We are on a mission to grow safer, healthier food by deploying autonomous, sustainable greenhouses outside every city on earth

Optimal

optimal

Table of Links Abstract and 1 Introduction 2 Preliminaries 3 Temporal Hierarchies 4 Rating Maps 5 Optimal Imprints for TL(AT) 6 Conclusion and References Appendix A. Appendix to Section 2 & Appendix B. Appendix to Section 3 Appendix C. Appendix to Section 4 & Appendix D. Appendix to Section 5 5. Optimal imprints for TL(AT) This paper is available on arxiv under CC BY 4.0 DEED license. Authors:
(1) Thomas Place;
(2) Marc Zaitoun. Table of Links Abstract and 1 Introduction Abstract and 1 Introduction 2 Preliminaries 2 Preliminaries 3 Temporal Hierarchies 3 Temporal Hierarchies 4 Rating Maps 4 Rating Maps 5 Optimal Imprints for TL(AT) 5 Optimal Imprints for TL(AT) 6 Conclusion and References 6 Conclusion and References Appendix A. Appendix to Section 2 & Appendix B. Appendix to Section 3 Appendix A. Appendix to Section 2 & Appendix B. Appendix to Section 3 Appendix C. Appendix to Section 4 & Appendix D. Appendix to Section 5 Appendix C. Appendix to Section 4 & Appendix D. Appendix to Section 5 5. Optimal imprints for TL(AT) This paper is available on arxiv under CC BY 4.0 DEED license. This paper is available on arxiv under CC BY 4.0 DEED license. available on arxiv Authors: (1) Thomas Place; (2) Marc Zaitoun. Authors: Authors: (1) Thomas Place; (2) Marc Zaitoun.

Optimal Imprints for TL(AT): Explaining Our Main Theorem

Authors:
(1) Jongmin Lee, Department of Mathematical Science, Seoul National University;
(2) Ernest K. Ryu, Department of Mathematical Science, Seoul National University and Interdisciplinary Program in Artificial Intelligence, Seoul National University. Abstract and 1 Introduction 1.1 Notations and preliminaries 1.2 Prior works 2 Anchored Value Iteration 2.1 Accelerated rate for Bellman consistency operator 2.2 Accelerated rate for Bellman optimality opera 3 Convergence when y=1 4 Complexity lower bound 5 Approximate Anchored Value Iteration 6 Gauss–Seidel Anchored Value Iteration 7 Conclusion, Acknowledgments and Disclosure of Funding and References A Preliminaries B Omitted proofs in Section 2 C Omitted proofs in Section 3 D Omitted proofs in Section 4 E Omitted proofs in Section 5 F Omitted proofs in Section 6 G Broader Impacts H Limitations A Preliminaries For notational unity, we use the symbol U when both V and Q can be used. This paper is available on arxiv under CC BY 4.0 DEED license. Authors: (1) Jongmin Lee, Department of Mathematical Science, Seoul National University; (2) Ernest K. Ryu, Department of Mathematical Science, Seoul National University and Interdisciplinary Program in Artificial Intelligence, Seoul National University. Authors: Authors: (1) Jongmin Lee, Department of Mathematical Science, Seoul National University; (2) Ernest K. Ryu, Department of Mathematical Science, Seoul National University and Interdisciplinary Program in Artificial Intelligence, Seoul National University. Abstract and 1 Introduction Abstract and 1 Introduction 1.1 Notations and preliminaries 1.1 Notations and preliminaries 1.2 Prior works 1.2 Prior works 2 Anchored Value Iteration 2 Anchored Value Iteration 2.1 Accelerated rate for Bellman consistency operator 2.1 Accelerated rate for Bellman consistency operator 2.2 Accelerated rate for Bellman optimality opera 2.2 Accelerated rate for Bellman optimality opera 3 Convergence when y=1 3 Convergence when y=1 4 Complexity lower bound 4 Complexity lower bound 5 Approximate Anchored Value Iteration 5 Approximate Anchored Value Iteration 6 Gauss–Seidel Anchored Value Iteration 6 Gauss–Seidel Anchored Value Iteration 7 Conclusion, Acknowledgments and Disclosure of Funding and References 7 Conclusion, Acknowledgments and Disclosure of Funding and References A Preliminaries A Preliminaries B Omitted proofs in Section 2 B Omitted proofs in Section 2 C Omitted proofs in Section 3 C Omitted proofs in Section 3 D Omitted proofs in Section 4 D Omitted proofs in Section 4 E Omitted proofs in Section 5 E Omitted proofs in Section 5 F Omitted proofs in Section 6 F Omitted proofs in Section 6 G Broader Impacts G Broader Impacts H Limitations H Limitations A Preliminaries For notational unity, we use the symbol U when both V and Q can be used. This paper is available on arxiv under CC BY 4.0 DEED license. This paper is available on arxiv under CC BY 4.0 DEED license. available on arxiv

Foundational Lemmas for Bellman Optimality and Anti-Optimality Operators

This is Part 6 of a 7-part series of the research paper “Towards Usability Guidelines for the Design of Effective Arabic Websites”. Use the table of links below to navigate to the other parts. Table of Links Abstract and I. Introduction II. Previous Works III. Research Methodology IV. Font and Image Inspection Studies V. Results VI. Discussion VII. Conclusions, Future Research Directions, and References VI. DISCUSSION Our comprehensive inspection of current practices concerning text formatting and image usage within the top visited Arabic websites in Saudi Arabia revealed various interesting findings. The usability inspection was performed to gather insights about the font types and sizes used to style Arabic text, especially that they could directly influence the legibility of text on websites. Let us review and attempt to answer the research questions posited in the introduction. What font types and font sizes are used by major Arabic websites? On the positive side, the selection of the Arabic websites included a large pool of websites, which were selected objectively by relying on Alexa Internet latest ranking. In effect, the inspection covered a total of 73 top viewed websites (52 local and 21 international) in Saudi Arabia. The websites' ranking is based on a set of metrics, primarily the average viewing time for the last three months. Typically, a font has several characteristics including type, size, width, weight, and serifs [37], [46]. However, for the purpose of this research, we directed our focus towards two key font characteristics namely type and size. On the web, font type usually refers to the font family that represents a certain typeface, including all sizes and styles, for example, Arial and Verdana. To style a particular family type, the size of text may be increased or decreased using the font size attribute. There are different ways to resize the font including Ems (em), pixels (px), points (pt), and percent (%). In our font size analysis, we used pixels (px) as the sole measurement for the font since it is the main measurement unit for media shown on computer screens. Moreover, web designers usually use pixels as their key measurement unit for font size. Points, however, are used to measure font size for print media. It is noted that more than half of the Arabic websites breached the principle of consistency when applying font types to the text. This means that multiple font types were used on the same web pages. Previous research, however, has already emphasized the role of consistency of user interface elements, such as font, in the overall usability of websites [35], [36]. On that basis, it is recommended that designers should adhere to the same font family to create attractive and consistent Arabic web designs. Moreover, there was no evident consensus amongst the websites in favoring a particular font type in order to display the Arabic text. More than 35 font types were used by the selected 73 websites. There are various potential theories that could explain this staggering variability; firstly, the lack of research and thereby guidelines with respect to styling Arabic text to guide the effective design of Arabic websites; secondly, the weak conformance to international design practices and recommendations; thirdly, the lack of awareness that text formatting might ultimately impact text legibility and thereby readers' mental load and overall satisfaction. Nonetheless, a pattern of font usage emerged within the Arabic websites; six font types recurred several times in the formatting of titles/headline, menus, and paragraphs. These font types were used differently according to the type of text element. For titles and menus, Droid Arabic Kufi, Tahoma, Helvetica, and Arial, emerged as favorites. It is no surprise that Droid Arabic Kufi came out as a winner for it is a unique font that reflects the Arabic calligraphy. This font gives a true feeling of the traditional Arabic scripts (Kufic scripts) that date back to the 7th century. For paragraphs, Tahoma, Helvetica, Arial and Times New Roman were used more frequently. International recommendations suggest using font type Verdana since it is one of the most legible fonts as rated by online readers of English websites [38]. Nonetheless, this font did not appear frequently in the Arabic websites that we tested. Moreover, other famous fonts that were found earlier to be legible or attractive by English readers, such as Georgia [18] and Courier [10], did not rank well in the Arabic websites. However, Arial emerged as one of the top six font types used by the Arabic websites. Previous research confirmed that font type Arial was read significantly faster and was perceived as legible [10]. Design guidelines have indicated that font size 12 points (~ 16 pixels) is the most suited size for displaying text on English websites [39]. This is somewhat disputable as subsequent research suggested the use of font size 14 points (~19 pixels) instead. For displaying the Arabic text, recommendations are inconclusive yet. For example, [17] proposed to use font 14 points (~19 pixels) whereas [4] argued that font size 16 (22 pixels) to 18 points (~24 pixels) must be used for better readability. These suggestions are in strike contrast with the current practices of the Arabic web design. More than 60% of the inspected websites used font size ranging between 12 pixels to 16 pixels (i.e. 9 points to 12 points) to style the paragraphs. Similarly, menu items are sized from 13 pixels to 14 pixels, which is still considerably illegible [17]. In respect to using images in web design, we aimed at answering the following question. What types of images are incorporated within the Saudi websites given the Saudi culture? All Arabic websites included images as part of their content. Authors in [40] and [41] suggested that graphics improve the overall attractiveness of websites. Moreover, 90% of the Arabic websites we tested included human images. This is known to improve user engagement, trust, and satisfaction [21]. However, 80% of the Arabic websites used conservative images that respect the Islamic identity and cultural values of the Saudi people. Research studies agree that web designs should adhere to the cultural values of its users to achieve success and acceptance [42], [43], [44]. Two-thirds of the websites used images of both genders. The remaining third, however, used images of men only. This could be explained by the masculine dimension of the Saudi society as indicated by Hofstede scores [45]. More than 80% of the websites included images containing groups of people. Again, this can be justified by the collectivism dimension of the Saudi society [45]. Finally, there was high usage of animations, possibly, in an attempt to engage web visitors and improve the aesthetics of the websites. Evidently, the high presence of images in these websites contributed to lower performance scores and increased site loading time. Optimization of images‟ size, using the appropriate image compression techniques, is therefore recommended as a result of our analysis. Authors:
(1) Abdallah Namoun, Department of Information Systems, Faculty of Computer and Information Systems, Madinah, Saudi Arabia;
(2) Ahmad B. Alkhodre, Department of Information Technology, Faculty of Computer and Information Systems, Madinah, Saudi Arabia. This paper is available on arxiv under CC BY 4.0 DEED license. This is Part 6 of a 7-part series of the research paper “Towards Usability Guidelines for the Design of Effective Arabic Websites”. Use the table of links below to navigate to the other parts. This is Part 6 of a 7-part series of the research paper “ Towards Usability Guidelines for the Design of Effective Arabic Websites ”. Use the table of links below to navigate to the other parts. Part 6 Towards Usability Guidelines for the Design of Effective Arabic Websites Table of Links Abstract and I. Introduction Abstract and I. Introduction II. Previous Works II. Previous Works III. Research Methodology III. Research Methodology IV. Font and Image Inspection Studies IV. Font and Image Inspection Studies V. Results V. Results VI. Discussion VI. Discussion VII. Conclusions, Future Research Directions, and References VII. Conclusions, Future Research Directions, and References VI. DISCUSSION Our comprehensive inspection of current practices concerning text formatting and image usage within the top visited Arabic websites in Saudi Arabia revealed various interesting findings. The usability inspection was performed to gather insights about the font types and sizes used to style Arabic text, especially that they could directly influence the legibility of text on websites. Let us review and attempt to answer the research questions posited in the introduction. What font types and font sizes are used by major Arabic websites? On the positive side, the selection of the Arabic websites included a large pool of websites, which were selected objectively by relying on Alexa Internet latest ranking. In effect, the inspection covered a total of 73 top viewed websites (52 local and 21 international) in Saudi Arabia. The websites' ranking is based on a set of metrics, primarily the average viewing time for the last three months. Typically, a font has several characteristics including type, size, width, weight, and serifs [37], [46]. However, for the purpose of this research, we directed our focus towards two key font characteristics namely type and size. On the web, font type usually refers to the font family that represents a certain typeface, including all sizes and styles, for example, Arial and Verdana. To style a particular family type, the size of text may be increased or decreased using the font size attribute. There are different ways to resize the font including Ems (em), pixels (px), points (pt), and percent (%). In our font size analysis, we used pixels (px) as the sole measurement for the font since it is the main measurement unit for media shown on computer screens. Moreover, web designers usually use pixels as their key measurement unit for font size. Points, however, are used to measure font size for print media. It is noted that more than half of the Arabic websites breached the principle of consistency when applying font types to the text. This means that multiple font types were used on the same web pages. Previous research, however, has already emphasized the role of consistency of user interface elements, such as font, in the overall usability of websites [35], [36]. On that basis, it is recommended that designers should adhere to the same font family to create attractive and consistent Arabic web designs. Moreover, there was no evident consensus amongst the websites in favoring a particular font type in order to display the Arabic text. More than 35 font types were used by the selected 73 websites. There are various potential theories that could explain this staggering variability; firstly, the lack of research and thereby guidelines with respect to styling Arabic text to guide the effective design of Arabic websites; secondly, the weak conformance to international design practices and recommendations; thirdly, the lack of awareness that text formatting might ultimately impact text legibility and thereby readers' mental load and overall satisfaction. Nonetheless, a pattern of font usage emerged within the Arabic websites; six font types recurred several times in the formatting of titles/headline, menus, and paragraphs. These font types were used differently according to the type of text element. For titles and menus, Droid Arabic Kufi, Tahoma, Helvetica, and Arial, emerged as favorites. It is no surprise that Droid Arabic Kufi came out as a winner for it is a unique font that reflects the Arabic calligraphy. This font gives a true feeling of the traditional Arabic scripts (Kufic scripts) that date back to the 7th century. For paragraphs, Tahoma, Helvetica, Arial and Times New Roman were used more frequently. International recommendations suggest using font type Verdana since it is one of the most legible fonts as rated by online readers of English websites [38]. Nonetheless, this font did not appear frequently in the Arabic websites that we tested. Moreover, other famous fonts that were found earlier to be legible or attractive by English readers, such as Georgia [18] and Courier [10], did not rank well in the Arabic websites. However, Arial emerged as one of the top six font types used by the Arabic websites. Previous research confirmed that font type Arial was read significantly faster and was perceived as legible [10]. Design guidelines have indicated that font size 12 points (~ 16 pixels) is the most suited size for displaying text on English websites [39]. This is somewhat disputable as subsequent research suggested the use of font size 14 points (~19 pixels) instead. For displaying the Arabic text, recommendations are inconclusive yet. For example, [17] proposed to use font 14 points (~19 pixels) whereas [4] argued that font size 16 (22 pixels) to 18 points (~24 pixels) must be used for better readability. These suggestions are in strike contrast with the current practices of the Arabic web design. More than 60% of the inspected websites used font size ranging between 12 pixels to 16 pixels (i.e. 9 points to 12 points) to style the paragraphs. Similarly, menu items are sized from 13 pixels to 14 pixels, which is still considerably illegible [17]. In respect to using images in web design, we aimed at answering the following question. What types of images are incorporated within the Saudi websites given the Saudi culture? All Arabic websites included images as part of their content. Authors in [40] and [41] suggested that graphics improve the overall attractiveness of websites. Moreover, 90% of the Arabic websites we tested included human images. This is known to improve user engagement, trust, and satisfaction [21]. However, 80% of the Arabic websites used conservative images that respect the Islamic identity and cultural values of the Saudi people. Research studies agree that web designs should adhere to the cultural values of its users to achieve success and acceptance [42], [43], [44]. Two-thirds of the websites used images of both genders. The remaining third, however, used images of men only. This could be explained by the masculine dimension of the Saudi society as indicated by Hofstede scores [45]. More than 80% of the websites included images containing groups of people. Again, this can be justified by the collectivism dimension of the Saudi society [45]. Finally, there was high usage of animations, possibly, in an attempt to engage web visitors and improve the aesthetics of the websites. Evidently, the high presence of images in these websites contributed to lower performance scores and increased site loading time. Optimization of images‟ size, using the appropriate image compression techniques, is therefore recommended as a result of our analysis. Authors: (1) Abdallah Namoun, Department of Information Systems, Faculty of Computer and Information Systems, Madinah, Saudi Arabia; (2) Ahmad B. Alkhodre, Department of Information Technology, Faculty of Computer and Information Systems, Madinah, Saudi Arabia. Authors : Authors (1) Abdallah Namoun, Department of Information Systems, Faculty of Computer and Information Systems, Madinah, Saudi Arabia; (2) Ahmad B. Alkhodre, Department of Information Technology, Faculty of Computer and Information Systems, Madinah, Saudi Arabia. This paper is available on arxiv under CC BY 4.0 DEED license. This paper is available on arxiv under CC BY 4.0 DEED license. available on arxiv available on arxiv

Design Arabic Websites with Consistent Fonts, Optimal Sizes, and Culturally Aligned Images

Authors:
(1) Jongmin Lee, Department of Mathematical Science, Seoul National University;
(2) Ernest K. Ryu, Department of Mathematical Science, Seoul National University and Interdisciplinary Program in Artificial Intelligence, Seoul National University. Abstract and 1 Introduction 1.1 Notations and preliminaries 1.2 Prior works 2 Anchored Value Iteration 2.1 Accelerated rate for Bellman consistency operator 2.2 Accelerated rate for Bellman optimality opera 3 Convergence when y=1 4 Complexity lower bound 5 Approximate Anchored Value Iteration 6 Gauss–Seidel Anchored Value Iteration 7 Conclusion, Acknowledgments and Disclosure of Funding and References A Preliminaries B Omitted proofs in Section 2 C Omitted proofs in Section 3 D Omitted proofs in Section 4 E Omitted proofs in Section 5 F Omitted proofs in Section 6 G Broader Impacts H Limitations 2.2 Accelerated rate for Bellman optimality opera We now present the accelerated convergence rate of Anc-VI for the Bellman optimality operator. Our analysis uses what we call the Bellman anti-optimality operator, define Anc-VI with the Bellman optimality operator exhibits the same accelerated convergence rate as Anc-VI with the Bellman consistency operator. As in Theorem 1, the rate of Theorem 2 also becomes O(1/k) when γ ≈ 1, while VI has a O(1)-rate. Proof outline of Theorem 2. The key technical challenge of the proof comes from the fact that the Bellman optimality operator is non-linear. Similar to the Bellman consistency operator case, we have This paper is available on arxiv under CC BY 4.0 DEED license. Authors: (1) Jongmin Lee, Department of Mathematical Science, Seoul National University; (2) Ernest K. Ryu, Department of Mathematical Science, Seoul National University and Interdisciplinary Program in Artificial Intelligence, Seoul National University. Authors: Authors: (1) Jongmin Lee, Department of Mathematical Science, Seoul National University; (2) Ernest K. Ryu, Department of Mathematical Science, Seoul National University and Interdisciplinary Program in Artificial Intelligence, Seoul National University. Abstract and 1 Introduction Abstract and 1 Introduction 1.1 Notations and preliminaries 1.1 Notations and preliminaries 1.2 Prior works 1.2 Prior works 2 Anchored Value Iteration 2 Anchored Value Iteration 2.1 Accelerated rate for Bellman consistency operator 2.1 Accelerated rate for Bellman consistency operator 2.2 Accelerated rate for Bellman optimality opera 2.2 Accelerated rate for Bellman optimality opera 3 Convergence when y=1 3 Convergence when y=1 4 Complexity lower bound 4 Complexity lower bound 5 Approximate Anchored Value Iteration 5 Approximate Anchored Value Iteration 6 Gauss–Seidel Anchored Value Iteration 6 Gauss–Seidel Anchored Value Iteration 7 Conclusion, Acknowledgments and Disclosure of Funding and References 7 Conclusion, Acknowledgments and Disclosure of Funding and References A Preliminaries A Preliminaries B Omitted proofs in Section 2 B Omitted proofs in Section 2 C Omitted proofs in Section 3 C Omitted proofs in Section 3 D Omitted proofs in Section 4 D Omitted proofs in Section 4 E Omitted proofs in Section 5 E Omitted proofs in Section 5 F Omitted proofs in Section 6 F Omitted proofs in Section 6 G Broader Impacts G Broader Impacts H Limitations H Limitations 2.2 Accelerated rate for Bellman optimality opera We now present the accelerated convergence rate of Anc-VI for the Bellman optimality operator. Our analysis uses what we call the Bellman anti-optimality operator, define Anc-VI with the Bellman optimality operator exhibits the same accelerated convergence rate as Anc-VI with the Bellman consistency operator. As in Theorem 1, the rate of Theorem 2 also becomes O(1/k) when γ ≈ 1, while VI has a O(1)-rate. Proof outline of Theorem 2. The key technical challenge of the proof comes from the fact that the Bellman optimality operator is non-linear. Similar to the Bellman consistency operator case, we have This paper is available on arxiv under CC BY 4.0 DEED license. This paper is available on arxiv under CC BY 4.0 DEED license. available on arxiv

How Anc-VI Helps AI Learn Faster with Optimality Operators

Table of Links Abstract and 1. Introduction 2. Preliminaries and 2.1. Blind deconvolution 2.2. Quadratic neural networks 3. Methodology 3.1. Time domain quadratic convolutional filter 3.2. Superiority of cyclic features extraction by QCNN 3.3. Frequency domain linear filter with envelope spectrum objective function 3.4. Integral optimization with uncertainty-aware weighing scheme 4. Computational experiments 4.1. Experimental configurations 4.2. Case study 1: PU dataset 4.3. Case study 2: JNU dataset 4.4. Case study 3: HIT dataset 5. Computational experiments 5.1. Comparison of BD methods 5.2. Classification results on various noise conditions 5.3. Employing ClassBD to deep learning classifiers 5.4. Employing ClassBD to machine learning classifiers 5.5. Feature extraction ability of quadratic and conventional networks 5.6. Comparison of ClassBD filters 6. Conclusions Appendix and References 5.6. Comparison of ClassBD filters Given that ClassBD comprises two filters, we explore their respective contributions in this experiment. Here we test four combinations: a standalone time domain filter (T-filter), a standalone frequency domain filter (F-filter), an F-filter followed by a T-filter, and our proposed scheme (a T-filter followed by an F-filter). The results are presented in Table 15. Primarily, our scheme exhibits superior performance, indicating that both filters contribute significantly to the classification. Secondly, when comparing the single T-filter and F-filter, their performances are found to be dataset-dependent. On the PU and HIT datasets, T-filters outperform F-filters, whereas their performance is inferior to F-filters on the JNU dataset. Authors:
(1) Jing-Xiao Liao, Department of Industrial and Systems Engineering, The Hong Kong Polytechnic University, Hong Kong, Special Administrative Region of China and School of Instrumentation Science and Engineering, Harbin Institute of Technology, Harbin, China;
(2) Chao He, School of Mechanical, Electronic and Control Engineering, Beijing Jiaotong University, Beijing, China;
(3) Jipu Li, Department of Industrial and Systems Engineering, The Hong Kong Polytechnic University, Hong Kong, Special Administrative Region of China;
(4) Jinwei Sun, School of Instrumentation Science and Engineering, Harbin Institute of Technology, Harbin, China;
(5) Shiping Zhang (Corresponding author), School of Instrumentation Science and Engineering, Harbin Institute of Technology, Harbin, China;
(6) Xiaoge Zhang (Corresponding author), Department of Industrial and Systems Engineering, The Hong Kong Polytechnic University, Hong Kong, Special Administrative Region of China. This paper is available on arxiv under CC by 4.0 Deed (Attribution 4.0 International) license. Table of Links Abstract and 1. Introduction Abstract and 1. Introduction 2. Preliminaries and 2.1. Blind deconvolution 2. Preliminaries and 2.1. Blind deconvolution 2.2. Quadratic neural networks 2.2. Quadratic neural networks 3. Methodology 3. Methodology 3.1. Time domain quadratic convolutional filter 3.1. Time domain quadratic convolutional filter 3.2. Superiority of cyclic features extraction by QCNN 3.2. Superiority of cyclic features extraction by QCNN 3.3. Frequency domain linear filter with envelope spectrum objective function 3.3. Frequency domain linear filter with envelope spectrum objective function 3.4. Integral optimization with uncertainty-aware weighing scheme 3.4. Integral optimization with uncertainty-aware weighing scheme 4. Computational experiments 4.1. Experimental configurations 4.1. Experimental configurations 4.2. Case study 1: PU dataset 4.2. Case study 1: PU dataset 4.3. Case study 2: JNU dataset 4.3. Case study 2: JNU dataset 4.4. Case study 3: HIT dataset 4.4. Case study 3: HIT dataset 5. Computational experiments 5.1. Comparison of BD methods 5.1. Comparison of BD methods 5.2. Classification results on various noise conditions 5.2. Classification results on various noise conditions 5.3. Employing ClassBD to deep learning classifiers 5.3. Employing ClassBD to deep learning classifiers 5.4. Employing ClassBD to machine learning classifiers 5.4. Employing ClassBD to machine learning classifiers 5.5. Feature extraction ability of quadratic and conventional networks 5.5. Feature extraction ability of quadratic and conventional networks 5.6. Comparison of ClassBD filters 5.6. Comparison of ClassBD filters 6. Conclusions 6. Conclusions Appendix and References Appendix and References 5.6. Comparison of ClassBD filters Given that ClassBD comprises two filters, we explore their respective contributions in this experiment. Here we test four combinations: a standalone time domain filter (T-filter), a standalone frequency domain filter (F-filter), an F-filter followed by a T-filter, and our proposed scheme (a T-filter followed by an F-filter). The results are presented in Table 15. Primarily, our scheme exhibits superior performance, indicating that both filters contribute significantly to the classification. Secondly, when comparing the single T-filter and F-filter, their performances are found to be dataset-dependent. On the PU and HIT datasets, T-filters outperform F-filters, whereas their performance is inferior to F-filters on the JNU dataset. Authors: (1) Jing-Xiao Liao, Department of Industrial and Systems Engineering, The Hong Kong Polytechnic University, Hong Kong, Special Administrative Region of China and School of Instrumentation Science and Engineering, Harbin Institute of Technology, Harbin, China; (2) Chao He, School of Mechanical, Electronic and Control Engineering, Beijing Jiaotong University, Beijing, China; (3) Jipu Li, Department of Industrial and Systems Engineering, The Hong Kong Polytechnic University, Hong Kong, Special Administrative Region of China; (4) Jinwei Sun, School of Instrumentation Science and Engineering, Harbin Institute of Technology, Harbin, China; (5) Shiping Zhang (Corresponding author), School of Instrumentation Science and Engineering, Harbin Institute of Technology, Harbin, China; (6) Xiaoge Zhang (Corresponding author), Department of Industrial and Systems Engineering, The Hong Kong Polytechnic University, Hong Kong, Special Administrative Region of China. Authors: Authors: (1) Jing-Xiao Liao, Department of Industrial and Systems Engineering, The Hong Kong Polytechnic University, Hong Kong, Special Administrative Region of China and School of Instrumentation Science and Engineering, Harbin Institute of Technology, Harbin, China; (2) Chao He, School of Mechanical, Electronic and Control Engineering, Beijing Jiaotong University, Beijing, China; (3) Jipu Li, Department of Industrial and Systems Engineering, The Hong Kong Polytechnic University, Hong Kong, Special Administrative Region of China; (4) Jinwei Sun, School of Instrumentation Science and Engineering, Harbin Institute of Technology, Harbin, China; (5) Shiping Zhang (Corresponding author), School of Instrumentation Science and Engineering, Harbin Institute of Technology, Harbin, China; (6) Xiaoge Zhang (Corresponding author), Department of Industrial and Systems Engineering, The Hong Kong Polytechnic University, Hong Kong, Special Administrative Region of China. This paper is available on arxiv under CC by 4.0 Deed (Attribution 4.0 International) license. This paper is available on arxiv under CC by 4.0 Deed (Attribution 4.0 International) license. available on arxiv

Researchers Discover Optimal Combination of Time and Frequency Domain Filters in ClassBD

Authors:
(1) Xian Liu, Snap Inc., CUHK with Work done during an internship at Snap Inc.;
(2) Jian Ren, Snap Inc. with Corresponding author: jren@snapchat.com;
(3) Aliaksandr Siarohin, Snap Inc.;
(4) Ivan Skorokhodov, Snap Inc.;
(5) Yanyu Li, Snap Inc.;
(6) Dahua Lin, CUHK;
(7) Xihui Liu, HKU;
(8) Ziwei Liu, NTU;
(9) Sergey Tulyakov, Snap Inc. Table of Links Abstract and 1 Introduction 2 Related Work 3 Our Approach and 3.1 Preliminaries and Problem Setting 3.2 Latent Structural Diffusion Model 3.3 Structure-Guided Refiner 4 Human Verse Dataset 5 Experiments 5.1 Main Results 5.2 Ablation Study 6 Discussion and References A Appendix and A.1 Additional Quantitative Results A.2 More Implementation Details and A.3 More Ablation Study Results A.4 More User Study Details A.5 Impact of Random Seed and Model Robustness and A.6 Boarder Impact and Ethical Consideration A.7 More Comparison Results and A.8 Additional Qualitative Results A.9 Licenses 5.2 ABLATION STUDY Simultaneous Denoise with Expert Branch. We explore whether latent structural diffusion model helps, and how many layers to replicate in the structural expert branches: 1) Denoise RGB, that only learns to denoise an image. 2) Denoise RGB + Depth, which also predicts depth. 3) Half DownBlock & UpBlock. We replicate half of the first DownBlock and the last UpBlock, which contains one down/up-sample ResBlock and one AttnBlock. 4) Two DownBlocks & UpBlocks, where we copy the first two DownBlocks and the last two UpBlocks. The results are shown in Tab. 2 (top), which prove that the joint learning of image appearance, spatial relationship, and geometry is beneficial. We also find that while fewer replicate layers give more spatially aligned results, the per-branch parameters are insufficient to capture distributions of each modality. In contrast, excessive replicate layers lead to less feature fusion across different targets, which fails to complement to each other branches. This paper is available on arxiv under CC BY 4.0 DEED license. Authors: (1) Xian Liu, Snap Inc., CUHK with Work done during an internship at Snap Inc.; (2) Jian Ren, Snap Inc. with Corresponding author: jren@snapchat.com; (3) Aliaksandr Siarohin, Snap Inc.; (4) Ivan Skorokhodov, Snap Inc.; (5) Yanyu Li, Snap Inc.; (6) Dahua Lin, CUHK; (7) Xihui Liu, HKU; (8) Ziwei Liu, NTU; (9) Sergey Tulyakov, Snap Inc. Authors: Authors: (1) Xian Liu, Snap Inc., CUHK with Work done during an internship at Snap Inc.; (2) Jian Ren, Snap Inc. with Corresponding author: jren@snapchat.com; (3) Aliaksandr Siarohin, Snap Inc.; (4) Ivan Skorokhodov, Snap Inc.; (5) Yanyu Li, Snap Inc.; (6) Dahua Lin, CUHK; (7) Xihui Liu, HKU; (8) Ziwei Liu, NTU; (9) Sergey Tulyakov, Snap Inc. Table of Links Abstract and 1 Introduction Abstract and 1 Introduction 2 Related Work 2 Related Work 3 Our Approach and 3.1 Preliminaries and Problem Setting 3 Our Approach and 3.1 Preliminaries and Problem Setting 3.2 Latent Structural Diffusion Model 3.2 Latent Structural Diffusion Model 3.3 Structure-Guided Refiner 3.3 Structure-Guided Refiner 4 Human Verse Dataset 4 Human Verse Dataset 5 Experiments 5 Experiments 5.1 Main Results 5.1 Main Results 5.2 Ablation Study 5.2 Ablation Study 6 Discussion and References 6 Discussion and References A Appendix and A.1 Additional Quantitative Results A Appendix and A.1 Additional Quantitative Results A.2 More Implementation Details and A.3 More Ablation Study Results A.2 More Implementation Details and A.3 More Ablation Study Results A.4 More User Study Details A.4 More User Study Details A.5 Impact of Random Seed and Model Robustness and A.6 Boarder Impact and Ethical Consideration A.5 Impact of Random Seed and Model Robustness and A.6 Boarder Impact and Ethical Consideration A.7 More Comparison Results and A.8 Additional Qualitative Results A.7 More Comparison Results and A.8 Additional Qualitative Results A.9 Licenses A.9 Licenses 5.2 ABLATION STUDY Simultaneous Denoise with Expert Branch. We explore whether latent structural diffusion model helps, and how many layers to replicate in the structural expert branches: 1) Denoise RGB, that only learns to denoise an image. 2) Denoise RGB + Depth, which also predicts depth. 3) Half DownBlock & UpBlock. We replicate half of the first DownBlock and the last UpBlock, which contains one down/up-sample ResBlock and one AttnBlock. 4) Two DownBlocks & UpBlocks, where we copy the first two DownBlocks and the last two UpBlocks. The results are shown in Tab. 2 (top), which prove that the joint learning of image appearance, spatial relationship, and geometry is beneficial. We also find that while fewer replicate layers give more spatially aligned results, the per-branch parameters are insufficient to capture distributions of each modality. In contrast, excessive replicate layers lead to less feature fusion across different targets, which fails to complement to each other branches. This paper is available on arxiv under CC BY 4.0 DEED license. This paper is available on arxiv under CC BY 4.0 DEED license. available on arxiv

HyperHuman Ablation Study: Optimal Expert Branch Design for Improved Image Generation

Authors:
(1) Shih-Tang Su, University of Michigan, Ann Arbor (shihtang@umich.edu);
(2) Vijay G. Subramanian, University of Michigan, Ann Arbor and (vgsubram@umich.edu);
(3) Grant Schoenebeck, University of Michigan, Ann Arbor (schoeneb@umich.edu). Table of Links Abstract and 1. Introduction 2. Problem Formulation 2.1 Model of Binary-Outcome Experiments in Two-Phase Trials 3 Binary-outcome Experiments in Two-phase Trials and 3.1 Experiments with screenings 3.2 Assumptions and induced strategies 3.3 Constraints given by phase-II experiments 3.4 Persuasion ratio and the optimal signaling structure 3.5 Comparison with classical Bayesian persuasion strategies 4 Binary-outcome Experiments in Multi-phase trials and 4.1 Model of binary-outcome experiments in multi-phase trials 4.2 Determined versus sender-designed experiments 4.3 Multi-phase model and classical Bayesian persuasion and References 3.5 Comparison with classical Bayesian persuasion strategies Given the optimal signaling strategy derived in Lemma 5, one natural followup question is the quantification of the sender’s utility improvement obtained by adopting the optimal signaling strategy in comparison to using strategies structurally similar to the optimal strategies in classical Bayesian persuasion for a binary state of the world. Owing the page limit, we directly define a class of strategies structurally similar to the classical Bayesian persuasion strategy below and provide the justification in our online version [23]. Definition 4. With binary states of the world, a (binary-state) Bayesian persuasion (BBP) strategy is a strategy that “mixes two possible states in one signal and reveals the true state on the other signal”. This paper is available on arxiv under CC 4.0 license. Authors: (1) Shih-Tang Su, University of Michigan, Ann Arbor (shihtang@umich.edu); (2) Vijay G. Subramanian, University of Michigan, Ann Arbor and (vgsubram@umich.edu); (3) Grant Schoenebeck, University of Michigan, Ann Arbor (schoeneb@umich.edu). Authors: Authors: (1) Shih-Tang Su, University of Michigan, Ann Arbor (shihtang@umich.edu); (2) Vijay G. Subramanian, University of Michigan, Ann Arbor and (vgsubram@umich.edu); (3) Grant Schoenebeck, University of Michigan, Ann Arbor (schoeneb@umich.edu). Table of Links Abstract and 1. Introduction Abstract and 1. Introduction 2. Problem Formulation 2. Problem Formulation 2.1 Model of Binary-Outcome Experiments in Two-Phase Trials 2.1 Model of Binary-Outcome Experiments in Two-Phase Trials 3 Binary-outcome Experiments in Two-phase Trials and 3.1 Experiments with screenings 3 Binary-outcome Experiments in Two-phase Trials and 3.1 Experiments with screenings 3.2 Assumptions and induced strategies 3.2 Assumptions and induced strategies 3.3 Constraints given by phase-II experiments 3.3 Constraints given by phase-II experiments 3.4 Persuasion ratio and the optimal signaling structure 3.4 Persuasion ratio and the optimal signaling structure 3.5 Comparison with classical Bayesian persuasion strategies 3.5 Comparison with classical Bayesian persuasion strategies 4 Binary-outcome Experiments in Multi-phase trials and 4.1 Model of binary-outcome experiments in multi-phase trials 4 Binary-outcome Experiments in Multi-phase trials and 4.1 Model of binary-outcome experiments in multi-phase trials 4.2 Determined versus sender-designed experiments 4.2 Determined versus sender-designed experiments 4.3 Multi-phase model and classical Bayesian persuasion and References 4.3 Multi-phase model and classical Bayesian persuasion and References 3.5 Comparison with classical Bayesian persuasion strategies Given the optimal signaling strategy derived in Lemma 5, one natural followup question is the quantification of the sender’s utility improvement obtained by adopting the optimal signaling strategy in comparison to using strategies structurally similar to the optimal strategies in classical Bayesian persuasion for a binary state of the world. Owing the page limit, we directly define a class of strategies structurally similar to the classical Bayesian persuasion strategy below and provide the justification in our online version [23]. Definition 4. With binary states of the world, a (binary-state) Bayesian persuasion (BBP) strategy is a strategy that “mixes two possible states in one signal and reveals the true state on the other signal”. Definition 4. With binary states of the world, a (binary-state) Bayesian persuasion (BBP) strategy is a strategy that “mixes two possible states in one signal and reveals the true state on the other signal”. This paper is available on arxiv under CC 4.0 license. This paper is available on arxiv under CC 4.0 license. available on arxiv

How Optimal Signaling Outperforms Classical Bayesian Strategies in Multi-Phase Trials

Authors:
(1) Shih-Tang Su, University of Michigan, Ann Arbor (shihtang@umich.edu);
(2) Vijay G. Subramanian, University of Michigan, Ann Arbor and (vgsubram@umich.edu);
(3) Grant Schoenebeck, University of Michigan, Ann Arbor (schoeneb@umich.edu). Table of Links Abstract and 1. Introduction 2. Problem Formulation 2.1 Model of Binary-Outcome Experiments in Two-Phase Trials 3 Binary-outcome Experiments in Two-phase Trials and 3.1 Experiments with screenings 3.2 Assumptions and induced strategies 3.3 Constraints given by phase-II experiments 3.4 Persuasion ratio and the optimal signaling structure 3.5 Comparison with classical Bayesian persuasion strategies 4 Binary-outcome Experiments in Multi-phase trials and 4.1 Model of binary-outcome experiments in multi-phase trials 4.2 Determined versus sender-designed experiments 4.3 Multi-phase model and classical Bayesian persuasion and References 3 Binary-outcome Experiments in Two-phase Trials In this section the sender’s optimization problem presented in (2) Section 2.1, is solved starting with the simplest non-trivial case. There are only two phases in the trial studied here, and from this we will develop more insight into how different types of experiments (determined versus sender-designed) influence the optimal signaling strategy of the sender. To be more specific, we will analyze how two determined experiments (in phase II) and one sender-designed experiment (in phase I) will impact the sender’s optimal signaling strategy. Before we present the general case, we discuss a subset class of two-phase trials that are similar to single-phase trials. In this class of two-phase trials, in one of the phase-II experiments, called a trivial experiment, the outcome distribution is independent of the true state. Trivial experiments [2], also called (Blackwell) non-informative experiments in some literature, are frequently used as benchmarks to compare the agents’ expected utility change under different signaling schemes/mechanisms, e.g., [22,20,21]. This two-phase model with a trivial experiment tries to capture real-world problems with one actual (and costly) experiment, e.g., clinical trials, venture capital investments, or space missions. Since the experiment is costly, a screening procedure is provided to decide whether it is worth conducting the experiment. We will then analyze the optimal signaling strategy in the general scenario, where both experiments in phase II are non-trivial. 3.1 Experiments with screenings We start by analyzing the sender’s optimal strategy (signaling structure) in a simple scenario where there is one non-trivial experiment conducted in phase II. The sender’s authority on choosing the probability pair (p1, p2) controls the screening process. To avoid any ambiguity, we first define what a trivial experiment is. When a trivial experiment (in phase II) is conducted, the posterior belief of the state stays the same as the interim belief derived in (1). When there exists a trivial experiment in the two phase-II trial options, then Lemma 1 states that the sender and the receiver’s expected utility under the optimal signaling strategy is the same as in the (single-phase) classical Bayesian persuasion problem. Lemma 1. When the state space is binary, both sender and receiver’s expected utilities are the same in the following two Bayesian persuasion schemes under each scheme’s optimal signaling strategy: Bayesian persuasion in a single-phase trial,


Bayesian persuasion in a two-phase trial with a sender-designed phase-I experiment and a trivial experiment in phase II. In the single-trial classical Bayesian persuasion setting, the optimal signaling strategy only mixes the two possible states in one outcome (e.g., when the prosecutor claims the suspect is guilty). On the other outcome, the sender reveals the true state with probability one (e.g., when the prosecutor says the suspect is innocent). When there is a trivial experiment in phase II, the other experiment (supposing that it will be conducted at outcome ωB) will be rendered defunct by the sender’s choice of experiments in phase I. This phenomenon occurs because the sender can always choose to reveal the true state when the non-trivial experiment is to be conducted, i.e., by setting P(θ1|EB) = 1 or P(θ2|EB) = 1; and the classical Bayesian persuasion strategy can be replicated. In essence, having a trivial experiment in the phase-II trial does not constrain the sender. This paper is available on arxiv under CC 4.0 license. Authors: (1) Shih-Tang Su, University of Michigan, Ann Arbor (shihtang@umich.edu); (2) Vijay G. Subramanian, University of Michigan, Ann Arbor and (vgsubram@umich.edu); (3) Grant Schoenebeck, University of Michigan, Ann Arbor (schoeneb@umich.edu). Authors: Authors: (1) Shih-Tang Su, University of Michigan, Ann Arbor (shihtang@umich.edu); (2) Vijay G. Subramanian, University of Michigan, Ann Arbor and (vgsubram@umich.edu); (3) Grant Schoenebeck, University of Michigan, Ann Arbor (schoeneb@umich.edu). Table of Links Abstract and 1. Introduction Abstract and 1. Introduction 2. Problem Formulation 2. Problem Formulation 2.1 Model of Binary-Outcome Experiments in Two-Phase Trials 2.1 Model of Binary-Outcome Experiments in Two-Phase Trials 3 Binary-outcome Experiments in Two-phase Trials and 3.1 Experiments with screenings 3 Binary-outcome Experiments in Two-phase Trials and 3.1 Experiments with screenings 3.2 Assumptions and induced strategies 3.2 Assumptions and induced strategies 3.3 Constraints given by phase-II experiments 3.3 Constraints given by phase-II experiments 3.4 Persuasion ratio and the optimal signaling structure 3.4 Persuasion ratio and the optimal signaling structure 3.5 Comparison with classical Bayesian persuasion strategies 3.5 Comparison with classical Bayesian persuasion strategies 4 Binary-outcome Experiments in Multi-phase trials and 4.1 Model of binary-outcome experiments in multi-phase trials 4 Binary-outcome Experiments in Multi-phase trials and 4.1 Model of binary-outcome experiments in multi-phase trials 4.2 Determined versus sender-designed experiments 4.2 Determined versus sender-designed experiments 4.3 Multi-phase model and classical Bayesian persuasion and References 4.3 Multi-phase model and classical Bayesian persuasion and References 3 Binary-outcome Experiments in Two-phase Trials In this section the sender’s optimization problem presented in (2) Section 2.1, is solved starting with the simplest non-trivial case. There are only two phases in the trial studied here, and from this we will develop more insight into how different types of experiments (determined versus sender-designed) influence the optimal signaling strategy of the sender. To be more specific, we will analyze how two determined experiments (in phase II) and one sender-designed experiment (in phase I) will impact the sender’s optimal signaling strategy. Before we present the general case, we discuss a subset class of two-phase trials that are similar to single-phase trials. In this class of two-phase trials, in one of the phase-II experiments, called a trivial experiment, the outcome distribution is independent of the true state. Trivial experiments [2], also called (Blackwell) non-informative experiments in some literature, are frequently used as benchmarks to compare the agents’ expected utility change under different signaling schemes/mechanisms, e.g., [22,20,21]. This two-phase model with a trivial experiment tries to capture real-world problems with one actual (and costly) experiment, e.g., clinical trials, venture capital investments, or space missions. Since the experiment is costly, a screening procedure is provided to decide whether it is worth conducting the experiment. We will then analyze the optimal signaling strategy in the general scenario, where both experiments in phase II are non-trivial. 3.1 Experiments with screenings We start by analyzing the sender’s optimal strategy (signaling structure) in a simple scenario where there is one non-trivial experiment conducted in phase II. The sender’s authority on choosing the probability pair (p1, p2) controls the screening process. To avoid any ambiguity, we first define what a trivial experiment is. When a trivial experiment (in phase II) is conducted, the posterior belief of the state stays the same as the interim belief derived in (1). When there exists a trivial experiment in the two phase-II trial options, then Lemma 1 states that the sender and the receiver’s expected utility under the optimal signaling strategy is the same as in the (single-phase) classical Bayesian persuasion problem. Lemma 1. When the state space is binary, both sender and receiver’s expected utilities are the same in the following two Bayesian persuasion schemes under each scheme’s optimal signaling strategy: Lemma 1. When the state space is binary, both sender and receiver’s expected utilities are the same in the following two Bayesian persuasion schemes under each scheme’s optimal signaling strategy: Bayesian persuasion in a single-phase trial, Bayesian persuasion in a two-phase trial with a sender-designed phase-I experiment and a trivial experiment in phase II. Bayesian persuasion in a single-phase trial, Bayesian persuasion in a single-phase trial, Bayesian persuasion in a single-phase trial, Bayesian persuasion in a two-phase trial with a sender-designed phase-I experiment and a trivial experiment in phase II. Bayesian persuasion in a two-phase trial with a sender-designed phase-I experiment and a trivial experiment in phase II. Bayesian persuasion in a two-phase trial with a sender-designed phase-I experiment and a trivial experiment in phase II. In the single-trial classical Bayesian persuasion setting, the optimal signaling strategy only mixes the two possible states in one outcome (e.g., when the prosecutor claims the suspect is guilty). On the other outcome, the sender reveals the true state with probability one (e.g., when the prosecutor says the suspect is innocent). When there is a trivial experiment in phase II, the other experiment (supposing that it will be conducted at outcome ωB) will be rendered defunct by the sender’s choice of experiments in phase I. This phenomenon occurs because the sender can always choose to reveal the true state when the non-trivial experiment is to be conducted, i.e., by setting P(θ1|EB) = 1 or P(θ2|EB) = 1; and the classical Bayesian persuasion strategy can be replicated. In essence, having a trivial experiment in the phase-II trial does not constrain the sender. This paper is available on arxiv under CC 4.0 license. This paper is available on arxiv under CC 4.0 license. available on arxiv

Analyzing Optimal Signaling with Binary-outcome Experiments in Two-phase Trials

Ontleed optimale sein met binêre uitkoms-eksperimente in twee-fase proewe

Análisis de la señalización óptima con experimentos de resultados binarios en ensayos de dos fases

تجزیه و تحلیل سیگنال دهی بهینه با آزمایش های باینری نتیجه در آزمایشات دو فازی

Analiza optimalnog signaliziranja s eksperimentima s binarnim ishodom u dvofaznim ispitivanjima

2段階試験におけるバイナリ結果実験による最適なシグナル伝達の分析

ოპტიმალური სიგნალიზაციის ანალიზი ორფაზიან ცდებში ორფაზიანი ექსპერიმენტებით

Екі фазалық сынақтардағы екілік нәтиже эксперименттерімен оңтайлы сигналды талдау

Go sekaseka Matshwao a Mabotse ka Diteko tša dipoelo tša Binary ka Ditekong tša Megato ye Mebedi

Анализ оптимальной сигнализации с помощью экспериментов с бинарным результатом в двухфазных испытаниях

Gusesengura Ibimenyetso Byiza hamwe na Binary-ibisubizo Ubushakashatsi Mubice bibiri

Анализа оптималне сигнализације са експериментима са бинарним исходом у двофазним испитивањима

دو فیز ٹرائلز میں بائنری نتائج کے تجربات کے ساتھ بہترین سگنلنگ کا تجزیہ کرنا

Authors:
(1) Shih-Tang Su, University of Michigan, Ann Arbor (shihtang@umich.edu);
(2) Vijay G. Subramanian, University of Michigan, Ann Arbor and (vgsubram@umich.edu);
(3) Grant Schoenebeck, University of Michigan, Ann Arbor (schoeneb@umich.edu). Table of Links Abstract and 1. Introduction 2. Problem Formulation 2.1 Model of Binary-Outcome Experiments in Two-Phase Trials 3 Binary-outcome Experiments in Two-phase Trials and 3.1 Experiments with screenings 3.2 Assumptions and induced strategies 3.3 Constraints given by phase-II experiments 3.4 Persuasion ratio and the optimal signaling structure 3.5 Comparison with classical Bayesian persuasion strategies 4 Binary-outcome Experiments in Multi-phase trials and 4.1 Model of binary-outcome experiments in multi-phase trials 4.2 Determined versus sender-designed experiments 4.3 Multi-phase model and classical Bayesian persuasion and References 2 Problem Formulation Before the receiver takes his action, a trial consisting of multiple phases will be run, and the outcome in each phase will be revealed to him. In each phase, one experiment will be conducted, which is chosen according to the outcomes in earlier phases. Hence, the experiment outcomes in earlier phases not only affect the interim belief but also influence the possible (sequence of) experiments that will be conducted afterward. In the most sender-friendly setup where the sender can choose any experiment in each phase without any constraints, the problem is equivalent to the classical Bayesian persuasion problem with an enlarged signal space. However, when some experiments are pre-determined conditional on a set of outcomes, the sender must take these constraints into account to design her optimal signaling structure. To present our results on the influence of multiple phases on the sender’s signaling strategy, we start with a model of two-phase trials with binary-outcome experiments in the rest of this section. We then analyze the optimal signaling strategy of this model in Section 3. After that, we will introduce the general model of multiple-phase trials with binary-outcome experiments and propose a systematic approach to analyze the optimal signaling structure in Section 4. This paper is available on arxiv under CC 4.0 license. Authors: (1) Shih-Tang Su, University of Michigan, Ann Arbor (shihtang@umich.edu); (2) Vijay G. Subramanian, University of Michigan, Ann Arbor and (vgsubram@umich.edu); (3) Grant Schoenebeck, University of Michigan, Ann Arbor (schoeneb@umich.edu). Authors: Authors: (1) Shih-Tang Su, University of Michigan, Ann Arbor (shihtang@umich.edu); (2) Vijay G. Subramanian, University of Michigan, Ann Arbor and (vgsubram@umich.edu); (3) Grant Schoenebeck, University of Michigan, Ann Arbor (schoeneb@umich.edu). Table of Links Abstract and 1. Introduction Abstract and 1. Introduction 2. Problem Formulation 2. Problem Formulation 2.1 Model of Binary-Outcome Experiments in Two-Phase Trials 2.1 Model of Binary-Outcome Experiments in Two-Phase Trials 3 Binary-outcome Experiments in Two-phase Trials and 3.1 Experiments with screenings 3 Binary-outcome Experiments in Two-phase Trials and 3.1 Experiments with screenings 3.2 Assumptions and induced strategies 3.2 Assumptions and induced strategies 3.3 Constraints given by phase-II experiments 3.3 Constraints given by phase-II experiments 3.4 Persuasion ratio and the optimal signaling structure 3.4 Persuasion ratio and the optimal signaling structure 3.5 Comparison with classical Bayesian persuasion strategies 3.5 Comparison with classical Bayesian persuasion strategies 4 Binary-outcome Experiments in Multi-phase trials and 4.1 Model of binary-outcome experiments in multi-phase trials 4 Binary-outcome Experiments in Multi-phase trials and 4.1 Model of binary-outcome experiments in multi-phase trials 4.2 Determined versus sender-designed experiments 4.2 Determined versus sender-designed experiments 4.3 Multi-phase model and classical Bayesian persuasion and References 4.3 Multi-phase model and classical Bayesian persuasion and References 2 Problem Formulation Before the receiver takes his action, a trial consisting of multiple phases will be run, and the outcome in each phase will be revealed to him. In each phase, one experiment will be conducted, which is chosen according to the outcomes in earlier phases. Hence, the experiment outcomes in earlier phases not only affect the interim belief but also influence the possible (sequence of) experiments that will be conducted afterward. In the most sender-friendly setup where the sender can choose any experiment in each phase without any constraints, the problem is equivalent to the classical Bayesian persuasion problem with an enlarged signal space. However, when some experiments are pre-determined conditional on a set of outcomes, the sender must take these constraints into account to design her optimal signaling structure. To present our results on the influence of multiple phases on the sender’s signaling strategy, we start with a model of two-phase trials with binary-outcome experiments in the rest of this section. We then analyze the optimal signaling strategy of this model in Section 3. After that, we will introduce the general model of multiple-phase trials with binary-outcome experiments and propose a systematic approach to analyze the optimal signaling structure in Section 4. This paper is available on arxiv under CC 4.0 license. This paper is available on arxiv under CC 4.0 license. available on arxiv

Formulating Optimal Signaling Strategies in Constrained Bayesian Persuasion Trials

Achieving Optimal Service Reliability: Insights Into Service Level Objectives (SLOs)

Have you ever found yourself staring at an image spotted somewhere on the internet and wondering whether it results from human or artificial creative labor? Since the breakthrough in image generation technology, I’ve been captivated by interior designs, nature scenery, fashion photographs, and futuristic cityscapes made with AI that look like professional artwork. As someone with a creative eye yet no artistic skills, I was excited about the opportunity to transform ideas from my mind into visuals based solely on text input. I tried out several popular text-to-image tools, like MidJourney and DreamStudio on the web and ARTA on mobile. Still, while they all provided a good starting point and a straightforward user experience, the generation outcomes often fell short of my expectations and differed from what I envisioned — until I learned to tell AI what to draw in the language it understands. If you’re new to AI-generated art and need assistance streamlining the creative process, I’ll provide a step-by-step guide below to help you compose concise and well-structured text prompts that the AI models can effectively interpret and translate into the desired images. In the bottom line, I will share an example of both a correct and an incorrect prompt to illustrate how significantly they can impact the generation output in practice. First things first, two common prompt-writing mistakes you should avoid when using any text-to-image generator are being too wordy and using complex grammar. In fact, the more words you incorporate and the more complicated your grammar, the more difficult it is for AI to understand your prompt and adequately depict your concept. Therefore, communicate concisely, carefully choosing keywords, and list your ideas explicitly and separately rather than trying to cram them into one sentence. Step 1. Choose the Content Type Ask yourself how you want your image to look overall. Do you see it as a photograph, illustration, painting, sketch, or other artwork type? This initial decision puts you in control of the final result and helps align all the elements with this general framework. For instance, choosing a sketch will typically produce pencil images, while opting for a painting will add colors and likely create a more vintage appearance. Step 2. Define the Subject AI image generators require a specific subject for rendering, so you must indicate the main subject of your future image, whether a person, an animal, or a landscape. Stick to one subject per prompt and opt for concrete nouns like girl, dog, train, rose, ocean, temple, etc., for more accurate results. You can most likely render something using abstract keywords like love, peace, or joy, but the results may appear very inconsistent in what they depict. Step 3. Add Subject Description Now, it’s time to detail the concept with modifiers – adjectives or attributive nouns that add to the sense of a head subject. Modifiers can completely change the perspective of your image and boost its overall quality, so the more descriptive you are, the better the generated output. Define what the subject looks like, what the subject is doing, and other characteristics essential to representing your concept. Step 4. Describe the Context To help AI create the exact atmosphere and surroundings you need, give attention to aspects like lightning (studio, soft, cinematic, volumetric, accent lighting, sunlight, frontlight, backlight, ambient, moonlight, etc.), color theme (pastel, vibrant, neon pink, dark, etc.), environment/scene (in the sky, indoor, underwater, at night, etc.), and background (forest, beach, solid color, nebula, etc.). Additionally, consider the mood and vibe you want to convey. Simple feeling modifiers can set the scene’s atmosphere, whether you opt for positive (energetic, cozy, romantic, satisfaction, etc.) or negative (depressive, loneliness, regret, fear, etc.) ones. Step 5. Define Perspective Add a point of view to determine the angle from which you are looking at the image, such as side, overhead, or front. Other essential modifiers for creating photo-like images involve lenses and cameras. Here are a few examples: close-up, macro, lens flare, wide angle, microscopic, bokeh, isometric, depth of field, ultra-wide angle, fisheye lens, and panorama. Step 6. Add Art Style, Art Mediums, and Artists Proceed to aesthetic settings and define the overall artistic style. Also, specify the art medium. These aspects can greatly contribute to the value of the generated output, making it more consistent and expressive. Here are some of the common keywords: geometrical art, pop art, watercolor, line drawing, line art, 3D sculpture, crayon drawing, painting, oil painting, pastel drawing, medieval art, photography, digital art, stained glass, cave painting, polaroid, vector art, retro, illustration, comics, editorial fashion photography, Japanese anime style, surreal, travel photography, pencil sketch, steampunk, cartoon, futurism, vaporwave, art deco, interior design, psychedelic, street art. Consider including artistic influences. Adding the name of a specific artist whose signature artwork aligns with your chosen art genre can enhance the final image. Note, however, that finding the right artist is crucial so as not to mess up the output. Some artists affect the generation only subtly, while others can alter it significantly depending on their distinctive manner. For example, Claude Monet can infuse impressionism into landscapes, while mentioning Salvador Dali adds a surrealistic touch. Step 7. Add “Magic” Words Certain words can make a dramatic difference in the outcomes of the generation. The keywords like highly detailed, ultra-realistic, 4K, 8K, UHD, and HDR are the game changers for the overall quality of the image. Adding “studio lighting” will introduce appealing textures to the image, while “accent lighting” can draw attention to specific features. Describing the image as “professional” can enhance color contrast and detail, while mentioning “vivid colors” will bring life to your image. Using terms like ultra-wide angle, panoramic, or long-shot will help guide the camera. Packing your prompt with phrases related to artistic techniques and materials (such as trending on artstation, precise line-art, golden ratio, fine art, etc.) and those associated with artistic value (such as most beautiful image ever seen, epic composition, etc.) can also bring sophisticated improvements. Step 8. Consider Adding Negative Prompts Negative prompts are parameters that inform the generation model about what you do not want to see in the final image. They help prevent AI from generating specific elements, fix image abnormalities, and improve overall quality. Here are some universal examples: blurry, cropped, cloned face, duplicate, error, ugly, wrong proportions, deform, fused fingers, extra arms, law quality res, watermark, and more. Step 9. Define Correct Word Order and Keyword Weight Input The order is almost as important as the vocabulary, guiding the AI in generating the desired output. Combine keywords to direct the focus of your prompt and note key phrases that influence image preference. Emphasize essential keywords with a full colon and decimal number, use parentheses for added importance, and brackets for less importance. Typically, the earlier a word appears in the sentence, the more importance it is given. If the AI model didn’t take in some key phrase and failed to depict it in the generated image, try rearranging the order of words, placing the missing element earlier in the prompt. Bad vs. Good Prompt Example Bad prompt: portrait of a woman looking directly at the camera, neck tattoo, urban pink background. Good prompt: head and shoulders realistic photo portrait of a beautiful woman looking at the camera, white skin, pink lips, red hair, blue eyes, black tattoos on her neck, neon punk, highly detailed, pink neon city background. Creating effective prompts requires both artistic imagination and technical skills. By including the necessary building blocks and following the proper prompt structure you ensure that the text-to-image generation model understands your vision and produces optimal output. However, don’t be afraid to experiment; the more you practice, the more adept you become, and the more remarkable your creations will be. Have you ever found yourself staring at an image spotted somewhere on the internet and wondering whether it results from human or artificial creative labor? Since the breakthrough in image generation technology, I’ve been captivated by interior designs, nature scenery, fashion photographs, and futuristic cityscapes made with AI that look like professional artwork. Have you ever found yourself staring at an image spotted somewhere on the internet and wondering whether it results from human or artificial creative labor? Since the breakthrough in image generation technology, I’ve been captivated by interior designs, nature scenery, fashion photographs, and futuristic cityscapes made with AI that look like professional artwork. As someone with a creative eye yet no artistic skills, I was excited about the opportunity to transform ideas from my mind into visuals based solely on text input. I tried out several popular text-to-image tools, like MidJourney and DreamStudio on the web and ARTA on mobile. Still, while they all provided a good starting point and a straightforward user experience, the generation outcomes often fell short of my expectations and differed from what I envisioned — until I learned to tell AI what to draw in the language it understands. If you’re new to AI-generated art and need assistance streamlining the creative process, I’ll provide a step-by-step guide below to help you compose concise and well-structured text prompts that the AI models can effectively interpret and translate into the desired images. In the bottom line, I will share an example of both a correct and an incorrect prompt to illustrate how significantly they can impact the generation output in practice. First things first, two common prompt-writing mistakes you should avoid when using any text-to-image generator are being too wordy and using complex grammar. In fact, the more words you incorporate and the more complicated your grammar, the more difficult it is for AI to understand your prompt and adequately depict your concept. Therefore, communicate concisely, carefully choosing keywords, and list your ideas explicitly and separately rather than trying to cram them into one sentence. Step 1. Choose the Content Type Ask yourself how you want your image to look overall. Do you see it as a photograph, illustration, painting, sketch, or other artwork type? This initial decision puts you in control of the final result and helps align all the elements with this general framework. For instance, choosing a sketch will typically produce pencil images, while opting for a painting will add colors and likely create a more vintage appearance. Step 2. Define the Subject AI image generators require a specific subject for rendering, so you must indicate the main subject of your future image, whether a person, an animal, or a landscape. Stick to one subject per prompt and opt for concrete nouns like girl, dog, train, rose, ocean, temple, etc., for more accurate results. You can most likely render something using abstract keywords like love, peace, or joy, but the results may appear very inconsistent in what they depict. Step 3. Add Subject Description Now, it’s time to detail the concept with modifiers – adjectives or attributive nouns that add to the sense of a head subject. Modifiers can completely change the perspective of your image and boost its overall quality, so the more descriptive you are, the better the generated output. Define what the subject looks like, what the subject is doing, and other characteristics essential to representing your concept. Step 4. Describe the Context To help AI create the exact atmosphere and surroundings you need, give attention to aspects like lightning (studio, soft, cinematic, volumetric, accent lighting, sunlight, frontlight, backlight, ambient, moonlight, etc.), color theme (pastel, vibrant, neon pink, dark, etc.), environment/scene (in the sky, indoor, underwater, at night, etc.), and background (forest, beach, solid color, nebula, etc.). Additionally, consider the mood and vibe you want to convey. Simple feeling modifiers can set the scene’s atmosphere, whether you opt for positive (energetic, cozy, romantic, satisfaction, etc.) or negative (depressive, loneliness, regret, fear, etc.) ones. Step 5. Define Perspective Add a point of view to determine the angle from which you are looking at the image, such as side, overhead, or front. Other essential modifiers for creating photo-like images involve lenses and cameras. Here are a few examples: close-up, macro, lens flare, wide angle, microscopic, bokeh, isometric, depth of field, ultra-wide angle, fisheye lens, and panorama. Step 6. Add Art Style, Art Mediums, and Artists Proceed to aesthetic settings and define the overall artistic style. Also, specify the art medium. These aspects can greatly contribute to the value of the generated output, making it more consistent and expressive. Here are some of the common keywords: geometrical art, pop art, watercolor, line drawing, line art, 3D sculpture, crayon drawing, painting, oil painting, pastel drawing, medieval art, photography, digital art, stained glass, cave painting, polaroid, vector art, retro, illustration, comics, editorial fashion photography, Japanese anime style, surreal, travel photography, pencil sketch, steampunk, cartoon, futurism, vaporwave, art deco, interior design, psychedelic, street art. Consider including artistic influences. Adding the name of a specific artist whose signature artwork aligns with your chosen art genre can enhance the final image. Note, however, that finding the right artist is crucial so as not to mess up the output. Some artists affect the generation only subtly, while others can alter it significantly depending on their distinctive manner. For example, Claude Monet can infuse impressionism into landscapes, while mentioning Salvador Dali adds a surrealistic touch. Step 7. Add “Magic” Words Certain words can make a dramatic difference in the outcomes of the generation. The keywords like highly detailed, ultra-realistic, 4K, 8K, UHD, and HDR are the game changers for the overall quality of the image. Adding “studio lighting” will introduce appealing textures to the image, while “accent lighting” can draw attention to specific features. Describing the image as “professional” can enhance color contrast and detail, while mentioning “vivid colors” will bring life to your image. Using terms like ultra-wide angle, panoramic, or long-shot will help guide the camera. Packing your prompt with phrases related to artistic techniques and materials (such as trending on artstation, precise line-art, golden ratio, fine art, etc.) and those associated with artistic value (such as most beautiful image ever seen, epic composition, etc.) can also bring sophisticated improvements. Step 8. Consider Adding Negative Prompts Negative prompts are parameters that inform the generation model about what you do not want to see in the final image. They help prevent AI from generating specific elements, fix image abnormalities, and improve overall quality. Here are some universal examples: blurry, cropped, cloned face, duplicate, error, ugly, wrong proportions, deform, fused fingers, extra arms, law quality res, watermark, and more. Step 9. Define Correct Word Order and Keyword Weight Input The order is almost as important as the vocabulary, guiding the AI in generating the desired output. Combine keywords to direct the focus of your prompt and note key phrases that influence image preference. Emphasize essential keywords with a full colon and decimal number, use parentheses for added importance, and brackets for less importance. Typically, the earlier a word appears in the sentence, the more importance it is given. If the AI model didn’t take in some key phrase and failed to depict it in the generated image, try rearranging the order of words, placing the missing element earlier in the prompt. Bad vs. Good Prompt Example Bad prompt: portrait of a woman looking directly at the camera, neck tattoo, urban pink background. Good prompt: head and shoulders realistic photo portrait of a beautiful woman looking at the camera, white skin, pink lips, red hair, blue eyes, black tattoos on her neck, neon punk, highly detailed, pink neon city background. Creating effective prompts requires both artistic imagination and technical skills. By including the necessary building blocks and following the proper prompt structure you ensure that the text-to-image generation model understands your vision and produces optimal output. However, don’t be afraid to experiment; the more you practice, the more adept you become, and the more remarkable your creations will be.

How to Write Text Prompts for AI Image Generators to Get Optimal Results with Ease

Author:
(1) Yigit Ege Bayiz, Electrical and Computer Engineering The University of Texas at Austin Austin, Texas, USA (Email: egebayiz@utexas.edu);
(2) Ufuk Topcu, Aerospace Engineering and Engineering Mechanics The University of Texas at Austin Austin, Texas, USA (Email: utopcu@utexas.edu). Table of Links Abstract and Introduction Related Works Preliminaries Optimal Prebunking Problem Deterministic Baseline Policies Temporally Equidistant Prebunking Numerical Results Conclusion and References IV. OPTIMAL PREBUNKING PROBLEM To guard user c against misinformation, we employ prebunking. Prebunking relies on inoculating the users in the network by providing the users with correct information before they encounter a misinformation that contradicts the correct information. The idea of prebunking is similar to that of vaccination, where an early intervention to misinformation can immunize some users against it, reducing misinformation spread in the population. Fig. 1 shows the effect of prebunking in a small network of users. Lastly, we note that it is impossible to guard the center user c against a cascading misinformation k if the misinformation starts from c. As there is no way of estimating when a new misinformation cascade will start, there is no way to preemptively provide a prebunk to the central user c if a misinformation cascade starts on it. Thus, for theoretical analysis it is often necessary to assume that a misinformation cascade never starts at c. We rephrase this assumption as follows: This paper is available on arxiv under CC 4.0 license. Author: (1) Yigit Ege Bayiz, Electrical and Computer Engineering The University of Texas at Austin Austin, Texas, USA (Email: egebayiz@utexas.edu); (2) Ufuk Topcu, Aerospace Engineering and Engineering Mechanics The University of Texas at Austin Austin, Texas, USA (Email: utopcu@utexas.edu). Author: Author: (1) Yigit Ege Bayiz, Electrical and Computer Engineering The University of Texas at Austin Austin, Texas, USA (Email: egebayiz@utexas.edu); (2) Ufuk Topcu, Aerospace Engineering and Engineering Mechanics The University of Texas at Austin Austin, Texas, USA (Email: utopcu@utexas.edu). Table of Links Abstract and Introduction Abstract and Introduction Related Works Related Works Preliminaries Preliminaries Optimal Prebunking Problem Optimal Prebunking Problem Deterministic Baseline Policies Deterministic Baseline Policies Temporally Equidistant Prebunking Temporally Equidistant Prebunking Numerical Results Numerical Results Conclusion and References Conclusion and References IV. OPTIMAL PREBUNKING PROBLEM To guard user c against misinformation, we employ prebunking. Prebunking relies on inoculating the users in the network by providing the users with correct information before they encounter a misinformation that contradicts the correct information. The idea of prebunking is similar to that of vaccination, where an early intervention to misinformation can immunize some users against it, reducing misinformation spread in the population. Fig. 1 shows the effect of prebunking in a small network of users. Lastly, we note that it is impossible to guard the center user c against a cascading misinformation k if the misinformation starts from c. As there is no way of estimating when a new misinformation cascade will start, there is no way to preemptively provide a prebunk to the central user c if a misinformation cascade starts on it. Thus, for theoretical analysis it is often necessary to assume that a misinformation cascade never starts at c. We rephrase this assumption as follows: This paper is available on arxiv under CC 4.0 license. This paper is available on arxiv under CC 4.0 license. available on arxiv

Enhancing User Protection with Optimal Prebunking in Social Networks

The Transformer Algorithm with the Lowest Optimal Time Complexity Possible

সম্ভাব্য সর্বনিম্ন সর্বোত্তম সময়ের জটিলতা সহ ট্রান্সফরমার অ্যালগরিদম

Der Transformer-Algorithmus mit der geringstmöglichen optimalen Zeitkomplexität

El algoritmo de transformador con la menor complejidad de tiempo óptima posible

L'algorithme de transformateur avec la complexité temporelle optimale la plus faible possible

सबसे कम संभव इष्टतम समय जटिलता वाला ट्रांसफार्मर एल्गोरिदम

可能な限り最小の時間計算量を実現するトランスフォーマーアルゴリズム

가능한 가장 낮은 최적의 시간 복잡도를 갖는 변환기 알고리즘

O algoritmo do transformador com a menor complexidade de tempo ideal possível

Алгоритм трансформатора с минимально возможной оптимальной временной сложностью

Mümkün Olan En Düşük Optimal Zaman Karmaşıklığına Sahip Transformatör Algoritması

Thuật toán máy biến áp có độ phức tạp thời gian tối ưu thấp nhất có thể

具有最低最优时间复杂度的 Transformer 算法

**PHILADELPHIA, Pennsylvania, May 8th, 2024/CyberNewsWire/--**Security Risk Advisors (SRA) announces the launch of their OT/XIoT Detection Selection Workshop, a complimentary offering designed to assist organizations in selecting the most suitable operational technology (OT) and Extended Internet of Things (XIoT) security tools for their unique environments. Led by seasoned OT/XIoT security consultants, the workshop provides participants with an invaluable opportunity to gain insights into both best-in-class and novel solutions and to identify those closest aligned to their specific needs .In today’s increasingly interconnected digital landscape, the importance of choosing the right OT/XIoT security tools cannot be overstated. These tools serve as the first line of risk reduction and defense against cyber threats targeting critical industrial processes and infrastructure. Making informed decisions, whether adding a new solution or replacing an incumbent, significantly impacts an organization’s ability to mitigate threats and protect its assets. During the half-day consultation, participants will delve deep into their OT/XIoT security environments, examining current tools and analyzing their infrastructure. The free workshop will result in personalized recommendations of the best-fit solutions from industry vendors. “We recognize the importance of selecting the right security tools for cyber-physical environments,” says Jason Rivera, Director of OT/XIoT Security at SRA. “Our workshop empowers organizations to make informed decisions, giving confidence that their selection is fit for purpose.” Submit your application here. About Security Risk Advisors Security Risk Advisors offers Purple Teams, Cloud Security, Penetration Testing, OT Security, and 24x7x365 Cybersecurity Operations. Based in Philadelphia, SRA operates across the USA, Ireland and Australia. For more information, visit SRA’s website at https://sra.io. Contact Marketing Manager Douglas Webster news@sra.io 215-867-9051 This story was distributed as a release by Cyberwire under HackerNoon’s Business Blogging Program. Learn more about the program here. **PHILADELPHIA, Pennsylvania, May 8th, 2024/CyberNewsWire/--**Security Risk Advisors (SRA) announces the launch of their OT/XIoT Detection Selection Workshop, a complimentary offering designed to assist organizations in selecting the most suitable operational technology (OT) and Extended Internet of Things (XIoT) security tools for their unique environments. Led by seasoned OT/XIoT security consultants, the workshop provides participants with an invaluable opportunity to gain insights into both best-in-class and novel solutions and to identify those closest aligned to their specific needs .In today’s increasingly interconnected digital landscape, the importance of choosing the right OT/XIoT security tools cannot be overstated. These tools serve as the first line of risk reduction and defense against cyber threats targeting critical industrial processes and infrastructure. Making informed decisions, whether adding a new solution or replacing an incumbent, significantly impacts an organization’s ability to mitigate threats and protect its assets. During the half-day consultation, participants will delve deep into their OT/XIoT security environments, examining current tools and analyzing their infrastructure. The free workshop will result in personalized recommendations of the best-fit solutions from industry vendors. “We recognize the importance of selecting the right security tools for cyber-physical environments,” says Jason Rivera, Director of OT/XIoT Security at SRA. “Our workshop empowers organizations to make informed decisions, giving confidence that their selection is fit for purpose.” “We recognize the importance of selecting the right security tools for cyber-physical environments,” says Jason Rivera, Director of OT/XIoT Security at SRA. “Our workshop empowers organizations to make informed decisions, giving confidence that their selection is fit for purpose.” Submit your application here. Submit your application here. Submit your application here. About Security Risk Advisors Security Risk Advisors offers Purple Teams, Cloud Security, Penetration Testing, OT Security, and 24x7x365 Cybersecurity Operations. Based in Philadelphia, SRA operates across the USA, Ireland and Australia. For more information, visit SRA’s website at https://sra.io . https://sra.io https://sra.io Contact Marketing Manager Douglas Webster news@sra.io 215-867-9051 This story was distributed as a release by Cyberwire under HackerNoon’s Business Blogging Program. Learn more about the program here. This story was distributed as a release by Cyberwire under HackerNoon’s Business Blogging Program. Learn more about the program here . here here

Free Workshop From Security Risk Advisors Empowers Organizations To Select Optimal OT Security Tools

নিরাপত্তা ঝুঁকি উপদেষ্টাদের থেকে বিনামূল্যে কর্মশালা সর্বোত্তম OT নিরাপত্তা সরঞ্জাম নির্বাচন করার জন্য সংস্থাগুলিকে ক্ষমতা দেয়

Kostenloser Workshop von Security Risk Advisors unterstützt Unternehmen bei der Auswahl optimaler OT-Sicherheitstools

El taller gratuito de Security Risk Advisors permite a las organizaciones seleccionar herramientas de seguridad OT óptimas

Un atelier gratuit organisé par des conseillers en risques de sécurité permet aux organisations de sélectionner les outils de sécurité OT optimaux

सुरक्षा जोखिम सलाहकारों की ओर से निःशुल्क कार्यशाला संगठनों को इष्टतम OT सुरक्षा उपकरण चुनने में सक्षम बनाती है

セキュリティリスクアドバイザーによる無料ワークショップで、組織は最適な OT セキュリティツールを選択できるようになります。

보안 위험 자문가의 무료 워크숍을 통해 조직이 최적의 OT 보안 도구를 선택할 수 있도록 지원

Workshop gratuito de consultores de risco de segurança capacita organizações a selecionar ferramentas de segurança TO ideais

Бесплатный семинар от консультантов по рискам безопасности дает организациям возможность выбирать оптимальные инструменты безопасности OT

Güvenlik Riski Danışmanlarından Ücretsiz Atölye Çalışması Kuruluşlara En İyi OT Güvenlik Araçlarını Seçme Gücü Veriyor

Hội thảo miễn phí từ các cố vấn rủi ro bảo mật trao quyền cho các tổ chức lựa chọn các công cụ bảo mật OT tối ưu

安全风险顾问举办的免费研讨会帮助组织选择最佳 OT 安全工具

In these intensely competitive times, every application needs to be aesthetically appealing in addition to providing seamless functionality to satisfy the users. If an app does not function properly because of a visual interface error or if the site is unreadable, users may uninstall or leave the app. This can ultimately lead to a loss of customers and a drop in revenues. To avoid this and ensure the best possible user experience, companies are prioritizing visual regression testing. Let us study a couple of examples of visual regression testing to understand its importance: When you click on a drop-down image the menu does not slide down after adding more options.
You have reworked the complete layout of the page, and the submit button on the page is broken. These UI errors need to be fixed since changes in the elements can lead to the breakdown of the visual aesthetics. These illustrations clearly highlight the importance of conducting thorough visual regression testing before software releases. Visual regression testing checks the UI of an application after code changes and ensures that these different visual elements, like buttons, images, and text, all render correctly. Through this blog, we will examine visual regression, the different techniques used, the challenges testers face when performing the tests, and the best practices to overcome them. Common Visual Regression Techniques Visual testing ensures that visual glitches are identified early and do not spill over to the production stage. Let us now briefly examine the commonly used methods for regression testing: Manual visual testing: In this method, testers manually compare UI screenshots before and after making changes in the code.
Comparing layouts: It requires comparing the UI layout before and after changes are made and accounts for changes in the UI’s font, color, and other visual elements.
Comparing pixel-by-pixel: Used to test small, complex UI elements, this method involves comparing the UI’s pixels before and after changes.
Structural comparison: It compares the UI’s Document Object Model (DOM) before and after making changes.
Inserting visual checkpoints: In this technique, checkpoints are inserted into the UI to check the UI’s visual state at specific points in time. Manual Regression Testing Manual regression testing is recommended in the early testing stages when the UI is unstable. It is suitable for ad hoc testing and conducting quick on-the-spot checks. In this method, the testers manually check the layout and appearance of the visual elements. It involves taking the latest screenshots and comparing them with baseline screenshots to unearth any gaps. Benefits of Automated Visual Regression Testing Over Manual Methods The manual technique can be time-consuming and lead to a waste of resources because of its repetitive nature. The scale of manual testing grows with every new feature addition, thereby increasing the time spent by a human tester pouring over screenshots to identify bugs. It is impractical to manually conduct visual regression testing when there are tight deadlines to meet. In contrast, automated visual regression testing helps you automate repetitive tasks like checking the page following every code change. Even with the heavy initial investment, automated testing, especially with AI-powered features, helps you save time and money in the long run. Though automated visual regression testing reaps many benefits for testers and developers, it has to be properly implemented if they are to receive its benefits. Let us examine the best practices that go into a proper visual regression testing process. What To Remember While Conducting Visual Regression Testing Following these best practices will help optimize your automated visual regression testing process and help you gain its maximum benefits: Develop Appropriate Test Scenarios Clearly define what to record in the snapshots and the time to take them while testing. Remember to include user interactions in such scenarios since the applications will need to deal with them in the real world. Validate the Entire UI Page Instead of only validating individual components, ensure to validate the entire UI page. This practice will increase the test coverage and improve it. Pick the Right Automated Tool The visual regression testing tool you choose should be capable of ignoring false positives. It should be able to take care of pixel offsets, anti-aliasing, and other issues while ensuring the tests don’t fail. The automated algorithm must be able to analyze the page’s structure and perform layout comparisons. It should also be able to take care of content that is dynamic and moving. Compare Screenshots Testers should compare screenshots with recent ones to identify the disparities. This will help ensure that the UI remains the same, improving the user experience and product quality. Identify and Resolve Bugs Ensure to resolve bugs that the testing tool identifies or send them to the respective developers for fixing them. Remember to update screenshots to be used as a baseline for future regression tests after it is done. Choose the Right Situation To Perform Automated Testing Automated visual regression testing may not be appropriate for all scenarios. In some situations, using a combination of manual and automated methods is advisable. For example, when new features are added, they can be validated using an automation technique and then checked manually. Conduct a Detailed Review A team of reviewers or a single reviewer can examine how adjustments are made without causing interruptions in the desired outcome and make a report accordingly. Learn From Your Mistakes Learning from your successes and failures is crucial in visual regression testing. You need to identify the root causes and impacts of the visual changes detected by your tool. Testers must also identify false negatives and positives and adjust the tool settings and test cases accordingly. Conclusion In conclusion, successful implementation of visual regression testing in Agile teams requires a holistic approach that encompasses automation, collaboration, scalability, and comprehensive analysis. Visual regression testing can be a game-changer if you choose an appropriate automated testing tool with the right features and advantages. By adhering to these best practices, Agile teams can effectively leverage visual regression testing to deliver high-quality user interfaces in an iterative and efficient manner. In these intensely competitive times, every application needs to be aesthetically appealing in addition to providing seamless functionality to satisfy the users. If an app does not function properly because of a visual interface error or if the site is unreadable, users may uninstall or leave the app. This can ultimately lead to a loss of customers and a drop in revenues. To avoid this and ensure the best possible user experience, companies are prioritizing visual regression testing . visual regression testing Let us study a couple of examples of visual regression testing to understand its importance: Let us study a couple of examples of visual regression testing to understand its importance: When you click on a drop-down image the menu does not slide down after adding more options. You have reworked the complete layout of the page, and the submit button on the page is broken. When you click on a drop-down image the menu does not slide down after adding more options. You have reworked the complete layout of the page, and the submit button on the page is broken. These UI errors need to be fixed since changes in the elements can lead to the breakdown of the visual aesthetics. These illustrations clearly highlight the importance of conducting thorough visual regression testing before software releases. Visual regression testing checks the UI of an application after code changes and ensures that these different visual elements, like buttons, images, and text, all render correctly. Through this blog, we will examine visual regression, the different techniques used, the challenges testers face when performing the tests, and the best practices to overcome them. Common Visual Regression Techniques Visual testing ensures that visual glitches are identified early and do not spill over to the production stage. Let us now briefly examine the commonly used methods for regression testing: Manual visual testing: In this method, testers manually compare UI screenshots before and after making changes in the code. Comparing layouts: It requires comparing the UI layout before and after changes are made and accounts for changes in the UI’s font, color, and other visual elements. Comparing pixel-by-pixel: Used to test small, complex UI elements, this method involves comparing the UI’s pixels before and after changes. Structural comparison: It compares the UI’s Document Object Model (DOM) before and after making changes. Inserting visual checkpoints: In this technique, checkpoints are inserted into the UI to check the UI’s visual state at specific points in time. Manual visual testing: In this method, testers manually compare UI screenshots before and after making changes in the code. Manual visual testing: Comparing layouts: It requires comparing the UI layout before and after changes are made and accounts for changes in the UI’s font, color, and other visual elements. Comparing layouts: Comparing pixel-by-pixel: Used to test small, complex UI elements, this method involves comparing the UI’s pixels before and after changes. Comparing pixel-by-pixel: Structural comparison: It compares the UI’s Document Object Model (DOM) before and after making changes. Structural comparison: Inserting visual checkpoints: In this technique, checkpoints are inserted into the UI to check the UI’s visual state at specific points in time. Inserting visual checkpoints: Manual Regression Testing Manual regression testing is recommended in the early testing stages when the UI is unstable. It is suitable for ad hoc testing and conducting quick on-the-spot checks. In this method, the testers manually check the layout and appearance of the visual elements. It involves taking the latest screenshots and comparing them with baseline screenshots to unearth any gaps. Benefits of Automated Visual Regression Testing Over Manual Methods The manual technique can be time-consuming and lead to a waste of resources because of its repetitive nature. The scale of manual testing grows with every new feature addition, thereby increasing the time spent by a human tester pouring over screenshots to identify bugs. It is impractical to manually conduct visual regression testing when there are tight deadlines to meet. In contrast, automated visual regression testing helps you automate repetitive tasks like checking the page following every code change. Even with the heavy initial investment, automated testing, especially with AI-powered features, helps you save time and money in the long run. Though automated visual regression testing reaps many benefits for testers and developers, it has to be properly implemented if they are to receive its benefits. Let us examine the best practices that go into a proper visual regression testing process. What To Remember While Conducting Visual Regression Testing Following these best practices will help optimize your automated visual regression testing process and help you gain its maximum benefits: Develop Appropriate Test Scenarios Clearly define what to record in the snapshots and the time to take them while testing. Remember to include user interactions in such scenarios since the applications will need to deal with them in the real world. Validate the Entire UI Page Instead of only validating individual components, ensure to validate the entire UI page. This practice will increase the test coverage and improve it. Pick the Right Automated Tool The visual regression testing tool you choose should be capable of ignoring false positives. It should be able to take care of pixel offsets, anti-aliasing, and other issues while ensuring the tests don’t fail. The automated algorithm must be able to analyze the page’s structure and perform layout comparisons. It should also be able to take care of content that is dynamic and moving. Compare Screenshots Testers should compare screenshots with recent ones to identify the disparities. This will help ensure that the UI remains the same, improving the user experience and product quality. Identify and Resolve Bugs Ensure to resolve bugs that the testing tool identifies or send them to the respective developers for fixing them. Remember to update screenshots to be used as a baseline for future regression tests after it is done. Choose the Right Situation To Perform Automated Testing Automated visual regression testing may not be appropriate for all scenarios. In some situations, using a combination of manual and automated methods is advisable. For example, when new features are added, they can be validated using an automation technique and then checked manually. Conduct a Detailed Review A team of reviewers or a single reviewer can examine how adjustments are made without causing interruptions in the desired outcome and make a report accordingly. Learn From Your Mistakes Learning from your successes and failures is crucial in visual regression testing. You need to identify the root causes and impacts of the visual changes detected by your tool. Testers must also identify false negatives and positives and adjust the tool settings and test cases accordingly. Conclusion In conclusion, successful implementation of visual regression testing in Agile teams requires a holistic approach that encompasses automation, collaboration, scalability, and comprehensive analysis. Visual regression testing can be a game-changer if you choose an appropriate automated testing tool with the right features and advantages. By adhering to these best practices, Agile teams can effectively leverage visual regression testing to deliver high-quality user interfaces in an iterative and efficient manner.

Optimal Strategies for Integrating Visual Regression Testing into Agile Teams

Efficient Neural Network Approaches for Conditional Optimal Transport: Discussion and Reference

Efficient Neural Network Approaches for Conditional Optimal Transport: Numerical Experiments

This paper is available on arxiv under CC 4.0 license.
Authors:
(1) Zheyu Oliver Wang, Department of Aeronautics and Astronautics, Massachusetts Institute of Technology, Cambridge, MA and olivrw@mit.edu;
(2)  Ricardo Baptista, Computing + Mathematical Sciences, California Institute of Technology, Pasadena, CA and rsb@caltech.edu;
(3) Youssef Marzouk, Department of Aeronautics and Astronautics, Massachusetts Institute of Technology, Cambridge, MA and ymarz@mit.edu;
(4) Lars Ruthotto, Department of Mathematics, Emory University, Atlanta, GA and lruthotto@emory.edu;
(5) Deepanshu Verma, Department of Mathematics, Emory University, Atlanta, GA and deepanshu.verma@emory.edu. Table of Links Abstract & Introduction
Background and Related Work
Partially Convex Potential Maps (PCP-Map) for Conditional OT
Conditional OT flow (COT-Flow)
Implementation and Experimental Setup
Numerical Experiments
Discussion and Reference 4. Conditional OT flow (COT-Flow). In this section, we extend the OT-regularized continuous normalizing flows in [36] to the conditional generative modeling problem introduced in section 2. Training Problem. Following the general approach of continuous normalizing flows [11, 19], we express the transport map that pushes forward the reference distribution ρz to the target π(x|y) via the flow map of an ODE. That is, we define g(z, y) = u(1) as the terminal state of the ODE where the evolution of u: [0, 1] → R n depends on the velocity field v : [0, 1] × R n × R m → R n and will be parameterized with a neural network below. When the velocity is trained to minimize the negative log-likelihood loss in (3.2), the resulting mapping is called a continuous normalizing flow [19]. We add y as an additional input to the velocity field to enable conditional sampling. Consequently, the resulting flow map and generator g depend on y. One advantage of defining the generator through an ODE is that the loss function can be evaluated efficiently for a wide range of velocity functions. Recall that the loss function requires the inverse of the generator and the log-determinant of its Jacobian. For sufficiently regular velocity fields, the inverse of the generator can be obtained by integrating backward in time. To be precise, we define g −1 (x, y) = p(0) where p : [0, 1] → R n satisfies (4.1) with the terminal condition p(1) = x. As derived in [58, 19, 56], constructing the generator through an ODE also simplifies computing the log-determinant of the Jacobian, i.e., Penalizing transport costs during training leads to theoretical and numerical advantages; see, for example, [58, 56, 36, 17]. Hence, we consider the OT-regularized training problem where α1 > 0 is a regularization parameter that trades off matching the distributions (for α1 ≪ 1) and minimizing the transport costs (for α1 ≫ 0) given by the dynamic transport cost penalty This penalty is stronger than the static counterpart in (3.4), in other words However, the values of both penalties agree when the velocity field in (4.1) is constant along the trajectories, which is the case for the optimal transport map. Hence, we expect the solution of the dynamic problem to be close to that of the static formulation when α1 is chosen well. To provide additional theoretical insight and motivate our numerical method, we note that (4.3) is related to the potential mean field game (MFG) Here, the terminal and running costs in the objective functional are the L2 anti-derivatives of JNLL and PDOT, respectively, and the continuity equation is used to represent the density evolution under the velocity v. To be precise, (4.3) can be seen as a discretization of (4.6) in the Lagrangian coordinates defined by the reversed ODE (4.14). Note that both formulations differ in the way the transport costs are measured: (4.4) computes the cost of pushing the conditional distribution to the Gaussian, while (4.6) penalizes the costs of pushing the Gaussian to the conditional. While these two terms do not generally agree, they coincide for the L2 optimal transport map; see [16, Corollary 2.5.13] for a proof for unconditional optimal transport. For more insights into MFGs and their relation to optimal transport and generative modeling, we refer to our prior work [43] and the more recent work [57, Sec 3.4]. The fact that the solutions of the microscopic version in (4.3) and the macroscopic version in (4.6) agree is remarkable and was first shown in the seminal work [28]. By Pontryagin’s maximum principle, the solution of (4.3) satisfies the feedback form where Φ : [0, 1] × R n × R m → R and Φ(·, ·, y) can be seen as the value function of the MFG and, alternatively, as the Lagrange multiplier in (4.6) for a fixed y. Therefore, we model the velocity as a conservative vector field as also proposed in [36, 43]. This also simplifies the computation of the log-determinant since the Jacobian of v is symmetric, and we note that Another consequence of optimal control theory is that the value function satisfies the Hamilton Jacobi Bellman (HJB) equations with the terminal condition which is only tractable if the joint density, π(x, y), is available. These n-dimensional PDEs are parameterized by y ∈ R m. Neural network approach. We parameterize the value function, Φ, with a scalar-valued neural network. In contrast to the static approach in the previous section, the choice of function approximator is more flexible in the dynamic approach. The approach can be effective as long as Φ is parameterized with any function approximation tool that is effective in high dimensions, allows efficient evaluation of its gradient and Laplacian, and the training problem can be solved sufficiently well. For our numerical experiments, we use the architecture considered in [36] and model Φ as the sum of a simple feed-forward neural network and a quadratic term. That is, As in [36], we model the neural network as a two-layer residual network of width w that reads Sample generation. After training, we draw i.i.d. samples from the approximated conditional distribution for a given y by sampling z ∼ ρz and solving the ODE (4.1). Since we train the inverse generator using a fixed number of integration steps, nt, it is interesting to investigate how close our solution is to the continuous problem. One indicator is to compare the samples obtained with different number of integration steps during sampling. Another indicator is to compute the variance of ∇Φ along the trajectories. Hyperparameters. As described in section 5, we randomly sample the width, w, of the neural network, the number of time integration steps during training, the penalty parameters α1, α2, and the hyperparameters of the Adam optimizer (batch size and initial learning rate) from the values listed in Table 2. This paper is available on arxiv under CC 4.0 license. Authors: (1) Zheyu Oliver Wang, Department of Aeronautics and Astronautics, Massachusetts Institute of Technology, Cambridge, MA and olivrw@mit.edu; (2)  Ricardo Baptista, Computing + Mathematical Sciences, California Institute of Technology, Pasadena, CA and rsb@caltech.edu; (3) Youssef Marzouk, Department of Aeronautics and Astronautics, Massachusetts Institute of Technology, Cambridge, MA and ymarz@mit.edu; (4) Lars Ruthotto, Department of Mathematics, Emory University, Atlanta, GA and lruthotto@emory.edu; (5) Deepanshu Verma, Department of Mathematics, Emory University, Atlanta, GA and deepanshu.verma@emory.edu. This paper is available on arxiv under CC 4.0 license. Authors: Authors: (1) Zheyu Oliver Wang, Department of Aeronautics and Astronautics, Massachusetts Institute of Technology, Cambridge, MA and olivrw@mit.edu; (2)  Ricardo Baptista, Computing + Mathematical Sciences, California Institute of Technology, Pasadena, CA and rsb@caltech.edu; (3) Youssef Marzouk, Department of Aeronautics and Astronautics, Massachusetts Institute of Technology, Cambridge, MA and ymarz@mit.edu; (4) Lars Ruthotto, Department of Mathematics, Emory University, Atlanta, GA and lruthotto@emory.edu; (5) Deepanshu Verma, Department of Mathematics, Emory University, Atlanta, GA and deepanshu.verma@emory.edu. Table of Links Abstract & Introduction Background and Related Work Partially Convex Potential Maps (PCP-Map) for Conditional OT Conditional OT flow (COT-Flow) Implementation and Experimental Setup Numerical Experiments Discussion and Reference Abstract & Introduction Abstract & Introduction Background and Related Work Background and Related Work Partially Convex Potential Maps (PCP-Map) for Conditional OT Partially Convex Potential Maps (PCP-Map) for Conditional OT Conditional OT flow (COT-Flow) Conditional OT flow (COT-Flow) Implementation and Experimental Setup Implementation and Experimental Setup Numerical Experiments Numerical Experiments Discussion and Reference Discussion and Reference 4. Conditional OT flow (COT-Flow). In this section, we extend the OT-regularized continuous normalizing flows in [36] to the conditional generative modeling problem introduced in section 2. Training Problem. Following the general approach of continuous normalizing flows [11, 19], we express the transport map that pushes forward the reference distribution ρz to the target π(x|y) via the flow map of an ODE. That is, we define g(z, y) = u(1) as the terminal state of the ODE where the evolution of u: [0, 1] → R n depends on the velocity field v : [0, 1] × R n × R m → R n and will be parameterized with a neural network below. When the velocity is trained to minimize the negative log-likelihood loss in (3.2), the resulting mapping is called a continuous normalizing flow [19]. We add y as an additional input to the velocity field to enable conditional sampling. Consequently, the resulting flow map and generator g depend on y. One advantage of defining the generator through an ODE is that the loss function can be evaluated efficiently for a wide range of velocity functions. Recall that the loss function requires the inverse of the generator and the log-determinant of its Jacobian. For sufficiently regular velocity fields, the inverse of the generator can be obtained by integrating backward in time. To be precise, we define g −1 (x, y) = p(0) where p : [0, 1] → R n satisfies (4.1) with the terminal condition p(1) = x. As derived in [58, 19, 56], constructing the generator through an ODE also simplifies computing the log-determinant of the Jacobian, i.e., Penalizing transport costs during training leads to theoretical and numerical advantages; see, for example, [58, 56, 36, 17]. Hence, we consider the OT-regularized training problem where α1 > 0 is a regularization parameter that trades off matching the distributions (for α1 ≪ 1) and minimizing the transport costs (for α1 ≫ 0) given by the dynamic transport cost penalty This penalty is stronger than the static counterpart in (3.4), in other words However, the values of both penalties agree when the velocity field in (4.1) is constant along the trajectories, which is the case for the optimal transport map. Hence, we expect the solution of the dynamic problem to be close to that of the static formulation when α1 is chosen well. To provide additional theoretical insight and motivate our numerical method, we note that (4.3) is related to the potential mean field game (MFG) Here, the terminal and running costs in the objective functional are the L2 anti-derivatives of JNLL and PDOT, respectively, and the continuity equation is used to represent the density evolution under the velocity v. To be precise, (4.3) can be seen as a discretization of (4.6) in the Lagrangian coordinates defined by the reversed ODE (4.14). Note that both formulations differ in the way the transport costs are measured: (4.4) computes the cost of pushing the conditional distribution to the Gaussian, while (4.6) penalizes the costs of pushing the Gaussian to the conditional. While these two terms do not generally agree, they coincide for the L2 optimal transport map; see [16, Corollary 2.5.13] for a proof for unconditional optimal transport. For more insights into MFGs and their relation to optimal transport and generative modeling, we refer to our prior work [43] and the more recent work [57, Sec 3.4]. The fact that the solutions of the microscopic version in (4.3) and the macroscopic version in (4.6) agree is remarkable and was first shown in the seminal work [28]. By Pontryagin’s maximum principle, the solution of (4.3) satisfies the feedback form where Φ : [0, 1] × R n × R m → R and Φ(·, ·, y) can be seen as the value function of the MFG and, alternatively, as the Lagrange multiplier in (4.6) for a fixed y. Therefore, we model the velocity as a conservative vector field as also proposed in [36, 43]. This also simplifies the computation of the log-determinant since the Jacobian of v is symmetric, and we note that Another consequence of optimal control theory is that the value function satisfies the Hamilton Jacobi Bellman (HJB) equations with the terminal condition which is only tractable if the joint density, π(x, y), is available. These n-dimensional PDEs are parameterized by y ∈ R m. Neural network approach. We parameterize the value function, Φ, with a scalar-valued neural network. In contrast to the static approach in the previous section, the choice of function approximator is more flexible in the dynamic approach. The approach can be effective as long as Φ is parameterized with any function approximation tool that is effective in high dimensions, allows efficient evaluation of its gradient and Laplacian, and the training problem can be solved sufficiently well. For our numerical experiments, we use the architecture considered in [36] and model Φ as the sum of a simple feed-forward neural network and a quadratic term. That is, As in [36], we model the neural network as a two-layer residual network of width w that reads Sample generation. After training, we draw i.i.d. samples from the approximated conditional distribution for a given y by sampling z ∼ ρz and solving the ODE (4.1). Since we train the inverse generator using a fixed number of integration steps, nt, it is interesting to investigate how close our solution is to the continuous problem. One indicator is to compare the samples obtained with different number of integration steps during sampling. Another indicator is to compute the variance of ∇Φ along the trajectories. Hyperparameters. As described in section 5, we randomly sample the width, w, of the neural network, the number of time integration steps during training, the penalty parameters α1, α2, and the hyperparameters of the Adam optimizer (batch size and initial learning rate) from the values listed in Table 2.

Stories, News & Mentions about OPTIMAL

Optimal’s Stories on HackerNoon