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2023

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Articles 1351 - 1380 of 3503

Full-Text Articles in Computer Sciences

Bertastic At Semeval-2023 Task 3: Fine-Tuning Pretrained Multilingual Transformers – Does Order Matter?, Tarek Mahmoud, Preslav Nakov Jul 2023

Bertastic At Semeval-2023 Task 3: Fine-Tuning Pretrained Multilingual Transformers – Does Order Matter?, Tarek Mahmoud, Preslav Nakov

Natural Language Processing Faculty Publications

The naïve approach for fine-tuning pretrained deep learning models on downstream tasks involves feeding them mini-batches of randomly sampled data. In this paper, we propose a more elaborate method for fine-tuning Pretrained Multilingual Transformers (PMTs) on multilingual data. Inspired by the success of curriculum learning approaches, we investigate the significance of fine-tuning PMTs on multilingual data in a sequential fashion language by language. Unlike the curriculum learning paradigm where the model is presented with increasingly complex examples, we do not adopt a notion of “easy” and “hard” samples. Instead, our experiments draw insight from psychological findings on how the human …

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Conformal Prediction For Federated Uncertainty Quantification Under Label Shift, Vincent Plassier, Mehdi Makni, Aleksandr Rubashevskii, Eric Moulines, Maxim Panov Jul 2023

Conformal Prediction For Federated Uncertainty Quantification Under Label Shift, Vincent Plassier, Mehdi Makni, Aleksandr Rubashevskii, Eric Moulines, Maxim Panov

Machine Learning Faculty Publications

Federated Learning (FL) is a machine learning framework where many clients collaboratively train models while keeping the training data decentralized. Despite recent advances in FL, the uncertainty quantification topic (UQ) remains partially addressed. Among UQ methods, conformal prediction (CP) approaches provides distribution-free guarantees under minimal assumptions. We develop a new federated conformal prediction method based on quantile regression and take into account privacy constraints. This method takes advantage of importance weighting to effectively address the label shift between agents and provides theoretical guarantees for both valid coverage of the prediction sets and differential privacy. Extensive experimental studies demonstrate that this …

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How To Best Retrain A Neural Network If We Added One More Input Variable, Saeid Tizpaz-Niari, Vladik Kreinovich Jul 2023

How To Best Retrain A Neural Network If We Added One More Input Variable, Saeid Tizpaz-Niari, Vladik Kreinovich

Departmental Technical Reports (CS)

Often, once we have trained a neural network to estimate the value of a quantity y based on the available values of inputs x1, ..., xn, we learn to measure the values of an additional quantity that have some influence on y. In such situations, it is desirable to re-train the neural network, so that it will be able to take this extra value into account. A straightforward idea is to add a new input to the first layer and to update all the weights based on the patterns that include the values of the new input. The problem with …

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Topological Explanation Of Why Complex Numbers Are Needed In Quantum Physics, Julio C. Urenda, Vladik Kreinovich Jul 2023

Topological Explanation Of Why Complex Numbers Are Needed In Quantum Physics, Julio C. Urenda, Vladik Kreinovich

Departmental Technical Reports (CS)

In quantum computing, we only use states in which all amplitudes are real numbers. So why do we need complex numbers with non-zero imaginary part in quantum physics in general? In this paper, we provide a simple topological explanation for this need, explanation based on the Second Law of Thermodynamics.

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Numerical Design And Optimization Of Near-Infrared Band- Pass Filter, Hafiza Syeeda Faiza, Ghazi Aman Nowsherwan, Basem A. Abu Izneid, Muhammad Azhar, Saira Riaz, Syed Sajjad Hussain, Saira Ikram, Mohsin Khan, Shahzad Naseem, Mohammad Kanan, Ibrahim M. Mansour Jul 2023

Numerical Design And Optimization Of Near-Infrared Band- Pass Filter, Hafiza Syeeda Faiza, Ghazi Aman Nowsherwan, Basem A. Abu Izneid, Muhammad Azhar, Saira Riaz, Syed Sajjad Hussain, Saira Ikram, Mohsin Khan, Shahzad Naseem, Mohammad Kanan, Ibrahim M. Mansour

Applied Mathematics & Information Sciences

Band-pass filters functioning in the near-infrared (IR) range are desired for laser technology, multi-photon fluorescence, and IR imaging applications. In this study, we have designed four band-pass filters in the near Infrared spectrum (900-1200 nm) by vertically stacking different high and low-index materials. The band-pass filters are modelled by Essential Macleod software with different thicknesses. The layer’s thicknesses were optimized in such a way to provide the negligible reflectance and maximum transmission on the front side. All the simulated band-pass filters exhibit high transmittance, but TiO2/Al2O3 and Ta2O5/Al2O3 outperforms other modelled structure in terms of performance due to the better …

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A Universal Unbiased Method For Classification From Aggregate Observations, Zixi Wei, Lei Feng, Bo Han, Tongliang Liu, Gang Niu, Xiaofeng Zhu, Heng Tao Shen Jul 2023

A Universal Unbiased Method For Classification From Aggregate Observations, Zixi Wei, Lei Feng, Bo Han, Tongliang Liu, Gang Niu, Xiaofeng Zhu, Heng Tao Shen

Machine Learning Faculty Publications

In conventional supervised classification, true labels are required for individual instances. However, it could be prohibitive to collect the true labels for individual instances, due to privacy concerns or unaffordable annotation costs. This motivates the study on classification from aggregate observations (CFAO), where the supervision is provided to groups of instances, instead of individual instances. CFAO is a generalized learning framework that contains various learning problems, such as multiple-instance learning and learning from label proportions. The goal of this paper is to present a novel universal method of CFAO, which holds an unbiased estimator of the classification risk for arbitrary …

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Diversity-Enhancing Generative Network For Few-Shot Hypothesis Adaptation, Ruijiang Dong, Feng Liu, Haoang Chi, Tongliang Liu, Mingming Gong, Gang Niu, Masashi Sugiyama, Bo Han Jul 2023

Diversity-Enhancing Generative Network For Few-Shot Hypothesis Adaptation, Ruijiang Dong, Feng Liu, Haoang Chi, Tongliang Liu, Mingming Gong, Gang Niu, Masashi Sugiyama, Bo Han

Machine Learning Faculty Publications

Generating unlabeled data has been recently shown to help address the few-shot hypothesis adaptation (FHA) problem, where we aim to train a classifier for the target domain with a few labeled target-domain data and a well-trained source-domain classifier (i.e., a source hypothesis), for the additional information of the highly-compatible unlabeled data. However, the generated data of the existing methods are extremely similar or even the same. The strong dependency among the generated data will lead the learning to fail. In this paper, we propose a diversity-enhancing generative network (DEG-Net) for the FHA problem, which can generate diverse unlabeled data with …

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Identifiability Of Label Noise Transition Matrix, Yang Liu, Hao Cheng, Kun Zhang Jul 2023

Identifiability Of Label Noise Transition Matrix, Yang Liu, Hao Cheng, Kun Zhang

Machine Learning Faculty Publications

The noise transition matrix plays a central role in the problem of learning with noisy labels. Among many other reasons, a large number of existing solutions rely on the knowledge of it. Identifying and estimating the transition matrix without ground truth labels is a critical and challenging task. When label noise transition depends on each instance, the problem of identifying the instance-dependent noise transition matrix becomes substantially more challenging. Despite recently proposed solutions for learning from instance-dependent noisy labels, the literature lacks a unified understanding of when such a problem remains identifiable. The goal of this paper is to characterize …

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Adaptive Compositional Continual Meta-Learning, Bin Wu, Jinyuan Fang, Xiangxiang Zeng, Shangsong Liang, Qiang Zhang Jul 2023

Adaptive Compositional Continual Meta-Learning, Bin Wu, Jinyuan Fang, Xiangxiang Zeng, Shangsong Liang, Qiang Zhang

Machine Learning Faculty Publications

This paper focuses on continual meta-learning, where few-shot tasks are heterogeneous and sequentially available. Recent works use a mixture model for meta-knowledge to deal with the heterogeneity. However, these methods suffer from parameter inefficiency caused by two reasons: (1) the underlying assumption of mutual exclusiveness among mixture components hinders sharing meta-knowledge across heterogeneous tasks. (2) they only allow increasing mixture components and cannot adaptively filter out redundant components. In this paper, we propose an Adaptive Compositional Continual Meta-Learning (ACML) algorithm, which employs a compositional premise to associate a task with a subset of mixture components, allowing meta-knowledge sharing among heterogeneous …

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Fast Rates For Maximum Entropy Exploration, Daniil Tiapkin, Denis Belomestny, Daniele Calandriello, Éric Moulines, Rémi Munos, Alexey Naumov, Pierre Perrault, Yunhao Tang, Michal Valko, Pierre Ménard Jul 2023

Fast Rates For Maximum Entropy Exploration, Daniil Tiapkin, Denis Belomestny, Daniele Calandriello, Éric Moulines, Rémi Munos, Alexey Naumov, Pierre Perrault, Yunhao Tang, Michal Valko, Pierre Ménard

Machine Learning Faculty Publications

We address the challenge of exploration in reinforcement learning (RL) when the agent operates in an unknown environment with sparse or no rewards. In this work, we study the maximum entropy exploration problem of two different types. The first type is visitation entropy maximization previously considered by Hazan et al. (2019) in the discounted setting. For this type of exploration, we propose a game-theoretic algorithm that has Oe(H3S2A/ε2) sample complexity thus improving the ε-dependence upon existing results, where S is a number of states, A is a number of actions, H is an episode length, and ε is a desired …

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Evolving Semantic Prototype Improves Generative Zero-Shot Learning, Shiming Chen, Wenjin Hou, Ziming Hong, Xiaohan Ding, Yibing Song, Xinge You, Tongliang Liu, Kun Zhang Jul 2023

Evolving Semantic Prototype Improves Generative Zero-Shot Learning, Shiming Chen, Wenjin Hou, Ziming Hong, Xiaohan Ding, Yibing Song, Xinge You, Tongliang Liu, Kun Zhang

Machine Learning Faculty Publications

In zero-shot learning (ZSL), generative methods synthesize class-related sample features based on predefined semantic prototypes. They advance the ZSL performance by synthesizing unseen class sample features for better training the classifier. We observe that each class's predefined semantic prototype (also referred to as semantic embedding or condition) does not accurately match its real semantic prototype. So the synthesized visual sample features do not faithfully represent the real sample features, limiting the classifier training and existing ZSL performance. In this paper, we formulate this mismatch phenomenon as the visual-semantic domain shift problem. We propose a dynamic semantic prototype evolving (DSP) method …

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Coco: A Coupled Contrastive Framework For Unsupervised Domain Adaptive Graph Classification, Nan Yin, Li Shen, Mengzhu Wang, Long Lan, Zeyu Ma, Chong Chen, Xian Sheng Hua, Xiao Luo Jul 2023

Coco: A Coupled Contrastive Framework For Unsupervised Domain Adaptive Graph Classification, Nan Yin, Li Shen, Mengzhu Wang, Long Lan, Zeyu Ma, Chong Chen, Xian Sheng Hua, Xiao Luo

Machine Learning Faculty Publications

Although graph neural networks (GNNs) have achieved impressive achievements in graph classification, they often need abundant task-specific labels, which could be extensively costly to acquire. A credible solution is to explore additional labeled graphs to enhance unsupervised learning on the target domain. However, how to apply GNNs to domain adaptation remains unsolved owing to the insufficient exploration of graph topology and the significant domain discrepancy. In this paper, we propose Coupled Contrastive Graph Representation Learning (CoCo), which extracts the topological information from coupled learning branches and reduces the domain discrepancy with coupled contrastive learning. CoCo contains a graph convolutional network …

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Convergence Of Proximal Point And Extragradient-Based Methods Beyond Monotonicity: The Case Of Negative Comonotonicity, Eduard Gorbunov, Adrien Taylor, Samuel Horváth, Gauthier Gidel Jul 2023

Convergence Of Proximal Point And Extragradient-Based Methods Beyond Monotonicity: The Case Of Negative Comonotonicity, Eduard Gorbunov, Adrien Taylor, Samuel Horváth, Gauthier Gidel

Machine Learning Faculty Publications

Algorithms for min-max optimization and variational inequalities are often studied under monotonicity assumptions. Motivated by non-monotone machine learning applications, we follow the line of works (Diakonikolas et al., 2021; Lee & Kim, 2021; Pethick et al., 2022; Böhm, 2022) aiming at going beyond monotonicity by considering the weaker negative comonotonicity assumption. In this work, we provide tight complexity analyses for the Proximal Point (PP), Extragradient (EG), and Optimistic Gradient (OG) methods in this setup, closing several questions on their working guarantees beyond monotonicity. In particular, we derive the first non-asymptotic convergence rates for PP under negative comonotonicity and star-negative comonotonicity …

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Unleashing Mask: Explore The Intrinsic Out-Of-Distribution Detection Capability, Jianing Zhu, Hengzhuang Li, Jiangchao Yao, Tongliang Liu, Jianliang Xu, Bo Han Jul 2023

Unleashing Mask: Explore The Intrinsic Out-Of-Distribution Detection Capability, Jianing Zhu, Hengzhuang Li, Jiangchao Yao, Tongliang Liu, Jianliang Xu, Bo Han

Machine Learning Faculty Publications

Out-of-distribution (OOD) detection is an indispensable aspect of secure AI when deploying machine learning models in real-world applications. Previous paradigms either explore better scoring functions or utilize the knowledge of outliers to equip the models with the ability of OOD detection. However, few of them pay attention to the intrinsic OOD detection capability of the given model. In this work, we generally discover the existence of an intermediate stage of a model trained on in-distribution (ID) data having higher OOD detection performance than that of its final stage across different settings, and further identify one critical data-level attribution to be …

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A Unified Optimization Framework Of Ann-Snn Conversion: Towards Optimal Mapping From Activation Values To Firing Rates, Haiyan Jiang, Srinivas Anumasa, Giulia De Masi, Huan Xiong, Bin Gu Jul 2023

A Unified Optimization Framework Of Ann-Snn Conversion: Towards Optimal Mapping From Activation Values To Firing Rates, Haiyan Jiang, Srinivas Anumasa, Giulia De Masi, Huan Xiong, Bin Gu

Machine Learning Faculty Publications

Spiking Neural Networks (SNNs) have gained significant attention for their energy-efficient and fast-inference capabilities, but training SNNs from scratch can be challenging due to the discrete nature of spikes. One alternative method is to convert an Artificial Neural Network (ANN) into an SNN, known as ANN-SNN conversion. Currently, existing ANN-SNN conversion methods often involve redesigning the ANN with a new activation function, rather than utilizing the traditional ReLU, and converting it to an SNN. However, these methods do not take into account the potential performance loss between the regular ANN with ReLU and the tailored ANN. In this work, we …

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Linear Classifier: An Often-Forgotten Baseline For Text Classification, Yu Chen Lin, Si An Chen, Jie Jyun Liu, Chih Jen Lin Jul 2023

Linear Classifier: An Often-Forgotten Baseline For Text Classification, Yu Chen Lin, Si An Chen, Jie Jyun Liu, Chih Jen Lin

Machine Learning Faculty Publications

Large-scale pre-trained language models such as BERT are popular solutions for text classification. Due to the superior performance of these advanced methods, nowadays, people often directly train them for a few epochs and deploy the obtained model. In this opinion paper, we point out that this way may only sometimes get satisfactory results. We argue the importance of running a simple baseline like linear classifiers on bag-of-words features along with advanced methods. First, for many text data, linear methods show competitive performance, high efficiency, and robustness. Second, advanced models such as BERT may only achieve the best results if properly …

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Exploring Model Dynamics For Accumulative Poisoning Discovery, Jianing Zhu, Xiawei Guo, Jiangchao Yao, Chao Du, Li He, Shuo Yuan, Tongliang Liu, Liang Wang, Bo Han Jul 2023

Exploring Model Dynamics For Accumulative Poisoning Discovery, Jianing Zhu, Xiawei Guo, Jiangchao Yao, Chao Du, Li He, Shuo Yuan, Tongliang Liu, Liang Wang, Bo Han

Machine Learning Faculty Publications

Adversarial poisoning attacks pose huge threats to various machine learning applications. Especially, the recent accumulative poisoning attacks show that it is possible to achieve irreparable harm on models via a sequence of imperceptible attacks followed by a trigger batch. Due to the limited data-level discrepancy in real-time data streaming, current defensive methods are indiscriminate in handling the poison and clean samples. In this paper, we dive into the perspective of model dynamics and propose a novel information measure, namely, Memorization Discrepancy, to explore the defense via the model-level information. By implicitly transferring the changes in the data manipulation to that …

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Causal Discovery With Latent Confounders Based On Higher-Order Cumulants, Ruichu Cai, Zhiyi Huang, Wei Chen, Zhifeng Hao, Kun Zhang Jul 2023

Causal Discovery With Latent Confounders Based On Higher-Order Cumulants, Ruichu Cai, Zhiyi Huang, Wei Chen, Zhifeng Hao, Kun Zhang

Machine Learning Faculty Publications

Causal discovery with latent confounders is an important but challenging task in many scientific areas. Despite the success of some overcomplete independent component analysis (OICA) based methods in certain domains, they are computationally expensive and can easily get stuck into local optima. We notice that interestingly, by making use of higher-order cumulants, there exists a closed-form solution to OICA in specific cases, e.g., when the mixing procedure follows the One-Latent-Component structure. In light of the power of the closed-form solution to OICA corresponding to the One-Latent-Component structure, we formulate a way to estimate the mixing matrix using the higher-order cumulants, …

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Feature Expansion For Graph Neural Networks, Jiaqi Sun, Lin Zhang, Guangyi Chen, Peng Xu, Kun Zhang, Yujiu Yang Jul 2023

Feature Expansion For Graph Neural Networks, Jiaqi Sun, Lin Zhang, Guangyi Chen, Peng Xu, Kun Zhang, Yujiu Yang

Machine Learning Faculty Publications

Graph neural networks aim to learn representations for graph-structured data and show impressive performance, particularly in node classification. Recently, many methods have studied the representations of GNNs from the perspective of optimization goals and spectral graph theory. However, the feature space that dominates representation learning has not been systematically studied in graph neural networks. In this paper, we propose to fill this gap by analyzing the feature space of both spatial and spectral models. We decompose graph neural networks into determined feature spaces and trainable weights, providing the convenience of studying the feature space explicitly using matrix space analysis. In …

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Team Thesyllogist At Semeval-2023 Task 3: Language-Agnostic Framing Detection In Multi-Lingual Online News: A Zero-Shot Transfer Approach, Osama Mohammed Afzal, Preslav Nakov Jul 2023

Team Thesyllogist At Semeval-2023 Task 3: Language-Agnostic Framing Detection In Multi-Lingual Online News: A Zero-Shot Transfer Approach, Osama Mohammed Afzal, Preslav Nakov

Natural Language Processing Faculty Publications

We describe our system for SemEval-2022 Task 3 subtask 2 which on detecting the frames used in a news article in a multi-lingual setup. We propose a multi-lingual approach based on machine translation of the input, followed by an English prediction model. Our system demonstrated good zero-shot transfer capability, achieving micro-F1 scores of 53% for Greek (4th on the leaderboard) and 56.1% for Georgian (3rd on the leaderboard), without any prior training on translated data for these languages. Moreover, our system achieved comparable performance on seven other languages, including German, English, French, Russian, Italian, Polish, and Spanish. Our results demonstrate …

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Semeval-2023 Task 3: Detecting The Category, The Framing, And The Persuasion Techniques In Online News In A Multi-Lingual Setup, Jakub Piskorski, Nicolas Stefanovitch, Giovanni Da San Martino, Preslav Nakov Jul 2023

Semeval-2023 Task 3: Detecting The Category, The Framing, And The Persuasion Techniques In Online News In A Multi-Lingual Setup, Jakub Piskorski, Nicolas Stefanovitch, Giovanni Da San Martino, Preslav Nakov

Natural Language Processing Faculty Publications

We describe SemEval-2023 task 3 on Detecting the Category, the Framing, and the Persuasion Techniques in Online News in a Multilingual Setup: the dataset, the task organization process, the evaluation setup, the results, and the participating systems. The task focused on news articles in nine languages (six known to the participants upfront: English, French, German, Italian, Polish, and Russian), and three additional ones revealed to the participants at the testing phase: Spanish, Greek, and Georgian). The task featured three subtasks: (1) determining the genre of the article (opinion, reporting, or satire), (2) identifying one or more frames used in an …

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Multilingual Multifaceted Understanding Of Online News In Terms Of Genre, Framing And Persuasion Techniques, Jakub Piskorski, Nicolas Stefanovitch, Nikolaos Nikolaidis, Giovanni Da San Martino, Preslav Nakov Jul 2023

Multilingual Multifaceted Understanding Of Online News In Terms Of Genre, Framing And Persuasion Techniques, Jakub Piskorski, Nicolas Stefanovitch, Nikolaos Nikolaidis, Giovanni Da San Martino, Preslav Nakov

Natural Language Processing Faculty Publications

We present a new multilingual multifacet dataset of news articles, each annotated for genre (objective news reporting vs. opinion vs. satire), framing (what key aspects are highlighted), and persuasion techniques (logical fallacies, emotional appeals, ad hominem attacks, etc.). The persuasion techniques are annotated at the span level, using a taxonomy of 23 fine-grained techniques grouped into 6 coarse categories. The dataset contains 1,612 news articles covering recent news on current topics of public interest in six European languages (English, French, German, Italian, Polish, and Russian), with more than 37k annotated spans of persuasion techniques. We describe the dataset and the …

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Model Transferability With Responsive Decision Subjects, Yatong Chen, Zeyu Tang, Kun Zhang, Yang Liu Jul 2023

Model Transferability With Responsive Decision Subjects, Yatong Chen, Zeyu Tang, Kun Zhang, Yang Liu

Machine Learning Faculty Publications

Given an algorithmic predictor that is accurate on some source population consisting of strategic human decision subjects, will it remain accurate if the population respond to it? In our setting, an agent or a user corresponds to a sample (X, Y ) drawn from a distribution D and will face a model h and its classification result h(X). Agents can modify X to adapt to h, which will incur a distribution shift on (X, Y ). Our formulation is motivated by applications where the deployed machine learning models are subjected to human agents, and will ultimately face responsive and interactive …

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Detecting Out-Of-Distribution Data Through In-Distribution Class Prior, Xue Jiang, Feng Liu, Zhen Fang, Hong Chen, Tongliang Liu, Feng Zheng, Bo Han Jul 2023

Detecting Out-Of-Distribution Data Through In-Distribution Class Prior, Xue Jiang, Feng Liu, Zhen Fang, Hong Chen, Tongliang Liu, Feng Zheng, Bo Han

Machine Learning Faculty Publications

Given a pre-trained in-distribution (ID) model, the inference-time out-of-distribution (OOD) detection aims to recognize OOD data during the inference stage. However, some representative methods share an unproven assumption that the probability that OOD data belong to every ID class should be the same, i.e., these OOD-to-ID probabilities actually form a uniform distribution. In this paper, we show that this assumption makes the above methods incapable when the ID model is trained with class-imbalanced data. Fortunately, by analyzing the causal relations between ID/OOD classes and features, we identify several common scenarios where the OOD-to-ID probabilities should be the ID-class-prior distribution and …

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How To Make Decision Under Interval Uncertainty: Description Of All Reasonable Partial Orders On The Set Of All Intervals, Tiago M. Costa, Olga Kosheleva, Vladik Kreinovich Jul 2023

How To Make Decision Under Interval Uncertainty: Description Of All Reasonable Partial Orders On The Set Of All Intervals, Tiago M. Costa, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

In many practical situations, we need to make a decision while for each alternative, we only know the corresponding value of the objective function with interval uncertainty. To help a decision maker in this situation, we need to know the (in general, partial) order on the set of all intervals that corresponds to the preferences of the decision maker. For this purpose, in this paper, we provide a description of all such partial orders -- under some reasonable conditions. It turns out that each such order is characterized by two linear inequalities relating the endpoints of the corresponding intervals, and …

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Which Fuzzy Implications Operations Are Polynomial? A Theorem Proves That This Can Be Determined By A Finite Set Of Inequalities, Sebastia Massanet, Olga Kosheleva, Vladik Kreinovich Jul 2023

Which Fuzzy Implications Operations Are Polynomial? A Theorem Proves That This Can Be Determined By A Finite Set Of Inequalities, Sebastia Massanet, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

To adequately represent human reasoning in a computer-based systems, it is desirable to select fuzzy operations that are as close to human reasoning as possible. In general, every real-valued function can be approximated, with any desired accuracy, by polynomials; it is therefore reasonable to use polynomial fuzzy operations as the appropriate approximations. We thus need to select, among all polynomial operations that satisfy corresponding properties -- like associativity -- the ones that best fit the empirical data. The challenge here is that properties like associativity mean satisfying infinitely many constraints (corresponding to infinitely many possible triples of values), while most …

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Fuzzy Mathematics Under Non-Minimal "And"-Operations (T-Norms): Equivalence Leads To Metric, Order Leads To Kinematic Metric, Topology Leads To Area Or Volume, Purbita Jana, Olga Kosheleva, Vladik Kreinovich Jul 2023

Fuzzy Mathematics Under Non-Minimal "And"-Operations (T-Norms): Equivalence Leads To Metric, Order Leads To Kinematic Metric, Topology Leads To Area Or Volume, Purbita Jana, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

Most formulas analyzed in fuzzy mathematics assume -- explicitly or implicitly -- that the corresponding "and"-operation (t-norm) is the simplest minimum operation. In this paper, we analyze what happens if instead, we use other "and"-operations. It turns out that for such operations, a fuzzification of a mathematical theory naturally leads to a more complex mathematical setting: fuzzification of equivalence relation leads to metric, fuzzification of order leads to kinematic metric, and fuzzification of topology leads to area or volume.

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Why Deep Learning Is Under-Determined? Why Usual Numerical Methods For Solving Partial Differential Equations Do Not Preserve Energy? The Answers May Be Related To Chevalley-Warning Theorem (And Thus To Fermat Last Theorem), Julio C. Urenda, Olga Kosheleva, Vladik Kreinovich Jul 2023

Why Deep Learning Is Under-Determined? Why Usual Numerical Methods For Solving Partial Differential Equations Do Not Preserve Energy? The Answers May Be Related To Chevalley-Warning Theorem (And Thus To Fermat Last Theorem), Julio C. Urenda, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

In this paper, we provide a possible explanation to two seemingly unrelated phenomena: (1) that in deep learning, under-determined systems of equations perform much better than the over-determined one -- which are typical in data processing, and that (2) usual numerical methods for solving partial differential equations do not preserve energy. Our explanation is related to the intuition of Fermat behind his Last Theorem and of Euler about more general statements, intuition that led to the proof of Chevalley-Warning Theorem in number theory.

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Methodological Lesson Of Pythagorean Triples, Julio C. Urenda, Olga Kosheleva, Vladik Kreinovich Jul 2023

Methodological Lesson Of Pythagorean Triples, Julio C. Urenda, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

There are many right triangles in which all three sides a, b, and c have integer lengths. The triples (a,b,c) formed by such lengths are known as Pythagorean triples. Since ancient times, it is known how to generate all Pythagorean triples: we can enumerate primitive Pythagorean triples -- in which the three numbers have no common divisors -- by considering all pairs of natural numbers m>n in which m and n have no common divisors, and taking a =m2 − n2, b = 2mn, and c = m2 + n2. Multiplying all elements of a triple by the same …

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Why Resilient Modulus Is Proportional To The Square Root Of Unconfined Compressive Strength (Ucs): A Qualitative Explanation, Edgar Daniel Rodriguez Velasquez, Vladik Kreinovich Jul 2023

Why Resilient Modulus Is Proportional To The Square Root Of Unconfined Compressive Strength (Ucs): A Qualitative Explanation, Edgar Daniel Rodriguez Velasquez, Vladik Kreinovich

Departmental Technical Reports (CS)

The strength of the pavement is determine by its resilient modulus, i.e., by its ability to withstand (practically) instantaneous stresses caused by the passing traffic. However, the resilient modulus is not easy to measure: its measurement requires a special expensive equipment that many labs do not have. So, instead of measuring it, practitioners often measure easier-to-measure Unconfined Compressive Strength (UCS) -- that describes the effect of a continuously applied force -- and estimate the resilient modulus based on the result of this measurement. An empirical formula shows that the resilient modulus is proportional to the square root of the Unconfined …

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