There has been a surge of interest in language model agents that can navigate virtual environments such as the web or desktop. To navigate such environments, agents benefit from information on the various elements (e.g., buttons, text, or images) present. It remains unclear which element attributes have the greatest impact on agent performance, especially in environments that only provide a graphical representation (i.e., pixels). Here we find that the ordering in which elements are presented to the language model is surprisingly impactful--randomizing element ordering in a webpage degrades agent performance comparably to removing all visible text from an agent's state representation. While a webpage provides a hierarchical ordering of elements, there is no such ordering when parsing elements directly from pixels. Moreover, as tasks become more challenging and models more sophisticated, our experiments suggest that the impact of ordering increases. Finding an effective ordering is non-trivial. We investigate the impact of various element ordering methods in web and desktop environments. We find that dimensionality reduction provides a viable ordering for pixel-only environments. We train a UI element detection model to derive elements from pixels and apply our findings to an agent benchmark--OmniACT--where we only have access to pixels. Our method completes more than two times as many tasks on average relative to the previous state-of-the-art.
{"title":"The Impact of Element Ordering on LM Agent Performance","authors":"Wayne Chi, Ameet Talwalkar, Chris Donahue","doi":"arxiv-2409.12089","DOIUrl":"https://doi.org/arxiv-2409.12089","url":null,"abstract":"There has been a surge of interest in language model agents that can navigate\u0000virtual environments such as the web or desktop. To navigate such environments,\u0000agents benefit from information on the various elements (e.g., buttons, text,\u0000or images) present. It remains unclear which element attributes have the\u0000greatest impact on agent performance, especially in environments that only\u0000provide a graphical representation (i.e., pixels). Here we find that the\u0000ordering in which elements are presented to the language model is surprisingly\u0000impactful--randomizing element ordering in a webpage degrades agent performance\u0000comparably to removing all visible text from an agent's state representation.\u0000While a webpage provides a hierarchical ordering of elements, there is no such\u0000ordering when parsing elements directly from pixels. Moreover, as tasks become\u0000more challenging and models more sophisticated, our experiments suggest that\u0000the impact of ordering increases. Finding an effective ordering is non-trivial.\u0000We investigate the impact of various element ordering methods in web and\u0000desktop environments. We find that dimensionality reduction provides a viable\u0000ordering for pixel-only environments. We train a UI element detection model to\u0000derive elements from pixels and apply our findings to an agent\u0000benchmark--OmniACT--where we only have access to pixels. Our method completes\u0000more than two times as many tasks on average relative to the previous\u0000state-of-the-art.","PeriodicalId":501301,"journal":{"name":"arXiv - CS - Machine Learning","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142261781","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Safety is one of the key issues preventing the deployment of reinforcement learning techniques in real-world robots. While most approaches in the Safe Reinforcement Learning area do not require prior knowledge of constraints and robot kinematics and rely solely on data, it is often difficult to deploy them in complex real-world settings. Instead, model-based approaches that incorporate prior knowledge of the constraints and dynamics into the learning framework have proven capable of deploying the learning algorithm directly on the real robot. Unfortunately, while an approximated model of the robot dynamics is often available, the safety constraints are task-specific and hard to obtain: they may be too complicated to encode analytically, too expensive to compute, or it may be difficult to envision a priori the long-term safety requirements. In this paper, we bridge this gap by extending the safe exploration method, ATACOM, with learnable constraints, with a particular focus on ensuring long-term safety and handling of uncertainty. Our approach is competitive or superior to state-of-the-art methods in final performance while maintaining safer behavior during training.
{"title":"Handling Long-Term Safety and Uncertainty in Safe Reinforcement Learning","authors":"Jonas Günster, Puze Liu, Jan Peters, Davide Tateo","doi":"arxiv-2409.12045","DOIUrl":"https://doi.org/arxiv-2409.12045","url":null,"abstract":"Safety is one of the key issues preventing the deployment of reinforcement\u0000learning techniques in real-world robots. While most approaches in the Safe\u0000Reinforcement Learning area do not require prior knowledge of constraints and\u0000robot kinematics and rely solely on data, it is often difficult to deploy them\u0000in complex real-world settings. Instead, model-based approaches that\u0000incorporate prior knowledge of the constraints and dynamics into the learning\u0000framework have proven capable of deploying the learning algorithm directly on\u0000the real robot. Unfortunately, while an approximated model of the robot\u0000dynamics is often available, the safety constraints are task-specific and hard\u0000to obtain: they may be too complicated to encode analytically, too expensive to\u0000compute, or it may be difficult to envision a priori the long-term safety\u0000requirements. In this paper, we bridge this gap by extending the safe\u0000exploration method, ATACOM, with learnable constraints, with a particular focus\u0000on ensuring long-term safety and handling of uncertainty. Our approach is\u0000competitive or superior to state-of-the-art methods in final performance while\u0000maintaining safer behavior during training.","PeriodicalId":501301,"journal":{"name":"arXiv - CS - Machine Learning","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142269707","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Air pollution, particularly particulate matter (PM2.5), poses significant risks to public health and the environment, necessitating accurate prediction and continuous monitoring for effective air quality management. However, air quality monitoring (AQM) data often suffer from missing records due to various technical difficulties. This study explores the application of Sparse Identification of Nonlinear Dynamics (SINDy) for imputing missing PM2.5 data by predicting, using training data from 2016, and comparing its performance with the established Soft Impute (SI) and K-Nearest Neighbors (KNN) methods.
{"title":"Enhancing PM2.5 Data Imputation and Prediction in Air Quality Monitoring Networks Using a KNN-SINDy Hybrid Model","authors":"Yohan Choi, Boaz Choi, Jachin Choi","doi":"arxiv-2409.11640","DOIUrl":"https://doi.org/arxiv-2409.11640","url":null,"abstract":"Air pollution, particularly particulate matter (PM2.5), poses significant\u0000risks to public health and the environment, necessitating accurate prediction\u0000and continuous monitoring for effective air quality management. However, air\u0000quality monitoring (AQM) data often suffer from missing records due to various\u0000technical difficulties. This study explores the application of Sparse\u0000Identification of Nonlinear Dynamics (SINDy) for imputing missing PM2.5 data by\u0000predicting, using training data from 2016, and comparing its performance with\u0000the established Soft Impute (SI) and K-Nearest Neighbors (KNN) methods.","PeriodicalId":501301,"journal":{"name":"arXiv - CS - Machine Learning","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142261957","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This paper proposes Hamiltonian Learning, a novel unified framework for learning with neural networks "over time", i.e., from a possibly infinite stream of data, in an online manner, without having access to future information. Existing works focus on the simplified setting in which the stream has a known finite length or is segmented into smaller sequences, leveraging well-established learning strategies from statistical machine learning. In this paper, the problem of learning over time is rethought from scratch, leveraging tools from optimal control theory, which yield a unifying view of the temporal dynamics of neural computations and learning. Hamiltonian Learning is based on differential equations that: (i) can be integrated without the need of external software solvers; (ii) generalize the well-established notion of gradient-based learning in feed-forward and recurrent networks; (iii) open to novel perspectives. The proposed framework is showcased by experimentally proving how it can recover gradient-based learning, comparing it to out-of-the box optimizers, and describing how it is flexible enough to switch from fully-local to partially/non-local computational schemes, possibly distributed over multiple devices, and BackPropagation without storing activations. Hamiltonian Learning is easy to implement and can help researches approach in a principled and innovative manner the problem of learning over time.
{"title":"A Unified Framework for Neural Computation and Learning Over Time","authors":"Stefano Melacci, Alessandro Betti, Michele Casoni, Tommaso Guidi, Matteo Tiezzi, Marco Gori","doi":"arxiv-2409.12038","DOIUrl":"https://doi.org/arxiv-2409.12038","url":null,"abstract":"This paper proposes Hamiltonian Learning, a novel unified framework for\u0000learning with neural networks \"over time\", i.e., from a possibly infinite\u0000stream of data, in an online manner, without having access to future\u0000information. Existing works focus on the simplified setting in which the stream\u0000has a known finite length or is segmented into smaller sequences, leveraging\u0000well-established learning strategies from statistical machine learning. In this\u0000paper, the problem of learning over time is rethought from scratch, leveraging\u0000tools from optimal control theory, which yield a unifying view of the temporal\u0000dynamics of neural computations and learning. Hamiltonian Learning is based on\u0000differential equations that: (i) can be integrated without the need of external\u0000software solvers; (ii) generalize the well-established notion of gradient-based\u0000learning in feed-forward and recurrent networks; (iii) open to novel\u0000perspectives. The proposed framework is showcased by experimentally proving how\u0000it can recover gradient-based learning, comparing it to out-of-the box\u0000optimizers, and describing how it is flexible enough to switch from fully-local\u0000to partially/non-local computational schemes, possibly distributed over\u0000multiple devices, and BackPropagation without storing activations. Hamiltonian\u0000Learning is easy to implement and can help researches approach in a principled\u0000and innovative manner the problem of learning over time.","PeriodicalId":501301,"journal":{"name":"arXiv - CS - Machine Learning","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142261827","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Nathan Wolfrath, Joel Wolfrath, Hengrui Hu, Anjishnu Banerjee, Anai N. Kothari
Machine Learning (ML) research has increased substantially in recent years, due to the success of predictive modeling across diverse application domains. However, well-known barriers exist when attempting to deploy ML models in high-stakes, clinical settings, including lack of model transparency (or the inability to audit the inference process), large training data requirements with siloed data sources, and complicated metrics for measuring model utility. In this work, we show empirically that including stronger baseline models in healthcare ML evaluations has important downstream effects that aid practitioners in addressing these challenges. Through a series of case studies, we find that the common practice of omitting baselines or comparing against a weak baseline model (e.g. a linear model with no optimization) obscures the value of ML methods proposed in the research literature. Using these insights, we propose some best practices that will enable practitioners to more effectively study and deploy ML models in clinical settings.
近年来，由于预测建模在不同应用领域取得了成功，机器学习（ML）研究大幅增加。然而，在高风险的临床环境中尝试部署 ML 模型时存在众所周知的障碍，包括缺乏模型透明度（或无法审计推理过程）、孤立数据源的大量训练数据要求以及衡量模型效用的复杂指标。在这项工作中，我们通过实证研究表明，在医疗保健 ML 评估中纳入更强的基线模型具有重要的下游效应，有助于实践者应对这些挑战。通过一系列案例研究，我们发现省略基线模型或与弱基线模型（如未优化的线性模型）进行比较的常见做法掩盖了研究文献中提出的 ML 方法的价值。利用这些洞察力，我们提出了一些最佳实践，使从业人员能够在临床环境中更有效地研究和部署 ML 模型。
{"title":"Stronger Baseline Models -- A Key Requirement for Aligning Machine Learning Research with Clinical Utility","authors":"Nathan Wolfrath, Joel Wolfrath, Hengrui Hu, Anjishnu Banerjee, Anai N. Kothari","doi":"arxiv-2409.12116","DOIUrl":"https://doi.org/arxiv-2409.12116","url":null,"abstract":"Machine Learning (ML) research has increased substantially in recent years,\u0000due to the success of predictive modeling across diverse application domains.\u0000However, well-known barriers exist when attempting to deploy ML models in\u0000high-stakes, clinical settings, including lack of model transparency (or the\u0000inability to audit the inference process), large training data requirements\u0000with siloed data sources, and complicated metrics for measuring model utility.\u0000In this work, we show empirically that including stronger baseline models in\u0000healthcare ML evaluations has important downstream effects that aid\u0000practitioners in addressing these challenges. Through a series of case studies,\u0000we find that the common practice of omitting baselines or comparing against a\u0000weak baseline model (e.g. a linear model with no optimization) obscures the\u0000value of ML methods proposed in the research literature. Using these insights,\u0000we propose some best practices that will enable practitioners to more\u0000effectively study and deploy ML models in clinical settings.","PeriodicalId":501301,"journal":{"name":"arXiv - CS - Machine Learning","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142269705","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This work considers the problem of estimating the distance between two covariance matrices directly from the data. Particularly, we are interested in the family of distances that can be expressed as sums of traces of functions that are separately applied to each covariance matrix. This family of distances is particularly useful as it takes into consideration the fact that covariance matrices lie in the Riemannian manifold of positive definite matrices, thereby including a variety of commonly used metrics, such as the Euclidean distance, Jeffreys' divergence, and the log-Euclidean distance. Moreover, a statistical analysis of the asymptotic behavior of this class of distance estimators has also been conducted. Specifically, we present a central limit theorem that establishes the asymptotic Gaussianity of these estimators and provides closed form expressions for the corresponding means and variances. Empirical evaluations demonstrate the superiority of our proposed consistent estimator over conventional plug-in estimators in multivariate analytical contexts. Additionally, the central limit theorem derived in this study provides a robust statistical framework to assess of accuracy of these estimators.
{"title":"Consistent Estimation of a Class of Distances Between Covariance Matrices","authors":"Roberto Pereira, Xavier Mestre, Davig Gregoratti","doi":"arxiv-2409.11761","DOIUrl":"https://doi.org/arxiv-2409.11761","url":null,"abstract":"This work considers the problem of estimating the distance between two\u0000covariance matrices directly from the data. Particularly, we are interested in\u0000the family of distances that can be expressed as sums of traces of functions\u0000that are separately applied to each covariance matrix. This family of distances\u0000is particularly useful as it takes into consideration the fact that covariance\u0000matrices lie in the Riemannian manifold of positive definite matrices, thereby\u0000including a variety of commonly used metrics, such as the Euclidean distance,\u0000Jeffreys' divergence, and the log-Euclidean distance. Moreover, a statistical\u0000analysis of the asymptotic behavior of this class of distance estimators has\u0000also been conducted. Specifically, we present a central limit theorem that\u0000establishes the asymptotic Gaussianity of these estimators and provides closed\u0000form expressions for the corresponding means and variances. Empirical\u0000evaluations demonstrate the superiority of our proposed consistent estimator\u0000over conventional plug-in estimators in multivariate analytical contexts.\u0000Additionally, the central limit theorem derived in this study provides a robust\u0000statistical framework to assess of accuracy of these estimators.","PeriodicalId":501301,"journal":{"name":"arXiv - CS - Machine Learning","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142261838","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
To mitigate the susceptibility of neural networks to adversarial attacks, adversarial training has emerged as a prevalent and effective defense strategy. Intrinsically, this countermeasure incurs a trade-off, as it sacrifices the model's accuracy in processing normal samples. To reconcile the trade-off, we pioneer the incorporation of null-space projection into adversarial training and propose two innovative Null-space Projection based Adversarial Training(NPAT) algorithms tackling sample generation and gradient optimization, named Null-space Projected Data Augmentation (NPDA) and Null-space Projected Gradient Descent (NPGD), to search for an overarching optimal solutions, which enhance robustness with almost zero deterioration in generalization performance. Adversarial samples and perturbations are constrained within the null-space of the decision boundary utilizing a closed-form null-space projector, effectively mitigating threat of attack stemming from unreliable features. Subsequently, we conducted experiments on the CIFAR10 and SVHN datasets and reveal that our methodology can seamlessly combine with adversarial training methods and obtain comparable robustness while keeping generalization close to a high-accuracy model.
{"title":"NPAT Null-Space Projected Adversarial Training Towards Zero Deterioration","authors":"Hanyi Hu, Qiao Han, Kui Chen, Yao Yang","doi":"arxiv-2409.11754","DOIUrl":"https://doi.org/arxiv-2409.11754","url":null,"abstract":"To mitigate the susceptibility of neural networks to adversarial attacks,\u0000adversarial training has emerged as a prevalent and effective defense strategy.\u0000Intrinsically, this countermeasure incurs a trade-off, as it sacrifices the\u0000model's accuracy in processing normal samples. To reconcile the trade-off, we\u0000pioneer the incorporation of null-space projection into adversarial training\u0000and propose two innovative Null-space Projection based Adversarial\u0000Training(NPAT) algorithms tackling sample generation and gradient optimization,\u0000named Null-space Projected Data Augmentation (NPDA) and Null-space Projected\u0000Gradient Descent (NPGD), to search for an overarching optimal solutions, which\u0000enhance robustness with almost zero deterioration in generalization\u0000performance. Adversarial samples and perturbations are constrained within the\u0000null-space of the decision boundary utilizing a closed-form null-space\u0000projector, effectively mitigating threat of attack stemming from unreliable\u0000features. Subsequently, we conducted experiments on the CIFAR10 and SVHN\u0000datasets and reveal that our methodology can seamlessly combine with\u0000adversarial training methods and obtain comparable robustness while keeping\u0000generalization close to a high-accuracy model.","PeriodicalId":501301,"journal":{"name":"arXiv - CS - Machine Learning","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142261837","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Few-shot class-incremental learning is crucial for developing scalable and adaptive intelligent systems, as it enables models to acquire new classes with minimal annotated data while safeguarding the previously accumulated knowledge. Nonetheless, existing methods deal with continuous data streams in a centralized manner, limiting their applicability in scenarios that prioritize data privacy and security. To this end, this paper introduces federated few-shot class-incremental learning, a decentralized machine learning paradigm tailored to progressively learn new classes from scarce data distributed across multiple clients. In this learning paradigm, clients locally update their models with new classes while preserving data privacy, and then transmit the model updates to a central server where they are aggregated globally. However, this paradigm faces several issues, such as difficulties in few-shot learning, catastrophic forgetting, and data heterogeneity. To address these challenges, we present a synthetic data-driven framework that leverages replay buffer data to maintain existing knowledge and facilitate the acquisition of new knowledge. Within this framework, a noise-aware generative replay module is developed to fine-tune local models with a balance of new and replay data, while generating synthetic data of new classes to further expand the replay buffer for future tasks. Furthermore, a class-specific weighted aggregation strategy is designed to tackle data heterogeneity by adaptively aggregating class-specific parameters based on local models performance on synthetic data. This enables effective global model optimization without direct access to client data. Comprehensive experiments across three widely-used datasets underscore the effectiveness and preeminence of the introduced framework.
{"title":"Few-Shot Class-Incremental Learning with Non-IID Decentralized Data","authors":"Cuiwei Liu, Siang Xu, Huaijun Qiu, Jing Zhang, Zhi Liu, Liang Zhao","doi":"arxiv-2409.11657","DOIUrl":"https://doi.org/arxiv-2409.11657","url":null,"abstract":"Few-shot class-incremental learning is crucial for developing scalable and\u0000adaptive intelligent systems, as it enables models to acquire new classes with\u0000minimal annotated data while safeguarding the previously accumulated knowledge.\u0000Nonetheless, existing methods deal with continuous data streams in a\u0000centralized manner, limiting their applicability in scenarios that prioritize\u0000data privacy and security. To this end, this paper introduces federated\u0000few-shot class-incremental learning, a decentralized machine learning paradigm\u0000tailored to progressively learn new classes from scarce data distributed across\u0000multiple clients. In this learning paradigm, clients locally update their\u0000models with new classes while preserving data privacy, and then transmit the\u0000model updates to a central server where they are aggregated globally. However,\u0000this paradigm faces several issues, such as difficulties in few-shot learning,\u0000catastrophic forgetting, and data heterogeneity. To address these challenges,\u0000we present a synthetic data-driven framework that leverages replay buffer data\u0000to maintain existing knowledge and facilitate the acquisition of new knowledge.\u0000Within this framework, a noise-aware generative replay module is developed to\u0000fine-tune local models with a balance of new and replay data, while generating\u0000synthetic data of new classes to further expand the replay buffer for future\u0000tasks. Furthermore, a class-specific weighted aggregation strategy is designed\u0000to tackle data heterogeneity by adaptively aggregating class-specific\u0000parameters based on local models performance on synthetic data. This enables\u0000effective global model optimization without direct access to client data.\u0000Comprehensive experiments across three widely-used datasets underscore the\u0000effectiveness and preeminence of the introduced framework.","PeriodicalId":501301,"journal":{"name":"arXiv - CS - Machine Learning","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142261956","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The loss landscape of neural networks is a critical aspect of their training, and understanding its properties is essential for improving their performance. In this paper, we investigate how the loss surface changes when the sample size increases, a previously unexplored issue. We theoretically analyze the convergence of the loss landscape in a fully connected neural network and derive upper bounds for the difference in loss function values when adding a new object to the sample. Our empirical study confirms these results on various datasets, demonstrating the convergence of the loss function surface for image classification tasks. Our findings provide insights into the local geometry of neural loss landscapes and have implications for the development of sample size determination techniques.
{"title":"Unraveling the Hessian: A Key to Smooth Convergence in Loss Function Landscapes","authors":"Nikita Kiselev, Andrey Grabovoy","doi":"arxiv-2409.11995","DOIUrl":"https://doi.org/arxiv-2409.11995","url":null,"abstract":"The loss landscape of neural networks is a critical aspect of their training,\u0000and understanding its properties is essential for improving their performance.\u0000In this paper, we investigate how the loss surface changes when the sample size\u0000increases, a previously unexplored issue. We theoretically analyze the\u0000convergence of the loss landscape in a fully connected neural network and\u0000derive upper bounds for the difference in loss function values when adding a\u0000new object to the sample. Our empirical study confirms these results on various\u0000datasets, demonstrating the convergence of the loss function surface for image\u0000classification tasks. Our findings provide insights into the local geometry of\u0000neural loss landscapes and have implications for the development of sample size\u0000determination techniques.","PeriodicalId":501301,"journal":{"name":"arXiv - CS - Machine Learning","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142261829","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This manuscript presents a novel framework that integrates higher-order symmetries and category theory into machine learning. We introduce new mathematical constructs, including hyper-symmetry categories and functorial representations, to model complex transformations within learning algorithms. Our contributions include the design of symmetry-enriched learning models, the development of advanced optimization techniques leveraging categorical symmetries, and the theoretical analysis of their implications for model robustness, generalization, and convergence. Through rigorous proofs and practical applications, we demonstrate that incorporating higher-dimensional categorical structures enhances both the theoretical foundations and practical capabilities of modern machine learning algorithms, opening new directions for research and innovation.
{"title":"Symmetry-Enriched Learning: A Category-Theoretic Framework for Robust Machine Learning Models","authors":"Ronald Katende","doi":"arxiv-2409.12100","DOIUrl":"https://doi.org/arxiv-2409.12100","url":null,"abstract":"This manuscript presents a novel framework that integrates higher-order\u0000symmetries and category theory into machine learning. We introduce new\u0000mathematical constructs, including hyper-symmetry categories and functorial\u0000representations, to model complex transformations within learning algorithms.\u0000Our contributions include the design of symmetry-enriched learning models, the\u0000development of advanced optimization techniques leveraging categorical\u0000symmetries, and the theoretical analysis of their implications for model\u0000robustness, generalization, and convergence. Through rigorous proofs and\u0000practical applications, we demonstrate that incorporating higher-dimensional\u0000categorical structures enhances both the theoretical foundations and practical\u0000capabilities of modern machine learning algorithms, opening new directions for\u0000research and innovation.","PeriodicalId":501301,"journal":{"name":"arXiv - CS - Machine Learning","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142261826","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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