Yarema Boryshchak
We take a closer look at some theoretical challenges of Machine Learning as a function approximation, gradient descent as the default optimization algorithm, limitations of fixed length and width networks and a different approach to RNNs from a mathematical perspective.
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There has been a lot of recent interest in adopting machine learning methods for scientific and engineering applications. This has in large part been inspired by recent successes and advances in the domains of Natural Language Processing (NLP) and Image Classification (IC). However, scientific and engineering problems have their own unique characteristics and requirements raising new challenges for effective design and deployment of machine learning approaches. There is a strong need for further mathematical developments on the foundations of machine learning methods to increase the level of r…
In this work, we introduce the concept of bandlimiting into the theory of machine learning because all physical processes are bandlimited by nature, including real-world machine learning tasks. After the bandlimiting constraint is taken into account, our theoretical analysis has shown that all practical machine learning tasks are asymptotically solvable in a perfect sense. Furthermore, the key towards this solvability almost solely relies on two factors: i) a sufficiently large amount of training samples beyond a threshold determined by a difficulty measurement of the underlying task; ii) a su…
Similarity-based fuzzy clustering scientific articles: potentials and challenges from mathematical and computational perspectives
本文研究科学文章模糊聚类问题，将其建模为约束优化模型，建立二阶最优性条件并提出基于 GPU 并行加速的梯度投影求解方法，以应对 OpenAlex 等亿级规模数据库的计算挑战。
Mathematical conjecture generation using machine intelligence
本研究提出一种借助机器智能生成数学不等式猜想的系统性方法，通过几何化构建猜想空间并证明其同构于巴拿赫流形，设计几何梯度下降算法流水线，生成了素数计数函数等相关新猜想，部分已获证。
Abstract In this work, we build two environments, namely the modified QLBS and RLOP models, from a mathematics perspective which enables RL methods in option pricing through replicating by portfolio. We implement the environment specifications (the source code can be found at https://github.com/owen8877/RLOP), the learning algorithm, and agent parametrization by a neural network. The learned optimal hedging strategy is compared against the BS prediction. The effect of various factors is considered and studied based on how they affect the optimal price and position.
Attention Meets Post-hoc Interpretability: A Mathematical Perspective
针对注意力权重能否作为模型解释的争论，本文从数学上分析简单注意力架构，比较事后解释与注意力解释，证明事后方法虽有局限，却能提供更有用的内部行为洞见。
A mathematical perspective on Transformers
本文从数学角度将 Transformer 建模为相互作用粒子系统，分析其长时间行为中的聚类现象，为数学家和计算机科学家提供新的理论视角。
Interactive model analysis, the process of understanding, diagnosing, and refining a machine learning model with the help of interactive visualization, is very important for users to efficiently solve real-world artificial intelligence and data mining problems. Dramatic advances in big data analytics has led to a wide variety of interactive model analysis tasks. In this paper, we present a comprehensive analysis and interpretation of this rapidly developing area. Specifically, we classify the relevant work into three categories: understanding, diagnosis, and refinement. Each category is exempl…
On the Conditions for Domain Stability for Machine Learning: a Mathematical Approach
本文用函数、拓扑与度量空间理论刻画机器学习模型的稳定性，给出验证、证明和测试稳定性的充分条件及等价关系。
With the increasing pervasive use of machine learning in social and economic settings, there has been an interest in the notion of machine bias in the AI community. Models trained on historic data reflect biases that exist in society and propagated them to the future through their decisions. There are three prominent metrics of machine fairness used in the community, and it has been shown statistically that it is impossible to satisfy them all at the same time. This has led to an ambiguity with regards to the definition of fairness. In this report, a causal perspective to the impossibility the…
A review of the main fairness definitions and fair learning methodologies proposed in the literature over the last years is presented from a mathematical point of view. Following our independence-based approach, we consider how to build fair algorithms and the consequences on the degradation of their performance compared to the possibly unfair case. This corresponds to the price for fairness given by the criteria $\textit{statistical parity}$ or $\textit{equality of odds}$. Novel results giving the expressions of the optimal fair classifier and the optimal fair predictor (under a linear regres…
Automatic differentiation, as implemented today, does not have a simple mathematical model adapted to the needs of modern machine learning. In this work we articulate the relationships between differentiation of programs as implemented in practice and differentiation of nonsmooth functions. To this end we provide a simple class of functions, a nonsmooth calculus, and show how they apply to stochastic approximation methods. We also evidence the issue of artificial critical points created by algorithmic differentiation and show how usual methods avoid these points with probability one.
Knowledge graph embedding (KGE) is an increasingly popular technique that aims to represent entities and relations of knowledge graphs into low-dimensional semantic spaces for a wide spectrum of applications such as link prediction, knowledge reasoning and knowledge completion. In this paper, we provide a systematic review of existing KGE techniques based on representation spaces. Particularly, we build a fine-grained classification to categorise the models based on three mathematical perspectives of the representation spaces: (1) Algebraic perspective, (2) Geometric perspective, and (3) Analy…
Machine learning develops rapidly, which has made many theoretical breakthroughs and is widely applied in various fields. Optimization, as an important part of machine learning, has attracted much attention of researchers. With the exponential growth of data amount and the increase of model complexity, optimization methods in machine learning face more and more challenges. A lot of work on solving optimization problems or improving optimization methods in machine learning has been proposed successively. The systematic retrospect and summary of the optimization methods from the perspective of m…
Many machine learning (ML) approaches are widely used to generate bioclimatic models for prediction of geographic range of organism as a function of climate. Applications such as prediction of range shift in organism, range of invasive species influenced by climate change are important parameters in understanding the impact of climate change. However, success of machine learning-based approaches depends on a number of factors. While it can be safely said that no particular ML technique can be effective in all applications and success of a technique is predominantly dependent on the application…
This paper reviews recent advances in the field of optimization under uncertainty via a modern data lens, highlights key research challenges and promise of data-driven optimization that organically integrates machine learning and mathematical programming for decision-making under uncertainty, and identifies potential research opportunities. A brief review of classical mathematical programming techniques for hedging against uncertainty is first presented, along with their wide spectrum of applications in Process Systems Engineering. A comprehensive review and classification of the relevant publ…
When and Why Does Unsupervised RL Succeed in Mathematical Reasoning? A Manifold Envelopment Perspective
本文研究无监督强化学习在数学推理中的成功条件，提出通过流形包裹视角分析其稳定性与失效原因，设计内在奖励机制并揭示基础逻辑先验对性能的影响。
Recent years have witnessed the rapid growth of machine learning in a wide range of fields such as image recognition, text classification, credit scoring prediction, recommendation system, etc. In spite of their great performance in different sectors, researchers still concern about the mechanism under any machine learning (ML) techniques that are inherently black-box and becoming more complex to achieve higher accuracy. Therefore, interpreting machine learning model is currently a mainstream topic in the research community. However, the traditional interpretable machine learning focuses on th…
There is a strong consensus that combining the versatility of machine learning with the assurances given by formal verification is highly desirable. It is much less clear what verified machine learning should mean exactly. We consider this question from the (unexpected?) perspective of computable analysis. This allows us to define the computational tasks underlying verified ML in a model-agnostic way, and show that they are in principle computable.
Continuous-Time Machine Learning: A Unified Mathematical Perspective
该综述提出统一数学视角，通过分类法组织连续时间机器学习各分支，规范其公式并比较算法与权衡，识别开放挑战。
Based on interviews with 28 organizations, we found that industry practitioners are not equipped with tactical and strategic tools to protect, detect and respond to attacks on their Machine Learning (ML) systems. We leverage the insights from the interviews and we enumerate the gaps in perspective in securing machine learning systems when viewed in the context of traditional software security development. We write this paper from the perspective of two personas: developers/ML engineers and security incident responders who are tasked with securing ML systems as they are designed, developed and …
Does machine learning and AI ensure that social biases thrive ? This paper aims to analyse this issue. Indeed, as algorithms are informed by data, if these are corrupted, from a social bias perspective, good machine learning algorithms would learn from the data provided and reverberate the patterns learnt on the predictions related to either the classification or the regression intended. In other words, the way society behaves whether positively or negatively, would necessarily be reflected by the models. In this paper, we analyse how social biases are transmitted from the data into banks loan…
Navigation through Non-Compact Symmetric Spaces: a mathematical perspective on Cartan Neural Networks
本文从数学角度阐释 Cartan Neural Networks，分析非紧对称空间上网络层的几何性质及层间映射，说明其协变性与几何可解释性。
In the early 2010s, a crisis of reproducibility rocked the field of psychology. Following a period of reflection, the field has responded with radical reform of its scientific practices. More recently, similar questions about the reproducibility of machine learning research have also come to the fore. In this short paper, we present select ideas from psychology's reformation, translating them into relevance for a machine learning audience.
With the exploding popularity of machine learning, domain knowledge in various forms has been playing a crucial role in improving the learning performance, especially when training data is limited. Nonetheless, there is little understanding of to what extent domain knowledge can affect a machine learning task from a quantitative perspective. To increase the transparency and rigorously explain the role of domain knowledge in machine learning, we study the problem of quantifying the values of domain knowledge in terms of its contribution to the learning performance in the context of informed mac…
Recently, increased computational power and data availability, as well as algorithmic advances, have led machine learning techniques to impressive results in regression, classification, data-generation and reinforcement learning tasks. Despite these successes, the proximity to the physical limits of chip fabrication alongside the increasing size of datasets are motivating a growing number of researchers to explore the possibility of harnessing the power of quantum computation to speed-up classical machine learning algorithms. Here we review the literature in quantum machine learning and discus…
Deep Learning Meets Sparse Regularization: A Signal Processing Perspective
本文从信号处理视角提出融合稀疏正则化、Radon 变换与逼近理论的数学框架，解释神经网络的函数特性、架构设计及高维性能。
The purpose of this article is to review the achievements made in the last few years towards the understanding of the reasons behind the success and subtleties of neural network-based machine learning. In the tradition of good old applied mathematics, we will not only give attention to rigorous mathematical results, but also the insight we have gained from careful numerical experiments as well as the analysis of simplified models. Along the way, we also list the open problems which we believe to be the most important topics for further study. This is not a complete overview over this quickly m…
Instance-Level Difficulty: A Missing Perspective in Machine Unlearning
该研究针对当前机器遗忘研究忽视样本个体遗忘难度差异的问题，通过多算法多数据集的实例级分析，总结出四个影响遗忘难度的因素，证明其与算法无关、仅和目标模型及训练数据相关，呼吁学界关注实例级遗忘难度。
With advances in vision and perception architectures, we have realized that working with data is equally crucial, if not more, than the algorithms. Till today, we have trained machines based on our knowledge and perspective of the world. The entire concept of Dataset Structural Index(DSI) revolves around understanding a machine`s perspective of the dataset. With DSI, I show two meta values with which we can get more information over a visual dataset and use it to optimize data, create better architectures, and have an ability to guess which model would work best. These two values are the Varie…
Machine learning is a promising technique for many practical applications. In this perspective, we illustrate the development and application for machine learning. It is indicated that the theories and applications of machine learning method in the field of energy conservation and indoor environment are not mature, due to the difficulty of the determination for model structure with better prediction. In order to significantly contribute to the problems, we utilize the ANN model to predict the indoor culturable fungi concentration, which achieves the better accuracy and convenience. The proposa…
Machine learning techniques are being increasingly used as flexible non-linear fitting and prediction tools in the physical sciences. Fitting functions that exhibit multiple solutions as local minima can be analysed in terms of the corresponding machine learning landscape. Methods to explore and visualise molecular potential energy landscapes can be applied to these machine learning landscapes to gain new insight into the solution space involved in training and the nature of the corresponding predictions. In particular, we can define quantities analogous to molecular structure, thermodynamics,…
The effective representation, processing, analysis, and visualization of large-scale structured data, especially those related to complex domains such as networks and graphs, are one of the key questions in modern machine learning. Graph signal processing (GSP), a vibrant branch of signal processing models and algorithms that aims at handling data supported on graphs, opens new paths of research to address this challenge. In this article, we review a few important contributions made by GSP concepts and tools, such as graph filters and transforms, to the development of novel machine learning al…
PAQ8 is an open source lossless data compression algorithm that currently achieves the best compression rates on many benchmarks. This report presents a detailed description of PAQ8 from a statistical machine learning perspective. It shows that it is possible to understand some of the modules of PAQ8 and use this understanding to improve the method. However, intuitive statistical explanations of the behavior of other modules remain elusive. We hope the description in this report will be a starting point for discussions that will increase our understanding, lead to improvements to PAQ8, and fac…
A Perspective on Symbolic Machine Learning in Physical Sciences
本文从视角角度探讨符号机器学习在物理科学中的应用，强调其与数值机器学习互补，以应对深度神经网络不可解释性，并加速物理发现。
Many datasets represent a combination of different ways of looking at the same data that lead to different generalizations. For example, a corpus with examples generated by different people may be mixtures of many perspectives and can be viewed with different perspectives by others. It isnt always possible to represent the viewpoints by a clean separation, in advance, of examples representing each viewpoint and train a separate model for each viewpoint. We introduce lensing, a mixed initiative technique to extract lenses or mappings between machine learned representations and perspectives of h…
We review the recent programme of using machine-learning to explore the landscape of mathematical problems. With this paradigm as a model for human intuition - complementary to and in contrast with the more formalistic approach of automated theorem proving - we highlight some experiments on how AI helps with conjecture formulation, pattern recognition and computation.
Graph Machine Learning (GraphML), whereby classical machine learning is generalized to irregular graph domains, has enjoyed a recent renaissance, leading to a dizzying array of models and their applications in several domains. With its growing applicability to sensitive domains and regulations by governmental agencies for trustworthy AI systems, researchers have started looking into the issues of transparency and privacy of graph learning. However, these topics have been mainly investigated independently. In this position paper, we provide a unified perspective on the interplay of privacy and …
Inclusion of high throughput technologies in the field of biology has generated massive amounts of biological data in the recent years. Now, transforming these huge volumes of data into knowledge is the primary challenge in computational biology. The traditional methods of data analysis have failed to carry out the task. Hence, researchers are turning to machine learning based approaches for the analysis of high-dimensional big data. In machine learning, once a model is trained with a training dataset, it can be applied on a testing dataset which is independent. In current times, deep learning…
We review, for a general audience, a variety of recent experiments on extracting structure from machine-learning mathematical data that have been compiled over the years. Focusing on supervised machine-learning on labeled data from different fields ranging from geometry to representation theory, from combinatorics to number theory, we present a comparative study of the accuracies on different problems. The paradigm should be useful for conjecture formulation, finding more efficient methods of computation, as well as probing into certain hierarchy of structures in mathematics.
Algorithms learned from data are increasingly used for deciding many aspects in our life: from movies we see, to prices we pay, or medicine we get. Yet there is growing evidence that decision making by inappropriately trained algorithms may unintentionally discriminate people. For example, in automated matching of candidate CVs with job descriptions, algorithms may capture and propagate ethnicity related biases. Several repairs for selected algorithms have already been proposed, but the underlying mechanisms how such discrimination happens from the computational perspective are not yet scienti…
Mercer Large-Scale Kernel Machines from Ridge Function Perspective
本文从岭函数视角出发，研究大规模核机的Mercer性质，探讨了通过余弦函数的乘积之和近似核函数的可行性，并分析了该方法的障碍，应用于图像处理中的'一对一'方法。
Putnam's Critical and Explanatory Tendencies Interpreted from a Machine Learning Perspective
本文重构普特南批判性与解释性倾向之分的思想脉络，论证二者的双向必要性，并借机器学习视角将其概念化为介入理论选择争论的新工具。
Data scientists often develop machine learning models to solve a variety of problems in the industry and academy but not without facing several challenges in terms of Model Development. The problems regarding Machine Learning Development involves the fact that such professionals do not realize that they usually perform ad-hoc practices that could be improved by the adoption of activities presented in the Software Engineering Development Lifecycle. Of course, since machine learning systems are different from traditional Software systems, some differences in their respective development processe…
We are used to the availability of big data generated in nearly all fields of science as a consequence of technological progress. However, the analysis of such data possess vast challenges. One of these relates to the explainability of artificial intelligence (AI) or machine learning methods. Currently, many of such methods are non-transparent with respect to their working mechanism and for this reason are called black box models, most notably deep learning methods. However, it has been realized that this constitutes severe problems for a number of fields including the health sciences and crim…
Service level agreement (SLA) is an essential part of cloud systems to ensure maximum availability of services for customers. With a violation of SLA, the provider has to pay penalties. In this paper, we explore two machine learning models: Naive Bayes and Random Forest Classifiers to predict SLA violations. Since SLA violations are a rare event in the real world (~0.2 %), the classification task becomes more challenging. In order to overcome these challenges, we use several re-sampling methods. We find that random forests with SMOTE-ENN re-sampling have the best performance among other method…
Generative AI Agents in Autonomous Machines: A Safety Perspective
本文从安全视角研究生成式AI智能体集成到自主机器中的安全要求与挑战，并提出开发和实施全面安全记分卡以保障其安全部署。
This paper reviews the most notable works applying machine learning techniques (ML) in the context of geophysics and corresponding subbranches. We showcase both the progress achieved to date as well as the important future directions for further research while providing an adequate background in the fields of weather forecast, wind energy, wave energy, oil and gas exploration. The objective is to reflect on the previous successes and provide a comprehensive review of the synergy between these two fields in order to speed up the novel approaches of machine learning techniques in geophysics. Las…
Machine learning (ML) teams often work on a project just to realize the performance of the model is not good enough. Indeed, the success of ML-enabled systems involves aligning data with business problems, translating them into ML tasks, experimenting with algorithms, evaluating models, capturing data from users, among others. Literature has shown that ML-enabled systems are rarely built based on precise specifications for such concerns, leading ML teams to become misaligned due to incorrect assumptions, which may affect the quality of such systems and overall project success. In order to help…
A novel approach to the relationships between data features -- based on comprehensive examination of mathematical, technological, and causal methodology
针对现有AI特征关系分析方法易扭曲内在作用的问题，本研究提出整合多视角的收敛融合范式（CFP）理论，结合希尔伯特空间等方法解决共因问题，提升反事实推理下的AI透明度与治理能力。
Evaluating Mathematical Reasoning of Large Language Models: A Focus on Error Identification and Correction
本文针对LLMs数学推理评估缺乏考官视角的问题，提出包含错误识别与纠正四任务及基于AnnotatedErrorTypes数据集的评估框架，发现GPT-4优于所有模型，闭源模型表现最好，LlamaMA-2-7B和GPT-3.5，
This work presents a review of the current state of research in data-driven turbulence closure modeling. It offers a perspective on the challenges and open issues, but also on the advantages and promises of machine learning methods applied to parameter estimation, model identification, closure term reconstruction and beyond, mostly from the perspective of Large Eddy Simulation and related techniques. We stress that consistency of the training data, the model, the underlying physics and the discretization is a key issue that needs to be considered for a successful ML-augmented modeling strategy…
Quantum machine learning has emerged as an exciting and promising paradigm inside quantum technologies. It may permit, on the one hand, to carry out more efficient machine learning calculations by means of quantum devices, while, on the other hand, to employ machine learning techniques to better control quantum systems. Inside quantum machine learning, quantum reinforcement learning aims at developing "intelligent" quantum agents that may interact with the outer world and adapt to it, with the strategy of achieving some final goal. Another paradigm inside quantum machine learning is that of qu…
The application of machine learning to radiological images is an increasingly active research area that is expected to grow in the next five to ten years. Recent advances in machine learning have the potential to recognize and classify complex patterns from different radiological imaging modalities such as x-rays, computed tomography, magnetic resonance imaging and positron emission tomography imaging. In many applications, machine learning based systems have shown comparable performance to human decision-making. The applications of machine learning are the key ingredients of future clinical d…
Machine learning is playing an increasingly significant role in emerging mobile application domains such as AR/VR, ADAS, etc. Accordingly, hardware architects have designed customized hardware for machine learning algorithms, especially neural networks, to improve compute efficiency. However, machine learning is typically just one processing stage in complex end-to-end applications, involving multiple components in a mobile Systems-on-a-chip (SoC). Focusing only on ML accelerators loses bigger optimization opportunity at the system (SoC) level. This paper argues that hardware architects should…
Federated learning is an emerging machine learning paradigm where clients train models locally and formulate a global model based on the local model updates. To identify the state-of-the-art in federated learning and explore how to develop federated learning systems, we perform a systematic literature review from a software engineering perspective, based on 231 primary studies. Our data synthesis covers the lifecycle of federated learning system development that includes background understanding, requirement analysis, architecture design, implementation, and evaluation. We highlight and summar…
Dynamics and Computational Principles of Echo State Networks: A Mathematical Perspective
本研究从数学视角系统探索储备池计算（RC），基于动力系统理论分析其回声状态特性、衰退记忆等基础特性，形式化输入与状态的相互作用条件，探讨计算权衡与应用，为RC理论发展提供见解。
It is beneficial to develop an efficient machine-learning based method for addition using embedded hexadecimal digits. Through a comparison between human-developed machine learning model and models sampled through Neural Architecture Search (NAS) we determine an efficient approach to solve this problem with a final testing loss of 0.2937 for a human-developed model.
As machine learning (ML) technologies and applications are rapidly changing many computing domains, security issues associated with ML are also emerging. In the domain of systems security, many endeavors have been made to ensure ML model and data confidentiality. ML computations are often inevitably performed in untrusted environments and entail complex multi-party security requirements. Hence, researchers have leveraged the Trusted Execution Environments (TEEs) to build confidential ML computation systems. We conduct a systematic and comprehensive survey by classifying attack vectors and miti…
Machine learning (ML) is used increasingly in real-world applications. In this paper, we describe our ongoing endeavor to define characteristics and challenges unique to Requirements Engineering (RE) for ML-based systems. As a first step, we interviewed four data scientists to understand how ML experts approach elicitation, specification, and assurance of requirements and expectations. The results show that changes in the development paradigm, i.e., from coding to training, also demands changes in RE. We conclude that development of ML systems demands requirements engineers to: (1) understand …
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