Research Papers

arXiv:2312.03644v3 Announce Type: replace Abstract: Offline Multi-agent Reinforcement Learning (MARL) is valuable in scenarios where online interaction is impractical or risky. While independent learning in MARL offers flexibility and scalability, accurately assigning credit to individual agents in offline settings poses challenges because interactions with an environment are prohibited. In this paper, we propose a new framework, namely Multi-Agent Causal Credit Assignment (MACCA), to address credit assignment in the offline MARL setting. Our approach, MACCA, characterizing the generative process as a Dynamic Bayesian Network, captures relationships between environmental variables, states, actions, and rewards. Estimating this model on offline data, MACCA can learn each agent's contribution by analyzing the causal relationship of their individual rewards, ensuring accurate and interpretable credit assignment. Additionally, the modularity of our approach allows it to integrate with vari

arXiv:2408.11266v5 Announce Type: replace Abstract: Deep learning is now common across many scientific fields, including the study of partial differential equations. This article provides a brief, accessible introduction to core deep learning concepts, including neural networks, backpropagation, and the universal approximation theorem. It mainly covers how to use deep learning in solving differential equations. The article aims to help undergraduate and graduate students in mathematics, physics, and related areas learn how to use Deep Learning to solve partial differential equations. Instructors in mathematics or physics can also use this article to introduce students to Deep Galerkin method and scientific deep learning. We focus on key questions: What is deep learning, and how can it help solve mathematical or physical problems? How can you implement a neural network and choose the right numerical method to solve differential equations? How do you select the best hyperparameters? How

arXiv:2410.09737v2 Announce Type: replace Abstract: A popular way to improve the expressive power of graph neural networks (GNNs) is to use Laplacian eigenvectors as additional node features, since they can serve both as structural identifiers and global coordinates of nodes. Properly handling the orthogonal group symmetry among eigenvectors is crucial for the stability and generalizability of Laplacian eigenvector augmented GNNs. Previous studies have shown that using a naive $O(p)$-group invariant encoder for each $p$-dimensional eigenspace often leads to expressivity loss and numerical instability. In this paper, we propose a novel method exploiting Laplacian eigenvectors to generate \emph{stable} and globally \emph{expressive} graph representations. The main difference from previous works is that (i) our method utilizes \textbf{learnable} $O(p)$-invariant representations for each Laplacian eigenspace of dimension $p$, which are built upon powerful orthogonal group equivariant neura

arXiv:2412.04177v2 Announce Type: replace Abstract: Recently, there has been an increasing interest in performing post-hoc uncertainty estimation about the predictions of pre-trained deep neural networks (DNNs). Given a pre-trained DNN via back-propagation, these methods enhance the original network by adding output confidence measures, such as error bars, without compromising its initial accuracy. In this context, we introduce a novel family of sparse variational Gaussian processes (GPs), where the posterior mean is fixed to any continuous function when using a universal kernel. Specifically, we fix the mean of this GP to the output of the pre-trained DNN, allowing our approach to effectively fit the GP's predictive variances to estimate the DNN prediction uncertainty. Our approach leverages variational inference (VI) for efficient stochastic optimization, with training costs that remain independent of the number of training points, scaling efficiently to large datasets such as ImageN

arXiv:2412.16209v5 Announce Type: replace Abstract: When using machine learning for imbalanced binary classification problems, it is common to subsample the majority class to create a (more) balanced training dataset. This biases the model's predictions because the model learns from data that is not fully representative of the underlying population of interest. One way of accounting for this bias is analytically mapping the resulting predictions to new values based on the sampling rate for the majority class. We show that calibrating a random forest this way has negative consequences, including prevalence estimates that depend on both the number of predictors considered at each split in the random forest and the sampling rate used. We explain the former using known properties of random forests and analytical calibration and the latter by demonstrating a bias in decision trees. In contradiction with much of the existing literature, we show that decision trees can be biased towards the m

arXiv:2412.19444v2 Announce Type: replace Abstract: Optimization algorithms such as AdaGrad and Adam have significantly advanced the training of deep models by dynamically adjusting the learning rate during the optimization process. However, ad-hoc tuning of learning rates poses a challenge and leads to inefficiencies in practice. To address this issue, recent research has focused on developing ``parameter-free'' algorithms that operate effectively without the need for learning rate tuning. Despite these efforts, existing parameter-free variants of AdaGrad and Adam tend to be overly complex and/or lack formal convergence guarantees. In this paper, we present AdaGrad++ and Adam++, novel and simple parameter-free variants of AdaGrad and Adam with convergence guarantees. We prove that AdaGrad++ achieves comparable convergence rates to AdaGrad in convex optimization without predefined learning rate assumptions. Similarly, Adam++ matches the convergence rate of Adam without relying on any c

arXiv:2501.08640v2 Announce Type: replace Abstract: We propose a way to bound the generalisation errors of several classes of quantum reservoirs using the Rademacher complexity. We give specific, parameter-dependent bounds for two particular quantum reservoir classes. We analyse how the generalisation bounds scale with growing numbers of qubits. Applying our results to classes with polynomial readout functions, we find that the risk bounds converge in the number of training samples. The explicit dependence on the quantum reservoir and readout parameters in our bounds can be used to control the generalisation error to a certain extent. It should be noted that the bounds scale exponentially with the number of qubits n. The upper bounds on the Rademacher complexity can be applied to other reservoir classes that fulfill a few hypotheses on the quantum dynamics and the readout function.

arXiv:2502.20016v2 Announce Type: replace Abstract: Sustainability encompasses three key facets: economic, environmental, and social. However, the nascent discourse on sustainable artificial intelligence (AI) predominantly focuses on the environmental sustainability of AI, neglecting the economic and social aspects. Achieving truly sustainable AI necessitates addressing the tension between its environmental sustainability, which emphasises mitigating AI's climate impact, and its social sustainability, hinging on equitable access to AI development resources. This push for increased accessibility, however, often overlooks the environmental costs of expanding such resource usage. This position paper argues that reconciling climate awareness and resource awareness is essential to realising truly sustainable AI, and neglecting these factors fuels a global AI arms race. Applying Karl Marx's base-superstructure framework from historical materialism, we analyse how the material conditions are

arXiv:2503.22939v4 Announce Type: replace Abstract: The integration of heterogeneous multi-omics datasets at a systems level remains a central challenge for developing analytical and computational models in precision cancer diagnostics. This paper introduces Multi-Omics Graph Kolmogorov-Arnold Network (MOGKAN), a deep learning framework that utilizes messenger-RNA, micro-RNA sequences, and DNA methylation samples together with Protein-Protein Interaction (PPI) networks for cancer classification across 31 different cancer types. The proposed approach combines differential gene expression with DESeq2, Linear Models for Microarray (LIMMA), and Least Absolute Shrinkage and Selection Operator (LASSO) regression to reduce multi-omics data dimensionality while preserving relevant biological features. The model architecture is based on the Kolmogorov-Arnold theorem principle and uses trainable univariate functions to enhance interpretability and feature analysis. MOGKAN achieves classification

arXiv:2503.24183v3 Announce Type: replace Abstract: The expansion of ride-sourcing services such as Uber and Lyft has reshaped urban transportation by offering flexible, on-demand mobility via mobile applications. Despite convenience, these platforms confront significant operational challenges, particularly vehicle rebalancing-strategic repositioning of a fleet of vehicles to address spatiotemporal mismatches in supply and demand. Inadequate rebalancing results in prolonged rider waiting times and inefficient vehicle utilization, but also leads to fairness issues, such as the inequitable distribution of service and disparities in driver income. To tackle these, we introduce continuous-state mean-field control (MFC) and mean-field reinforcement learning (MFRL) models with continuous repositioning actions. MFC and MFRL offer scalable solutions by modeling each vehicle's behavior through interaction with the vehicle distribution, rather than with individual vehicles. This mitigates the cu

arXiv:2504.19419v3 Announce Type: replace Abstract: Local clustering aims to identify specific substructures within a large graph without any additional structural information of the graph. These substructures are typically small compared to the overall graph, enabling the problem to be approached by finding a sparse solution to a linear system associated with the graph Laplacian. In this work, we first propose a method for identifying specific local clusters when very few labeled data are given, which we term semi-supervised local clustering. We then extend this approach to the unsupervised setting when no prior information on labels is available. The proposed methods involve randomly sampling the graph, applying diffusion through local cluster extraction, then examining the overlap among the results to find each cluster. We establish the co-membership conditions for any pair of nodes, and rigorously prove the correctness of our methods. Additionally, we conduct extensive experiments

arXiv:2505.10882v2 Announce Type: replace Abstract: Principal component analysis classically requires full $d$-dimensional samples, yet in various applications hardware limits acquisition to a few scalar measurements per sample. We analyze a compressed variant of Oja's algorithm for estimating the principal eigenvector of the data covariance matrix using only two adaptive measurements per sample. At each iteration, we observe one measurement along the current estimate and one in a random orthogonal direction. We prove that after $t$ iterations, the expected sine-squared error to the true eigenvector is $\mathcal{O}(\lambda_1\lambda_2 d^2 / (\Delta^2 t))$, where $d$ is the ambient dimension, $\lambda_1, \lambda_2$ are the leading eigenvalues, and $\Delta = \lambda_1 - \lambda_2$ is the eigengap. We complement this with a matching information-theoretic lower bound of $\Omega(\lambda_1\lambda_2 d^2 / (\Delta^2 t))$ -- the first for compressed eigenvector estimation -- proving that the $d^

arXiv:2505.14411v4 Announce Type: replace Abstract: Existing time series tokenization methods predominantly encode a constant number of samples into individual tokens. This inflexible approach can generate excessive tokens for even simple patterns like extended constant values, resulting in substantial computational overhead. Inspired by the success of byte pair encoding, we propose the first pattern-centric tokenization scheme for time series analysis. Based on a discrete vocabulary of frequent motifs, our method merges samples with underlying patterns into tokens, compressing time series adaptively. Exploiting our finite set of motifs and the continuous properties of time series, we further introduce conditional decoding as a lightweight yet powerful post-hoc optimization method, which requires no gradient computation and adds no computational overhead. On recent time series foundation models, our motif-based tokenization improves forecasting performance by 40% and boosts efficiency

arXiv:2505.15354v2 Announce Type: replace Abstract: Time series forecasting models often produce systematic, predictable errors even in critical domains such as energy, finance, and healthcare. We introduce a novel post training adaptive optimization framework that improves forecast accuracy without retraining or architectural changes. Our method automatically applies expressive transformations optimized via reinforcement learning, contextual bandits, or genetic algorithms to correct model outputs in a lightweight and model agnostic way. Theoretically, we prove that affine corrections always reduce the mean squared error; practically, we extend this idea with dynamic action based optimization. The framework also supports an optional human in the loop component: domain experts can guide corrections using natural language, which is parsed into actions by a language model. Across multiple benchmarks (e.g., electricity, weather, traffic), we observe consistent accuracy gains with minimal c

arXiv:2505.18113v2 Announce Type: replace Abstract: Training quantized neural networks requires addressing the non-differentiable and discrete nature of the underlying optimization problem. To tackle this challenge, the straight-through estimator (STE) has become the most widely adopted heuristic, allowing backpropagation through discrete operations by introducing biased yet valid surrogate gradients. However, its theoretical properties remain largely unexplored, with few existing analyses focus on the generalization error by assuming an infinite amount of training data. In contrast, this work presents the first sample complexity analysis of STE in the context of neural network quantization. Our theoretical results highlight the critical role of sample size in the success of STE, a key insight absent from existing studies. Specifically, by analyzing the quantization-aware training of a two-layer neural network with binary weights and activations, we derive the sample complexity bounds