News & Research

arXiv:2606.02427v1 Announce Type: cross Abstract: Existing evaluations of neural operators and in-context operator learning rely primarily on prediction error, but accurate output prediction does not guarantee the correct local dynamical structure. A model may match solutions while exhibiting incorrect sensitivities, distorted frequency response, spurious mode coupling, or unstable tangent behavior. We introduce a Jacobian-based spectral audit for in-context operator learning. For a fixed prompt, we differentiate the network output with respect to the query function and view the resulting Jacobian as a learned tangent operator. Projecting it onto Fourier modes, we obtain a local spectral characterization of the inferred operator, including frequency-dependent gains, phase structure, and cross-mode coupling. The audit complements standard prediction metrics by testing whether the model reproduces local mechanisms of the underlying PDE operator rather than only outputs. Across benchmarks

arXiv:2606.02475v1 Announce Type: cross Abstract: Classical finite-difference solvers remain reliable tools for partial differential equations, but their efficiency depends on where mesh resolution is placed. Uniform refinement can waste degrees of freedom when solution difficulty is localised near sharp gradients, fronts, oscillations, or constraint-sensitive regions. This paper studies a hybrid strategy in which a physics-informed neural network (PINN) is used not as the final solver, but as an off-grid residual probe for adaptive mesh refinement. The PINN residual is sampled over the domain, converted into cellwise indicators, and used to guide refinement before the final approximation is computed by a finite-difference solver. The method is evaluated on three benchmarks. The main full-solver validation uses the one-dimensional viscous Burgers equation with a nonuniform finite-difference solve on the adapted meshes. PINN-threshold refinement attains final relative $L^2$ error $0.021

arXiv:2606.02507v1 Announce Type: cross Abstract: Inverse materials design is shifting materials discovery from forward prediction to targeted proposal of candidates that satisfy objectives under physical constraints. Here, we review recent advances in generative crystal structure modeling, multimodal learning, and closed-loop design pipelines for crystalline solids. We survey how modern generators learn chemical-structural priors from large databases to enable controllable sampling of periodic structures, and compare leading model classes including variational autoencoders, normalizing flows, autoregressive formulations, and diffusion models. Particular attention is given to how feasibility constraints and physical priors are enforced across the workflow, through representation choices, training objectives, sampling-time guidance, and post-generation screening and relaxation. We also discuss how multimodal learning fuses diverse materials modalities, including crystal structures, ther

arXiv:2606.02528v1 Announce Type: cross Abstract: Large language models now power robo-advisors and trading agents, yet whether they carry built-in biases toward specific assets is largely untested. We ask three questions: do LLMs systematically prefer certain financial instruments; can an internal representation with causal leverage over those preferences be identified; and does that representation affect downstream financial decisions? We develop a three-level audit protocol and apply it to Bitcoin. First, a behavioral audit of eight frontier LLMs shows that Bitcoin's ranking among money-like instruments is frame-dependent: models place it around rank 5 of 8 as "reliable money" but near the top under crisis and autonomous-agent frames, and an attribute-swap experiment confirms rankings track functional properties, not names. Second, we open a model's internals: a search across thousands of sparse-autoencoder features in Gemma 3 identifies a dominant Bitcoin-selective feature. Amplify

arXiv:2303.04345v2 Announce Type: replace Abstract: Federated learning (FL) is a promising framework that models distributed machine learning while protecting the privacy of clients. However, FL suffers performance degradation from heterogeneous and limited data. To alleviate the degradation, we present a novel personalized Bayesian FL approach named pFedBayes. By using the trained global distribution from the server as the prior distribution of each client, each client adjusts its own distribution by minimizing the sum of the reconstruction error over its personalized data and the KL divergence with the downloaded global distribution. Then, we propose a sparse personalized Bayesian FL approach named sFedBayes to enhance the inference efficiency. To overcome the extreme heterogeneity in non-i.i.d. data, we propose a clustered Bayesian FL model named cFedbayes by learning different prior distributions for different clients. Theoretical analysis gives the generalization error bound of th

arXiv:2310.20545v3 Announce Type: replace Abstract: We present a multi-task optimization approach based on a deep learning architecture for time series forecasting. We leverage large collections of time series to identify the weights of forecasting models that can be combined to produce forecasts for each series. This method jointly addresses two tasks: the selection of different forecasting models, and their effective combination. In doing so, it keeps into account, in an original way, both the accuracy and diversity of the forecasting methods. For a given time series, the model combination module extracts features and uses them to optimize the weights of the forecasting methods. Simultaneously, the model selection module extracts other features to identify the subset of methods to be used for the prediction. This selection process is framed as a classification problem, with the labels representing the set of models to be used for a series. These labels are determined by solving an au

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