Deep neural networks (DNNs) and Kolmogorov-Arnold networks (KANs) are popular methods for function approximation due to their flexibility and expressivity. However, they typically require a large number of trainable parameters to produce a suitable approximation. Beyond making the resulting network less transparent, overparameterization creates a large optimization space, likely producing local minima in training that have quite different generalization errors. In this case, network initialization can have an outsize impact on the model's out-of-sample accuracy. For these reasons, we propose shallow universal polynomial networks (SUPNs). These networks replace all but the last hidden layer with a single layer of polynomials with learnable coefficients, leveraging the strengths of DNNs and polynomials to achieve sufficient expressivity with far fewer parameters. We prove that SUPNs converge at the same rate as the best polynomial approximation of the same degree, and we derive explicit formulas for quasi-optimal SUPN parameters. We complement theory with an extensive suite of numerical experiments involving SUPNs, DNNs, KANs, and polynomial projection in one, two, and ten dimensions, consisting of over 13,000 trained models. On the target functions we numerically studied, for a given number of trainable parameters, the approximation error and variability are often lower for SUPNs than for DNNs and KANs by an order of magnitude. In our examples, SUPNs even outperform polynomial projection on non-smooth functions.

Recovering meaningful concepts from language model activations is a central aim of interpretability. While existing feature extraction methods aim to identify concepts that are independent directions, it is unclear if this assumption can capture the rich temporal structure of language. Specifically, via a Bayesian lens, we demonstrate that Sparse Autoencoders (SAEs) impose priors that assume independence of concepts across time, implying stationarity. Meanwhile, language model representations exhibit rich temporal dynamics, including systematic growth in conceptual dimensionality, context-dependent correlations, and pronounced non-stationarity, in direct conflict with the priors of SAEs. Taking inspiration from computational neuroscience, we introduce a new interpretability objective -- Temporal Feature Analysis -- which possesses a temporal inductive bias to decompose representations at a given time into two parts: a predictable component, which can be inferred from the context, and a residual component, which captures novel information unexplained by the context. Temporal Feature Analyzers correctly parse garden path sentences, identify event boundaries, and more broadly delineate abstract, slow-moving information from novel, fast-moving information, while existing SAEs show significant pitfalls in all the above tasks. Overall, our results underscore the need for inductive biases that match the data in designing robust interpretability tools.

Recent work on neural scaling laws demonstrates that model performance scales predictably with compute budget, model size, and dataset size. In this work, we develop scaling laws based on problem complexity. We analyze two fundamental complexity measures: solution space size and representation space size. Using the Traveling Salesman Problem (TSP) as a case study, we show that combinatorial optimization promotes smooth cost trends, and therefore meaningful scaling laws can be obtained even in the absence of an interpretable loss. We then show that suboptimality grows predictably for fixed-size models when scaling the number of TSP nodes or spatial dimensions, independent of whether the model was trained with reinforcement learning or supervised fine-tuning on a static dataset. We conclude with an analogy to problem complexity scaling in local search, showing that a much simpler gradient descent of the cost landscape produces similar trends.

We propose a method for discovering and visualizing the differences between two learned representations, enabling more direct and interpretable model comparisons. We validate our method, which we call Representational Differences Explanations (RDX), by using it to compare models with known conceptual differences and demonstrate that it recovers meaningful distinctions where existing explainable AI (XAI) techniques fail. Applied to state-of-the-art models on challenging subsets of the ImageNet and iNaturalist datasets, RDX reveals both insightful representational differences and subtle patterns in the data. Although comparison is a cornerstone of scientific analysis, current tools in machine learning, namely post hoc XAI methods, struggle to support model comparison effectively. Our work addresses this gap by introducing an effective and explainable tool for contrasting model representations.

Large language models have transformed natural language processing, yet supervised fine-tuning (SFT) remains computationally intensive. This paper formally proves that capabilities acquired through SFT can be approximated by a base transformer model using inference-time techniques, specifically in-context learning (ICL), without altering model parameters, under idealized assumptions including unbounded computational resources and access to the fine-tuning dataset. We extend these results to practical scenarios with finite context lengths and partial dataset access. For text generation tasks with fixed output length $l$, datasets of size $\mathrm{O}\left( \frac{m V}{\varepsilon^2} \log \frac{m}δ \right)$ or, with bounded context, $\mathrm{O}\left( \frac{l \log V}{\varepsilon^2} \log \frac{1}δ \right)$ suffice to approximate fine-tuned behavior across $m$ contexts within error $\varepsilon$, where $V$ is the vocabulary size and $δ$ is the failure probability. For linear classification, datasets of size $\mathrm{O}\left( \frac{d}{\varepsilon} \right)$ or, with fixed context, $\mathrm{O}\left( \frac{1}{\varepsilon^2} \log \frac{1}δ \right)$ are sufficient, where $d$ is the input dimension. Grounded in the Turing completeness of transformers, these results provide a theoretical foundation for resource-efficient deployment of large language models, with practical techniques like retrieval-augmented generation bridging theory to real-world applications.

In medical imaging, the primary challenge is collecting large-scale labeled data due to privacy concerns, logistics, and high labeling costs. In this work, we present the UK Biobank Organs and Bones (UKBOB), the largest labeled dataset of body organs, comprising 51,761 MRI 3D samples (equivalent to 17.9 million 2D images) and more than 1.37 billion 2D segmentation masks of 72 organs, all based on the UK Biobank MRI dataset. We utilize automatic labeling, introduce an automated label cleaning pipeline with organ-specific filters, and manually annotate a subset of 300 MRIs with 11 abdominal classes to validate the quality (referred to as UKBOB-manual). This approach allows for scaling up the dataset collection while maintaining confidence in the labels. We further confirm the validity of the labels by demonstrating zero-shot generalization of trained models on the filtered UKBOB to other small labeled datasets from similar domains (e.g., abdominal MRI). To further mitigate the effect of noisy labels, we propose a novel method called Entropy Test-time Adaptation (ETTA) to refine the segmentation output. We use UKBOB to train a foundation model, Swin-BOB, for 3D medical image segmentation based on the Swin-UNetr architecture, achieving state-of-the-art results in several benchmarks in 3D medical imaging, including the BRATS brain MRI tumor challenge (with a 0.4% improvement) and the BTCV abdominal CT scan benchmark (with a 1.3% improvement). The pre-trained models and the code are available at https://emmanuelleb985.github.io/ukbob , and the filtered labels will be made available with the UK Biobank.

We consider the non-convex non-concave objective function in two-player zero-sum continuous games. The existence of pure Nash equilibrium requires stringent conditions, posing a major challenge for this problem. To circumvent this difficulty, we examine the problem of identifying a mixed Nash equilibrium, where strategies are randomized and characterized by probability distributions over continuous domains.To this end, we propose PArticle-based Primal-dual ALgorithm (PAPAL) tailored for a weakly entropy-regularized min-max optimization over probability distributions. This algorithm employs the stochastic movements of particles to represent the updates of random strategies for the $\epsilon$-mixed Nash equilibrium. We offer a comprehensive convergence analysis of the proposed algorithm, demonstrating its effectiveness. In contrast to prior research that attempted to update particle importance without movements, PAPAL is the first implementable particle-based algorithm accompanied by non-asymptotic quantitative convergence results, running time, and sample complexity guarantees. Our framework contributes novel insights into the particle-based algorithms for continuous min-max optimization in the general non-convex non-concave setting.

The United Nations has identified improving food security and reducing hunger as essential components of its sustainable development goals. As of 2021, approximately 828 million people worldwide are experiencing hunger and malnutrition, with numerous fatalities reported. Climate change significantly impacts agricultural land suitability, potentially leading to severe food shortages and subsequent social and political conflicts. To address this pressing issue, we have developed a machine learning-based approach to predict the risk of substantial land suitability degradation and changes in irrigation patterns. Our study focuses on Central Eurasia, a region burdened with economic and social challenges. This study represents a pioneering effort in utilizing machine learning methods to assess the impact of climate change on agricultural land suitability under various carbon emissions scenarios. Through comprehensive feature importance analysis, we unveil specific climate and terrain characteristics that exert influence on land suitability. Our approach achieves remarkable accuracy, offering policymakers invaluable insights to facilitate informed decisions aimed at averting a humanitarian crisis, including strategies such as the provision of additional water and fertilizers. This research underscores the tremendous potential of machine learning in addressing global challenges, with a particular emphasis on mitigating hunger and malnutrition.

In this paper, we propose a novel network framework for indoor 3D object detection to handle variable input frame numbers in practical scenarios. Existing methods only consider fixed frames of input data for a single detector, such as monocular RGB-D images or point clouds reconstructed from dense multi-view RGB-D images. While in practical application scenes such as robot navigation and manipulation, the raw input to the 3D detectors is the RGB-D images with variable frame numbers instead of the reconstructed scene point cloud. However, the previous approaches can only handle fixed frame input data and have poor performance with variable frame input. In order to facilitate 3D object detection methods suitable for practical tasks, we present a novel 3D detection framework named AnyView for our practical applications, which generalizes well across different numbers of input frames with a single model. To be specific, we propose a geometric learner to mine the local geometric features of each input RGB-D image frame and implement local-global feature interaction through a designed spatial mixture module. Meanwhile, we further utilize a dynamic token strategy to adaptively adjust the number of extracted features for each frame, which ensures consistent global feature density and further enhances the generalization after fusion. Extensive experiments on the ScanNet dataset show our method achieves both great generalizability and high detection accuracy with a simple and clean architecture containing a similar amount of parameters with the baselines.

Graph neural networks (GNNs) have emerged as a state-of-the-art approach to model and draw inferences from large scale graph-structured data in various application settings such as social networking. The primary goal of a GNN is to learn an embedding for each graph node in a dataset that encodes both the node features and the local graph structure around the node. Embeddings generated by a GNN for a graph node are unique to that GNN. Prior work has shown that GNNs are prone to model extraction attacks. Model extraction attacks and defenses have been explored extensively in other non-graph settings. While detecting or preventing model extraction appears to be difficult, deterring them via effective ownership verification techniques offer a potential defense. In non-graph settings, fingerprinting models, or the data used to build them, have shown to be a promising approach toward ownership verification. We present GrOVe, a state-of-the-art GNN model fingerprinting scheme that, given a target model and a suspect model, can reliably determine if the suspect model was trained independently of the target model or if it is a surrogate of the target model obtained via model extraction. We show that GrOVe can distinguish between surrogate and independent models even when the independent model uses the same training dataset and architecture as the original target model. Using six benchmark datasets and three model architectures, we show that consistently achieves low false-positive and false-negative rates. We demonstrate that is robust against known fingerprint evasion techniques while remaining computationally efficient.