Sparse-Aware Neural Networks for Nonlinear Functionals: Mitigating the Exponential Dependence on Dimension

Deep neural networks have emerged as powerful tools for learning operators defined over infinite-dimensional function spaces. However, existing theories frequently encounter difficulties related to dimensionality and limited interpretability. This work investigates how sparsity can help address these challenges in functional learning, a central ingredient in operator learning. We propose a framework that employs convolutional architectures to extract sparse features from a finite number of samples, together with deep fully connected networks to effectively approximate nonlinear functionals. Using universal discretization methods, we show that sparse approximators enable stable recovery from discrete samples. In addition, both the deterministic and the random sampling schemes are sufficient for our analysis. These findings lead to improved approximation rates and reduced sample sizes in various function spaces, including those with fast frequency decay and mixed smoothness. They also provide new theoretical insights into how sparsity can alleviate the curse of dimensionality in functional learning.

FlowTouch: View-Invariant Visuo-Tactile Prediction

Tactile sensation is essential for contact-rich manipulation tasks. It provides direct feedback on object geometry, surface properties, and interaction forces, enhancing perception and enabling fine-grained control. An inherent limitation of tactile sensors is that readings are available only when an object is touched. This precludes their use during planning and the initial execution phase of a task. Predicting tactile information from visual information can bridge this gap. A common approach is to learn a direct mapping from camera images to the output of vision-based tactile sensors. However, the resulting model will depend strongly on the specific setup and on how well the camera can capture the area where an object is touched. In this work, we introduce FlowTouch, a novel model for view-invariant visuo-tactile prediction. Our key idea is to use an object's local 3D mesh to encode rich information for predicting tactile patterns while abstracting away from scene-dependent details. FlowTouch integrates scene reconstruction and Flow Matching-based models for image generation. Our results show that FlowTouch is able to bridge the sim-to-real gap and generalize to new sensor instances. We further show that the resulting tactile images can be used for downstream grasp stability prediction. Our code, datasets and videos are available at https://flowtouch.github.io/

The Price of Robustness: Stable Classifiers Need Overparameterization

The relationship between overparameterization, stability, and generalization remains incompletely understood in the setting of discontinuous classifiers. We address this gap by establishing a generalization bound for finite function classes that improves inversely with class stability, defined as the expected distance to the decision boundary in the input domain (margin). Interpreting class stability as a quantifiable notion of robustness, we derive as a corollary a law of robustness for classification that extends the results of Bubeck and Sellke beyond smoothness assumptions to discontinuous functions. In particular, any interpolating model with $p \approx n$ parameters on $n$ data points must be unstable, implying that substantial overparameterization is necessary to achieve high stability. We obtain analogous results for parameterized infinite function classes by analyzing a stronger robustness measure derived from the margin in the codomain, which we refer to as the normalized co-stability. Experiments support our theory: stability increases with model size and correlates with test performance, while traditional norm-based measures remain largely uninformative.

Adaptive-CaRe: Adaptive Causal Regularization for Robust Outcome Prediction

Accurate prediction of outcomes is crucial for clinical decision-making and personalized patient care. Supervised machine learning algorithms, which are commonly used for outcome prediction in the medical domain, optimize for predictive accuracy, which can result in models latching onto spurious correlations instead of robust predictors. Causal structure learning methods on the other hand have the potential to provide robust predictors for the target, but can be too conservative because of algorithmic and data assumptions, resulting in loss of diagnostic precision. Therefore, we propose a novel model-agnostic regularization strategy, Adaptive-CaRe, for generalized outcome prediction in the medical domain. Adaptive-CaRe strikes a balance between both predictive value and causal robustness by incorporating a penalty that is proportional to the difference between the estimated statistical contribution and estimated causal contribution of the input features for model predictions. Our experiments on synthetic data establish the efficacy of the proposed Adaptive-CaRe regularizer in finding robust predictors for the target while maintaining competitive predictive accuracy. With experiments on a standard causal benchmark, we provide a blueprint for navigating the trade-off between predictive accuracy and causal robustness by tweaking the regularization strength, $λ$. Validation using real-world dataset confirms that the results translate to practical, real-domain settings. Therefore, Adaptive-CaRe provides a simple yet effective solution to the long-standing trade-off between predictive accuracy and causal robustness in the medical domain. Future work would involve studying alternate causal structure learning frameworks and complex classification models to provide deeper insights at a larger scale.

DRAW2ACT: Turning Depth-Encoded Trajectories into Robotic Demonstration Videos

Video diffusion models provide powerful real-world simulators for embodied AI but remain limited in controllability for robotic manipulation. Recent works on trajectory-conditioned video generation address this gap but often rely on 2D trajectories or single modality conditioning, which restricts their ability to produce controllable and consistent robotic demonstrations. We present DRAW2ACT, a depth-aware trajectory-conditioned video generation framework that extracts multiple orthogonal representations from the input trajectory, capturing depth, semantics, shape and motion, and injects them into the diffusion model. Moreover, we propose to jointly generate spatially aligned RGB and depth videos, leveraging cross-modality attention mechanisms and depth supervision to enhance the spatio-temporal consistency. Finally, we introduce a multimodal policy model conditioned on the generated RGB and depth sequences to regress the robot's joint angles. Experiments on Bridge V2, Berkeley Autolab, and simulation benchmarks show that DRAW2ACT achieves superior visual fidelity and consistency while yielding higher manipulation success rates compared to existing baselines.

CHEM: Estimating and Understanding Hallucinations in Deep Learning for Image Processing

U-Net and other U-shaped architectures have achieved significant success in image deconvolution tasks. However, challenges have emerged, as these methods might generate unrealistic artifacts or hallucinations, which can interfere with analysis in safety-critical scenarios. This paper introduces a novel approach for quantifying and comprehending hallucination artifacts to ensure trustworthy computer vision models. Our method, termed the Conformal Hallucination Estimation Metric (CHEM), is applicable to any image reconstruction model, enabling efficient identification and quantification of hallucination artifacts. It offers two key advantages: it leverages wavelet and shearlet representations to efficiently extract hallucinations of image features and uses conformalized quantile regression to assess hallucination levels in a distribution-free manner. Furthermore, from an approximation theoretical perspective, we explore the reasons why U-shaped networks are prone to hallucinations. We test the proposed approach on the CANDELS astronomical image dataset with models such as U-Net, SwinUNet, and Learnlets, and provide new perspectives on hallucination from different aspects in deep learning-based image processing.

When is a System Discoverable from Data? Discovery Requires Chaos

The deep learning revolution has spurred a rise in advances of using AI in sciences. Within physical sciences the main focus has been on discovery of dynamical systems from observational data. Yet the reliability of learned surrogates and symbolic models is often undermined by the fundamental problem of non-uniqueness. The resulting models may fit the available data perfectly, but lack genuine predictive power. This raises the question: under what conditions can the systems governing equations be uniquely identified from a finite set of observations? We show, counter-intuitively, that chaos, typically associated with unpredictability, is crucial for ensuring a system is discoverable in the space of continuous or analytic functions. The prevalence of chaotic systems in benchmark datasets may have inadvertently obscured this fundamental limitation. More concretely, we show that systems chaotic on their entire domain are discoverable from a single trajectory within the space of continuous functions, and systems chaotic on a strange attractor are analytically discoverable under a geometric condition on the attractor. As a consequence, we demonstrate for the first time that the classical Lorenz system is analytically discoverable. Moreover, we establish that analytic discoverability is impossible in the presence of first integrals, common in real-world systems. These findings help explain the success of data-driven methods in inherently chaotic domains like weather forecasting, while revealing a significant challenge for engineering applications like digital twins, where stable, predictable behavior is desired. For these non-chaotic systems, we find that while trajectory data alone is insufficient, certain prior physical knowledge can help ensure discoverability. These findings warrant a critical re-evaluation of the fundamental assumptions underpinning purely data-driven discovery.

Improved probabilistic regression using diffusion models

Probabilistic regression models the entire predictive distribution of a response variable, offering richer insights than classical point estimates and directly allowing for uncertainty quantification. While diffusion-based generative models have shown remarkable success in generating complex, high-dimensional data, their usage in general regression tasks often lacks uncertainty-related evaluation and remains limited to domain-specific applications. We propose a novel diffusion-based framework for probabilistic regression that learns predictive distributions in a nonparametric way. More specifically, we propose to model the full distribution of the diffusion noise, enabling adaptation to diverse tasks and enhanced uncertainty quantification. We investigate different noise parameterizations, analyze their trade-offs, and evaluate our framework across a broad range of regression tasks, covering low- and high-dimensional settings. For several experiments, our approach shows superior performance against existing baselines, while delivering calibrated uncertainty estimates, demonstrating its versatility as a tool for probabilistic prediction.

RoboSwap: A GAN-driven Video Diffusion Framework For Unsupervised Robot Arm Swapping

Recent advancements in generative models have revolutionized video synthesis and editing. However, the scarcity of diverse, high-quality datasets continues to hinder video-conditioned robotic learning, limiting cross-platform generalization. In this work, we address the challenge of swapping a robotic arm in one video with another: a key step for crossembodiment learning. Unlike previous methods that depend on paired video demonstrations in the same environmental settings, our proposed framework, RoboSwap, operates on unpaired data from diverse environments, alleviating the data collection needs. RoboSwap introduces a novel video editing pipeline integrating both GANs and diffusion models, combining their isolated advantages. Specifically, we segment robotic arms from their backgrounds and train an unpaired GAN model to translate one robotic arm to another. The translated arm is blended with the original video background and refined with a diffusion model to enhance coherence, motion realism and object interaction. The GAN and diffusion stages are trained independently. Our experiments demonstrate that RoboSwap outperforms state-of-the-art video and image editing models on three benchmarks in terms of both structural coherence and motion consistency, thereby offering a robust solution for generating reliable, cross-embodiment data in robotic learning.

Conflicting Biases at the Edge of Stability: Norm versus Sharpness Regularization

A widely believed explanation for the remarkable generalization capacities of overparameterized neural networks is that the optimization algorithms used for training induce an implicit bias towards benign solutions. To grasp this theoretically, recent works examine gradient descent and its variants in simplified training settings, often assuming vanishing learning rates. These studies reveal various forms of implicit regularization, such as $\ell_1$-norm minimizing parameters in regression and max-margin solutions in classification. Concurrently, empirical findings show that moderate to large learning rates exceeding standard stability thresholds lead to faster, albeit oscillatory, convergence in the so-called Edge-of-Stability regime, and induce an implicit bias towards minima of low sharpness (norm of training loss Hessian). In this work, we argue that a comprehensive understanding of the generalization performance of gradient descent requires analyzing the interaction between these various forms of implicit regularization. We empirically demonstrate that the learning rate balances between low parameter norm and low sharpness of the trained model. We furthermore prove for diagonal linear networks trained on a simple regression task that neither implicit bias alone minimizes the generalization error. These findings demonstrate that focusing on a single implicit bias is insufficient to explain good generalization, and they motivate a broader view of implicit regularization that captures the dynamic trade-off between norm and sharpness induced by non-negligible learning rates.