Related papers: Why Deep Jacobian Spectra Separate: Depth-Induced …

We prove sharp uniqueness results for a wide class of one-dimensional discrete evolutions. The proof is based on a construction from the theory of complex Jacobi matrices combined with growth estimates of entire functions.

Flow matching learns a velocity field that transports a base distribution to data. We study how small latent perturbations propagate through these flows and show that Jacobian-vector products (JVPs) provide a practical lens on dependency…

Recently, there has been a growing interest in the problem of learning rich implicit models - those from which we can sample, but can not evaluate their density. These models apply some parametric function, such as a deep network, to a base…

Deep neural networks (DNNs) are known to be vulnerable to adversarial examples that are crafted with imperceptible perturbations, i.e., a small change in an input image can induce a mis-classification, and thus threatens the reliability of…

For a two-parameter family of Jacobi matrices exhibiting first-order spectral phase transitions, we prove discreteness of the spectrum in the positive real axis when the parameters are in one of the transition boundaries. To this end we…

Neural networks are trained primarily based on their inputs and outputs, without regard for their internal mechanisms. These neglected mechanisms determine properties that are critical for safety, like (i) transparency; (ii) the absence of…

We present a unified framework called deep dependency networks (DDNs) that combines dependency networks and deep learning architectures for multi-label classification, with a particular emphasis on image and video data. The primary…

We present a postprocessing layer for deformable image registration to make a registration field more diffeomorphic by encouraging Jacobians of the transformation to be positive. Diffeomorphic image registration is important for medical…

Generative models based on static scalar energy functions represent an emerging paradigm in which a single time independent potential drives sample generation through its gradient field, eliminating the need for time conditioning entirely.…

In recent years, discriminative self-supervised methods have made significant strides in advancing various visual tasks. The central idea of learning a data encoder that is robust to data distortions/augmentations is straightforward yet…

Training a deep neural network with the outputs of selected layers satisfying linear constraints is required in many contemporary data-driven applications. While this can be achieved by incorporating projection layers into the neural…

Deep learning models achieve high predictive performance but lack intrinsic interpretability, hindering our understanding of the learned prediction behavior. Existing local explainability methods focus on associations, neglecting the causal…

The implicit biases of gradient-based optimization algorithms are conjectured to be a major factor in the success of modern deep learning. In this work, we investigate the implicit bias of gradient flow and gradient descent in two-layer…

How to balance training accuracy and adversarial robustness has become a challenge since the birth of deep learning. Here, we introduce a geometry-aware deep learning framework that leverages layer-wise local training to sculpt the internal…

In this paper we introduce an iterative Jacobi algorithm for solving distributed model predictive control (DMPC) problems, with linear coupled dynamics and convex coupled constraints. The algorithm guarantees stability and persistent…

Neural networks, whice have had a profound effect on how researchers study complex phenomena, do so through a complex, nonlinear mathematical structure which can be difficult for human researchers to interpret. This obstacle can be…

Hyperparameter optimization of neural networks can be elegantly formulated as a bilevel optimization problem. While research on bilevel optimization of neural networks has been dominated by implicit differentiation and unrolling,…

While modern representation learning relies heavily on global error signals, decentralized algorithms driven by local interactions offer a fundamental distributed alternative. However, the macroscopic convergence properties of these…

Most self-supervised learning (SSL) methods learn continuous visual representations by aligning different views of the same input, offering limited control over how information is structured across representation dimensions. In this work,…

Training reliable deep learning models which avoid making overconfident but incorrect predictions is a longstanding challenge. This challenge is further exacerbated when learning has to be differentially private: protection provided to…