Related papers: On Correctness of Automatic Differentiation for No…

Human reasoning can distill principles from observed patterns and generalize them to explain and solve novel problems. The most powerful artificial intelligence systems lack explainability and symbolic reasoning ability, and have therefore…

With the emergence of powerful representations of continuous data in the form of neural fields, there is a need for discretization invariant learning: an approach for learning maps between functions on continuous domains without being…

Diffusion-based classifiers such as those relying on the Personalized PageRank and the Heat kernel, enjoy remarkable classification accuracy at modest computational requirements. Their performance however is affected by the extent to which…

Deep Convolutional Neural Networks (DCNNs) are currently the method of choice both for generative, as well as for discriminative learning in computer vision and machine learning. The success of DCNNs can be attributed to the careful…

Neural networks are versatile tools for computation, having the ability to approximate a broad range of functions. An important problem in the theory of deep neural networks is expressivity; that is, we want to understand the functions that…

We present differentiable particle filters (DPFs): a differentiable implementation of the particle filter algorithm with learnable motion and measurement models. Since DPFs are end-to-end differentiable, we can efficiently train their…

We proposed a framework for solving inverse problems in differential equations based on neural networks and automatic differentiation. Neural networks are used to approximate hidden fields. We analyze the source of errors in the framework…

Offline reinforcement learning, which aims at optimizing sequential decision-making strategies with historical data, has been extensively applied in real-life applications. State-Of-The-Art algorithms usually leverage powerful function…

Computer-aided diagnosis systems must make critical decisions from medical images that are often noisy, ambiguous, or conflicting, yet today's models are trained on overly simplistic labels that ignore diagnostic uncertainty. One-hot labels…

Deep learning is currently reaching outstanding performances on different tasks, including image classification, especially when using large neural networks. The success of these models is tributary to the availability of large collections…

Diffusion models have achieved remarkable results in image generation, and have similarly been used to learn high-performing policies in sequential decision-making tasks. Decision-making diffusion models can be trained on lower-quality…

A central problem in machine learning is often formulated as follows: Given a dataset $\{(x_j, y_j)\}_{j=1}^M$, which is a sample drawn from an unknown probability distribution, the goal is to construct a functional model $f$ such that…

Non-determinism and non-reproducibility present significant challenges in deep learning, leading to inconsistent results across runs and platforms. These issues stem from two origins: random number generation and floating-point computation.…

Depth separation -- why a deeper network is more powerful than a shallower one -- has been a major problem in deep learning theory. Previous results often focus on representation power. For example, arXiv:1904.06984 constructed a function…

AI Safety is a major concern in many deep learning applications such as autonomous driving. Given a trained deep learning model, an important natural problem is how to reliably verify the model's prediction. In this paper, we propose a…

We propose a categorical semantics of gradient-based machine learning algorithms in terms of lenses, parametrised maps, and reverse derivative categories. This foundation provides a powerful explanatory and unifying framework: it…

Differential linear logic (DiLL) provides a fine analysis of resource consumption in cut-elimination. We investigate the subsystem of DiLL without promotion in a deep inference formalism, where cuts are at an atomic level. In our system…

Taylor's formula holds significant importance in function representation, such as solving differential difference equations, ordinary differential equations, partial differential equations, and further promotes applications in visual…

The successes of deep learning, variational inference, and many other fields have been aided by specialized implementations of reverse-mode automatic differentiation (AD) to compute gradients of mega-dimensional objectives. The AD…

We consider the problem of computing dense correspondences between non-rigid shapes with potentially significant partiality. Existing formulations tackle this problem through heavy manifold optimization in the spectral domain, given…