Related papers: Softmax as a Lagrangian-Legendrian Seam

Deep metric learning (DML) aims to minimize empirical expected loss of the pairwise intra-/inter- class proximity violations in the embedding space. We relate DML to feasibility problem of finite chance constraints. We show that minimizer…

Many biological examples of fluid-structure interaction, including the transit of red blood cells through the narrow slits in the spleen and the intracellular trafficking of vesicles into dendritic spines, involve the near-contact of…

Many real world sequences such as protein secondary structures or shell logs exhibit a rich internal structures. Traditional probabilistic models of sequences, however, consider sequences of flat symbols only. Logical hidden Markov models…

This paper addresses the challenge of geometric quality assurance in manufacturing, particularly when human assessment is required. It proposes using Blender, an open-source simulation tool, to create synthetic datasets for machine learning…

Hilbert's sixth problem calls for the axiomatization of physics, particularly the derivation of macroscopic statistical laws from microscopic mechanical principles. A conceptual difficulty arises in classical probability theory: in…

Lagrangian Relaxation (LR) is a powerful technique for solving large-scale Mixed Integer Linear Programming (MILP), particularly those with decomposable structures, such as vehicle routing or unit commitment problems. By relaxing the…

Analyzing embedded simplicial complexes, such as triangular meshes and graphs, is an important problem in many fields. We propose a new approach for analyzing embedded simplicial complexes in a subdivision-invariant and isometry-invariant…

We introduce a novel approach to simulate the interaction between fluids and thin elastic solids without any penetration. Our approach is centered around an optimization system augmented with barriers, which aims to find a configuration…

Entropy-based inference methods have gained traction for improving the reliability of Large Language Models (LLMs). However, many existing approaches, such as entropy minimization techniques, suffer from high computational overhead and fail…

Softmax is popular normalization method used in machine learning. Deep learning solutions like Transformer or BERT use the softmax function intensively, so it is worthwhile to optimize its performance. This article presents our methodology…

The dynamics of supercooled liquids slow down and become increasingly heterogeneous as they are cooled. Recently, local structural variables identified using machine learning, such as "softness", have emerged as predictors of local…

Neural Network Language Models (NNLMs) generate probability distributions by applying a softmax function to a distance metric formed by taking the dot product of a prediction vector with all word vectors in a high-dimensional embedding…

Large language models (LLMs) have numerous real-life applications across various domains, such as natural language translation, sentiment analysis, language modeling, chatbots and conversational agents, creative writing, text…

In modern computational materials science, deep learning has shown the capability to predict interatomic potentials, thereby supporting and accelerating conventional simulations. However, existing models typically sacrifice either accuracy…

The proximal gradient algorithm for minimizing the sum of a smooth and a nonsmooth convex function often converges linearly even without strong convexity. One common reason is that a multiple of the step length at each iteration may…

Soft solids and their surface deformations control the response of many natural and artificial systems. Yet, their underlying properties are vigorously debated, particularly for polymer networks. While molecular-scale theories predict no…

Spherical symmetry is ubiquitous in nature. It's therefore unfortunate that spherical system simulations are so hard, and require complete spheres with millions of interacting particles. Here we introduce an approach to model spherical…

The extraction of useful deep features is important for many computer vision tasks. Deep features extracted from classification networks have proved to perform well in those tasks. To obtain features of greater usefulness, end-to-end…

Large Language Models are increasingly used as zero-shot classifiers in complex reasoning tasks. However, standard constrained decoding suffers from a phenomenon we define as Renormalization Bias. When a model is restricted to a small set…

Elastohydrodynamic lubrication, or simply soft lubrication, refers to the motion of deformable objects near a boundary lubricated by a fluid, and is one of the key physical mechanisms to minimise friction and wear in natural and engineered…