Related papers: Neural Algorithmic Reasoning with Multiple Correct…

In recent years, advanced deep neural networks have required a large number of parameters for training. Therefore, finding a method to reduce the number of parameters has become crucial for achieving efficient training. This work proposes a…

Designing effective neural networks is fundamentally important in deep multimodal learning. Most existing works focus on a single task and design neural architectures manually, which are highly task-specific and hard to generalize to…

These notes focus on the minimization of convex functionals using first-order optimization methods, which are fundamental in many areas of applied mathematics and engineering. The primary goal of this document is to introduce and analyze…

Recently an algorithm, was discovered, which separates points in n-dimension by planes in such a manner that no two points are left un-separated by at least one plane{[}1-3{]}. By using this new algorithm we show that there are two ways of…

Deep learning, a branch of artificial intelligence, is a data-driven method that uses multiple layers of interconnected units or neurons to learn intricate patterns and representations directly from raw input data. Empowered by this…

In this paper, we consider both first- and second-order techniques to address continuous optimization problems arising in machine learning. In the first-order case, we propose a framework of transition from deterministic or…

Neural networks are increasingly used to construct numerical solution methods for partial differential equations. In this expository review, we introduce and contrast three important recent approaches attractive in their simplicity and…

While Large Language Models (LLMs) form the cornerstone of sequential decision-making agent development, they have inherent limitations in high-frequency decision tasks. Existing research mainly focuses on discrete embodied decision…

Large language models (LLMs) can face factual limitations when responding to time-sensitive queries about recent events that arise after their knowledge thresholds in the training corpus. Existing search-augmented approaches fall into two…

Neural networks (NN) have achieved state-of-the-art performance in various applications. Unfortunately in applications where training data is insufficient, they are often prone to overfitting. One effective way to alleviate this problem is…

Feed-forward, fully-connected Artificial Neural Networks (ANNs) or the so-called Multi-Layer Perceptrons (MLPs) are well-known universal approximators. However, their learning performance varies significantly depending on the function or…

Recent advancements in artificial intelligence (AI) have positioned deep learning (DL) as a pivotal technology in fields like computer vision, data mining, and natural language processing. A critical factor in DL performance is the…

Large Language Models (LLMs) have emerged as powerful tools capable of accomplishing a broad spectrum of tasks. Their abilities span numerous areas, and one area where they have made a significant impact is in the domain of code generation.…

Recent work on neural algorithmic reasoning has demonstrated that graph neural networks (GNNs) could learn to execute classical algorithms. Doing so, however, has always used a recurrent architecture, where each iteration of the GNN aligns…

Deep neural networks typically treat nonlinearities as fixed primitives (e.g., ReLU), limiting both interpretability and the granularity of control over the induced function class. While recent additive models (like KANs) attempt to address…

Large Language Models (LLMs) have shown remarkable reasoning capabilities, while their practical applications are limited by severe factual hallucinations due to limitations in the timeliness, accuracy, and comprehensiveness of their…

Multimodal Mathematical Reasoning (MMR) has recently attracted increasing attention for its capability to solve mathematical problems involving both textual and visual modalities. However, current models still face significant challenges in…

In this paper we introduce two algorithms for neural architecture search (NASGD and NASAGD) following the theoretical work by two of the authors [5] which used the geometric structure of optimal transport to introduce the conceptual basis…

Designing effective neural architectures poses a significant challenge in deep learning. While Neural Architecture Search (NAS) automates the search for optimal architectures, existing methods are often constrained by predetermined search…

We propose the Neural Logic Machine (NLM), a neural-symbolic architecture for both inductive learning and logic reasoning. NLMs exploit the power of both neural networks---as function approximators, and logic programming---as a symbolic…