Related papers: Composing Global Solutions to Reasoning Tasks via …

Neural architecture search has attracted wide attentions in both academia and industry. To accelerate it, researchers proposed weight-sharing methods which first train a super-network to reuse computation among different operators, from…

Neural networks are powerful models that solve a variety of complex real-world problems. However, the stochastic nature of training and large number of parameters in a typical neural model makes them difficult to evaluate via inspection.…

Large Language Models (LLMs) have demonstrated remarkable reasoning capabilities but often grapple with reliability challenges like hallucinations. While Knowledge Graphs (KGs) offer explicit grounding, existing paradigms of KG-augmented…

Understanding the fundamental mechanism behind the success of deep neural networks is one of the key challenges in the modern machine learning literature. Despite numerous attempts, a solid theoretical analysis is yet to be developed. In…

Recent advances in pixel-level tasks (e.g. segmentation) illustrate the benefit of of long-range interactions between aggregated region-based representations that can enhance local features. However, such aggregated representations, often…

We consider the approximation of functions by 2-layer neural networks with a small number of hidden weights based on the squared loss and small datasets. Due to the highly non-convex energy landscape, gradient-based training often suffers…

Large Language Models (LLMs) demonstrate strong reasoning abilities but face limitations such as hallucinations and outdated knowledge. Knowledge Graph (KG)-based Retrieval-Augmented Generation (RAG) addresses these issues by grounding LLM…

A quadratic approximation of neural network loss landscapes has been extensively used to study the optimization process of these networks. Though, it usually holds in a very small neighborhood of the minimum, it cannot explain many…

Areas of computational mechanics such as uncertainty quantification and optimization usually involve repeated evaluation of numerical models that represent the behavior of engineering systems. In the case of complex nonlinear systems…

In this paper, we introduce a novel analysis of neural networks based on geometric (Clifford) algebra and convex optimization. We show that optimal weights of deep ReLU neural networks are given by the wedge product of training samples when…

Retrieval-Augmented Generation (RAG) effectively enhances Large Language Models (LLMs) by incorporating retrieved external knowledge into the generation process. Reasoning models improve LLM performance in multi-hop QA tasks, which require…

Large Language Models (LLMs) demonstrate strong reasoning capabilities but struggle with hallucinations and limited transparency. Recently, KG-enhanced LLMs that integrate knowledge graphs (KGs) have been shown to improve reasoning…

Retrieval-Augmented Generation (RAG) enhances the reasoning ability of Large Language Models (LLMs) by dynamically integrating external knowledge, thereby mitigating hallucinations and strengthening contextual grounding for structured data…

Unsupervised representation learning methods are widely used for gaining insight into high-dimensional, unstructured, or structured data. In some cases, users may have prior topological knowledge about the data, such as a known cluster…

Neural networks have historically been built layerwise from the set of functions in ${f: \mathbb{R}^n \to \mathbb{R}^m }$, i.e. with activations and weights/parameters represented by real numbers, $\mathbb{R}$. Our work considers a richer…

Large Language Models (LLMs) struggle with knowledge-intensive tasks due to hallucinations and fragmented reasoning over dispersed information. While Retrieval-Augmented Generation (RAG) grounds generation in external sources, existing…

Retrieval-Augmented Generation (RAG) enhances the response quality and domain-specific performance of large language models (LLMs) by incorporating external knowledge to combat hallucinations. In recent research, graph structures have been…

Chain-of-thought (CoT) reasoning boosts large language models' (LLMs) performance on complex tasks but faces two key limitations: a lack of reliability when solely relying on LLM-generated reasoning chains and lower reasoning performance…

Accurate quantification of uncertainty in neural network predictions remains a central challenge for scientific applications involving high-dimensional, correlated data. While existing methods capture either aleatoric or epistemic…

Can a neural network minimizing cross-entropy learn linearly separable data? Despite progress in the theory of deep learning, this question remains unsolved. Here we prove that SGD globally optimizes this learning problem for a two-layer…