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In this paper we propose a generalization of deep neural networks called deep function machines (DFMs). DFMs act on vector spaces of arbitrary (possibly infinite) dimension and we show that a family of DFMs are invariant to the dimension of…

Large language models (LLMs) have shown great success in text modeling tasks across domains. However, natural language exhibits inherent semantic hierarchies and nuanced geometric structure, which current LLMs do not capture completely…

Large language models (LLM) are advanced AI systems trained on extensive textual data, leveraging deep learning techniques to understand and generate human-like language. Today's LLMs with billions of parameters are so huge that hardly any…

Recent advancements in building domain-specific large language models (LLMs) have shown remarkable success, especially in tasks requiring reasoning abilities like logical inference over complex relationships and multi-step problem solving.…

Artificial Neural Networks(ANN) has been phenomenally successful on various pattern recognition tasks. However, the design of neural networks rely heavily on the experience and intuitions of individual developers. In this article, the…

Reinforcement learning (RL) promises a framework for near-universal problem-solving. In practice however, RL algorithms are often tailored to specific benchmarks, relying on carefully tuned hyperparameters and algorithmic choices. Recently,…

Ensembles over neural network weights trained from different random initialization, known as deep ensembles, achieve state-of-the-art accuracy and calibration. The recently introduced batch ensembles provide a drop-in replacement that is…

Large language models (LLMs) have shown impressive capabilities across tasks such as mathematics, coding, and reasoning, yet their learning ability, which is crucial for adapting to dynamic environments and acquiring new knowledge, remains…

Machine learning force fields (MLFFs) are a promising approach to balance the accuracy of quantum mechanics with the efficiency of classical potentials, yet selecting an optimal model amid increasingly diverse architectures that delivers…

Large language models (LLMs) are prone to hallucination stemming from misaligned self-awareness, particularly when processing queries exceeding their knowledge boundaries. While existing mitigation strategies employ uncertainty estimation…

Deep neural networks represent the gold standard for image classification. However, they usually need large amounts of data to reach superior performance. In this work, we focus on image classification problems with a few labeled examples…

The increased computerization in recent years has resulted in the production of a variety of different software, however measures need to be taken to ensure that the produced software isn't defective. Many researchers have worked in this…

Deep neural networks (DNNs) have been shown to outperform traditional machine learning algorithms in a broad variety of application domains due to their effectiveness in modeling complex problems and handling high-dimensional datasets. Many…

Based on its great successes in inference and denosing tasks, Dictionary Learning (DL) and its related sparse optimization formulations have garnered a lot of research interest. While most solutions have focused on single layer…

We show the existence of a deep neural network capable of approximating a wide class of high-dimensional approximations. The construction of the proposed neural network is based on a quasi-optimal polynomial approximation. We show that this…

Deep learning methods have played a more and more important role in hyperspectral image classification. However, the general deep learning methods mainly take advantage of the information of sample itself or the pairwise information between…

Convolutional neural network (CNN) has achieved impressive success in computer vision during the past few decades. The image convolution operation helps CNNs to get good performance on image-related tasks. However, it also has high…

Large language models (LLMs) have substantially advanced machine learning research, including natural language processing, computer vision, data mining, etc., yet they still exhibit critical limitations in explainability, reliability,…

Overparameterized machine learning (ML) methods such as neural networks may be prohibitively resource intensive for devices with limited computational capabilities. Hyperdimensional computing (HDC) is an emerging resource efficient and…

Symbolic regression is a powerful technique that can discover analytical equations that describe data, which can lead to explainable models and generalizability outside of the training data set. In contrast, neural networks have achieved…