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The field of neural machine translation (NMT) has changed with the advent of large language models (LLMs). Much of the recent emphasis in natural language processing (NLP) has been on modeling machine translation and many other problems…

Transformers excel at discovering patterns in sequential data, yet their fundamental limitations and learning mechanisms remain crucial topics of investigation. In this paper, we study the ability of Transformers to learn pseudo-random…

The state of the art in machine translation (MT) is governed by neural approaches, which typically provide superior translation accuracy over statistical approaches. However, on the closely related task of word alignment, traditional…

In this article we prove that the general transformer neural model undergirding modern large language models (LLMs) is Turing complete under reasonable assumptions. This is the first work to directly address the Turing completeness of the…

Recent advancements in Transformer-based architectures have led to impressive breakthroughs in natural language processing tasks, with models such as GPT-4, Claude, and Gemini demonstrating human-level reasoning abilities. However, despite…

A growing body of work explores how Large Language Models (LLMs) can be embedded in trading systems as agents that perceive market information, retrieve context, reason about decisions, emit tradable actions, and adapt under market…

The transformer structure employed in large language models (LLMs), as a specialized category of deep neural networks (DNNs) featuring attention mechanisms, stands out for their ability to identify and highlight the most relevant aspects of…

Trained transformer models have been found to implement interpretable procedures for tasks like arithmetic and associative recall, but little is understood about how the circuits that implement these procedures originate during training. To…

In the last decade, the generalization and adaptation abilities of deep learning models were typically evaluated on fixed training and test distributions. Contrary to traditional deep learning, large language models (LLMs) are (i) even more…

Transformer-based large language models have displayed impressive in-context learning capabilities, where a pre-trained model can handle new tasks without fine-tuning by simply augmenting the query with some input-output examples from that…

The Transformer has quickly become the dominant architecture for various pattern recognition tasks due to its capacity for long-range representation. However, transformers are data-hungry models and need large datasets for training. In…

Researchers have made notable progress in applying Large Language Models (LLMs) to solve math problems, as demonstrated through efforts like GSM8k, ProofNet, AlphaGeometry, and MathOdyssey. This progress has sparked interest in their…

The transformer has revolutionized modern AI across language, vision, and beyond. It consists of $L$ layers, each running $H$ attention heads in parallel and feeding the combined output to the subsequent layer. In attention, the input…

Large Language Models (LLMs) demonstrate exceptional reasoning abilities, enabling strong generalization across diverse tasks such as commonsense reasoning and instruction following. However, as LLMs scale, inference costs become…

Large Language Models (LLMs) have demonstrated exceptional capabilities in various natural language tasks, often achieving performances that surpass those of humans. Despite these advancements, the domain of mathematics presents a…

Although state-of-the-art LLMs can solve math problems, we find that they make errors on numerical comparisons with mixed notation: "Which is larger, $5.7 \times 10^2$ or $580$?" This raises a fundamental question: Do LLMs even know how big…

Transformers, the backbone of modern large language models (LLMs), face inherent architectural limitations that impede their reasoning capabilities. Unlike recurrent networks, Transformers lack recurrent connections, confining them to…

Many NLP applications require models to be interpretable. However, many successful neural architectures, including transformers, still lack effective interpretation methods. A possible solution could rely on building explanations from…

Large language models (LLMs) like GPT-4 and LLaMA-3 utilize the powerful in-context learning (ICL) capability of Transformer architecture to learn on the fly from limited examples. While ICL underpins many LLM applications, its full…

Large Language Models (LLMs) often exhibit a gap between their internal knowledge and their explicit linguistic outputs. In this report, we empirically investigate whether Looped Transformers (LTs)--architectures that increase computational…