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Transformers have demonstrated remarkable capabilities in multi-step reasoning tasks. However, understandings of the underlying mechanisms by which they acquire these abilities through training remain limited, particularly from a…

Test-time scaling improves the reasoning capabilities of large language models (LLMs) by allocating extra compute to generate longer Chains-of-Thoughts (CoTs). This enables models to tackle more complex problem by breaking them down into…

Chain-of-Thought (CoT) is a technique that guides Large Language Models (LLMs) to decompose complex tasks into multi-step reasoning through intermediate steps in natural language form. Briefly, CoT enables LLMs to think step by step.…

Constant bit-size Transformers are known to be Turing complete, but existing constructions require $\Omega(s(n))$ chain-of-thought (CoT) steps per simulated Turing machine (TM) step, leading to impractical reasoning lengths. In this paper,…

Analyzing the similarity of internal representations has been an important technique for understanding the behavior of deep neural networks. Most existing methods for analyzing the similarity between representations of high dimensions, such…

In this paper, we consider the supervised pre-trained transformer for a class of sequential decision-making problems. The class of considered problems is a subset of the general formulation of reinforcement learning in that there is no…

Recent years have witnessed increasing interests in prompt-based learning in which models can be trained on only a few annotated instances, making them suitable in low-resource settings. When using prompt-based learning for text…

Chain-of-Thought (CoT) prompting has demonstrably enhanced the performance of Large Language Models on tasks requiring multi-step inference. This success has led to widespread claims of emergent reasoning capabilities in these models. In…

As reasoning modules, such as the chain-of-thought mechanism, are applied to large language models, they achieve strong performance on various tasks such as answering common-sense questions and solving math problems. The main challenge now…

Solving mathematical problems using computer-verifiable languages like Lean has significantly impacted the mathematical and computer science communities. State-of-the-art methods utilize a single Large Language Model (LLM) to generate…

Chain of Thought (CoT) reasoning has demonstrated remarkable deep reasoning capabilities in both large language models (LLMs) and multimodal large language models (MLLMs). However, its reliability is often undermined by the accumulation of…

This paper presents "Predictive Pipelined Decoding (PPD)," an approach that speeds up greedy decoding in Large Language Models (LLMs) while maintaining the exact same output as the original decoding. Unlike conventional strategies, PPD…

Recent advances in large language models (LLMs) have popularized test-time scaling, where models generate additional reasoning tokens before producing final answers. These approaches have demonstrated significant performance improvements on…

The Transformer model is widely used in various application areas of machine learning, such as natural language processing. This paper investigates the approximation of the H\"older continuous function class…

Large language models (LLMs) exhibit failure modes on seemingly trivial tasks. We propose a formalisation of LLM interaction using a deterministic multi-tape Turing machine, where each tape represents a distinct component: input characters,…

Chain-of-Thought (CoT) prompting has achieved remarkable success in unlocking the reasoning capabilities of Large Language Models (LLMs). Although CoT prompting enhances reasoning, its verbosity imposes substantial computational overhead.…

The expressive power and computational complexity of deep visual generative models, such as flow-based and autoregressive (AR) models, have gained considerable interest for their wide-ranging applications in generative tasks. However, the…

Chain-of-thought (CoT) via prompting is the de facto method for eliciting reasoning capabilities from large language models (LLMs). But for what kinds of tasks is this extra ``thinking'' really helpful? To analyze this, we conducted a…

Recently, Diffusion Large Language Models (DLLMs) have offered high throughput and effective sequential reasoning, making them a competitive alternative to autoregressive LLMs (ALLMs). However, parallel decoding, which enables simultaneous…

Padding is often used in tuning LLM models by adding special tokens to shorter training examples to match the length of the longest sequence in each batch. While this ensures uniformity for batch processing, it introduces inefficiencies by…