Related papers: The Counting Power of Transformers

What is the computational model behind a Transformer? Where recurrent neural networks have direct parallels in finite state machines, allowing clear discussion and thought around architecture variants or trained models, Transformers have no…

Finding human-understandable circuits in language models is a central goal of the field of mechanistic interpretability. We train models to have more understandable circuits by constraining most of their weights to be zeros, so that each…

Deep architectures such as Transformers are sometimes criticized for having uninterpretable "black-box" representations. We use causal intervention analysis to show that, in fact, some linguistic features are represented in a linear,…

Recently, the transformer architecture has enabled substantial progress in many areas of pattern recognition and machine learning. However, as with other neural network models, there is currently no general method available to explain their…

We examine the convergence properties of sequences of nonnegative real numbers that satisfy a particular class of recursive inequalities, from the perspective of proof theory and computability theory. We first establish a number of results…

A wide variety of deep learning techniques from style transfer to multitask learning rely on training affine transformations of features. Most prominent among these is the popular feature normalization technique BatchNorm, which normalizes…

Transformers generate valid and diverse chemical structures, but little is known about the mechanisms that enable these models to capture the rules of molecular representation. We present a mechanistic analysis of autoregressive…

We investigate the mechanisms that arise when transformers are trained to solve arithmetic on sequences where tokens are variables whose meaning is determined only through their interactions in-context. While prior work has studied…

Transformer has become the dominant architecture for sequence modeling, yet a detailed understanding of how its structural parameters influence expressive power remains limited. In this work, we study the approximation properties of…

Using more test-time computation during language model inference, such as generating more intermediate thoughts or sampling multiple candidate answers, has proven effective in significantly improving model performance. This paper takes an…

Algorithm extraction aims to synthesize executable programs directly from models trained on algorithmic tasks, enabling de novo algorithm discovery without relying on human-written code. However, applying this paradigm to Transformer is…

Previous work on the learnability of transformers \textemdash\ focused primarily on examining their ability to approximate specific algorithmic patterns through training \textemdash\ has largely been data-driven, offering only probabilistic…

Despite the popularity of transformers in practice, their architectures are empirically designed and neither mathematically justified nor interpretable. Moreover, as indicated by many empirical studies, some components of transformer…

Despite the remarkable success of transformer architectures in natural language processing, their scalability limitations remain poorly understood through systematic empirical analysis. This paper presents the first comprehensive…

Implicit models, an emerging model class, compute outputs by iterating a single parameter block to a fixed point. This architecture realizes an infinite-depth, weight-tied network that trains with constant memory, significantly reducing…

It has been found that Transformer-based language models have the ability to perform basic quantitative reasoning. In this paper, we propose a method for studying how these models internally represent numerical data, and use our proposal to…

With the exponentially faster computation for certain problems, quantum computing has garnered significant attention in recent years. Variational quantum algorithms are crucial methods to implement quantum computing, and an appropriate…

The remarkable capability of Transformers to do reasoning and few-shot learning, without any fine-tuning, is widely conjectured to stem from their ability to implicitly simulate a multi-step algorithms -- such as gradient descent -- with…

The Transformer architecture has become prominent in developing large causal language models. However, mechanisms to explain its capabilities are not well understood. Focused on the training process, here we establish a meta-learning view…

In this text we develop the formalism of products and powers of linear codes under componentwise multiplication. As an expanded version of the author's talk at AGCT-14, focus is put mostly on basic properties and descriptive statements that…