Related papers: Overcoming a Theoretical Limitation of Self-Attent…
Understanding what neural architectures can and cannot compute is a central challenge in the theory of AI. One of the fundamental problems in this context is the PARITY task, which asks whether the number of 1s in a binary input sequence is…
Transformers struggle with length generalisation, displaying poor performance even on basic tasks. We test whether these limitations can be explained through two key failures of the self-attention mechanism. The first is the inability to…
Identifying words that impact a task's performance more than others is a challenge in natural language processing. Transformers models have recently addressed this issue by incorporating an attention mechanism that assigns greater attention…
Empirical studies have identified a range of learnability biases and limitations of transformers, such as a persistent difficulty in learning to compute simple formal languages such as PARITY, and a bias towards low-degree functions.…
Language recognition tasks are fundamental in natural language processing (NLP) and have been widely used to benchmark the performance of large language models (LLMs). These tasks also play a crucial role in explaining the working…
This work provides the first theoretical analysis of training transformers to solve complex problems by recursively generating intermediate states, analogous to fine-tuning for chain-of-thought (CoT) reasoning. We consider training a…
Transformers are emerging as the new workhorse of NLP, showing great success across tasks. Unlike LSTMs, transformers process input sequences entirely through self-attention. Previous work has suggested that the computational capabilities…
Chain-of-Thought (CoT) has been shown to empirically improve Transformers' performance, and theoretically increase their expressivity to Turing completeness. However, whether Transformers can learn to generalize to CoT traces longer than…
It has been observed in recent years that transformers have problems with length generalization for certain types of reasoning and arithmetic tasks. In particular, the performance of a transformer model trained on tasks (say addition) up to…
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…
Increasing the input length has been a driver of progress in language modeling with transformers. We identify conditions where shorter inputs are not harmful, and achieve perplexity and efficiency improvements through two new methods that…
Despite the fact that Transformers perform well in NLP tasks, recent studies suggest that self-attention is theoretically limited in learning even some regular and context-free languages. These findings motivated us to think about their…
This paper investigates the limitations of transformers for entity-tracking tasks in large language models. We identify a theoretical constraint, showing that transformers require at least $\log_2 (n+1)$ layers to handle entity tracking…
Despite the empirical success of prompt tuning in adapting pretrained language models to new tasks, theoretical analyses of its capabilities remain limited. Existing theoretical work primarily addresses universal approximation properties,…
Exactly solving first-order constraints (i.e., first-order formulas over a certain predefined structure) can be a very hard, or even undecidable problem. In continuous structures like the real numbers it is promising to compute approximate…
Transformers have supplanted recurrent models in a large number of NLP tasks. However, the differences in their abilities to model different syntactic properties remain largely unknown. Past works suggest that LSTMs generalize very well on…
The remarkable capability of over-parameterised neural networks to generalise effectively has been explained by invoking a ``simplicity bias'': neural networks prevent overfitting by initially learning simple classifiers before progressing…
Transformers allow attention between all pairs of tokens, but there is reason to believe that most of these connections - and their quadratic time and memory - may not be necessary. But which ones? We evaluate the impact of sparsification…
We propose the first method to show theoretical limitations for one-layer softmax transformers with arbitrarily many precision bits (even infinite). We establish those limitations for three tasks that require advanced reasoning. The first…
The Transformer model is widely successful on many natural language processing tasks. However, the quadratic complexity of self-attention limit its application on long text. In this paper, adopting a fine-to-coarse attention mechanism on…