Universal In-Context Approximation By Prompting Fully Recurrent Models

TL;DR

This paper proves that various fully recurrent neural architectures, including RNNs, LSTMs, and SSMs, can serve as universal in-context approximators, extending previous transformer-based results to a broader class of models.

Contribution

It introduces a formal framework and a programming language, LSRL, to demonstrate the universal in-context approximation capability of fully recurrent models.

Findings

Recurrent models like RNNs, LSTMs, and SSMs can approximate any function in-context.

Gated architectures such as LSTMs and GRUs offer more stable operation implementations.

The LSRL language facilitates further analysis and interpretability of recurrent models.

Abstract

Zero-shot and in-context learning enable solving tasks without model fine-tuning, making them essential for developing generative model solutions. Therefore, it is crucial to understand whether a pretrained model can be prompted to approximate any function, i.e., whether it is a universal in-context approximator. While it was recently shown that transformer models do possess this property, these results rely on their attention mechanism. Hence, these findings do not apply to fully recurrent architectures like RNNs, LSTMs, and the increasingly popular SSMs. We demonstrate that RNNs, LSTMs, GRUs, Linear RNNs, and linear gated architectures such as Mamba and Hawk/Griffin can also serve as universal in-context approximators. To streamline our argument, we introduce a programming language called LSRL that compiles to these fully recurrent architectures. LSRL may be of independent interest for further studies of fully recurrent models, such as constructing interpretability benchmarks. We also study the role of multiplicative gating and observe that architectures incorporating such gating (e.g., LSTMs, GRUs, Hawk/Griffin) can implement certain operations more stably, making them more viable candidates for practical in-context universal approximation.