Fourier Head: Helping Large Language Models Learn Complex Probability Distributions

• URL: http://arxiv.org/abs/2410.22269v1
• Date: Tue, 29 Oct 2024 17:27:58 GMT
• Title: Fourier Head: Helping Large Language Models Learn Complex Probability Distributions
• Authors: Nate Gillman, Daksh Aggarwal, Michael Freeman, Saurabh Singh, Chen Sun,
• Abstract summary: We introduce a neural network layer, constructed using Fourier series, which we can easily substitute for any linear layer if we want the outputs to have a more continuous structure. We perform extensive analysis on synthetic datasets, as well as on large-scale decision making and time series forecasting tasks. All of our results support the effectiveness of our proposed Fourier head in scenarios where the underlying data distribution has a natural continuous structure.
• Score: 7.074506869260538
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: As the quality of large language models has improved, there has been increased interest in using them to model non-linguistic tokens. For example, the Decision Transformer recasts agentic decision making as a sequence modeling problem, using a decoder-only LLM to model the distribution over the discrete action space for an Atari agent. However, when adapting LLMs to non-linguistic domains, it remains unclear if softmax over discrete bins captures the continuous structure of the tokens and the potentially complex distributions needed for high quality token generation. We introduce a neural network layer, constructed using Fourier series, which we can easily substitute for any linear layer if we want the outputs to have a more continuous structure. We perform extensive analysis on synthetic datasets, as well as on large-scale decision making and time series forecasting tasks. We also provide theoretical evidence that this layer can better learn signal from data while ignoring high-frequency noise. All of our results support the effectiveness of our proposed Fourier head in scenarios where the underlying data distribution has a natural continuous structure. For example, the Fourier head improves a Decision Transformer agent's returns by 46% on the Atari Seaquest game, and increases a state-of-the-art times series foundation model's forecasting performance by 3.5% across 20 benchmarks unseen during training.

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