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Learning Universal Predictors
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Meta-learning has emerged as a powerful approach to train neural networks to learn new tasks quickly from limited data. Broad exposure to different tasks leads to versatile representations enabling general problem solving. But, what are the limits of meta-learning? In this work, we explore the potential of amortizing the most powerful universal predictor, namely Solomonoff Induction (SI), into neural networks via leveraging meta-learning to its limits. We use Universal Turing Machines (UTMs) to generate training data used to expose networks to a broad range of patterns. We provide theoretical analysis of the UTM data generation processes and meta-training protocols. We conduct comprehensive experiments with neural architectures (e.g. LSTMs, Transformers) and algorithmic data generators of varying complexity and universality. Our results suggest that UTM data is a valuable resource for meta-learning, and that it can be used to train neural networks capable of learning universal prediction strategies.
Forward citations
Cited by 5 Pith papers
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Next-Token Prediction Should be Ambiguity-Sensitive: A Meta-Learning Perspective
Transformers systematically deviate from the Bayes-optimal predictor under high-ambiguity contexts on a new HMM benchmark, and a Monte Carlo predictor that decouples task inference from token prediction partly closes ...
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Transformers Pretrained on Procedural Data Contain Modular Structures for Algorithmic Reasoning
Different procedural pretraining tasks create complementary, transferable structures in a transformer's attention and MLP weights, and structures from different tasks can be combined into one initialization.
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Hierarchical Solomonoff Induction: An Unbounded Machine Learning Model
HSI, a hyperprior over all Solomonoff priors, is shown equivalent to Solomonoff Induction while enabling dataset-conditioned prediction and a training-set error bound.
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Procedural Pretraining: Warming Up Language Models with Abstract Data
A short warm-up on procedural data (brackets, sorting, sets) makes language models more accurate and more data-efficient on language, code, and informal math.
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Large Language Models as Computable Approximations to Solomonoff Induction
The paper argues LLMs are computable approximations of Solomonoff induction, but its central derivation recovers the model's own probabilities by construction.
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