It has long been established that predictive models can be transformed into lossless compressors and vice versa. Incidentally, in recent years, the machine learning community has focused on training increasingly large and powerful self-supervised (language) models. Since these large language models exhibit impressive predictive capabilities, they are well-positioned to be strong compressors. In this work, we advocate for viewing the prediction problem through the lens of compression and evaluate the compression capabilities of large (foundation) models. We show that large language models are powerful general-purpose predictors and that the compression viewpoint provides novel insights into scaling laws, tokenization, and in-context learning. For example, Chinchilla 70B, while trained primarily on text, compresses ImageNet patches to 43.4% and LibriSpeech samples to 16.4% of their raw size, beating domain-specific compressors like PNG (58.5%) or FLAC (30.3%), respectively. Finally, we show that the prediction-compression equivalence allows us to use any compressor (like gzip) to build a conditional generative model.

Meta-learning has emerged as a powerful approach to train neural networks to learn new tasks quickly from limited data by pre-training them on a broad set of tasks. 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 (memory-based) 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.

We propose a novel algorithmic framework for distributional reinforcement learning, based on learning finite-dimensional mean embeddings of return distributions. The framework reveals a wide variety of new algorithms for dynamic programming and temporal-difference algorithms that rely on the sketch Bellman operator, which updates mean embeddings with simple linear-algebraic computations. We provide asymptotic convergence theory, and examine the empirical performance of the algorithms on a suite of tabular tasks. Further, we show that this approach can be straightforwardly combined with deep reinforcement learning.

This paper uses chess, a landmark planning problem in AI, to assess transformers’ performance on a planning task where memorization is futile — even at a large scale. To this end, we release ChessBench, a large-scale benchmark dataset of 10 million chess games with legal move and value annotations (15 billion data points) provided by Stockfish 16, the state-of-the-art chess engine. We train transformers with up to 270 million parameters on ChessBench via supervised learning and perform extensive ablations to assess the impact of dataset size, model size, architecture type, and different prediction targets (state-values, action-values, and behavioral cloning). Our largest models learn to predict action-values for novel boards quite accurately, implying highly non-trivial generalization. Despite performing no explicit search, our resulting chess policy solves challenging chess puzzles and achieves a surprisingly strong Lichess blitz Elo of 2895 against humans (grandmaster level). We also compare to Leela Chess Zero and AlphaZero (trained without supervision via self-play) with and without search. We show that, although a remarkably good approximation of Stockfish’s search-based algorithm can be distilled into large-scale transformers via supervised learning, perfect distillation is still beyond reach, thus making ChessBench well-suited for future research.

Memory-based meta-learning is a technique for approximating Bayes-optimal predictors. Under fairly general conditions, minimizing sequential prediction error, measured by the log loss, leads to implicit meta-learning. The goal of this work is to investigate how far this interpretation can be realized by current sequence prediction models and training regimes. The focus is on piecewise stationary sources with unobserved switching-points, which arguably capture an important characteristic of natural language and action-observation sequences in partially observable environments. We show that various types of memory-based neural models, including Transformers, LSTMs, and RNNs can learn to accurately approximate known Bayes-optimal algorithms and behave as if performing Bayesian inference over the latent switching-points and the latent parameters governing the data distribution within each segment.

Reinforcement Learning (RL) algorithms typically utilize learning and/or planning techniques to derive effective policies. The integration of both approaches has proven to be highly successful in addressing complex sequential decision-making challenges, as evidenced by algorithms such as AlphaZero and MuZero, which consolidate the planning process into a parametric search-policy. AIXI, the most potent theoretical universal agent, leverages planning through comprehensive search as its primary means to find an optimal policy. Here we define an alternative universal agent, which we call Self-AIXI, that on the contrary to AIXI, maximally exploits learning to obtain good policies. It does so by self-predicting its own stream of action data, which is generated, similarly to other TD(0) agents, by taking an action maximization step over the current on-policy (universal mixture-policy) Q-value estimates. We prove that Self-AIXI converges to AIXI, and inherits a series of properties like maximal Legg-Hutter intelligence and the self-optimizing property.

Memory-based meta-learning is a powerful technique to build agents that adapt fast to any task within a target distribution. A previous theoretical study has argued that this remarkable performance is because the meta-training protocol incentivises agents to behave Bayes-optimally. We empirically investigate this claim on a number of prediction and bandit tasks. Inspired by ideas from theoretical computer science, we show that meta-learned and Bayes-optimal agents not only behave alike, but they even share a similar computational structure, in the sense that one agent system can approximately simulate the other. Furthermore, we show that Bayes-optimal agents are fixed points of the meta-learning dynamics. Our results suggest that memory-based meta-learning is a general technique for numerically approximating Bayes-optimal agents; that is, even for task distributions for which we currently don't possess tractable models.