Christopher Mattern

Grégoire Delétang, Anian Ruoss, Paul-Ambroise Duquenne et al.

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.

Jordi Grau-Moya, Tim Genewein, Marcus Hutter et al.

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.

Christopher Mattern

In this work we consider a new family of algorithms for sequential prediction, Hierarchical Partitioning Forecasters (HPFs). Our goal is to provide appealing theoretical - regret guarantees on a powerful model class - and practical - empirical performance comparable to deep networks - properties at the same time. We built upon three principles: hierarchically partitioning the feature space into sub-spaces, blending forecasters specialized to each sub-space and learning HPFs via local online learning applied to these individual forecasters. Following these principles allows us to obtain regret guarantees, where Constant Partitioning Forecasters (CPFs) serve as competitor. A CPF partitions the feature space into sub-spaces and predicts with a fixed forecaster per sub-space. Fixing a hierarchical partition $\mathcal H$ and considering any CPF with a partition that can be constructed using elements of $\mathcal H$ we provide two guarantees: first, a generic one that unveils how local online learning determines regret of learning the entire HPF online; second, a concrete instance that considers HPF with linear forecasters (LHPF) and exp-concave losses where we obtain $O(k \log T)$ regret for sequences of length $T$ where $k$ is a measure of complexity for the competing CPF. Finally, we provide experiments that compare LHPF to various baselines, including state of the art deep learning models, in precipitation nowcasting. Our results indicate that LHPF is competitive in various settings.

Joel Veness, Tor Lattimore, David Budden et al.

This paper presents a new family of backpropagation-free neural architectures, Gated Linear Networks (GLNs). What distinguishes GLNs from contemporary neural networks is the distributed and local nature of their credit assignment mechanism; each neuron directly predicts the target, forgoing the ability to learn feature representations in favor of rapid online learning. Individual neurons can model nonlinear functions via the use of data-dependent gating in conjunction with online convex optimization. We show that this architecture gives rise to universal learning capabilities in the limit, with effective model capacity increasing as a function of network size in a manner comparable with deep ReLU networks. Furthermore, we demonstrate that the GLN learning mechanism possesses extraordinary resilience to catastrophic forgetting, performing comparably to a MLP with dropout and Elastic Weight Consolidation on standard benchmarks. These desirable theoretical and empirical properties position GLNs as a complementary technique to contemporary offline deep learning methods.

Joel Veness, Tor Lattimore, Avishkar Bhoopchand et al.

This paper describes a family of probabilistic architectures designed for online learning under the logarithmic loss. Rather than relying on non-linear transfer functions, our method gains representational power by the use of data conditioning. We state under general conditions a learnable capacity theorem that shows this approach can in principle learn any bounded Borel-measurable function on a compact subset of euclidean space; the result is stronger than many universality results for connectionist architectures because we provide both the model and the learning procedure for which convergence is guaranteed.