Why We Care About Understanding: Competence through Predictive Compression

Despite the increasing prevalence of large language models (LLMs), we still have a limited understanding of how their representational spaces are structured. This limits our ability to interpret how and what they learn or relate them to learning in humans. We argue LLMs are best seen as an instance of lossy compression, where over training they learn by retaining only information in their training data relevant to their objective(s). We show pre-training results in models that are optimally compressed for next-sequence prediction, approaching the Information Bottleneck bound on compression. Across an array of open weights models, each compresses differently, likely due to differences in the data and training recipes used. However even across different families of LLMs the optimality of a model's compression, and the information present in it, can predict downstream performance on across a wide array of benchmarks, letting us directly link representational structure to actionable insights about model performance. In the general case the work presented here offers a unified Information-Theoretic framing for how these models learn that is deployable at scale.

Model compression makes large language models deployable, but today's evaluation tells an incomplete story. Standard practice measures retained task performance and stops there. This misses a critical fact: compression perturbs the distributed knowledge embedded across billions of weights, and task scores alone cannot reveal which underlying abilities survive and which quietly collapse. To solve this question, we introduce ACE-Compression, an ability-centric evaluation framework. Instead of asking only "does the compressed model still answer correctly?", we ask "which of its core abilities remain intact?" Our framework probes four deployment-facing dimensions: procedural reasoning and constraint execution, knowledge grounding and truthfulness, social cognition and affective understanding, and persona fidelity and stylistic consistency. Across more than 35 compressed checkpoints from six open-weight LLMs-covering quantization and pruning-we find that compression redistributes ability profiles. Coarse, local, and surface-level signals often persist, while fine-grained, long-tail, and context-dependent abilities become fragile. Quantization consistently outperforms pruning in retention, but the practical meaning of that gap depends entirely on which ability an application requires. Based on our findings, deployers can choose compression methods by the ability profile their application needs, not just by a leaderboard average. And algorithm designers gain diagnostic signals to build compression methods that preserve what matters. We believe that ACE-Compression turns compression from a black-box accuracy drop into an interpretable intervention-one we can measure, understand, and ultimately improve.

A long-standing hypothesis in artificial intelligence and neuroscience posits that intelligence is closely related to compression: the ability to compress information efficiently intuitively reflects capacities associated with intelligence and learning. Indeed, recent experimental works verify this intuition by showing connections between the capabilities of large language models (LLMs) and their ability as compressors: for instance, Deletang et al. (ICLR'24) demonstrate that LLMs can be used as powerful compressors, and Huang et al. (COLM'24) show that the compression ability of LLMs is highly correlated with their performance on benchmarks for knowledge and reasoning. In this work, we initiate a theoretical study of this connection. Our main result is that LLMs (formally modeled as next-token predictors) are equivalent to monotone (a.k.a. order-preserving) compression algorithms---namely, compression algorithms where the encoding process preserves the ordering of the inputs---in the sense that the one can be constructed from the other while preserving the same error up to an additive gap of 2. We next show that the monotonicity is required for this equivalence to hold if and only if cryptographic (infinitely-often) one-way functions exist. As a direct corollary, we get a cryptographic result of independent interest: the notion of next-bit pseudoentropy (a computational analogue of entropy) of a distribution is equivalent to monotone incompressibility of the distribution. (Previously, it was only known (Haitner et al., ITCS'23) that incompressibility implies next-bit pseudoentropy.)