Language Modeling is Monotone Compression

LLM pipelines waste substantial token budgets on low-information content: repeated context, verbose responses, and redundant boilerplate. We introduce Entropy Gate, a token compression framework applying entropy quenching $-$ a thermodynamic process that progressively freezes out low-energy tokens while preserving semantic fidelity. Each token receives a multi-factor information energy $E(t)$ combining statistical, structural, and positional components. An adaptive quenching schedule $T(τ) = T_0 / (1 + ατ)$ removes tokens whose Boltzmann survival probability $p_i = \exp(-E_i / kT)$ falls below threshold, with a fidelity gate halting compression when energy-weighted similarity drops below $θ$. We prove token selection by descending $E(t)$ maximizes expected semantic preservation, that quenching produces nested survival sets, and that achievable compression approaches the information-theoretic limit $\text{CR} \to 1 - I(P; T)/H(P)$. A Phase 1 heuristic achieves 40-60% compression across five prompt categories while maintaining $S_E > 0.80$, with energy-squared amplification $E \to E^2$ adding 10-25 percentage points. Context deduplication adds 50-70% savings on repeated blocks. Output-side quenching, motivated by findings that brevity improves accuracy, further reduces response overhead. Combined with external memory, reduction composes multiplicatively to 88-96% for agentic workloads. The framework is stateless, model-agnostic, and deploys as an OpenAI-compatible HTTP proxy.

Compression is fundamental to intelligence. A model that can represent its training data as a short code has discovered regularities that enable generalization. Large neural networks may learn functions far simpler than their parameter counts suggest, but it is challenging to construct codes that realize this simplicity. Parameter-based methods such as quantization produce code lengths that scale with model size, insensitive to how much information the parameters store. Prequential coding bypasses this issue by compressing the training trajectory, but codes the exact data sequence regardless of how much the model learns, yielding large codes when the data has high entropy. We introduce requential coding, where a teacher model selects training samples drawn from the student's own distribution. The student's code records only these selections, which cost bits only where teacher and student disagree. The resulting code length is independent of parameter count and data entropy, and often orders of magnitude shorter than the prequential counterpart, with an advantage that grows with scale. This compression sheds light on phenomena inaccessible to prior compressors. Holding loss fixed, larger models and ensembles compress to much smaller sizes despite more parameters. Plugged into a PAC-Bayes bound, the requential code yields state-of-the-art generalization guarantees for billion-parameter LLMs, outperforming bounds built on aggressive post-training quantization even granted zero error. The bound tightens with scale in the compute-optimal regime, as models become increasingly compressible relative to dataset size. The same code predicts that models gradually overfit when trained for multiple epochs. It also isolates the learnable information in a dataset from its unpredictable, random content, revealing that lower-entropy text holds far more learnable structure than higher-entropy image data.

We study the problem of lossless text compression, motivated by the rapid growth in the collection and storage of digital textual data - including plain text, source code, and structured formats such as XML - and by recent advances in neural language model-based compression. In particular, recent LLM-based approaches, whether built on symbol-ranking pipelines or paired with a statistical compressor, have demonstrated compression ratios significantly superior to general-purpose compressors such as zstd, gzip, or bzip on text and code. However, these neural approaches suffer from severe throughput limitations, making them not yet practically usable. For the first time in the context of lossless neural text compression, we introduce Diffusion Language Models (DLMs) as an alternative inference paradigm to autoregressive LLM-based approaches. We argue that replacing autoregressive LLMs with DLMs within the same compression framework could overcome the throughput bottleneck caused by their one-symbol-per-step limitation. However, achieving these improvements requires addressing algorithmic challenges introduced by applying DLMs to lossless compression, where the architecture allows the number and positions of symbols encoded at each forward pass to be decided independently. We design efficient and effective strategies to solve these challenges and evaluate them experimentally against LLM-based and general-purpose compressors on enwik8, a well-established textual benchmark. Our results show that the newly proposed DLM-based framework advances the state of the art in lossless text compression. Moreover, as DLMs are still a relatively young paradigm, recent advances toward increasingly capable and efficient models suggest substantial room for further improvements.