The State-Prediction Separation Hypothesis

Hybrid language models that mix attention and recurrent layers have shown promise: theoretically, recurrent layers ameliorate the limitations of pure transformers on state tracking, and empirically, hybrids can outperform pure transformers in loss and downstream evaluations \citep{waleffe2024empirical,merrill2026olmohybrid}. Yet it remains unclear which data or capabilities drive these gains, and to what degree they reflect the theoretical advantages motivating hybrid models. We address this question using the open weights from Olmo 3 \citep{olmo2025olmo3} and Olmo Hybrid \citep{merrill2026olmohybrid}: we compare the loss of a matched transformer and hybrid at the same target tokens under the same prefixes, stratifying the results by natural token tags, copy features, delimiter structure, and controlled synthetic probes. The hybrid has lower loss on most tag families, but the gains are not uniform: they are largest for open-class content words and smaller for many closed-class function words. Across prose, code, and markup, the hybrid's loss advantage is larger on opening delimiters than on the corresponding closing delimiters, and nearly vanishes on repeated $n$-grams. Synthetic probes show the same split: the hybrid is favored on pronoun-memory and entity-tracking tasks, whereas the transformer is favored on bracket-matching tasks that require choosing closing delimiters. These patterns suggest that the recurrent layers in hybrids improve predictions that leverage the semantic state of a document, whereas attention helps on tokens predictable by $n$-gram copying or syntactic bracket matching. We conclude with proof-of-concept filtered evaluations showing how token-level decompositions can sharpen pretraining diagnostics for hybrid architectures.

Trained transformer models develop privileged bases: coordinate axes whose statistics differ from the rest of the residual stream. But what kind of direction does such a basis select? We investigate the prediction direction, the unembedding direction of the token a model currently predicts, and find that it functions as a content-defined privileged anchor. Measured with respect to this anchor, residual-stream variation is geometrically and behaviorally stratified by proximity to the prediction. The stratification holds in all eighteen models tested (dense and mixture-of-experts, 7B-120B, base and instruction-tuned). A narrow, scale-invariant prediction interface concentrates readout-relevant structure, while the vast prediction-distal complement expands with model scale. Because the prediction direction sits nearly orthogonal to the principal variance axes, variance-based analyses recover this organization only partly, and the shortfall grows with prompt heterogeneity. Anchoring reveals a steep geometric gradient: prediction-proximal regions are highly structured and cluster related prompts, while the complement is flatter and anti-discriminates among prompt groups. The interface is a narrow slice but functionally decisive. Disrupting the variance directions closest to the prediction causes immediate divergence and frequent task-frame shifts; disrupting the next level down delays divergence and preserves framing. The complement is weakly readout-aligned per direction yet causally and temporally load-bearing, and behavior is driven by direction rather than magnitude. These results establish the prediction direction as a privileged anchor distinct from previously described coordinate axes, and give a geometric account of how high-dimensional computation coexists with linear readout.

Transformer language models process sequences token by token in an autoregressive manner, making growing contexts increasingly expensive. Yet many adjacent token spans are highly predictable or frequently occur as stable units, suggesting that their representations may be compressible. We introduce a method for distilling sequential computation by replacing spans of input tokens with collapsed representations, computed on the fly by a lightweight merge module. This module generates a single surrogate embedding from a sequence of static token embeddings that captures the functional role of the multiple tokens, allowing pretrained models to operate on compressed inputs without architectural changes or re-training. We apply this approach during inference to compress both prompts and intermediate decoding steps, using a rollback mechanism to substitute stored multi-token KV cache entries with their single-step surrogates. Experiments across diverse models show that the merge module can be used to reduce effective sequence length by up to 40% with minimal accuracy degradation across language modeling evaluations and downstream tasks, including question answering, summarization, commonsense reasoning, and long-form mathematical reasoning. Additional lightweight adaptation of the merge module further improves the accuracy-compression trade-off in selected settings. These results demonstrate that sequential token computation in Transformers can be effectively approximated through condensed surrogate representations that approximate the original behavior without model updating.