A Single-Layer Model Can Do Language Modeling

Language modeling using Transformers has become commonplace despite their fixed computational depth and quadratic runtime with respect to input tokens. Recurrent models on the other hand offer linear depth but no parallel execution. In this work, we extend balanced-tree recursive operators from sequence encoding to autoregressive prediction, enabling all prefix representations to be computed with logarithmic depth and linear runtime. Our experiments provide an initial characterization of this model class, demonstrating robust length extrapolation and performance approaching that of ALiBi-based Transformers, highlighting its potential as an alternative architecture for language modeling.

Modern language models, including transformer, recurrent, and memory-based variants, share a common chassis: a stack of identical layers in which parameters are allocated uniformly across depth. This is a default inherited from the original transformer and largely unchanged since, yet a growing body of evidence suggests that layers contribute non-uniformly to the final output, with later layers refining the residual stream rather than transforming it. We ask whether parameter capacity should reflect this asymmetry. Our controlled experiment shows that, under a fixed budget, allocating more capacity to earlier layers and less to later layers improves perplexity over a uniform-width baseline, while the reverse allocation hurts. Building on this result, we introduce Tapered Language Models (TLMs), an architectural principle in which a parameter-bearing component is monotonically tapered across depth under a fixed total budget. MLPs are the natural site for this instantiation: they dominate parameter count across all modern LM families and expose width as a single, clean axis of variation. Across three model scales and four architectures (Transformer, Gated Attention, Hope-attention, and Titans), tapering MLP width via a smooth cosine schedule consistently improves perplexity and downstream benchmark performance over uniform baselines, at no additional parameter or compute cost. These findings establish depth-aware capacity allocation as a simple, architecture-agnostic axis of language model design, a free lever hidden in plain sight.

We introduce a simple architectural modification to decoder-only transformers: a persistent recurrent state that observes hidden representations via cross-attention, updates itself through a GRU, and modulates subsequent processing via gated addition. Inserted between the lower and upper halves of a 6-layer transformer, this module adds only 3.7% additional parameters while reducing evaluation loss from $2.438 \pm 0.004$ to $1.743 \pm 0.018$, corresponding to a 28.5% reduction on held-out language modeling data. The improvement is statistically significant across 5 random seeds ($p < 0.01$) and corresponds to reduced overfitting (generalization gap 0.12 vs 0.26). Through controlled ablations, we demonstrate that the improvement stems entirely from the persistent memory topology, not from auxiliary self-prediction objectives. A model with identical topology but no auxiliary loss performs equivalently, while a random auxiliary loss provides no benefit. Representation probing reveals that the persistent state encodes narrative position (52% vs 33% chance level)---information that standard attention maintains less efficiently. Our results suggest that bridging transformer layers with a lightweight recurrent memory is a simple, effective approach to improving generalization in small-scale language models.