The Ratchet Effect in Silico: How Interaction Drives Cumulative Intelligence in Large Language Models

Large language models provide a tractable system for asking how intelligence itself emerges, rather than only how LLMs can be engineered. Although progress is usually attributed to scale, data and architecture, we show that parameter initialization is a gene-like determinant of training and, in particular, of model capacity. Reducing the initialization scale consistently improves pretraining, with the largest gains on reasoning-demanding tasks. We identify two widely used empirical settings that restrain the advantage of small initialization, and show how relaxing them restores favorable scaling. We further uncover a critical initialization that balances the reasoning and training. Mechanistically, small initialization drives a distinct developmental trajectory: parameters first condense into low-complexity structures and later expand into richer representations, giving concrete form to the idea that compression is intelligence. Token-level analyses show that the gains concentrate on non-trivial, context-constrained predictions rather than all tokens uniformly. These results motivate a simple $γ$-initialization rule: expose initialization rage as an explicit knob and use small initialization by default, an almost cost-free intervention that improves pretraining and strengthens reasoning across model scales.

Inference-time multi-agent LLM scaling lacks a shared unit: counting nominal agents conflates cost with independent evidence. We derive a two-parameter scaling law $R(N) = N_\text{eff}/N = 1/(1+c(N-1)N^{-β})$ where the regime exponent $β$ classifies any configuration into one of three asymptotic regimes -- hard-ceiling at $1/c$ ($β= 0$), sublinear at $N^β/c$ ($0 < β< 1$), or linear ($β\ge 1$), and a mean-field theorem predicts that peer count $k$ and rounds $τ$ during agent debate enter the dynamics only through their product $kτ$. The law applies at two levels: answer diversity and correctness redundancy. Across 44 (model $\times$ task $\times$ condition) cells spanning peer debate, self-correction, random-noise placebo, self-consistency, three open-weight families (Qwen, Llama, Ministral) at scales from 7B to 32B with a frontier API check (Gemini), thinking models, heterogeneous teams, and sparse communication, the functional form fits every condition at $R^2 > 0.99$; only $(c, β)$ shifts. On free-form math, dense peer influence collapses the answer-level regime from sublinear into hard-ceiling; correctness-level fits remain hard-ceiling throughout. Three findings have practical implications. \emph{(i)}~Thirty dense debating agents produce no more answer diversity than one on MMLU-Hard. \emph{(ii)}~A noise placebo tracks self-correction on free-form math and at $4\times$ scale, so within homogeneous teams the gain commonly attributed to ``debate'' comes from re-evaluation, not peer content. \emph{(iii)}~A single $N \le 5$ pilot predicts the $N=30$ structural ceiling, and within the configurations tested only architectural diversity (heterogeneous teams) lowers $c$ and escapes the hard-ceiling regime, communication-mode interventions do not.

Current large language models reason in isolation. Although it is common to sample multiple reasoning paths in parallel, these trajectories do not interact, and often fail in the same redundant ways. We introduce LACE, a framework that transforms reasoning from a collection of independent trials into a coordinated, parallel process. By repurposing the model architecture to enable cross-thread attention, LACE allows concurrent reasoning paths to share intermediate insights and correct one another during inference. A central challenge is the absence of natural training data that exhibits such collaborative behavior. We address this gap with a synthetic data pipeline that explicitly teaches models to communicate and error-correct across threads. Experiments show that this unified exploration substantially outperforms standard parallel search, improving reasoning accuracy by over 7 points. Our results suggest that large language models can be more effective when parallel reasoning paths are allowed to interact.