Model families are typically trained size by size, each from scratch. Can a pretrained large model instead be converted into a smaller sibling? We characterize the 1.4B->410M conversion in Pythia end to end. Representations align strongly across sizes (ridge R^2=0.84) while parameters align weakly. Dense weight projection is functionally destructive, and a bit-exact control shows this is not an assembly artifact: basis mixing breaks rotary, per-head, GELU, and LayerNorm structure. After the best-fit linear operator, weight residuals are statistically indistinguishable from noise under shuffle controls. Conversion value therefore lives in initialization. In matched-budget continued pre-training we decompose conversion into two independent levers: least-squares compensation (function lever, best zero-shot) and variance-preserving rescale (dynamics lever, best endpoints). Compensation is a token-efficient, low-budget win rather than a universal one. At 30M tokens it beats the strongest subcloning variant on both a width-reduced pair (84.0 +/- 1.8 vs. 89.7 +/- 3.7, 3/3 seeds) and a held-out depth-reduced pair (109.3 vs. 117.9, 3/3 seeds), reaching a given quality with fewer tokens. At a 33x larger budget the two converge to parity (40.0 vs. 40.0), both far ahead of from-scratch, which transfer initialization always beats: by up to 18x at low budget, with the margin narrowing at convergence and at the largest scale. We also map the method's boundary. At about 5x the donor scale (6.9B->1.4B) stacking both levers over-corrects, consistent with ill-conditioning of the compensation solve at large width, which points to dimension-aware regularization as a fix. At matched budget our initialization also beats structured pruning with distillation, the standard pipeline, and improves further combined with it. Code, checkpoints, and the frozen evaluation corpus are released.
Low-rank adaptation (LoRA) fine-tunes large pretrained models at a fraction of the cost of full fine-tuning, but its performance depends strongly on how the adapters are initialized. Recent schemes initialize the adapters from the downstream loss gradient: some project the raw gradient onto its top directions, while others first whiten it with an estimate of the loss curvature. We show that these seemingly distinct methods are points on a single continuum: a two-parameter family of preconditioned gradient initializations, which we call Unified LoRA (ULoRA), governed by a spectral whitening exponent and an Adam-like diagonal exponent. Sweeping this family under a full learning-rate search, we find that no single fixed preconditioning strength dominates: the best operating point is task-dependent and frequently lies strictly inside the family, away from the published endpoints. Treated as an upper bound of this family, a tuned ULoRA configuration matches or exceeds full fine-tuning on all five GLUE tasks with RoBERTa-base and is competitive with the strongest baselines on GSM8K with LLaMA-2-7B. Our deployable, search-free variant, ULoRA-Auto, selects per-layer exponents from measured spectral statistics, approaches this upper bound at no additional search cost, and ranks at or near the top among deployable LoRA methods. Our results show that a principled design space for LoRA initialization and curvature preconditioning should be treated as a tunable dimension rather than a fixed design decision.
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.
Ekaterina Alimaskina, Gleb Molodtsov, Aleksandr Beznosikovcs.LG cs.AI
Hyper-Connections (HC) replace the single Transformer residual stream with multiple streams, introducing a permutation symmetry over stream indices. We study how this symmetry is resolved in practice: whether streams specialize in a balanced way or exhibit dominant-stream usage. Using fine-grained diagnostics for HC-based language models, we trace how multi-stream representations are actually used. We find that after an early seeding stage, residual mixing often remains close to identity, limiting a core HC mechanism for exchanging information between streams. Moreover, both signal and interpretable features concentrate in a dominant stream, and the nominally multi-stream residual connection can underutilize its capacity, behaving closer to a single-stream residual pathway. Finally, we show that breaking symmetry at stream initialization reduces dominant behavior and improves performance across \textit{m}HC variants. Our code is publicly available.