Understanding Layer Patching in Model Size Interpolation

We study distillation for large language models under explicit compute constraints, with the goal of producing student models that are not only cheaper to train, but structurally efficient at inference time. While prior approaches to parameter-efficient distillation, such as LoRA, reduce adaptation cost, they leave the dense backbone unchanged and therefore fail to deliver meaningful inference savings. We propose Budgeted LoRA, a distillation framework that treats model compression as a structured compute allocation problem. Instead of using a fixed student architecture, we introduce a global compute budget that sets the final target fraction of dense computation retained. Under this constraint, the model redistributes capacity across dense and low-rank pathways via (i) module-level dense retention coefficients, (ii) adaptive low-rank allocation, and (iii) post-training compression that selectively removes, approximates, or preserves dense components. This formulation yields a family of students controlled by a single budget dial. Empirically, Budgeted LoRA matches standard LoRA perplexity at a moderate budget with a 1.74x compressed-module speedup; at an aggressive budget it achieves a 4.05x speedup with moderate perplexity degradation, and it preserves higher accuracy on function-style in-context learning probes. These results suggest that, under compute-constrained distillation, retaining behavior is less about matching perplexity or removing more parameters than it is about controlling how dense computation is transferred to low-rank pathways.

Tokenizer-free language models eliminate the tokenizer step of the language modeling pipeline by operating directly on bytes; patch-based variants further aggregate contiguous byte spans into patches for efficiency. However, the average patch size chosen at the model design stage governs a tight trade-off: larger patches reduce compute and KV-cache footprint, but degrade modeling quality. We trace this trade-off to patch lag: until a patch is fully observed, byte predictions within it must rely on a stale representation from the previous patch to preserve causality; this lag widens as patches grow larger. We introduce Scratchpad Patching (SP), which inserts transient scratchpads inside each patch to aggregate the bytes seen so far and refresh patch-level context for subsequent predictions. SP triggers scratchpads using next-byte prediction entropy, selectively allocating compute to information-dense regions and enabling post-hoc adjustment of inference-time compute. Across experiments on natural language and code, SP improves model quality at the same patch size; for example, even at $16$ bytes per patch, SP-augmented models match or closely approach the byte-level baseline on downstream evaluations while using a $16\times$ smaller KV cache over patches and $3$-$4\times$ less inference compute.

Small language models are often the only option for deployment under tight latency, cost, and on-premises constraints, but they are rarely trained from scratch: a compressed model is usually recovered through knowledge distillation (KD). This recovery step largely decides the final quality, yet it is expensive. We present a practitioner's study of how to make distillation training efficient, organised around two systems contributions. First, we show that offline KD (caching the teacher's top-$K$ logits once and training the student against the cache) matches online distillation at near-identical training loss while removing the teacher from memory, running about 29% faster per iteration, and reaching up to 41% higher throughput on a single H200 GPU. Second, we introduce a \emph{fused, chunked KL loss} that never materialises the full vocabulary-sized logit tensor, making peak memory linear in the sequence length. This removes the memory spike that otherwise caps context length and lets us train at four times the context (32{,}768 tokens) on a single GPU. A separate output-head-only toy benchmark isolates the loss kernel and confirms its memory and iteration-rate scaling from 4K to 256K tokens. Together these make large-scale healing and hundreds of ablations affordable. We also report supporting ablations on loss design and sequence packing. We release our chunked-loss implementation: https://github.com/CompactifAI/Full-Chunked-KL-Loss.