Sensitivity-Positional Co-Localization in GQA Transformers

Decoding efficiency depends on KV-cache traffic, computation, and parallelism. Multi-head Latent Attention (MLA) offers absorbed and head-expanded forms, but its head-specific projections limit grouped KV sharing. We introduce Group-Query Latent Attention (GQLA), whose group-shared up-projections preserve a joint latent and enable a shardable expanded cache. The same weights support equivalent MQA-absorb and GQA execution using existing kernels. Roofline analysis relates path preference to GPU compute-to-bandwidth ratio and tensor parallelism (TP): absorption trades traffic for computation and replicates the latent across ranks; GQA shards KV groups. Pretraining with eight query heads per group yields terminal training losses close to MLA's across the tested model scales at matched tokens. TransGQLA converts GQA and MLA checkpoints using calibration data. Without gradient updates, converted DeepSeek-V3.1-Base achieves 77.79% eight-task accuracy versus the source's 77.84%, while WikiText-2 perplexity rises from 3.21 to 6.05. On eight H20-3e GPUs, its GQA path improves output throughput over MQA-absorb by 22.42--34.97% at matched resident batches across 8K--64K inputs. Its smaller per-rank cache permits larger batches, giving 50.07% in a separate capacity-tuned comparison. These results support multiple execution paths as an architectural means of adapting decoding to hardware and parallelism.

Self-attention is central to Transformer performance and is often the most expensive part of the Transformer at long context lengths because its pairwise token interactions scale quadratically with sequence length. Standard dense attention also applies the same set of attention heads to every token regardless of token difficulty or information content. This uniform activation can waste compute, especially as sequences grow longer and attention cost increases rapidly. We propose Grouped Query Experts (GQE), a mixture-of-experts layer on top of grouped-query attention (GQA). Within each GQA group, a router selects k query-head experts per token while all key-value (KV) heads remain dense and unchanged. Thus, GQE keeps the KV cache benefits of GQA and reduces only the active query-head computation. On a fixed 30B token budget at the 250M parameter scale, GQE matches the all-active GQA baseline in downstream accuracy while activating half the query heads per token.

Task arithmetic, sequential fine-tuning, activation steering, and first-order random search all operate through relatively small perturbations around an already trained checkpoint, and they rely on different local approximations: individual perturbations should be first-order predictable, task updates should compose with controlled interference, useful tangent structure should be stable and possible to estimate, and weight edits should have counterparts in representation space. We measure 8 such properties with the same harness around a multitask LoRA operating point, on 9 transformers (82M-7B), with a prospectively registered property list, thresholds, and test split. We find a shared one-direction validity window up to the tested scale $10^{-2}$, but no universal radius for pairwise composition or update ordering. Along individual directions, changes of the probe loss remain first-order predictable throughout the grid: a perturbation's effect on the loss is essentially its projection onto the gradient, which is also what makes local random search work. Pairwise structure, however, proves to be far more fragile: on over a third of the measured (model, task pair) combinations, two-update order sensitivity sets in strictly inside that window; task-gradient subspaces rotate within tens of steps; additivity under our fixed activation probe fails at full task-vector scale on several models, including both held-out 7B models; and no model median passes the registered global mean-vector weight-to-steering correspondence bar. For two sequential task-gradient steps, the leading order-dependent term is the Lie bracket $H_B\textbf{g}_A-H_A\textbf{g}_B$; its normalized prediction $c(η)=ηκ+O(η^2)$ tracks the measured defect at median ratio 1.002, while the onset scale $η^\dagger\approx0.10/κ$ spans three orders of magnitude across models and task pairs.