Exploiting Biases in Attention for Transformers

Transformers usually expose one inference cost per trained model, while deployed systems often need multiple cost-quality operating points. We study Budgeted Attention Allocation, a monotone head-gating mechanism conditioned on a requested attention budget. Dense warm-starting is important for stability: on a robust synthetic sequence task, one budgeted model reaches 99.7% accuracy at 0.303 estimated attention cost and 100.0% accuracy at 0.504 cost. On held-out AG News with a custom word-level transformer, hard-gate adaptation turns soft cost control into measured single-thread CPU speed, reaching 82.1% accuracy with 1.28x speedup at budget 0.50. In pretrained BERT-Mini AG News, budgeted structural pruning reaches 87.6% accuracy with 1.20x speedup at budget 0.50; a validation-ranked zero-shot dense post-hoc structural baseline reaches 86.1%, and one recovery epoch raises that per-budget specialist to 87.9%. On DBpedia14, BERT-Mini budgeted gates reach 97.4% at exact budget 0.50 versus 96.6% for dense full attention. Static fixed-budget gates and recovered dense specialists remain strong. The contribution is therefore not universal dominance, but a reproducible feasibility study of one controllable checkpoint across budgets that can trade attention cost for accuracy and be converted into measured structural speedups on small CPU benchmarks.

Pretrained transformers spend a large share of their inference compute inside self-attention, yet the per-head query-key interaction is structurally low-rank by construction. We ask a diagnostic question: across layers and architectures, which heads actually use the full rank budget on real data, and which do not? We propose SVD-Attention, a post-hoc method that decomposes the per-head interaction matrix $M_h$ and scores every singular mode by both its spectral magnitude and its activation variance across tokens on a small calibration set. The score keeps the modes the head can amplify and that real data actually activates, and discards the rest; the resulting factorization is exact for the retained modes and needs no finetuning. Across seven pretrained models and five task types, the diagnostic finds a task-dependent pattern: redundancy sits in the early to middle layers for sentiment and image classification and for generation, and in the late layers for dense prediction and extractive question answering. It is also predictive: truncating the layers it flags costs at most $1.75$ F1, while truncating the same number of layers elsewhere in the same model costs up to $50$ F1. SVD-Attention is an analysis tool rather than a compression method: acting on it reduces inference FLOPs by $0.8$-$1.5\%$ on its own and by $8$-$11\%$ when composed with weight pruning, with $0$-$4\%$ change in task quality.

We study efficient reasoning under tight compute. We ask how to make structured, correct decisions without increasing test time cost. We add two training only components to small and medium Transformers that also transfer to broader differentiable optimizers. First, a length aware attention prior built via fuzzy regime position alignment, RPA, yields a normalized pre softmax bias that guides attention like a structured regularizer while adding no new inference parameters. Second, a minimal gain aware controller, Guardian, nudges attention sharpness only when validation improvements warrant it, following a two timescale policy gradient view of nonconvex optimization. It is disabled at inference. A KL perspective shows softmax of z plus log pi as MAP with KL regularization, grounding the prior in a principled objective. Under strict compute parity on WikiText 2, we reduce validation cross entropy while matching baseline latency and memory. At inference, we add a precomputed, cached prior B of T as a single additive bias per head. The controller does not run. In practice, this incurs negligible overhead, a cached bias add per head, with no measurable p50 latency shift. Our results suggest that length aware priors and late phase gain control preserve scarce improvements, especially in long span, noisy logit regimes, while keeping test time costs effectively unchanged.