Budgeted Attention Allocation: Cost-Conditioned Compute Control for Efficient Transformers

Standard transformer architectures apply a single attention mechanism uniformly across all tokens and sequence positions, irrespective of local context or computational budget. We propose Meta-Attention, a framework that dynamically routes each token to the most appropriate attention strategy -- full softmax attention, linear (kernel) attention, or sliding-window local attention -- via a Bayesian Meta-Controller. Unlike prior routing approaches that use deterministic or prior-free learned routing, the Meta-Controller treats per-token mechanism selection as posterior inference under a compute-aware Dirichlet prior: routing weights are the output of an amortised variational posterior q(alpha | x_t; phi) trained with an Evidence Lower Bound (ELBO) objective that jointly encodes task performance and attention-mechanism cost. This design produces principled routing uncertainty estimates that govern the soft-to-hard routing transition, mitigates routing collapse without ad hoc load-balancing losses, and yields better compute-performance trade-offs than deterministic or prior-free learned routing at negligible overhead. Phase 1 empirical results on a Tiny LM benchmark confirm core predictions: the Bayesian controller's learned routing distribution implies a projected normalised FLOP cost of 25.1% under hard routing, vs. 59.3% for the prior-free baseline (-34.2 pp), and reduces routing entropy from 55.8% to 43.3% (-12.5 pp), demonstrating that the Dirichlet prior prevents routing collapse while the non-Bayesian model defaults to full attention. We present the Bayesian architecture, ELBO training objective, and a Phase 1 PyTorch prototype validating forward-pass correctness, posterior diversity, and a controlled ablation against a prior-free baseline. Code available at: https://github.com/KFEAL/meta-attention

Multi-head attention enables Transformers to capture diverse representations, but all attention heads are typically activated for every input, regardless of task complexity. For coarse-grained tasks such as text classification, where relevant information is often global, this fixed allocation can introduce unnecessary computation. We propose BudgetFormer, a Transformer architecture that dynamically allocates attention heads on a per-input basis. The model learns both a head budget and a relevance distribution to select the most informative heads. To support effective head selection, we introduce a training strategy that balances exploration and exploitation. Experiments on text classification tasks show that BudgetFormer reduces FLOPs and memory usage while matching or surpassing the performance of standard multi-head attention. These results highlight adaptive head allocation as an effective approach to improving Transformer efficiency and performance.

Feed-forward networks hold two thirds of a transformer's non-embedding parameters, yet the architecture has not received a necessity test that controls parameters, compute, and depth at once. We pretrain attention-only decoder transformers (Simple Attention Networks, SANs) against standard transformers matched separately for parameter count, training FLOPs, and depth (2 to 48 layers), for up to 105B tokens at 6M to 87M parameters. Deleting feed-forward layers in place is costly: the standard transformer leads by 0.47 nats at matched depth and 0.26 nats at matched FLOPs. Reallocating the freed budget into attention depth closes the gap: at matched parameters the difference is 0.006 nats (0.27 percent of loss), reproducible to one part in ten thousand across seed pairs, shrinking across 5B, 30B, and 105B budgets, and holding near 0.02 nats across a 29x size range. Three measurements localize the remaining gap to parametric recall: attention-only models are better on context-grounded answers and worse where knowledge must come from weights. Weight spectra show why: routing matrices (Q/K) crystallize early, content matrices accumulate rank slowly, and removing feed-forward layers relocates this accumulation to the attention output projection. QK-normalization, not feed-forward layers or residual gating, keeps 48-layer attention-only stacks trainable. The deficit concentrates on low-context query prediction and localizes there entirely by the largest budget. A pre-registered test confirms the account: it predicts a 0.02 to 0.05 nat gap on knowledge-dense web text; a matched pair trained on fineweb-edu measures 0.040. Within the tested regime, attention does the rest.