The paper demonstrates that any Transformer block—comprising attention, LayerNorm, and a GELU MLP—can be exactly compiled into a generic deep neural network using only fixed affine maps, routing, and a small set of nonlinear functions (square, sigmoid, inverse square root, and GELU or its sigmoid approximation). It shows that removing activation‑activation products incurs an $N^2$ cost per head for dense scores, but this can be avoided by using element‑wise operations available on most NPUs. Additionally, the authors prove that exact or conditional‑mean tail‑mass estimation provides an unbiased, low‑error approximation of top‑$k$ attention, and that clustering queries or agents into centroids reduces the number of computed scores from $N^2$ to $Nk$ per head, achieving comparable performance to reference models on DeiT‑Tiny, MambaIRv2‑Light, and Pythia‑70M.
arXiv:2606. 04032v1 Announce Type: cross Abstract: Transformers have become the standard solution for various AI tasks, with the query, key, and value (QKV) attention formulation playing a central role.
The paper examines how to allocate attention heads and head dimensions across Transformer layers to balance expressivity and efficiency. It provides a mathematical analysis of early layers’ role in information extraction and characterizes the trade‑off between head count and dimension under a fixed parameter budget. The authors prove a saturation effect of softmax activations, showing that increasing head dimensions yields diminishing returns, especially for long sequences, and propose strategies for efficient parameter allocation across layers.
arXiv:2607. 18363v1 Announce Type: cross Abstract: 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.
arXiv:2606. 07713v1 Announce Type: cross Abstract: The attention mechanism is the dominant computational bottleneck in modern transformer-based AI.
The paper introduces TANGO, a Token‑Aggregated Nonlinear Gating Operator that blends cross‑token mixing and token‑wise transformation in transformer architectures. By computing a nonlinear gate per source token and averaging these gates for each destination, TANGO forms a source‑conditioned linear operator that improves predictive performance. Experiments on web text, formal mathematics, and code show that full‑prefix TANGO achieves the lowest test negative log‑likelihood across 16 settings, while a narrower variant offers substantial throughput gains with only a modest increase in loss.
arXiv:2604. 17324v2 Announce Type: replace-cross Abstract: Global self-attention drives modern graph transformers, yet the softmax at its core imposes a structural constraint rarely examined directly: every attention row is non-negative and sums to one, so each per-head output is a mass-conserving convex combination of value vectors.
The paper presents a retraining‑free technique that transforms pre‑trained transformers into elastic models capable of adapting to any computational budget on the fly. By jointly ranking every MLP neuron and attention head on a common scale and applying soft pruning across multiple sparsity targets, the method achieves smooth performance degradation up to 60% sparsity while outperforming one‑shot baselines. Experiments on 27 vision and text transformer encoders show significant parameter reductions with minimal accuracy loss and notable throughput and latency gains on GPUs, all produced in minutes.
The paper investigates using short polynomial approximations to accelerate special‑function operations in large language models on NVIDIA Blackwell GPUs. By replacing native sigmoid, tanh, and SiLU with degree‑3 or degree‑4 bfloat16 programs, the authors achieve up to 2.19× speed‑ups in isolated FP16 benchmarks and modest training‑step throughput gains (2.7–8.0%) across four integration tasks. The study also evaluates model behavior, finding negligible training‑loss differences within 100 billion tokens.
arXiv:2607. 18759v1 Announce Type: new Abstract: Transformers with relative positional encodings often extrapolate to sequences longer than those seen during training, whereas transformers with learned absolute encodings typically do not.
arXiv:2606. 15036v1 Announce Type: new Abstract: We train a two-layer transformer encoder to classify rational elliptic curves $E/\mathbb{Q}$ of conductor $\leq 10000$ as either rank 0 or rank 1 from the first 128 normalized Frobenius traces.
Modern transformers pair impressive capabilities with substantial memory and compute demands. Low-rank weight factorization reduces both while keeping the matrices dense, and thus efficient on standar...
arXiv:2607. 20214v1 Announce Type: cross Abstract: The quadratic $N\times N$ attention score matrix remains a central obstacle to extending Transformers to longer input lengths.