arXiv Machine Learning
Sep 2

Performance-Efficiency Tradeoffs in Transformers: An Approximation Theory Perspective

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.

By Ruoxi Yu, Haotian Jiang, Jingpu Cheng, Penghao Yu, Qianxiao Li, Zhong Li
arXiv Machine Learning
Aug 19

Recirculation

The paper introduces recirculation, an inference‑time architectural enhancement for foundation models that reduces perplexity and improves accuracy on generation and reasoning tasks without adding significant latency. Recirculation adds a specific form of recurrence, enabling the model to function as a dynamical system that tracks belief states, and is distinct from chain‑of‑thought or depth‑recurrence methods. An adaptive variant requires minimal hyperparameter tuning and achieves notable gains on the Gemma3 family, including a 23% perplexity drop and a 21% accuracy increase on GSM8k.

By Michael C. Mozer, Shoaib Ahmed Siddiqui, Danny Sawyer, Sunny Sanyal, Rosanne Liu
arXiv Machine Learning
1d ago

Fixed Universal Transformers

The paper introduces fixed universal transformers, which are transformers with immutable internal parameters that can emulate any transformer within a specified class by encoding the target model’s description into the input embedding. The authors provide explicit sparse constructions that achieve universality when the embedding dimension is large enough, and demonstrate that universality is generic—randomly initialized transformers are almost surely universal. Empirical tests on parenthesis balancing and multi‑hop reasoning tasks support the theory, suggesting that a transformer’s expressive power largely stems from its input representation rather than its learned weights.

By Jingwen Liu, Alexandr Andoni, Daniel Hsu
arXiv Machine Learning
Sep 25

FlashLoop: Fast and Memory-Efficient Looped Transformers via Lazy Updates

FlashLoop is a training‑free inference framework for Looped Transformers that reduces cross‑loop redundancy by employing token‑sparse updates, sparse attention, and KV‑residual quantization. It exploits observations that, as loops progress, state changes concentrate on a small token subset, attention differences are dominated by a sparse key subset, and KV residuals become amenable to low‑bit quantization. The method achieves lossless accuracy with up to 1.64× speedup and 6× KV‑cache memory reduction across several Looped Transformer models.

By Wanqi Yang, Shiwei Liu