Quaternion Self-Attention with Shared Scores

We propose a parameter-efficient speech enhancement framework, Quaternion Conformer GAN (QC-GAN), which combines a Quaternion Conformer generator with MetricGAN-based training. The Hamilton product encodes the magnitude and phase via structured weight sharing, reducing the number of layer parameters while preserving their interdependencies. A metric-learning discriminator was employed to maximize perceptual quality by optimizing the approximate perceptual evaluation scores. On the VoiceBank+DEMAND dataset, QC-GAN achieved a Perceptual Evaluation of Speech Quality (PESQ) score of 3.48 with only 0.89M parameters, delivering a performance comparable to state-of-the-art models at less than half their size. A 35K-parameter variant achieved a PESQ score of 3.23, surpassing conventional methods with significantly fewer parameters. Evaluation on the DNS-Challenge 3 dataset further confirmed generalization to real-world conditions.

A standard self-attention layer consists of two interacting circuits: the query-key circuit that governs attention allocation, and the output-value circuit that maps attended representations to predictions. Collapsed and factorized parameterizations of the query-key and output-value circuits lead to qualitatively different attention patterns. In particular, some parameterizations give sharper attention to task-relevant tokens, at a similar training loss. We analyze how the parameterizations of these circuits shape the parameter trajectories in single-layer self-attention models trained for next-token prediction. Through gradient-flow analysis, we show that factorization induces implicit rescaling of the two circuits' learning rates. We derive closed-form dynamics showing that output-value and query-key parameters move along a line, with relative speeds determined by their learning rates. Faster query-key learning relative to output-value learning thus produces sharper attention, as the model compensates for slower output-value learning by increasing attention mass on relevant tokens. Experiments show that differences in the relative learning rates of the two circuits govern attention concentration. This improves attention interpretability proxies while maintaining comparable predictive performance.

Transformer models are increasingly used as computational models of cognition and neural representation, so the mechanism implemented by self-attention is of interest beyond engineering performance. A complementary tradition in cognitive science models coordination, binding, and memory through dynamical interactions such as oscillator synchrony; we bring this mechanism into self-attention by introducing the Kuramoto Attention layer, whose value update is a synchronization step. Each token carries a bank of phase oscillators, so its hidden state lives on a high-dimensional torus. The attention weights form an adaptive coupling graph, and using the raw phase states as values makes the value update exactly the Kuramoto coupling direction for fixed attention weights. The softmax selects which oscillators couple, while the value path moves each token toward the attention-weighted circular mean of the tokens it selects. We train Kuramoto Attention on enwiki8 and CodeParrot against parameter-matched RoPE and SwiGLU transformers. At 5M parameters on CodeParrot, it improves on the transformer by both median and mean, with mean gaps of 0.012 validation and 0.010 test bits per byte. At 5M on enwiki8, all six runs have lower validation/test medians than the transformer and all-seed means within 0.01 BPC; five of six also form a tight lower-mean cluster. At 1M, it trails by about 0.02 BPC on enwiki8 and by 0.013-0.015 bits per byte on CodeParrot. Ablations and phase diagnostics show how the layer's synchronization and geometry-motivated components shape model performance. The result is a self-attention mechanism whose learned computation can be read directly as adaptive synchronization on phase states.