Organizations: College of Computer Science and Technology, Jilin University, Changchun, 130012, China. · Key Laboratory of Symbolic Computation and Knowledge Engineering of Ministry of Education, Jilin University, Changchun, 130012, China. · Institute for Quantitative and Computational Biology, University of California, Los Angeles, 90024, United States of America. · Greenwich High School, Greenwich, CT, 06830, United States of America. · BCPM Data Limited, Chengdu 610041, China.
Abstract
Token aggregation is a common bottleneck in models that map token representations to sample-level predictions, yet most pooling methods operate only in the original token domain. We propose FLaG, a plug-in aggregation module that transforms token representations with the real FFT, summarizes spectral components with learnable latent queries, applies a channel-wise gate, and reconstructs enhanced time-domain tokens for final pooling. We evaluate FLaG on antimicrobial peptide (AMP) activity prediction with ESM2, image classification with ResNet18 on CIFAR-10 and CIFAR-100, and text classification with RoBERTa on IMDB and GLUE. FLaG achieves its clearest gains on the ESM2-8M antimicrobial peptide tasks and on CIFAR-100, while remaining competitive with strong text baselines on IMDB and GLUE. Then we probe its behavior on the AMP setting with band knockouts, gate summaries, residue perturbations, latent-query readouts, and structure-proxy stratification. We find that low-frequency bands contribute the most overall, and the remaining higher-band pattern is more sample-specific. The gate acts as a broadly shared spectral reweighting stage and the cross-attention patterns are sample-specific with mild query-wise differentiation, and higher-helix peptides exhibit stronger average spectral sensitivity in both bacteria. The supplementary materials, source code and data are released at https://www.healthinformaticslab.org/supp/ and https://github.com/Kewei2023/AMPCliff/tree/FLaG.
Token aggregation converts token-level representations into fixed-dimensional sample representations, but most pooling methods operate only in the original token space. We introduce Frequency-Domain Latent-attention Gated Pooling (FLaG), a plug-in aggregation module that re-expresses encoder outputs in the Fourier domain before final pooling. FLaG represents the nonredundant rFFT spectrum through concatenated real and imaginary components, summarizes spectral tokens with learnable latent queries, derives a sample-conditioned channel gate, and reconstructs modulated token representations for downstream aggregation. We evaluate the same architecture across ESM2-based antimicrobial peptide (AMP) activity prediction, ResNet18 image classification on CIFAR-10 and CIFAR-100, and three RoBERTa-based language tasks. FLaG achieves the best macro-averaged Spearman correlation coefficient, RMSE, and Recall@50 across four AMP backbone-species settings and the highest top-1 accuracy on CIFAR 10. It also achieves the best mean results on five of seven language metrics, although mean pooling remains strongest on STSBenchmark. AMP-side mechanistic analyses reveal low-frequency prediction sensitivity across most encoder layers, with increased relative high-frequency sensitivity in the final layer, and pronounced peptide-specific positional responses. The residual gate broadly amplifies spectral channels while preserving the low-frequency-dominated energy profile, whereas latent cross-attention exhibits sample- and species-specific spectral allocation. Overall, FLaG provides a transferable frequency-domain aggregation bias across protein, visual, and textual representations, with benefits that depend on the backbone and downstream task. Supplementary materials, source code, and data are available at https://www.healthinformaticslab.org/supp/ and https://github.com/Kewei2023/AMPCliff/tree/FLaG.
Standard transformer attention computes pairwise similarity between queries and keys, treating all tokens as equally salient regardless of their intrinsic informational content. In turbulent fluid dynamics, coherent structures -- the energetically dominant, spatially organized patterns that persist amid background chaos -- carry a disproportionate fraction of total energy and govern all transport. We propose that tokens play an analogous role in transformer attention: informationally dense positions (morphological boundaries, syntactic heads, discourse markers) concentrate spectral energy and should attract proportionally more attention than background tokens (function words, repeated patterns, low-information filler). We propose Energy-Gated Attention (EGA): a simple modification that gates value aggregation by the spectral energy of key token embeddings, computed by a single learned linear projection that discovers the dominant spectral mode of the embedding field. On TinyShakespeare, EGA achieves +0.103 validation loss improvement with only 12,480 additional parameters (<0.26% overhead) and no measurable computational cost. The result is consistent on Penn Treebank (+0.101), demonstrating dataset independence. A systematic ablation across three wavelet families (fixed Morlet, Daubechies db2/db4, and a parametric Morlet) establishes that fixed structured bases are suboptimal -- the optimal energy direction is data-adaptive and non-sinusoidal -- while identifying learned wavelet packets as a promising open direction. The learned energy threshold converges to tau ~= 0.35 independently of initialization, corresponding to the fraction (~36%) of tokens carrying above-average spectral energy in English text, a stable linguistic property consistent with the fraction of content words in running English text.
FFT-based spectral preprocessing of learned query-key (Q/K) projections substantially improves transformer attention on character-level language modelling. On TinyShakespeare: a fixed random spectral filter achieves val=1.031 (Delta=+0.443); a single learned frequency at paragraph scale achieves val=0.608 (Delta=+0.867); and four learned frequencies spanning paragraph to word scale achieve val=0.309 (Delta=+1.166), a 79% reduction over standard dot-product attention. The single-frequency result is confirmed across three random seeds (mean val=0.236, std=0.019). The four frequencies converge to a near-geometric multi-scale ordering (49, 27, 10, 6 tokens/cycle) corresponding to paragraph, sub-paragraph, phrase, and word scales. The gain is specific to spectral preprocessing: random orthogonal and non-orthogonal projections of Q/K produce no measurable improvement, suggesting the benefit comes from global frequency-domain mixing rather than metric distortion. All results are verified by a shuffled-validation diagnostic against positional leakage. Causal filters (Gaussian, Mexican Hat, Morlet) do not improve over standard attention at character-level tokenisation: the bilateral FFT kernel is structurally non-causal, coupling every position to future tokens. This defines an architectural boundary between bilateral spectral attention (this paper) and genuinely causal spectral attention at word-scale tokenisation (companion paper MorletQK). This work is architecturally distinct from FNet (Lee-Thorp et al., 2021), which replaces attention with Fourier mixing of token embeddings. Here, spectral preprocessing applies only to Q/K projections while the full attention score structure is preserved.