Language Through a Prism: A Spectral Approach for Multiscale Language Representations
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Abstract (arXiv)
Language exhibits structure at different scales, ranging from subwords to words, sentences, paragraphs, and documents. To what extent do deep models capture information at these scales, and can we force them to better capture structure across this hierarchy? We approach this question by focusing on individual neurons, analyzing the behavior of their activations at different timescales. We show that signal processing provides a natural framework for separating structure across scales, enabling us to 1) disentangle scale-specific information in existing embeddings and 2) train models to learn more about particular scales. Concretely, we apply spectral filters to the activations of a neuron across an input, producing filtered embeddings that perform well on part of speech tagging (word-level), dialog speech acts classification (utterance-level), or topic classification (document-level), while performing poorly on the other tasks. We also present a prism layer for training models, which uses spectral filters to constrain different neurons to model structure at different scales. Our proposed BERT + Prism model can better predict masked tokens using long-range context and produces multiscale representations that perform better at utterance- and document-level tasks. Our methods are general and readily applicable to other domains besides language, such as images, audio, and video.
Key facts. Cited by 39 papers in the map (data through 7 Oct 2026). First posted on arXiv 9 Nov 2020.
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Citing papers per year: 2021: 4; 2022: 6; 2023: 5; 2024: 7; 2025: 6; 2026: 11.
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- 2021FNet: Mixing Tokens with Fourier Transformscited by 343
- 2022Continuous diffusion for categorical datacited by 202
- 2023Codebook Features: Sparse and Discrete Interpretability for Neural Networkscited by 45
- 2021Audio Transformerscited by 41
- 2024Fourier Position Embedding: Enhancing Attention's Periodic Extension for Length Generalizationcited by 37
- 2024DCTdiff: Intriguing Properties of Image Generative Modeling in the DCT Spacecited by 32
- 2022Task Ambiguity in Humans and Language Modelscited by 27
- 2022Language modeling via stochastic processescited by 18
- 2023Learning a Fourier Transform for Linear Relative Positional Encodings in Transformerscited by 10
- 2021Deep Autoregressive Models with Spectral Attentioncited by 9
- 2022Feature Dropout: Revisiting the Role of Augmentations in Contrastive Learningcited by 9
- 2024Vim-F: Visual State Space Model Benefiting from Learning in the Frequency Domaincited by 8
27 more
- 2024Towards Signal Processing In Large Language Modelscited by 7
- 2024Extracting Sentence Embeddings from Pretrained Transformer Modelscited by 7
- 2025A quantitative analysis of semantic information in deep representations of text and imagescited by 7
- 2026Differential syntactic and semantic encoding in LLMscited by 6
- 2022Fast-FNet: Accelerating Transformer Encoder Models via Efficient Fourier Layerscited by 5
- 2026Energy-Gated Attention: Spectral Salience as an Inductive Bias for Transformer Attentioncited by 5
- 2025MGT-Prism: Enhancing Domain Generalization for Machine-Generated Text Detection via Spectral Alignmentcited by 4
- 2026Energy-Gated Attention and Wavelet Positional Encoding: Complementary Inductive Biases for Transformer Attentioncited by 4
- 2023SpectralCLIP: Preventing Artifacts in Text-Guided Style Transfer from a Spectral Perspectivecited by 3
- 2026Beyond Sinusoids: A Morlet Wavelet Framework for Transformer Positional Encodingcited by 3
- 2021Oscillatory Fourier Neural Network: A Compact and Efficient Architecture for Sequential Processingcited by 2
- 2025Exploiting Inter-Session Information with Frequency-enhanced Dual-Path Networks for Sequential Recommendationcited by 2
- 2025MS-SSM: A Multi-Scale State Space Model for Efficient Sequence Modelingcited by 2
- 2022Spectral Probingcited by 1
- 2023Conformer LLMs -- Convolution Augmented Large Language Modelscited by 1
- 2024Repurformer: Transformers for Repurposing-Aware Molecule Generationcited by 1
- 2024Wavelet GPT: Wavelet Inspired Large Language Modelscited by 1
- 2025A Free Probabilistic Framework for Analyzing the Transformer-based Language Modelscited by 1
- 2026FourierQK: Spectral Preprocessing of Query-Key Projections Improves Transformer Attentioncited by 1
- 2023Interpretable Spectral Variational AutoEncoder (ISVAE) for time series clusteringcited by 0
- 2025Towards Efficient Post-Training via Fourier-Driven Adapter Architecturescited by 0
- 2026DisenReason: Behavior Disentanglement and Latent Reasoning for Shared-Account Sequential Recommendationcited by 0
- 2026Latent Fourier Transformcited by 0
- 2026Frequency-Domain Latent Attention Gating for Cross-Domain Token Aggregationcited by 0
- 2026Denoising the Future: Context-Aware Spectral Diffusion for Temporal Knowledge Graph Extrapolationcited by 0
- 2026FLaG: Frequency-Domain Latent-attention Gated Pooling for Token Aggregationcited by 0
- 2026MS-GLA: Multi-Scale Gated Linear Attention for Addressing Representational Bottlenecks via Multi-Temporal Resolutioncited by 0
- 2026MS-GLA: Multi-Scale Gated Linear Attention for Addressing Representational Bottlenecks via Multi-Temporal Resolution28 Sep 2026
- 2026FLaG: Frequency-Domain Latent-attention Gated Pooling for Token Aggregation1 Sep 2026
- 2026Denoising the Future: Context-Aware Spectral Diffusion for Temporal Knowledge Graph Extrapolation21 Aug 2026
- 2026FourierQK: Spectral Preprocessing of Query-Key Projections Improves Transformer Attention8 Jul 2026
- 2026Frequency-Domain Latent Attention Gating for Cross-Domain Token Aggregation6 Jun 2026
- 2026Beyond Sinusoids: A Morlet Wavelet Framework for Transformer Positional Encoding31 May 2026
- 2026Energy-Gated Attention and Wavelet Positional Encoding: Complementary Inductive Biases for Transformer Attention25 May 2026
- 2026Energy-Gated Attention: Spectral Salience as an Inductive Bias for Transformer Attention21 May 2026
- 2026Latent Fourier Transform20 Apr 2026
- 2026DisenReason: Behavior Disentanglement and Latent Reasoning for Shared-Account Sequential Recommendation4 Mar 2026
- 2026Differential syntactic and semantic encoding in LLMs8 Jan 2026
- 2025MS-SSM: A Multi-Scale State Space Model for Efficient Sequence Modeling29 Dec 2025
27 more
- 2025Towards Efficient Post-Training via Fourier-Driven Adapter Architectures26 Dec 2025
- 2025Exploiting Inter-Session Information with Frequency-enhanced Dual-Path Networks for Sequential Recommendation9 Nov 2025
- 2025MGT-Prism: Enhancing Domain Generalization for Machine-Generated Text Detection via Spectral Alignment19 Aug 2025
- 2025A Free Probabilistic Framework for Analyzing the Transformer-based Language Models19 Jun 2025
- 2025A quantitative analysis of semantic information in deep representations of text and images21 May 2025
- 2024Fourier Position Embedding: Enhancing Attention's Periodic Extension for Length Generalization23 Dec 2024
- 2024DCTdiff: Intriguing Properties of Image Generative Modeling in the DCT Space19 Dec 2024
- 2024Wavelet GPT: Wavelet Inspired Large Language Models4 Sep 2024
- 2024Extracting Sentence Embeddings from Pretrained Transformer Models15 Aug 2024
- 2024Repurformer: Transformers for Repurposing-Aware Molecule Generation16 Jul 2024
- 2024Towards Signal Processing In Large Language Models10 Jun 2024
- 2024Vim-F: Visual State Space Model Benefiting from Learning in the Frequency Domain29 May 2024
- 2023Codebook Features: Sparse and Discrete Interpretability for Neural Networks26 Oct 2023
- 2023Interpretable Spectral Variational AutoEncoder (ISVAE) for time series clustering18 Oct 2023
- 2023Conformer LLMs -- Convolution Augmented Large Language Models2 Jul 2023
- 2023SpectralCLIP: Preventing Artifacts in Text-Guided Style Transfer from a Spectral Perspective16 Mar 2023
- 2023Learning a Fourier Transform for Linear Relative Positional Encodings in Transformers3 Feb 2023
- 2022Task Ambiguity in Humans and Language Models20 Dec 2022
- 2022Feature Dropout: Revisiting the Role of Augmentations in Contrastive Learning16 Dec 2022
- 2022Continuous diffusion for categorical data28 Nov 2022
- 2022Spectral Probing21 Oct 2022
- 2022Fast-FNet: Accelerating Transformer Encoder Models via Efficient Fourier Layers26 Sep 2022
- 2022Language modeling via stochastic processes21 Mar 2022
- 2021Oscillatory Fourier Neural Network: A Compact and Efficient Architecture for Sequential Processing14 Sep 2021
- 2021Deep Autoregressive Models with Spectral Attention13 Jul 2021
- 2021FNet: Mixing Tokens with Fourier Transforms9 May 2021
- 2021Audio Transformers1 May 2021
- 2022Continuous diffusion for categorical datacited by 202
- 2024DCTdiff: Intriguing Properties of Image Generative Modeling in the DCT Spacecited by 32
- 2024DCTdiff: Intriguing Properties of Image Generative Modeling in the DCT Space19 Dec 2024
- 2022Continuous diffusion for categorical data28 Nov 2022
- 2021FNet: Mixing Tokens with Fourier Transformscited by 343
- 2023Codebook Features: Sparse and Discrete Interpretability for Neural Networkscited by 45
- 2021Audio Transformerscited by 41
- 2024Fourier Position Embedding: Enhancing Attention's Periodic Extension for Length Generalizationcited by 37
- 2022Task Ambiguity in Humans and Language Modelscited by 27
- 2022Language modeling via stochastic processescited by 18
- 2023Learning a Fourier Transform for Linear Relative Positional Encodings in Transformerscited by 10
- 2021Deep Autoregressive Models with Spectral Attentioncited by 9
- 2022Feature Dropout: Revisiting the Role of Augmentations in Contrastive Learningcited by 9
- 2024Towards Signal Processing In Large Language Modelscited by 7
- 2024Extracting Sentence Embeddings from Pretrained Transformer Modelscited by 7
- 2025A quantitative analysis of semantic information in deep representations of text and imagescited by 7
12 most cited of 35 All 35 (JSON)
- 2026MS-GLA: Multi-Scale Gated Linear Attention for Addressing Representational Bottlenecks via Multi-Temporal Resolution28 Sep 2026
- 2026FLaG: Frequency-Domain Latent-attention Gated Pooling for Token Aggregation1 Sep 2026
- 2026Denoising the Future: Context-Aware Spectral Diffusion for Temporal Knowledge Graph Extrapolation21 Aug 2026
- 2026FourierQK: Spectral Preprocessing of Query-Key Projections Improves Transformer Attention8 Jul 2026
- 2026Frequency-Domain Latent Attention Gating for Cross-Domain Token Aggregation6 Jun 2026
- 2026Beyond Sinusoids: A Morlet Wavelet Framework for Transformer Positional Encoding31 May 2026
- 2026Energy-Gated Attention and Wavelet Positional Encoding: Complementary Inductive Biases for Transformer Attention25 May 2026
- 2026Energy-Gated Attention: Spectral Salience as an Inductive Bias for Transformer Attention21 May 2026
- 2026Latent Fourier Transform20 Apr 2026
- 2026DisenReason: Behavior Disentanglement and Latent Reasoning for Shared-Account Sequential Recommendation4 Mar 2026
- 2026Differential syntactic and semantic encoding in LLMs8 Jan 2026
- 2025MS-SSM: A Multi-Scale State Space Model for Efficient Sequence Modeling29 Dec 2025
12 newest of 35 All 35 (JSON)