# Language as a Wave Phenomenon: Semantic Phase Locking and Interference in Neural Networks

arXiv: https://arxiv.org/abs/2512.01208 · HTML: https://mlsanity.com/paper/2512.01208/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 19 of its 42 references that are in the map.
- First posted on arXiv 1 Dec 2025.

## Builds on (most cited first, 19 of 19)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [RoBERTa: A Robustly Optimized BERT Pretraining Approach](https://mlsanity.com/paper/1907.11692/) (2019)
- [Layer Normalization](https://mlsanity.com/paper/1607.06450/) (2016)
- [Mamba: Linear-Time Sequence Modeling with Selective State Spaces](https://mlsanity.com/paper/2312.00752/) (2023)
- [RoFormer: Enhanced Transformer with Rotary Position Embedding](https://mlsanity.com/paper/2104.09864/) (2021)
- [Pointer Sentinel Mixture Models](https://mlsanity.com/paper/1609.07843/) (2016)
- [Root Mean Square Layer Normalization](https://mlsanity.com/paper/1910.07467/) (2019)
- [In-context Learning and Induction Heads](https://mlsanity.com/paper/2209.11895/) (2022)
- [Progress measures for grokking via mechanistic interpretability](https://mlsanity.com/paper/2301.05217/) (2023)
- [FNet: Mixing Tokens with Fourier Transforms](https://mlsanity.com/paper/2105.03824/) (2021)
- [Unitary Evolution Recurrent Neural Networks](https://mlsanity.com/paper/1511.06464/) (2015)
- [Deep Complex Networks](https://mlsanity.com/paper/1705.09792/) (2017)
- [Transformers without Tears: Improving the Normalization of Self-Attention](https://mlsanity.com/paper/1910.05895/) (2019)
- [The Relational Bottleneck as an Inductive Bias for Efficient Abstraction](https://mlsanity.com/paper/2309.06629/) (2023)
- [Abstractors and relational cross-attention: An inductive bias for explicit relational reasoning in Transformers](https://mlsanity.com/paper/2304.00195/) (2023)
- [Disentangling and Integrating Relational and Sensory Information in Transformer Architectures](https://mlsanity.com/paper/2405.16727/) (2024)
- [Holographic Transformers for Complex-Valued Signal Processing: Integrating Phase Interference into Self-Attention](https://mlsanity.com/paper/2509.19331/) (2025)
- [A Lightweight Transformer with Phase-Only Cross-Attention for Illumination-Invariant Biometric Authentication](https://mlsanity.com/paper/2412.19160/) (2024)
- [ComplexFormer: Disruptively Advancing Transformer Inference Ability via Head-Specific Complex Vector Attention](https://mlsanity.com/paper/2505.10222/) (2025)

## Built on by (most cited first, 2 of 2)

- [The Importance of Phase in Neural Representations: An Internal Oppenheim-Lim Test of Image Classifiers](https://mlsanity.com/paper/2606.17037/) (2026)
- [Language Has Two Parameters: Narrative-Induced Semantic Plasticity and Phase-Sensitive Interpretation](https://mlsanity.com/paper/2608.18041/) (2026)

## Abstract (arXiv)

In standard Transformer architectures, semantic importance is often conflated with activation magnitude, obscuring the geometric structure of latent representations. To disentangle these factors, we introduce PRISM, a complex-valued architecture designed to isolate the computational role of phase. By enforcing a strict unit-norm constraint (|z| = 1) and replacing attention with gated harmonic convolutions, the model is encouraged to utilize subtractive interference in the frequency domain to suppress noise, rather than relying on magnitude-based gating. We utilize this constrained regime to study a hybrid architecture -- fusing phase-based routing with standard attention -- which achieves improved parameter efficiency and representation quality compared to baselines in our evaluated settings. Mechanistically, interventional ablations indicate that the model carries substantial task-relevant information in phase: preserving phase largely maintains performance, whereas disrupting phase causes severe degradation. Together, these results suggest that phase-based spectral interference is a usable computational mechanism for neural sequence modeling at the evaluated scale.