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Q-Interference: Memory-Efficient Phase-Aware Quantum-Inspired Attention

Emama Nahid, Tahmid Imtiaz Imu, Huayue Gu, Liran Ma, Zhipeng Cai, Honghui Xu

arXiv:2608.17288v1cs.CL

TL;DR

Standard attention captures feature similarity but not whether token features should reinforce or suppress one another, while naive phase-aware attention is memory-intensive. Q-Interference adds amplitudes and learned phases, then uses an exact factorization to compute the same score without the large intermediate tensor. Controlled experiments report a practical phase-aware model with favorable language-modeling quality and memory efficiency, while the reformulation is essential for practicality.

  • Problem

    Standard dot-product attention may miss context-dependent reinforcing or suppressive relationships between strong token features, while long-context attention creates memory pressures.

  • Method

    Q-Interference augments query and key features with amplitudes and learned phases, using an exact factorization that computes phase-aware scores with two matrix multiplications.

  • Results

    Across controlled benchmark experiments, Q-Interference was the strongest practical model in its phase-aware family, balancing language-modeling quality and memory efficiency.

  • Takeaways & Limitations

    The exact memory-efficient reformulation makes phase-aware attention practical within a standard GPT pipeline, while the phase component provides a small but consistent modeling benefit.

  • Takeaways & Limitations

    Naively implemented phase-aware interference introduces a large token-pair-feature intermediate structure, making it significantly more memory-intensive and potentially impractical at scale.

Abstract

from arXiv · show

GPT attention measures token compatibility through dot-product similarity. This mechanism is simple, effective, and memory-efficient. But it does not explicitly model whether strong token features should reinforce or suppress one another. We introduce Q-Interference, a fully classical quantum-inspired attention mechanism for autoregressive language modeling that augments each query and key feature with an amplitude and a learned phase. The resulting attention score is phase-aware which aligned phases contribute constructively while conflicting phases contribute destructively. Although Q-Interference yields a richer interaction rule than similarity alone, a naive implementation of Q-Interference requires a large token-pair-feature interaction tensor, making it memory-intensive and often impractical. To address this limitation, we propose an exact trigonometric factorization that computes the same score using two standard matrix multiplications avoiding materialization of the large intermediate tensor. Q-Interference fits directly into a Transformer block in GPT and leaves the remainder of the model architecture and next-token prediction objective unchanged. Experiments on public benchmark datasets and baseline models show that the proposed reformulation trains stably in a controlled GPT-style setting and provides a consistent memory advantage over naive phase-aware interference attention. These results support the specific contribution of this work: an exact memory-efficient reformulation that makes phase-aware interference attention practical within a standard GPT pipeline.

1 Introduction

The introduction identifies a limitation of dot-product attention in modeling constructive and destructive feature interactions and presents Q-Interference with an exact, memory-efficient reformulation for GPT-style language modeling.

  • Motivation: Standard causal self-attention compares token features through dot products, which may miss whether strong features should reinforce or suppress one another.GPT-style autoregressive models attend only to previous positions for next-token prediction.
  • Motivation: Dense attention becomes increasingly memory-intensive for long-context modeling because each token compares with many earlier tokens.The introduction connects this challenge to document question answering, scientific text modeling, and retrieval-augmented generation.
  • Q-Interference: Q-Interference augments each query and key feature with an amplitude and a learned phase to represent constructive and destructive token interactions.Amplitude controls feature strength, while aligned phases reinforce and conflicting phases suppress interactions.
  • Memory-efficient reformulation: The proposed exact reformulation computes the same phase-aware attention score using two standard matrix multiplications instead of materializing a large interaction tensor.This reformulation is intended to make phase-aware interference attention memory-efficient within a GPT-style architecture.

2 Q-Interference

Q-Interference replaces GPT’s dot-product attention score with a classical phase-aware interference score, while preserving the standard GPT architecture and training objective. An exact trigonometric factorization computes this richer score with two matrix multiplications, reducing the added memory cost from O(T^2dh) to O(Tdh).

  • Integration and Training: The proposed score is inserted into a standard GPT block without changing the remaining architecture or the standard autoregressive next-token prediction objective.Token and positional embeddings, residual connections, layer normalization, feed-forward blocks, and training remain inherited from baseline GPT.
  • Phase-Aware Interference Attention: Q-Interference augments magnitude-based query-key compatibility with relative phase alignment, allowing constructive reinforcement and destructive suppression between token features.Amplitudes control feature participation, while learned phases determine whether interactions reinforce or suppress one another.
  • Memory-Efficient Reformulation: The phase-aware score is richer than dot-product attention but naively requires a large token-pair-feature intermediate structure, increasing memory usage.This additional structure spans token pairs and feature dimensions, making direct implementation less practical at scale.
  • Memory-Efficient Reformulation: The exact factorization uses cos(α − β) = cos α cos β + sin α sin β to replace explicit pairwise interactions with two standard matrix multiplications and an addition.The reformulation introduces no approximation and avoids forming the T × T × d_h interaction tensor.
  • Memory-Efficient Reformulation: O(T^2d_h) to O(Td_h): the factorized form reduces the extra memory cost while retaining a standard attention-sized final score matrix.The method removes the additional intermediate-tensor overhead but does not eliminate the quadratic costs of dense attention.

3 Experiment and Evaluation

Q-Interference is evaluated in a controlled GPT-style language-modeling pipeline that isolates the phase-aware attention mechanism while measuring both language-modeling quality and computational practicality. Comparisons and ablations assess cross-dataset behavior, reference-model context, memory efficiency, and the contribution of phase.

  • Experimental setup: Q-Interference replaces standard scaled dot-product attention while keeping the GPT backbone and next-token objective unchanged.Token and positional embeddings, residual connections, layer normalization, and feed-forward blocks remain fixed.
  • Datasets and preprocessing: Experiments use WikiText-103, TinyStories, pile-10k, and small-C4 with GPT-2 tokenization and context length 512.WikiText-103 is the main controlled benchmark, while the other datasets probe behavior across different data regimes.
  • Evaluation metrics: Evaluation reports validation loss, test loss, test perplexity, peak GPU memory, elapsed execution time, and sequence-length scaling.Peak memory is measured under fixed batch size, context length, numerical precision, and hardware.
  • Model comparisons: Across datasets, Q-Interference is compared with standard GPT and Q-GPT, then contextualized against pretrained GPT-Neo-125M and OPT-125M references.The pretrained models are treated as reference points rather than parameter-matched direct competitors.
  • Overall results: Q-Interference is the strongest practical model in the proposed phase-aware family, with the best matched WikiText-103 result and the most favorable quality-memory trade-off among custom models.Its gains are not universal across datasets, but it remains more practical than Q-GPT.
  • Ablation studies: Ablations show that the exact memory-efficient reformulation is necessary for practicality, while the phase term provides a consistent but modest improvement in final test quality.The naive implementation can be highly memory-intensive or impractical under the full matched setting.

4 Related Work

Prior work has explored quantum-inspired attention for language modeling and memory-efficient adaptation or inference. Q-Interference is positioned differently by applying exact factorization to the intermediate memory introduced by phase-aware attention.

  • Quantum and quantum-inspired attention for language modeling: Quantum-inspired attention studies have applied quantum-style or quantum-state-based formulations to GPT-style attention and NLP, reporting improved representation quality in text transformer settings.Li et al. [2024] and Chen et al. [2025] introduced quantum self-attention mechanisms for NLP.
  • Quantum and quantum-inspired attention for language modeling: Hybrid quantum-classical attention has been studied for sequence generation and natural language generation, while Kuznetsov et al. [2026] incorporated classical quantum-inspired self-attention into an autoregressive GPT-1 pipeline.The cited studies include Smaldone et al. [2025] and Kong et al. [2025].
  • Memory optimization in quantum-inspired LLM research: Quantum-inspired memory optimization has targeted parameter-efficient LLM fine-tuning through schemes motivated by quantum circuits or quantum parameter generation.Chen et al. [2024], Liu et al. [2025], and Raj and Coyle [2026] aim to reduce fine-tuning cost.
  • Memory optimization in quantum-inspired LLM research: Kang et al. [2026] reduces inference memory by compressing the KV cache, addressing past-key-and-value storage rather than the intermediate memory targeted by Q-Interference.KV-cache compression is presented as related to efficient long-context language modeling but as addressing a different memory source.
  • Positioning of Q-Interference: Q-Interference starts from a more expressive phase-aware attention score and uses exact trigonometric factorization to avoid materializing the T × T × dh interaction tensor.The paper distinguishes this focus from removing the quadratic cost of dense attention altogether.

5 Conclusion · A Additional Related Work Summary

Q-Interference is a classical quantum-inspired, phase-aware attention mechanism whose exact trigonometric factorization makes richer token interactions practical within a standard GPT pipeline. Table 6 supplements the related-work discussion by comparing Q-Interference with representative prior work across key design and applicability dimensions.

  • 5 Conclusion: Q-Interference models autoregressive token interactions using feature amplitudes and learned phases.It is fully classical but quantum-inspired through a wave-interference principle.
  • 5 Conclusion: Aligned phases contribute constructively, while conflicting phases contribute destructively.This interference rule distinguishes supportive from suppressive token relationships.
  • 5 Conclusion: Phase-aware interaction provides a richer way to capture token relationships than standard similarity-based attention.Standard attention mainly measures similarity, whereas Q-Interference models both supportive and suppressive relationships.
  • 5 Conclusion: An exact trigonometric factorization avoids the high memory cost of naive phase-aware interaction while preserving the same interaction.The reformulation makes Q-Interference practical within a standard GPT pipeline.
  • 5 Conclusion: Controlled benchmark experiments identified Q-Interference as the strongest practical model within the proposed phase-aware approach.The supplied passage reports this result without specifying a numerical margin.
  • A Additional Related Work Summary: Table 6 provides a compact comparison of representative prior work with Q-Interference.It is presented as a supplementary overview of the related-work discussion.
  • A Additional Related Work Summary: The related-work comparison highlights GPT-style applicability, quantum-inspired design, phase-aware interaction, memory-awareness, and exact memory-efficient reformulation.These are the dimensions identified for comparing representative prior work and Q-Interference.

B Proofs and Derivations for Q-Interference · B.1 Notation and Assumptions

Appendix B establishes the notation and assumptions for proving Q-Interference’s exact algebraic reformulation and memory accounting. The analysis uses one attention head and preserves the standard T × T score matrix while avoiding the naive T × T × dh intermediate tensor.

  • B.1 Notation and Assumptions: The derivations analyze a single attention head, because multi-head attention applies the same computation independently to each head.
  • B.1 Notation and Assumptions: T denotes the sequence length in the proof notation.
  • B.1 Notation and Assumptions: dh denotes the dimension of one attention head.
  • B.1 Notation and Assumptions: For tokens i and j, aq and ak denote nonnegative query and key amplitude vectors in R^dh.
  • B.1 Notation and Assumptions: The proofs concern exact algebraic equivalence and memory accounting rather than generalization performance.
  • B.1 Notation and Assumptions: The factorized computation still produces a standard T × T attention score matrix.
  • B.1 Notation and Assumptions: The factorization avoids the additional T × T × dh token-pair-feature tensor required by the naive phase-aware implementation.

B.2 Derivation of the Phase-Aware Interference Score … B.5 Compatibility with Causal GPT Attention

Q-Interference derives a phase-aware score as a scaled real amplitude-phase inner product, enabling constructive or destructive feature interactions. An exact trigonometric factorization removes the naive token-pair-feature intermediate tensor while preserving causal GPT attention unchanged.

  • B.2 Derivation of the Phase-Aware Interference Score: The phase-aware interference score is the scaled real part of an amplitude-phase inner product over query and key features.This follows by summing the real-valued conjugate interactions across feature dimensions and applying standard attention scaling.
  • B.2 Derivation of the Phase-Aware Interference Score: Phase differences reinforce interactions when cosine terms are positive and suppress them when those terms decrease and become negative.Near-zero phase differences produce constructive interference, whereas large phase differences can produce destructive interference.
  • B.3 Exact Factorization of Phase-Aware Attention: The factorized score matrix is exactly equal to the naive phase-aware interference score matrix, introducing no approximation.The equality follows from applying cos(α − β) = cos α cos β + sin α sin β and rewriting the interaction as two inner products.
  • B.3 Exact Factorization of Phase-Aware Attention: The factorization avoids explicitly constructing the additional token-pair-feature tensor required by naive phase-aware attention but retains the standard T × T score matrix.Thus, it changes the computation of phase-specific interactions without eliminating ordinary dense attention scores.
  • B.4 Memory Cost of Naive and Factorized Computation: The naive implementation requires additional phase-specific storage of order T^2dh, whereas the factorized implementation requires order Tdh, excluding the standard attention score matrix.The factorized form stores transformed query and key matrices, with constant factors ignored in the order estimate.
  • B.5 Compatibility with Causal GPT Attention: Q-Interference changes only the score function and leaves causal masking, normalization, value aggregation, and the remaining GPT transformer block unchanged.Its factorized score matrix has the same shape as standard dot-product attention, allowing the existing causal attention interface to apply.
  • B.5 Compatibility with Causal GPT Attention: The proposed attention output has the same shape as a standard causal attention head, so residual connections, layer normalization, feed-forward blocks, and next-token prediction require no modification.The causal mask is applied before row-wise softmax, followed by value aggregation as in standard causal attention.

C Additional Main Result Analysis · C.1 Metric and Model Definitions

Appendix figures use defined quality and efficiency metrics for autoregressive next-token prediction under the fixed main-experiment training setup. These definitions establish how subsequent comparisons should be interpreted.

  • C.1 Metric and Model Definitions: Table 8 defines the main terms used throughout the appendix figures.These definitions provide the terminology for the following subsections.
  • C.1 Metric and Model Definitions: All quality metrics are computed for autoregressive next-token prediction.The metric scope is specifically next-token prediction in an autoregressive setting.
  • C.1 Metric and Model Definitions: Peak GPU memory is reported under the fixed training setup used in the main experiments.Memory comparisons therefore use the same stated training configuration.
  • C.1 Metric and Model Definitions: The appendix distinguishes quality measurements from efficiency measurements.The definitions cover both model quality and resource usage.
  • C.1 Metric and Model Definitions: The defined metrics provide the basis for interpreting quality comparisons in later subsections.Subsequent appendix figures rely on these metric definitions.
  • C.1 Metric and Model Definitions: The same definitions provide the basis for interpreting efficiency comparisons in later subsections.Peak GPU memory is the explicitly specified efficiency measure.

C.2 Controlled WikiText-103 Result

On controlled WikiText-103 experiments, Q-Interference achieved the lowest test perplexity among the internal models and substantially reduced peak training GPU memory versus the standard GPT baseline.

  • Controlled WikiText-103 Result: Q-Interference achieves the lowest test perplexity among the internal models on WikiText-103.Figure 3 reports test perplexity as the top metric ruler, where lower values are better.
  • Controlled WikiText-103 Result: Peak training GPU memory falls from 8055.76 MB for the standard GPT baseline to 4227.14 MB with Q-Interference.This corresponds to an approximate 47.5% reduction; lower peak memory is better.

C.3 Cross-Dataset Memory Behavior · C.4 Pretrained 125M Models

Across TinyStories, pile-10k, and small-C4, Q-Interference has the lowest peak training GPU memory among the custom models through exact factorization. Against pretrained 125M models, it remains a contextual comparison because Q-Interference is trained from scratch while pretrained models achieve stronger final test perplexity.

  • C.3 Cross-Dataset Memory Behavior: Q-Interference has the lowest peak training GPU memory among custom models across TinyStories, pile-10k, and small-C4.Its factorized computation avoids materializing the phase-aware token-pair-feature interaction tensor.
  • C.3 Cross-Dataset Memory Behavior: The naive interference model uses the largest memory because it directly materializes the phase-aware token-pair-feature interaction tensor.
  • C.3 Cross-Dataset Memory Behavior: Figure 4 reports the same cross-dataset memory pattern for Q-Interference across the three custom-model settings.
  • C.4 Pretrained 125M Models: Q-Interference is compared with GPT-Neo-125M and OPT-125M, both pretrained decoder-only language models.
  • C.4 Pretrained 125M Models: Because Q-Interference is trained from scratch, the pretrained-model comparison is contextual rather than parameter-matched.
  • C.4 Pretrained 125M Models: GPT-Neo-125M and OPT-125M achieve stronger final test perplexity, benefiting from large-scale pretraining.
  • C.4 Pretrained 125M Models: In the controlled WikiText-103 setting, Q-Interference achieves the best internal test perplexity and lowest peak GPU memory.
  • C.4 Pretrained 125M Models: Across the custom model family, Q-Interference uses less memory than the standard GPT baseline, naive interference, and Q-GPT.

D Limitations and Discussion · NeurIPS Paper Checklist

Q-Interference is presented as a practical phase-aware attention design whose exact reformulation enables standard GPT training with lower memory cost, while its evidence remains limited to controlled GPT-style language modeling. The checklist documents theoretical derivations and experimental setup, but identifies incomplete training details and absent statistical uncertainty reporting.

  • D Limitations and Discussion: The exact reformulation makes richer interference-based attention trainable in a standard GPT pipeline while reducing naive phase-aware computation’s additional memory cost.Ablations show that the phase term provides a small but consistent modeling benefit.
  • D Limitations and Discussion: Pretrained GPT-Neo-125M and OPT-125M achieve stronger final language-modeling quality, while Q-Interference uses lower peak GPU memory on three of four datasets.Q-Interference is trained from scratch in the controlled setup, so the comparison is contextual rather than parameter-matched.
  • D Limitations and Discussion: Q-Interference is not intended to replace all strong pretrained GPT transformer baselines and is evaluated in controlled GPT-style language modeling rather than large-scale pretraining or downstream transfer.The results instead motivate further study of phase-aware quantum-inspired interactions paired with an exact memory-efficient reformulation.
  • NeurIPS Paper Checklist: The paper provides assumptions and derivations in Appendix A for the phase-aware score, exact factorization, memory accounting, and compatibility with causal GPT attention.These materials support the paper’s theoretical results and implementation compatibility claims.
  • NeurIPS Paper Checklist: The submission states that public datasets and a project git link are provided, existing assets are cited, and the work involves neither high-risk released resources nor human-subjects research.It also states that the research conforms to ethics requirements, reports no current societal impact, introduces no new assets, and does not use LLMs as important non-standard components.
  • NeurIPS Paper Checklist: The paper describes datasets, model families, context length, hardware, precision, and evaluation metrics, but omits optimizer type, learning rate, batch size, epoch count, seed choice, and hyperparameter selection.The checklist therefore indicates that the core experimental setup is described without all training details needed for full reproducibility.
  • NeurIPS Paper Checklist: The main experimental results report single-run validation loss, test loss, test perplexity, and peak GPU memory without error bars, confidence intervals, significance tests, or multi-seed mean ± standard deviation.This limits assessment of experimental variability and statistical significance.
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