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| Format: | Preprint |
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2026
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| Accès en ligne: | https://arxiv.org/abs/2604.05030 |
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| _version_ | 1866917443852566528 |
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| author | Vishwakarma, Gowrav Agostino, Christopher J. |
| author_facet | Vishwakarma, Gowrav Agostino, Christopher J. |
| contents | Experiments probing natural language processing by both humans and LLMs suggest that the meaning of a semantic expression is indeterminate prior to the act of interpretation rather than being specifiable simply as the sum of its parts (i.e. compositionality). This observer-dependent act dynamically actualizes meaning under genuine contextuality more consistent with quantum logical mechanisms than with classical Boolean approaches that assume separability, motivating an approach to language modeling that utilizes a Hilbert space formalism. In this work, we introduce Phase-Associative Memory (PAM) -- a complex-valued sequence model whose state S_t \in \mathbb{C}^{d \times d} accumulates outer products of complex token embeddings retrieved through the conjugate inner product $\mathrm{Re}\langle K \mid Q\rangle / \sqrt{d}$ -- and evaluate it against a structurally matched real-valued ablation. Both architectures train stably across a 5M--100M parameter sweep on WikiText-103 under identical conditions; PAM sits at higher absolute loss at every measured scale but improves more rapidly with parameter count, with power-law exponents of $-0.15$ vs.\ $-0.12$ in loss and $-0.65$ vs.\ $-0.49$ in perplexity that narrow the gap between the two architectures monotonically. Further investigation of complex-valued sequence modeling at larger scales could reveal that the loss plateau characteristic of real-valued state-of-the-art language models (e.g. transformers) is reachable with PAM-style architectures with an order of magnitude fewer parameters than the current frontier ($\sim$1T), implying that similar capabilities are achievable at sizes runnable on consumer-grade hardware. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_05030 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Phase-Associative Memory: Sequence Modeling in Complex Hilbert Space Vishwakarma, Gowrav Agostino, Christopher J. Computation and Language Artificial Intelligence Machine Learning Experiments probing natural language processing by both humans and LLMs suggest that the meaning of a semantic expression is indeterminate prior to the act of interpretation rather than being specifiable simply as the sum of its parts (i.e. compositionality). This observer-dependent act dynamically actualizes meaning under genuine contextuality more consistent with quantum logical mechanisms than with classical Boolean approaches that assume separability, motivating an approach to language modeling that utilizes a Hilbert space formalism. In this work, we introduce Phase-Associative Memory (PAM) -- a complex-valued sequence model whose state S_t \in \mathbb{C}^{d \times d} accumulates outer products of complex token embeddings retrieved through the conjugate inner product $\mathrm{Re}\langle K \mid Q\rangle / \sqrt{d}$ -- and evaluate it against a structurally matched real-valued ablation. Both architectures train stably across a 5M--100M parameter sweep on WikiText-103 under identical conditions; PAM sits at higher absolute loss at every measured scale but improves more rapidly with parameter count, with power-law exponents of $-0.15$ vs.\ $-0.12$ in loss and $-0.65$ vs.\ $-0.49$ in perplexity that narrow the gap between the two architectures monotonically. Further investigation of complex-valued sequence modeling at larger scales could reveal that the loss plateau characteristic of real-valued state-of-the-art language models (e.g. transformers) is reachable with PAM-style architectures with an order of magnitude fewer parameters than the current frontier ($\sim$1T), implying that similar capabilities are achievable at sizes runnable on consumer-grade hardware. |
| title | Phase-Associative Memory: Sequence Modeling in Complex Hilbert Space |
| topic | Computation and Language Artificial Intelligence Machine Learning |
| url | https://arxiv.org/abs/2604.05030 |