Updated 5 h ago · first seen 11 Sept 2026
paper_01M294FS9JQ7J0TAN4ENSAKHS1
- Published
- 11 Sept 2026
- T1 · 5 h ago
- arXiv
- 2606.12059
- T1 · 5 h ago
- Category
- cs.LG
- T1 · 5 h ago
Abstract
We address transformer attention on energy-constrained physical substrates. Softmax attention requires exponentiation and global reduction, operations with high energy cost on von Neumann hardware and no natural physical analog. We show that Kuramoto synchronization dynamics (which arise in electrical, mechanical, superconducting, and charge-density-wave oscillator arrays, among other physical systems) implement a well-defined attention operation. The resulting mechanism, \emph{fixed-query oscillator attention}, replaces softmax's arithmetic with the equilibration of a gradient flow on the sphere: queries are learned anchors fixed on the sphere, and free oscillators evolve under Kuramoto--Lohe dynamics until they settle at positions encoding attention weights via cosine similarity. Because the computation is equilibration, no global exponential normalization is needed. The fixed point is provably unique and globally attractive from almost every initial condition, a guarantee that holds across every physical realization. Empirically, at the minimal hardware configuration (oscillator dimension $d_{\mathrm{osc}} = 2$), oscillator attention matches softmax on keyword spotting, and on subject-verb agreement it trains more reliably while reaching softmax's accuracy. Softmax retains an advantage on causal language modeling, but the gap decays as a power law in $d_{\mathrm{osc}}$. The main objective of this work is not to replace softmax in software but to provide a mathematically grounded blueprint for accurate attention on physical substrates.
Authors 2
Fabio Pasqualetti, Taosha Guo
Specification
- Official page
Source:arXiv (Atom API + RSS)T1observed 5 h agohigh
- Arxiv announce type
- replace
Source:arXiv (Atom API + RSS)T1observed 5 h agohigh
- arXiv id
- 2606.12059
Source:arXiv (Atom API + RSS)T1observed 5 h agohigh
- Categories
- cs.LG, cs.NE, nlin.AO
Source:arXiv (Atom API + RSS)T1observed 5 h agohigh
Source:arXiv (Atom API + RSS)T1observed 5 h agohigh
- Primary category
- cs.LG
Source:arXiv (Atom API + RSS)T1observed 5 h agohigh
- Published
- 11 Sept 2026
Source:arXiv (Atom API + RSS)T1observed 5 h agohigh
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Provenance
Attributed facts
9
Source tiers
T19
Freshest observation
5 h ago
Conflicts
None
No models linked to this paper yet.
- Authors
- Fabio Pasqualetti, Taosha Guo
As of
Rewind the record: see this entity's attributes exactly as AI Atlas knew them on a given day.
Claim history
Official pageofficial_url1
| Value | Valid from → to | Status | Source | Confidence | Extractor |
|---|---|---|---|---|---|
| https://arxiv.org/abs/2606.12059 | → current | current | arXiv (Atom API + RSS)T1 | high | deterministic |
Abstractabstract1
| Value | Valid from → to | Status | Source | Confidence | Extractor |
|---|---|---|---|---|---|
| We address transformer attention on energy-constrained physical substrates. Softmax attention requires exponentiation and global reduction, operations with high energy cost on von Neumann hardware and no natural physical analog. We show that Kuramoto synchronization dynamics (which arise in electrical, mechanical, superconducting, and charge-density-wave oscillator arrays, among other physical systems) implement a well-defined attention operation. The resulting mechanism, \emph{fixed-query oscillator attention}, replaces softmax's arithmetic with the equilibration of a gradient flow on the sphere: queries are learned anchors fixed on the sphere, and free oscillators evolve under Kuramoto--Lohe dynamics until they settle at positions encoding attention weights via cosine similarity. Because the computation is equilibration, no global exponential normalization is needed. The fixed point is provably unique and globally attractive from almost every initial condition, a guarantee that holds across every physical realization. Empirically, at the minimal hardware configuration (oscillator dimension $d_{\mathrm{osc}} = 2$), oscillator attention matches softmax on keyword spotting, and on subject-verb agreement it trains more reliably while reaching softmax's accuracy. Softmax retains an advantage on causal language modeling, but the gap decays as a power law in $d_{\mathrm{osc}}$. The main objective of this work is not to replace softmax in software but to provide a mathematically grounded blueprint for accurate attention on physical substrates. | → current | current | arXiv (Atom API + RSS)T1 | high | deterministic |
Arxiv announce typearxiv_announce_type1
| Value | Valid from → to | Status | Source | Confidence | Extractor |
|---|---|---|---|---|---|
| replace | → current | current | arXiv (Atom API + RSS)T1 | high | deterministic |
arXiv idarxiv_id1
| Value | Valid from → to | Status | Source | Confidence | Extractor |
|---|---|---|---|---|---|
| 2606.12059 | → current | current | arXiv (Atom API + RSS)T1 | high | deterministic |
Categoriescategories1
| Value | Valid from → to | Status | Source | Confidence | Extractor |
|---|---|---|---|---|---|
| cs.LG, cs.NE, nlin.AO | → current | current | arXiv (Atom API + RSS)T1 | high | deterministic |
PDFpdf_url1
| Value | Valid from → to | Status | Source | Confidence | Extractor |
|---|---|---|---|---|---|
| https://arxiv.org/pdf/2606.12059 | → current | current | arXiv (Atom API + RSS)T1 | high | deterministic |
Primary categoryprimary_category1
| Value | Valid from → to | Status | Source | Confidence | Extractor |
|---|---|---|---|---|---|
| cs.LG | → current | current | arXiv (Atom API + RSS)T1 | high | deterministic |
Publishedpublished_at1
| Value | Valid from → to | Status | Source | Confidence | Extractor |
|---|---|---|---|---|---|
| 11 Sept 2026 | → current | current | arXiv (Atom API + RSS)T1 | high | deterministic |
Claims are temporal and append-only: a new observation closes the previous claim (valid_to) instead of overwriting it. Conflicting claims from different sources are kept side by side and flagged — never averaged. Methodology →
New paper: Attention by Synchronization in Coupled Oscillator Networks
arxiv
| Source | Document | Type | Tier | Last observed | Snapshots |
|---|---|---|---|---|---|
| arXiv (Atom API + RSS) | rss.arxiv.org/rss/cs.LG | feed | T1· Official | 3 h ago | 1 |
Tier 1 = official/primary, 2 = quality secondary, 3 = community, 4 = unverified. Every snapshot is archived; see all sources and the methodology.