Closing the Theory-Practice Gap in Spiking Transformers via Effective Dimension

• URL: http://arxiv.org/abs/2604.15769v1
• Date: Fri, 17 Apr 2026 07:15:53 GMT
• Title: Closing the Theory-Practice Gap in Spiking Transformers via Effective Dimension
• Abstract summary: Spiking transformers achieve competitive accuracy with conventional transformers while offering $38$-$57times$ energy efficiency on neuromorphic hardware.<n>This paper establishes the first comprehensive expressivity theory for spiking self-attention.
• Score: 13.891522069967507
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Spiking transformers achieve competitive accuracy with conventional transformers while offering $38$-$57\times$ energy efficiency on neuromorphic hardware, yet no theoretical framework guides their design. This paper establishes the first comprehensive expressivity theory for spiking self-attention. We prove that spiking attention with Leaky Integrate-and-Fire neurons is a universal approximator of continuous permutation-equivariant functions, providing explicit spike circuit constructions including a novel lateral inhibition network for softmax normalization with proven $O(1/\sqrt{T})$ convergence. We derive tight spike-count lower bounds via rate-distortion theory: $\varepsilon$-approximation requires $Ω(L_f^2 nd/\varepsilon^2)$ spikes, with rigorous information-theoretic derivation. Our key insight is input-dependent bounds using measured effective dimensions ($d_{\text{eff}}=47$--$89$ for CIFAR/ImageNet), explaining why $T=4$ timesteps suffice despite worst-case $T \geq 10{,}000$ predictions. We provide concrete design rules with calibrated constants ($C=2.3$, 95\% CI: $[1.9, 2.7]$). Experiments on Spikformer, QKFormer, and SpikingResformer across vision and language benchmarks validate predictions with $R^2=0.97$ ($p<0.001$). Our framework provides the first principled foundation for neuromorphic transformer design.

Related papers

• Transformers Provably Learn to Internalize Chain-of-Thought [65.41010769606844]
  Implicit Chain-of-Thought (ICoT) trains models to internalize intermediate steps within their hidden states.<n>Log-ICoT removes thinking tokens one at a time, reducing the number of stages from linear in $k$ to logarithmic.<n>Experiments on multi-layer transformers confirm the theory and visualize how reasoning is progressively absorbed into deeper layers.
  arXiv  Detail & Related papers  (2026-05-27T15:17:06Z)
• Prism: Structural Symmetry Scanning via Duality-Constrained Laplacian Projection [0.0]
  We introduce textbfPrism, a framework for structural symmetry diagnosis in complex networks.<n>Prism computes the emphduality defect $(L,P) = |LP - PL|_F / |L|_F$ -- a scalar measuring how far the network deviates from structural self-consistency.
  arXiv  Detail & Related papers  (2026-05-18T04:20:05Z)
• OAM-Induced Lattice Rotation Reveals a Fractional Optimum in Fault-Tolerant GKP Quantum Sensing [0.0]
  We establish that orbital-angular-momentum encoding and Gottesman-Kitaev-Preskill (GKP) lattice geometry are structurally coupled.<n>Using an end-to-end differentiable Strawberry Fields--TensorFlow circuit, we jointly optimise $ell$, the lattice aspect ratio $r$, and the finite-energy envelope $$ to maximise quantum Fisher information.
  arXiv  Detail & Related papers  (2026-05-13T09:49:16Z)
• Wavelet Variance Equipartition as a Threshold for World-Model Quality and Quantum Kernel TN-Simulability [0.0]
  We identify the wavelet scaling exponent $$ as a critical diagnostic.<n>We establish $= 1/2$ as a sharp transition boundary for the classical simulability of amplitude-encoded quantum kernels.<n>We prove this variance scales strictly as $Var[X] = (d-2)$.
  arXiv  Detail & Related papers  (2026-05-12T05:41:12Z)
• The Spectral Edge Thesis: A Mathematical Framework for Intra-Signal Phase Transitions in Neural Network Training [0.0]
  We show that phase transitions in neural network training are controlled by the spectral gap of the rolling-window Gram matrix of parameter updates.<n>Adiabatic parameter $mathcalA = |G|_F / (, g2)$ controls circuit stability: $mathcalA ll 1$ (plateau), $mathcalA sim 1$ (phase transition), $mathcalA gg 1$ (forgetting)
  arXiv  Detail & Related papers  (2026-03-30T20:10:22Z)
• Exact Attention Sensitivity and the Geometry of Transformer Stability [0.0]
  Despite powering modern AI, transformers remain mysteriously brittle to train.<n>We develop a stability theory that explains why pre-LayerNorm works, why DeepNorm uses $N-1/4$ scaling, and why warmup is necessary.
  arXiv  Detail & Related papers  (2026-02-21T14:25:24Z)
• INC: An Indirect Neural Corrector for Auto-Regressive Hybrid PDE Solvers [61.84396402100827]
  We propose the Indirect Neural Corrector ($mathrmINC$), which integrates learned corrections into the governing equations.<n>$mathrmINC$ reduces the error amplification on the order of $t-1 + L$, where $t$ is the timestep and $L$ the Lipschitz constant.<n>We test $mathrmINC$ in extensive benchmarks, covering numerous differentiable solvers, neural backbones, and test cases ranging from a 1D chaotic system to 3D turbulence.
  arXiv  Detail & Related papers  (2025-11-16T20:14:28Z)
• Convergence Rate Analysis of LION [54.28350823319057]
  LION converges iterations of $cal(sqrtdK-)$ measured by gradient Karush-Kuhn-T (sqrtdK-)$. We show that LION can achieve lower loss and higher performance compared to standard SGD.
  arXiv  Detail & Related papers  (2024-11-12T11:30:53Z)
• Towards Understanding the Universality of Transformers for Next-Token Prediction [20.300660057193017]
  Causal Transformers are trained to predict the next token for a given context.<n>We take a step towards understanding this phenomenon by studying the approximation ability of Transformers for next-token prediction.
  arXiv  Detail & Related papers  (2024-10-03T21:42:21Z)
• Chain of Thought Empowers Transformers to Solve Inherently Serial Problems [57.58801785642868]
  Chain of thought (CoT) is a highly effective method to improve the accuracy of large language models (LLMs) on arithmetics and symbolic reasoning tasks. This work provides a theoretical understanding of the power of CoT for decoder-only transformers through the lens of expressiveness.
  arXiv  Detail & Related papers  (2024-02-20T10:11:03Z)
• Transformers as Support Vector Machines [54.642793677472724]
  We establish a formal equivalence between the optimization geometry of self-attention and a hard-margin SVM problem. We characterize the implicit bias of 1-layer transformers optimized with gradient descent. We believe these findings inspire the interpretation of transformers as a hierarchy of SVMs that separates and selects optimal tokens.
  arXiv  Detail & Related papers  (2023-08-31T17:57:50Z)
• Curse of Dimensionality on Randomized Smoothing for Certifiable Robustness [151.67113334248464]
  We show that extending the smoothing technique to defend against other attack models can be challenging. We present experimental results on CIFAR to validate our theory.
  arXiv  Detail & Related papers  (2020-02-08T22:02:14Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.