ELM Network 研究：表达性神经元循环网络中的缩放规律与权衡
Scaling Laws and Tradeoffs in Recurrent Networks of Expressive Neurons
AI 导读
一篇 arXiv 论文提出 ELM Network，其循环层由模拟皮层神经元功能的 Expressive Leaky Memory（ELM）神经元构成，可在参数预算 $P$ 下独立调节神经元数量 N、单元复杂度 k_e 和连接度 k_c。
正文 · 原文
Abstract:Cortical neurons are complex, multi-timescale processors wired into recurrent circuits, shaped by long evolutionary pressure under stringent biological constraints. Mainstream machine learning, by contrast, predominantly builds models from extremely simple units, a default inherited from early neural-network theory. We treat this as a normative architectural question. How should one split a fixed parameter budget $P$ between the number of units $N$, per-unit effective complexity $k_e$, and per-unit connectivity $k_c$? What controls the optimal allocation? This calls for a model in which per-unit complexity can be tuned independently of width and connectivity. Accordingly, we introduce the ELM Network, whose recurrent layer is built from Expressive Leaky Memory (ELM) neurons, chosen to mirror functional components of cortical neurons. The architecture allows for individually adjusting $N$, $k_e$, and $k_c$ and trains stably across orders of magnitude in scale. We evaluate the model on two qualitatively different sequence benchmarks: the neuromorphic SHD-Adding task and Enwik8 character-level language modeling. Performance improves monotonically along each of the three axes individually. Under a fixed budget, a clear non-trivial optimum emerges in their tradeoff, and larger budgets favor both more numerous \emph{and} more complex neurons. A closed-form information-theoretic proxy captures these tradeoffs and attributes the diminishing returns at two ends to: per-neuron signal-to-noise saturation and across-neuron redundancy. A hyperparameter sweep spanning three orders of magnitude in trainable parameters traces a near-Pareto-frontier scaling law consistent with the proxy. This suggests that the simple-unit default in ML is not obviously optimal once this tradeoff surface is probed, and offers a normative lens on cortex's reliance on complex spatio-temporal integrators.
| Comments: | 33 pages, 28 figures, 3 tables, including derivations. Submitted for peer review |
| Subjects: | Machine Learning (cs.LG); Artificial Intelligence (cs.AI); Information Theory (cs.IT); Neural and Evolutionary Computing (cs.NE) |
| Cite as: | arXiv:2605.12049 [cs.LG] |
| (or arXiv:2605.12049v2 [cs.LG] for this version) | |
| https://doi.org/10.48550/arXiv.2605.12049 arXiv-issued DOI via DataCite |
Submission history
From: Aaron Spieler [view email]
[v1]
Tue, 12 May 2026 12:29:33 UTC (1,313 KB)
[v2]
Mon, 26 Oct 2026 14:30:08 UTC (1,539 KB)
来源：arXiv cs.AI · arxiv.org