arXiv:2605.12049cs.LGcs.AI2026-05

探索神经网络中单元数量、复杂度与连接性的最优分配,发现复杂神经元更优。

Scaling Laws and Tradeoffs in Recurrent Networks of Expressive Neurons

论文配图:Scaling Laws and Tradeoffs in Recurrent Networks of Expressive Neurons
图 1 · 摘自论文原文
  • 用可调复杂度的表达性漏电记忆单元构建递归网络,独立控制三要素。
  • 固定参数下存在非平凡最优解,更大预算下倾向更多更复杂的神经元。
  • 提出信息论模型解释收益递减,适合对神经架构设计感兴趣的学者。

皮层神经元是复杂、多时间尺度的处理器,嵌入在递归回路中,历经长期进化压力并在严苛生物约束下形成。主流机器学习则主要使用极简单元,这一默认设置源于早期神经网络理论。我们将其视为一个规范性的架构问题:如何在固定参数预算 $P$ 下分配单元数 $N$、单个单元有效复杂度 $k_e$ 与连接度 $k_c$?什么决定最优分配?为此,我们引入 ELM 网络,其递归层由模仿皮层神经元功能特性的表达性漏电记忆(ELM)神经元构成,可独立调节 $N$、$k_e$ 与 $k_c$,并在跨数量级规模下稳定训练。我们在两个质异序列任务上评估:类脑的 SHD-Adding 任务和 Enwik8 字符级语言建模。性能在三个维度上均单调提升;固定预算下出现清晰的非平凡最优,更大预算更偏好更高数量与更高复杂度的神经元。一个闭式信息论模型捕捉了这些权衡,并将两端的收益递减归因于:单神经元信噪比饱和与跨神经元冗余。超参数扫描覆盖三个数量级的可训练参数,呈现出接近帕累托前沿的缩放规律,表明一旦探查该权衡面,简单单元默认并非显然最优,并为皮层依赖复杂时空整合器提供了规范性视角。

原文摘要 · Abstract (English)

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 and more complex neurons. A closed-form information-theoretic model 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 framework. 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.

神经网络架构设计缩放定律递归网络

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