Emergent Sparsity in Frozen Random CNN Feature Extractors for Deep Reinforcement Learning

[Submitted on 15 May 2026]

Title:Emergent Sparsity in Frozen Random CNN Feature Extractors for Deep Reinforcement Learning

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Abstract:We report a striking phenomenon: deep reinforcement learning agents trained with frozen, randomly initialized CNN feature extractors spontaneously develop extremely sparse fully-connected representations, without any sparsity-inducing objective. In the first fully-connected layer (FC1, $3{,}136 \to 64$), agents compress task-relevant information through as few as 1-3 neurons out of 64 for deterministic Pong (5-11 for stochastic Pong), while trainable CNNs activate 55-64 neurons under matched conditions. We establish four principal findings. First, FC1 sparsity scales with task complexity: 1-11 for Pong, 19-26 for Breakout, and $\sim$42 for Space Invaders. Width-scaling confirms this reflects task structure rather than a fixed capacity fraction. Second, within-game scaling emerges: three identical Pong seeds produce 5, 7, and 11 active neurons. The 5-neuron seed plateaus at $+14$ reward, while the others reach expert performance ($+18.4$, $+18.7$), suggesting the random projection's usable dimensionality bounds achievable performance. Third, ablation confirms necessity: removing these active neurons crashes performance across two PPO implementations and four games. Fourth, the information bottleneck commits early: a sweep shows the active set locks by 15-30M steps, while reward turns positive 35-105M steps later. A complementary finding in Breakout shows frozen and trainable CNNs reach competitive rewards via structurally different bottlenecks: frozen agents use 17-25 active neurons (participation ratio $\sim$10-14), while trainable agents use 51 (participation ratio $\sim$3.6). Finally, wherever input dimensionality dwarfs intrinsic task dimensionality, gradient descent on a frozen random projection may reveal the effective rank of the underlying problem without explicit sparsity machinery.

Comments: 24 pages, 4 figures

Subjects:

Machine Learning (cs.LG); Artificial Intelligence (cs.AI); Neural and Evolutionary Computing (cs.NE)

Cite as: arXiv:2607.26059 [cs.LG]

(or arXiv:2607.26059v1 [cs.LG] for this version)

https://doi.org/10.48550/arXiv.2607.26059

arXiv-issued DOI via DataCite

Submission history

From: Scott Norton [view email] [v1] Fri, 15 May 2026 00:01:05 UTC (180 KB)

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