RECAP: Local Hebbian Prototype Learning as a Self-Organizing Readout for Reservoir Dynamics

Heng Zhang

cs.NEFeb 25, 2026

RECAP: Local Hebbian Prototype Learning as a Self-Organizing Readout for Reservoir Dynamics

Authors: Heng Zhang

Organizations: International Research Center for Neurointelligence (IRCN), University of Tokyo, Japan

Abstract

Robust perception in brains is often attributed to high-dimensional population activity together with local plasticity mechanisms that reinforce recurring structure. In contrast, most modern image recognition systems are trained by error backpropagation and end-to-end gradient optimization, which are not naturally aligned with local computation and local plasticity. We introduce RECAP (Reservoir Computing with Hebbian Co-Activation Prototypes), a bio-inspired learning strategy for robust image classification that couples untrained reservoir dynamics with a self-organizing Hebbian prototype readout. RECAP discretizes time-averaged reservoir responses into activation levels, constructs a co-activation mask over reservoir unit pairs, and incrementally updates class-wise prototype matrices via a Hebbian-like potentiation-decay rule. Inference is performed by overlap-based prototype matching. The method avoids error backpropagation and is naturally compatible with online prototype updates. We illustrate the resulting robustness behavior on MNIST-C, where RECAP remains robust under diverse corruptions without exposure to corrupted training samples.

Figures & tables

Figure 1: RECAP for robust image classification. An input image drives an untrained echo-state reservoir, producing temporal population activity that is time-averaged and discretized into activation levels. The discretized population code is converted into a binary co-activation mask, which updates a class-wise continuous prototype state via a Hebbian-like potentiation–decay rule. After thresholding, inference is performed by matching the test mask against all class prototypes and selecting the highest-overlap class.

Figure 2: Corrupted examples of the MNIST-C dataset used in the experiments. The method consists of 15 types of algorithmically generated corruptions from noise ( top-left ), blur ( bottom-left ), weather ( top-right ), and digital categories ( bottom-right ). Each type has 5 levels of severity (i.e., 75 distinct corruptions).

Figure 3: Motivation and intuition for the RECAP readout. (a) Standard reservoir computing relies on a typically linear readout, which can be sensitive to feature distortions under input degradations. (b) Local Hebbian-style plasticity provides an inspiration for strengthening repeatedly co-activated relations [ 17 ] . (c) Repeated inputs can induce structured co-activation patterns in reservoir population responses. (d) RECAP leverages these ideas by learning class-wise relational prototypes from co-activation masks using a Hebbian-like potentiation–decay update and performing inference via prototype matching. Figures modified from [ 17 , 31 , 5 ] .

Figure 4: Workflow for prototype formation. An input image is processed by the reservoir for $T$ steps, yielding a time-averaged state vector that is quantized into $K$ discrete levels. This induces a binary co-activation mask over unit pairs. During training, each sample updates its class prototype via Hebbian potentiation–decay; prototypes are then thresholded into binary templates for inference.

Training data	Clean MNIST training set (no corruptions).
Test data	Clean MNIST test set and MNIST-C: 15 corruption types $\times$ 5 severity levels.
Corruption families	Noise, Blur, Weather, Digital (as in ImageNet-C) [ 9 ] .
Baselines	MLP, ResNet-18 [ 7 ] , AlexNet [ 15 ] , ESN-Ridge [ 13 , 10 ] .
Metrics	Clean error; per-corruption Relative CE; Relative mCE (mean over corruptions) [ 9 ] .

Table 1: Summary of the experimental setup.

Model	Component	Parameter	Value
RECAP	Reservoir	Number of neurons ( $N$ )	1024
		Spectral radius ( $\rho$ )	1.0
		Leaking rate ( $\lambda$ )	0.5
		Sparsity	0.9
	Dynamics	Time steps ( $T$ )	60
	Hebbian Learning	Potentiation rate ( $\eta_{+}$ )	0.6

Table 2: Hyperparameters for RECAP (proposed) and baseline models.

			Noise			Blur
Network	Clean Error	Relative mCE	Gauss.	Shot	Impulse	Defocus	Glass	Motion	Zoom
AlexNet	2.1	100.0	100	100	100	100	100	100	100
MLP	1.9	52.1	41	10	29	56	57	72	20
ResNet18	0.9	99.9	56	77	31	114	123	123	132
ESN-Ridge	6.3	55.0	44	14	44	58	60	81	41
RC-HeCaP	11.7	34.1	10	5	11	49	56	72	27

Table 3: Clean error (%) on clean MNIST and robustness scores on MNIST-C. We report Relative mCE (%) and per-corruption Relative CE (%), normalized by AlexNet as in [ 9 ] (AlexNet = 100% by construction; lower is better). Negative Relative CE values can occur when the average corrupted error is slightly lower than the clean error (Eq. ( 14 )).

		Weather				Digital
Network	Relative mCE	Snow	Frost	Fog	Bright	Contrast	Elastic	Pixelate	JPEG
AlexNet	100.0	100	100	100	100	100	100	100	100
MLP	52.1	82	93	98	100	78	30	6	5
ResNet18	99.9	78	95	108	100	116	93	118	127
ESN-Ridge	55.0	83	92	93	99	77	38	7	-13
RC-HeCaP	34.1	36	53	70	52	46	28	5	-15

Table 4: (Part 2) Weather, and Digital columns (%).

Figure 5: Radar plot of per-corruption Relative CE on MNIST-C across 15 types of corruption, each represented as a point on the circular chart. The concentric contour lines indicate Relative mCE scores. For visualization, the radial axis is inverted so that lower Relative CE values (better robustness) appear farther from the center. AlexNet, used as the standard, is represented by a perfect gray circle reflecting an mCE of 100% across all categories. The larger the area enclosed by a model’s line, the better the robustness. The RECAP model, highlighted in the chart in yellow, shows the largest area, indicating superior robustness compared to baseline.

Appendix figures & tables1 asset

Supplementary material from the paper’s appendix.

Appendix

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Hebbian Learning Recurrent Neural Networks Associative Memory

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Associative memory or content-addressable memory is an important component function in computer science and information processing, and at the same time a key concept in cognitive and computational brain science. Many different neural network architectures and learning rules have been proposed to model the brain's associative memory while investigating key component functions like figure-ground segmentation, perceptual reconstruction and rivalry. A less investigated but equally important capability of associative memory is prototype extraction where the training set comprises distorted prototype instances and the task is to recall the correct generating prototype given a new distorted instance. In this paper we benchmark associative memory function of seven different Hebbian learning rules employed in non-modular and modular recurrent networks with winner-take-all dynamics operating on moderately sparse binary patterns. We measure pattern storage and weight information capacity, prototype extraction capabilities, and sensitivity to correlations in data. The original additive Hebb rule comes out with worst capacity, covariance learning proves to be robust but with moderate capacity, and the Bayesian-Hebbian learning rules show highest capacity in almost all different conditions tested.

Abstract

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