Reward-Modulated Local Learning in Spiking Encoders: Controlled Benchmarks with STDP and Hybrid Rate Readouts

Debjyoti Chakraborty

cs.LGFeb 28, 2026

Reward-Modulated Local Learning in Spiking Encoders: Controlled Benchmarks with STDP and Hybrid Rate Readouts

Authors: Debjyoti Chakraborty

Organizations: Researcher

Abstract

This paper presents a controlled empirical study of biologically motivated local learning for handwritten digit recognition. We evaluate an STDP-inspired competitive proxy and a practical hybrid benchmark built on the same spiking population encoder. The proxy is motivated by leaky integrate-and-fire E/I circuit models with three-factor delayed reward modulation. The hybrid update is local in pre x post rates but uses supervised labels and no timing-based credit assignment. On sklearn digits, fixed-seed evaluation shows classical pixel baselines from 98.06 to 98.22% accuracy, while local spike-based models reach 86.39 +/- 4.75% (hybrid default) and 87.17 +/- 3.74% (STDP-style competitive proxy). Ablations identify normalization and reward-shaping settings as the strongest observed levers, with a best hybrid ablation of 95.52 +/- 1.11%. A network-free synthetic temporal benchmark supports the same timing-versus-rate interpretation under matched local-update training. A descriptive 2x2 analysis further shows reward-shaping effects can reverse sign across stabilization regimes, so reward-shaping conclusions should be reported jointly with normalization settings.

Figures & tables

Fig. 1: Schematic of the shared spiking encoder with two evaluated branches: STDP-inspired competitive proxy pathway and practical local rate-readout benchmark pathway (evaluated via proxy abstraction; no circuit simulation).

Parameter	Value
Hybrid epochs	18
Hybrid learning rate $\alpha$	0.003
Norm-on scaling / interval	0.98 / every epoch
Norm-gentle scaling / interval	0.995 / every 5 epochs
STDP-proxy epochs	9
STDP-proxy $\eta_{+}$ , $\eta_{-}$	0.08, 0.01

TABLE I: Key training and proxy hyperparameters used in this study.

Method	Accuracy (mean $\pm$ std, %)	95% CI half-width (%)	Macro F1
LogReg (pixels)	98.06 $\pm$ 0.00	0.00	0.98 $\pm$ 0.00
MLP (pixels)	98.22 $\pm$ 0.46	0.41	0.98 $\pm$ 0.00
LogReg (spike-encoded rates)	96.11 $\pm$ 0.68	0.60	0.96 $\pm$ 0.01
Hybrid local readout	86.39 $\pm$ 4.75	4.17	0.86 $\pm$ 0.06
STDP-style competitive	87.17 $\pm$ 3.74	3.28	0.87 $\pm$ 0.04

TABLE II: Baseline comparison over seeds. Accuracy is reported as mean

\pm

std, with 95% CI half-width shown separately.

Fig. 2: Accuracy trajectories for the population-coded hybrid learner, overlaying default norm-on and norm-off settings (representative model seed 23, split seed 2026).

Factor	Setting	Accuracy (mean $\pm$ std, %)	95% CI half-width (%)
K	1	81.50 $\pm$ 5.23	4.58
K	2	85.78 $\pm$ 4.64	4.07
K	4	86.39 $\pm$ 4.75	4.17
K	6	84.28 $\pm$ 6.01	5.27
$\sigma$	0.15	87.44 $\pm$ 2.76	2.42
$\sigma$	0.25	86.39 $\pm$ 4.75	4.17

TABLE III: Ablation results over seeds. Accuracy is reported as mean

\pm

std, with 95% CI half-width shown separately.

Condition	Accuracy (mean $\pm$ std, %)	95% CI half-width (%)	Notes
norm on + reward signed	84.44 $\pm$ 5.77	3.77	default
norm on + reward pos-only	91.70 $\pm$ 1.09	0.71	targeted run
norm off + reward signed	95.52 $\pm$ 1.11	0.72	ablation row
norm off + reward pos-only	91.98 $\pm$ 1.49	0.97	targeted run
$\Delta$ pos-only $-$ signed (norm on)	7.25	–	descriptive
$\Delta$ pos-only $-$ signed (norm off)	-3.55	–	descriptive

TABLE IV: Explicit 2

\times

2 interaction summary for normalization and reward shaping on sklearn digits (descriptive, no factorial significance claim).

Fig. 3: Seed-level diagnostic summary for normalization-heuristic and reward-shaping ablations (bars: mean $\pm$ std; points: per-seed values for seeds {11,23,37,41,53,67,79,83,97}).

Fig. 4: Normalization-schedule diagnostic: mean class-row norm trajectory across training epochs (mean $\pm$ std over seeds).

Split seed	Hybrid default Acc (mean $\pm$ std, %)	Hybrid best (norm off) Acc (mean $\pm$ std, %)	$\Delta$ (pp)
2026	86.39 $\pm$ 4.75	95.50 $\pm$ 0.84	+9.11
2027	85.39 $\pm$ 4.08	93.06 $\pm$ 0.81	+7.67
2028	81.50 $\pm$ 7.58	92.67 $\pm$ 1.83	+11.17
Across splits	84.43 $\pm$ 2.58	93.74 $\pm$ 1.54	+9.31 $\pm$ 1.76 ( $\Delta>0$ in 3/3)

TABLE V: Robustness across dataset splits (no retuning). Per-split values aggregate over five model seeds;

\Delta

denotes best minus default. Reward shaping is signed in both compared conditions; only the normalization heuristic is toggled.

Condition	Accuracy (mean $\pm$ std, %)	95% CI half-width (%)	Macro F1
Count readout local (timing-agnostic)	50.25 $\pm$ 0.96	0.84	0.37 $\pm$ 0.06
Time-bin readout local (timing-aware)	84.62 $\pm$ 1.22	1.07	0.85 $\pm$ 0.01

TABLE VI: Temporal synthetic benchmark (fixed seeds). Accuracy is reported as mean

\pm

std, with 95% CI half-width shown separately.

Condition	Accuracy (mean $\pm$ std, %)	95% CI half-width (%)	Macro F1
Hybrid default (norm on, signed)	79.28 $\pm$ 7.83	6.87	0.79 $\pm$ 0.08
Hybrid best (norm off, signed)	85.03 $\pm$ 1.82	1.59	0.85 $\pm$ 0.02
Hybrid norm on (pos-only)	84.60 $\pm$ 0.22	0.20	0.84 $\pm$ 0.00
Hybrid norm off (pos-only)	84.60 $\pm$ 2.15	1.88	0.85 $\pm$ 0.02
STDP proxy (norm on, signed)	57.34 $\pm$ 4.37	3.83	0.55 $\pm$ 0.07
LogReg (spike-encoded rates)	88.32 $\pm$ 0.14	0.12	0.88 $\pm$ 0.00

TABLE VII: OpenML external benchmark on MNIST (fixed split/seed protocol). Accuracy is reported as mean

\pm

std, with 95% CI half-width shown separately.

Cell	Accuracy (mean $\pm$ std)
Norm on + signed	79.28 $\pm$ 7.83
Norm on + pos-only	84.60 $\pm$ 0.22
Norm off + signed	85.03 $\pm$ 1.82
Norm off + pos-only	84.60 $\pm$ 2.15
$\Delta$ (pos-only $-$ signed — norm on)	5.32 $\pm$ 7.73
$\Delta$ (pos-only $-$ signed — norm off)	-0.44 $\pm$ 2.65

TABLE VIII: OpenML MNIST descriptive 2

\times

2 interaction context for hybrid reward shaping and normalization regime (accuracy, %).

Condition	seed 11	seed 23	seed 37	seed 41	seed 53
Hybrid default (norm on, signed)	79.435714	84.907143	79.692857	86.042857	66.321429
Hybrid best (norm off, signed)	85.035714	87.607143	83.442857	85.885714	83.200000
Hybrid norm on (pos-only)	84.392857	84.871429	84.807143	84.514286	84.421429
Hybrid norm off (pos-only)	80.828571	85.721429	85.664286	85.914286	84.864286
STDP proxy (norm on, signed)	61.478571	58.807143	60.971429	51.864286	53.592857
LogReg (spike-encoded rates)	88.164286	88.442857	88.421429	88.392857	88.164286

TABLE IX: OpenML MNIST per-seed accuracy values (%) for the six reported conditions (split seed 2026).

Fig. 5: Normalized confusion matrix on the held–out test set (representative model seed 23, split seed 2026).

Fig. 6: Random test digits with predicted labels (representative model seed 23, split seed 2026).

Metric	Value
Hybrid default: worst class F1 (digit 8)	0.63
Hybrid default: 2nd worst class F1 (digit 9)	0.74
Hybrid default: input spikes/sample (mean $\pm$ std across seeds)	2420.7 $\pm$ 2.4
STDP branch: weight saturation (% at lower bound)	2.55 $\pm$ 0.15
STDP branch: weight saturation (% at upper bound)	0.00 $\pm$ 0.00
STDP branch: winner margin (activation units, normalized dot-product)	0.0229 $\pm$ 0.0014

TABLE X: Additional SNN diagnostics (hybrid default; STDP rows explicitly marked). Inference timing is reported as median over 100 repeats on full-test vectorized batches (

N=360

): forward-only excludes encoding and I/O, while end-to-end includes encoding and forward pass; no learning/update steps are included. Parameter counts include model weights and threshold terms; STDP-style counts also include excitatory prototype vectors (

96\times 256

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Hebbian Learning Spiking Neural Networks Spike-Timing-Dependent Plasticity

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Supervised learning in spiking neural networks (SNNs) typically requires either gradient-based backpropagation, which sacrifices the Hebbian, spike-driven character of biological plasticity, or reward-modulated Spike-Timing-Dependent Plasticity (STDP), in which class supervision enters only as a scalar gate on an otherwise class-agnostic correlation signal. We propose Supervised Spike Agreement-Dependent Plasticity (Supervised SADP), a gradient-free supervised Hebbian learning algorithm in which class information is embedded directly into the Hebbian plasticity computation rather than introduced through reward modulation. SADP trains the output layer via a supervised Hebbian rule that encodes class labels into output spike patterns, then trains the hidden layer by measuring each hidden neuron's chance-corrected temporal agreement, Cohen's kappa, with the correct-class output spike train produced by the forward pass without gradient computation or external reward. A K-shift extension aggregates agreement over temporal offsets, providing robustness to spike-timing jitter at linear computational cost. We evaluate Supervised SADP against reward-modulated STDP across six benchmark and medical imaging datasets, four input encoding strategies, K_shift in {5,25}, and three reward modes (none, binary, margin). Supervised SADP outperforms STDP in a significant majority of comparisons. Under Poisson encoding, SADP achieves 86.46% on MNIST and 76.62% on Fashion-MNIST, outperforming the best STDP configurations by 23.66 and 23.29 percentage points, respectively. Across the encodings tested, including CNN-extracted features, SADP outperforms STDP in the large majority of cells and trains 1.47x faster on average, with up to 2.86x speedup under Poisson inputs. These results position Supervised SADP as a stable, efficient, gradient-free alternative to reward-modulated STDP for supervised SNN learning.

Abstract

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