It is proved that two canonical local synaptic learning rules, the potentiation arm of spike-timing-dependent plasticity and homeostatic plasticity and homeostatic plasticity together can implement the exact gradient of a SIGReg-like self-supervised learning objective.
Abstract
We prove that two canonical local synaptic learning rules, the potentiation arm of spike-timing-dependent plasticity (STDP$^+$) and homeostatic plasticity (instantiated here via flashlight granule-cell-like neurons), together can implement the exact gradient of a SIGReg-like self-supervised learning objective. The equivalence requires no gradient calculations, no global error signals, no weight transport, and no label information: the only inputs are pre- and post-synaptic firing rates, local firing statistics, and the temporal contiguity of natural sensory streams. On a synthetic clustering task designed to probe whether class structure can be recovered from temporal ordering of inputs alone, ordered presentation raised cluster separation (CSR) to 2.49 while random ordering left it near baseline (0.83), a roughly threefold ($\approx 3.5\sigma$) separation attributable solely to input ordering. On temporally ordered MNIST, a two-layer network trained entirely with these rules achieved 87.3% linear-probe accuracy, showing that the mechanism functions end-to-end.
Componentwise weak convergence of signed synaptic kernels does not, by itself, determine the fast-synapse limit of a sparse threshold-reset network. Within a causal event protocol with clamped refractoriness and smooth positive-delay kernels, we construct two families whose excitatory and inhibitory measures converge weakly to $\delta_0$ while their microscopic arrival orders are reversed. A target fires in the excitatory-first family and not in the inhibitory-first family precisely when $x+a-b<\theta\le x+a$. Strict margins preserve this response under perturbations of the target state, aggregate E/I pulse masses, and bounded drift. The macroscopic effect persists on a moderately sparse Dale-compatible random block graph with $q_N\to\infty$ and $q_N/N\to0$. The two systems share their graph and initial data. Along every deterministic joint scale $\varepsilon_N\downarrow0$, their population-averaged firing counts differ by $1/2+o_{L^1}(1)$. A bounded-degree construction and a later probe show that the discrepancy is macroscopic and can persist through reset. Fixed positive-delay kernels with finitely many classes admit a stable regime. Before grazing, typewise-mixing sparse networks converge to a delayed class mean-field system. Directed Erdos-Renyi graphs yield the bound $O_P(\lambda_N^{-1/2}+\|\pi_N-\pi\|_1)$ when $\lambda_N\to\infty$ and $\lambda_N/N\to0$. This separates stable averaging at a fixed delay from singular collapse. In the latter, componentwise weak convergence discards signed arrival-order information needed by the threshold-reset response.
This work presents a Hebbian local learning rule that models synaptic modification as a function of calcium traces tracking neuronal activity and demonstrates how spike timing and rate can be complementary in their role of shaping the connectivity of spiking neural networks.
Willian Soares Girāo, Nicoletta Risi, Caroline Geisler et al.· Neuromorphic Computing and E...· 0 citations
Findings show the impact of inference stage design decisions in STDP-based SNN-VPR on recall precision, although the separate contribution of each mechanism and implementation differences is only partially disentangled and needs further examination.
A DA-modulated STDP rule is proposed in which increasing DA progressively biases plasticity toward potentiation while receptor saturation limits further DA effects beyond a critical concentration, providing a biologically grounded model of DA-dependent plasticity and offering new insight into how abnormal dopamine signaling can impair learning in neurological disorders.
Biological intelligence naturally prevents catastrophic forgetting through Complementary Learning Systems (CLS) theory, a macroscopic consolidation process driven at the local level by synaptic metaplasticity: the continuous, history-dependent neuromodulation of individual synapses. While artificial neural networks struggle with the stability-plasticity dilemma in non-stationary environments, existing solutions often require task labels or incur massive memory overhead, diverging from biological reality. Re-framing this localized neuromodulation as an optimization-driven process, we introduce $\textbf{SynGAP}$: $\textbf{Syn}$aptic $\textbf{G}$eometric $\textbf{A}$daptive $\textbf{P}$reconditioning. SynGAP is a task-free continual learning framework based on adaptive gradient preconditioning. Rather than relying on explicit episodic triggers, SynGAP simulates real-time metaplasticity by maintaining an exponential moving average of the Fisher Information Matrix over a continuous data stream. During the optimization step, these dynamic metaplastic states are translated into a bounded multiplicative mask that preconditions raw gradients, selectively attenuating updates to critical historical parameters. Empirical evaluations demonstrate SynGAP's superior ability to mitigate catastrophic forgetting compared to established baselines. On the Split CIFAR-100 benchmark, SynGAP delivers a $4\times$ increase in accuracy compared to EWC++ and outperforms Experience Replay (ER) by almost $10\%$, while reducing the forgetting measure by over $10\%$ against both methods. Furthermore, on the CORe50 benchmark, SynGAP achieves about $68\%$, a $10\%$ improvement over optimizer baselines. By mathematically formalizing continuous biological metaplasticity as stable gradient-based regularization, SynGAP offers a highly robust and memory-efficient solution for adaptive intelligence at the edge.
Isabelle Aguilar, Zayn Andre Zainal, Omid Kavehei· 0 citations
This work studies the mean-field limit of large networks of interacting stochastic leaky integrate-and-fire (LIF) neurons subject to short-term synaptic depression (STD). The macroscopic dynamics of this system is governed by a two-dimensional, non-linear McKean-Vlasov equation that couples the evolution of the neurons'membrane potentials with a synaptic depression variable. We investigate the long-time behavior of this limit system. To this end, we introduce an auxiliary linearized Markov process by freezing the interaction non-linearity to a constant. By exploiting the regeneration of the membrane potential at spike times, we are able to explicitly compute the conditional expectation of the synaptic depression variable, conditionally on the potential value, under the invariant measure of this two-dimensional linear process. This is a crucial ingredient to study time-dependent local perturbations thereof. As a consequence we are able to identify an analytic criterion guaranteeing the local stability of any invariant probability measure of the fully non-linear system. This stability criterion is formulated in terms of the zeros of the Laplace transform of a specific linear response function. Finally, we provide numerical examples demonstrating that the two-dimensional framework induces a richer spectrum of long-time dynamics than purely one-dimensional models. For example, synaptic depression can lead to low-frequency oscillations around a unique, unstable invariant measure where the oscillations are much slower than the neurons'firing rates.
Q. Cormier, Eva Löcherbach, Valentin Schmutz· 0 citations