Local Pheromone Network: Sparse Local Learning with Multi-Scale Synaptic Trails, Consolidation, and Replay

Spiking Neural Networks (SNNs) provide a promising framework for energy-efficient and biologically grounded computation; however, scalable learning in deep recurrent architectures with sparse connectivity remains a major challenge. In this work, we propose a structured multi-layer recurrent SNN architecture composed of locally dense recurrent layers augmented with sparse small-world long-range projections to a readout population. The long-range connectivity is largely fixed, preserving routing efficiency and hardware scalability, while synaptic adaptation is performed using strictly local plasticity mechanisms. To enable supervised learning without backpropagation or surrogate gradients, we introduce a biologically motivated learning framework that combines: (i) population-based winner-take-all (WTA) teaching signals at the output layer, (ii) fixed random broadcast alignment feedback pathways, and (iii) low-dimensional modulatory neuron populations that gate synaptic updates through three-factor learning rules with eligibility traces. This design supports deep recurrent computation with sparse global communication and purely local synaptic updates. We analyze the algorithmic properties, computational complexity, and hardware feasibility of the proposed approach, and demonstrate stable learning and competitive performance on benchmark classification tasks. The results highlight the potential of structured recurrence and neuromodulatory learning to enable scalable, hardware-compatible SNN training beyond gradient-based methods.

A Noise-modulated Neural Network (NNN) learns and infers only in the presence of noise, treating noise as a computational resource rather than a disturbance. The noise lets it learn efficiently by backpropagation while transmitting spike-like signals, but backpropagation needs a reverse path through transposed weights, the weight transport problem, which undermines biological and neuromorphic plausibility. Forward-only alternatives typically substitute a different objective or fixed random feedback, sacrificing stability and accuracy. We show that backpropagation itself can be reconstructed in the NNN from forward-pass statistics alone: a weight mirror estimates each weight matrix from the covariance between a previous-layer unit's output and the next-layer unit's input, and combining it with local differential estimation inside the units propagates the output error recursively along the computational graph, with no transposed-weight readout and no backward data path. The resulting gradient is empirically near-unbiased, and with local per-weight Adam updates it matches the final accuracy of backpropagation on simple regression tasks. With uniformly distributed noise, the local operations reduce to polynomials and comparators, making the whole system, learning rule included, well suited to digital circuits. Thus, in the NNN, noise is a resource not only for inference but also for reconstructing backpropagation.

The brain learns abstract representations of high-dimensional sensory input, but the plasticity rules that enable such learning are unknown. We study biologically plausible algorithms on the Random Hierarchy Model (RHM), an artificial dataset designed to investigate how deep neural networks learn the intrinsic hierarchical structure of high-dimensional data. We focus on two types of local learning rules that avoid both a long convergence time and the use of a symmetric error network. The first type uses direct feedback signals to approximate error propagation from the output layer. The second type uses layerwise self-supervised contrastive or non-contrastive loss functions that do not explicitly approximate errors at the output layer. We show that all rules of the first type fail to solve the tasks of the RHM and trace this failure back to input-specific nonlinearities (`masking') that are implemented in full backpropagation and are essential for learning complex tasks. However, algorithms of the second type are able to learn the hierarchical hidden structure of the RHM tasks and are as data-efficient as supervised backpropagation training, while being compatible with known rules of synaptic plasticity in cortex.