local-synaptic-rules-sigreg-gradient

name	local-synaptic-rules-sigreg-gradient
description	Local synaptic learning rules (STDP+ and homeostatic plasticity) can implement exact SIGReg-like self-supervised learning gradients without backpropagation, global error signals, or weight transport.
version	1.0.0
author	Hermes Agent
license	MIT
metadata	{"hermes":{"tags":["neuroscience","spiking-neural-networks","synaptic-plasticity","gradient-learning","biologically-plausible"],"related_skills":["spiking-neural-network-analysis","stdp-bernoulli-message-passing","feedback-hebbian-continual-learning"]}}

Local Synaptic Rules Implement SIGReg Gradient

This skill implements the methodology from arXiv:2607.21622 "Local Synaptic Rules Can Implement a SIGReg Gradient Without Backpropagation" by Martin Andrews.

Core Insight

Two canonical local synaptic learning rules together can implement the exact gradient of a SIGReg-like self-supervised learning objective:

1. Potentiation arm of spike-timing-dependent plasticity (STDP⁺)
2. Homeostatic plasticity (instantiated via flashlight granule-cell-like neurons)

This equivalence requires:

• No gradient calculations
• No global error signals
• No weight transport
• No label information
• Only inputs: pre- and post-synaptic firing rates, local firing statistics, and temporal contiguity of natural sensory streams

Implementation Steps

1. Network Architecture Setup

# Two-layer network with appropriate neuron models
# Input layer: sensory neurons with temporal ordering
# Hidden layer: neurons with STDP⁺ and homeostatic plasticity

2. STDP⁺ Rule Implementation

# Potentiation-only STDP rule
def stdp_potentiation(pre_spike_time, post_spike_time, A_plus, tau_plus):
    if post_spike_time > pre_spike_time:  # Causal relationship
        delta_t = post_spike_time - pre_spike_time
        return A_plus * exp(-delta_t / tau_plus)
    return 0

3. Homeostatic Plasticity Implementation

# Flashlight granule-cell-like homeostatic mechanism
def homeostatic_plasticity(firing_rate, target_rate, eta_homeo):
    return eta_homeo * (target_rate - firing_rate)

4. Combined Weight Update Rule

def combined_update_rule(weight, pre_rate, post_rate, local_stats, temporal_context):
    # STDP⁺ component based on spike timing
    stdp_component = compute_stdp_potentiation(pre_rate, post_rate, temporal_context)
    
    # Homeostatic component based on firing rate deviation
    homeo_component = homeostatic_plasticity(post_rate, target_rate, eta_homeo)
    
    # Total weight change implements SIGReg gradient
    delta_weight = stdp_component + homeo_component
    
    return weight + learning_rate * delta_weight

5. Temporal Ordering Requirement

• Input presentation must preserve temporal contiguity of natural sensory streams
• Random ordering fails to recover class structure
• Ordered presentation enables cluster separation through temporal statistics alone

Validation Tasks

Synthetic Clustering Task

• Purpose: Probe whether class structure can be recovered from temporal ordering alone
• Metric: Cluster Separation Ratio (CSR)
• Expected Results:
  • Ordered presentation: CSR ≈ 2.49 (≈3.5σ separation)
  • Random ordering: CSR ≈ 0.83 (near baseline)

Temporally Ordered MNIST

• Architecture: Two-layer network trained entirely with local rules
• Evaluation: Linear-probe accuracy on learned representations
• Expected Result: ~87.3% accuracy

Biological Plausibility Advantages

1. No weight transport problem: Updates use only locally available information
2. No global error signals: Learning driven by local firing statistics and temporal contiguity
3. Biologically realistic mechanisms: Uses established synaptic plasticity rules
4. Self-supervised: No labels required, learns from natural temporal structure

Applications

• Biologically plausible deep learning: Bridge between neuroscience and AI
• Neuromorphic hardware: Energy-efficient learning without backpropagation
• Unsupervised representation learning: Extract structure from temporal data streams
• Continual learning: Natural integration with online learning scenarios

Activation Keywords

• local synaptic rules
• STDP gradient learning
• biologically plausible backpropagation
• SIGReg without backprop
• temporal ordering clustering
• homeostatic plasticity gradient

References

• Andrews, M. (2026). Local Synaptic Rules Can Implement a SIGReg Gradient Without Backpropagation. arXiv:2607.21622
• Original SIGReg framework: Self-supervised learning through temporal prediction
• Biological STDP: Caporale & Dan (2008), Markram et al. (1997)
• Homeostatic plasticity: Turrigiano (2012), Zenke et al. (2013)