Dual-Timescale Hebbian Accumulators for Online Spiking Neural Network Decoding in Intracortical Brain Machine Interfaces

1. Problem Statement

Intracortical Brain-Machine Interfaces (BMIs) face a critical trade-off between decoding accuracy and online adaptability under strict hardware constraints:

• Signal Instability: Neural signals recorded via Utah arrays degrade over time due to electrode encapsulation, micromotion, and neural plasticity. This necessitates continuous, real-time decoder adaptation.
• Memory Constraints: Implantable devices have severe memory and power budgets.
• Current Limitations:
  • Recurrent Neural Networks (LSTM/GRU): Achieve high accuracy but require Backpropagation Through Time (BPTT), which demands $O(T)$ activation memory (growing with sequence length) and batch retraining, making them unsuitable for long-term, memory-constrained implants.
  • Linear Filters (Kalman Filters): Adapt online with constant memory but fail to capture the non-linear temporal structures of intracortical signals.
  • Existing SNNs: Often rely on global optimizers (Adam) or replay buffers, which are computationally expensive and incompatible with true online, per-timestep learning on neuromorphic hardware.

The Gap: There is no existing method that provides nonlinear temporal modeling, per-timestep online updates, and constant memory usage (independent of sequence length) without adaptive gradient optimizers.

2. Methodology

The authors propose a Dual-Timescale Hebbian Accumulator learning rule for Spiking Neural Networks (SNNs) designed for online BMI decoding.

A. Network Architecture

• Model: A three-layer Leaky Integrate-and-Fire (LIF) network.
• Input: Raw spike count vectors from intracortical electrodes (no rate normalization).
• Output: 2D velocity predictions ($\hat{y}_t$).
• Recurrence: The first hidden layer contains recurrent connections to capture temporal dynamics.
• Surrogate Gradient: Since the Heaviside spike function is non-differentiable, a fast sigmoid surrogate is used locally to estimate neuronal sensitivity ($d_{LIF}$) without unrolling a computational graph.

B. The Learning Rule: Dual-Timescale Hebbian Accumulation

The core innovation replaces BPTT with a local, three-factor learning rule that accumulates updates over time using two distinct eligibility traces:

1. Three-Factor Update:
   Plasticity is driven by the coincidence of:

   • Presynaptic activity ($pre_t$).
   • Postsynaptic sensitivity ($d_{LIF}$).
   • Layer-local error signal ($\tilde{e}_t$), computed via weight-transpose propagation and RMS normalization.
     $$\Delta W_{hebb} = (\tilde{e}_t \odot d_{LIF}) \cdot pre_t^T$$

2. Dual Eligibility Traces:
   Instead of applying $\Delta W_{hebb}$ immediately, each synapse accumulates it in two traces with different decay timescales:

   • Fast Trace ($E_{fast}$): Captures recent updates for rapid adaptation to abrupt changes.
   • Slow Trace ($E_{slow}$): Averages over a longer history to preserve stable structural knowledge.
   • Combination: $E_{comb} = \alpha E_{fast} + (1-\alpha) E_{slow}$.

3. Update Mechanism:

   • Fast Update: Applied every timestep using the combined trace for immediate adaptation.
   • Slow Consolidation: A momentum-smoothed accumulator ($G$) is updated continuously. Every $K$ timesteps, a slow weight update is applied to $G$ to stabilize the weights.

C. Stability and Hardware Efficiency

• RMS Homeostasis: An integer-friendly Root Mean Square (RMS) normalization is applied to error signals and pre-synaptic activities using exponential moving averages and a lookup table. This prevents gradient explosion/vanishing without adaptive optimizers (like Adam).
• Weight Projection: L2 norms of incoming weights are checked against a threshold; exceeding weights are rescaled using bitshift operations (power-of-two division) to maintain stability on neuromorphic hardware.
• Memory Complexity: The method stores only fixed-size buffers (parameters + traces), resulting in $O(P)$ memory (where $P$ is parameter count), completely independent of sequence length $T$. This eliminates the $O(T)$ activation storage required by BPTT.

3. Key Contributions

1. Dual-Timescale Hebbian Rule: Introduces a learning rule that replaces BPTT with synapse-specific fast and slow eligibility traces, enabling constant-memory online learning.
2. Hardware-Optimized Implementation: Utilizes bitshift RMS homeostasis and integer-friendly operations, removing the need for adaptive gradient optimizers (Adam/RMSProp) and replay buffers.
3. Comprehensive Evaluation: Validated on two primate intracortical datasets (MC Maze and Zenodo Indy) and closed-loop simulations, demonstrating robustness to neural disruptions and the ability to learn from scratch without offline calibration.

4. Experimental Results

A. Offline Decoding Performance

• Datasets: MC Maze (Macaque, 182 channels) and Zenodo Indy (Macaque, 96 channels).
• Metrics: Pearson Correlation ($R$) between predicted and true velocity.
• Performance:
  • MC Maze: $R \ge 0.81$ (Online SNN) vs. $R \approx 0.90$ (BPTT-SNN).
  • Zenodo Indy: $R \ge 0.63$ (Online SNN) vs. $R \approx 0.68$ (BPTT-SNN).
  • Comparison: The Online SNN outperforms Kalman Filters significantly ($+0.22$ on Zenodo) and approaches the performance of LSTM/GRU models, despite lacking adaptive optimizers and multi-step gradient flow.

B. Memory Efficiency

• Reduction: At sequence length $T=1000$, the Online SNN achieves 63–86% memory reduction compared to BPTT.
• Scalability: Memory usage remains constant as $T$ increases, whereas BPTT memory grows linearly.

C. Closed-Loop Adaptation

• Disruption Recovery: In simulations involving 90% neuron remapping, drift, or dropout, the Online SNN recovered to pre-disruption performance within 15–20 reaches.
• Baseline Failure: Fixed-parameter decoders (LSTM, BPTT-SNN, Kalman) remained impaired (time-to-target > 1.5s) after disruptions.
• Learning from Scratch: The Online SNN could learn to control a cursor from random initialization using only self-generated data, whereas other decoders required offline batch retraining to achieve similar performance.

D. Ablation Studies

• Dual-Timescale: Essential for robustness; single timescales were optimal for one dataset but suboptimal for the other. The dual configuration provided near-optimal performance across both.
• Synapse-Specific vs. Factorized: Synapse-specific traces ($O(N^2)$) outperformed neuron-level factorized traces ($O(N)$) by ~0.06–0.08 in correlation, highlighting the importance of distinct temporal dynamics for heterogeneous electrode inputs.
• Three-Factor Rule: Crucial for datasets with broad error signals (Zenodo), acting as a "gating" mechanism to confine plasticity to moments when neurons are near threshold.

5. Significance and Conclusion

This work bridges the gap between high-accuracy deep learning and the strict constraints of implantable BMIs.

• Clinical Relevance: It offers a path toward self-calibrating, adaptive BMIs that do not require daily offline recalibration sessions, a major burden in current clinical systems (e.g., BrainGate).
• Hardware Viability: By removing BPTT and adaptive optimizers, the method is directly deployable on low-power neuromorphic chips (e.g., Loihi), enabling continuous, lifelong adaptation to neural signal drift.
• Trade-off: The authors acknowledge a moderate offline accuracy gap (~13–18%) compared to BPTT-trained models due to the lack of per-parameter adaptive learning rates and temporal credit assignment. However, they argue this trade-off is acceptable and necessary for the online adaptability required in real-world, long-term neural implants.

In summary, the proposed Dual-Timescale Hebbian Accumulator provides a theoretically grounded, memory-efficient, and experimentally validated solution for continuous, online decoding in intracortical BMIs, paving the way for more robust and user-friendly neuroprosthetics.