Online dynamical learning and sequence memory with neuromorphic nanowire networks

Neuromorphic computing seeks brain-inspired architectures for efficient information processing. Beyond CMOS spiking implementations, an alternate approach exploits the intrinsic, brain-like physical properties of nanomaterials, particularly memristive switching. This work focuses on memristive nanowire networks (NWNs), which comprise metal nanowires forming heterogeneous, recurrent networks with junctions that undergo electrochemically driven conductance changes. NWNs exhibit collective, brain-like dynamics (e.g., switching synchronisation and avalanche criticality) and can project temporal inputs into rich, high-dimensional dynamical feature spaces suitable for reservoir computing (RC). While prior physical RC studies typically used batch (offline) training of readout weights after full input delivery—requiring retraining under distribution shifts—online training can adapt readout weights incrementally to non-stationary features and support continual learning. Here, the research objective is to demonstrate online dynamical learning with an NWN device using streams of dynamical features for (i) MNIST digit classification and (ii) a sequence memory recall task, and to analyse learning using information-theoretic measures.

Previous experimental and simulation studies established that NWNs possess fading memory and effectively embed temporal inputs into higher-dimensional feature spaces, enabling their use as physical reservoirs. Batch-trained readouts on physical reservoirs have limitations with evolving feature distributions. Online approaches promise better adaptability. Prior NWN simulation work achieved MNIST classification (e.g., Milano et al. reported 90.4% with a simulated NWN mapped to a ReRAM array), while other memristor crossbar reservoirs reported lower accuracies; NWN simulations reached ~98% with preprocessing or deep architectures. Information-theoretic analyses (e.g., mutual information, transfer entropy, active information storage) have been used to characterise learning dynamics in reservoirs and ANNs, motivating the MI-based analysis here. Sequence memory and attractor dynamics are well-studied in neuroscience and have been emulated in algorithmic spiking recurrent networks and ReRAM-based systems; this study introduces a hardware NWN sequence memory recall using online learning.

MNIST 28×28 images are normalised and converted to 1-D temporal voltage pulse streams (784 time steps, Δt = 0.001 s per pixel) delivered to a designated source electrode on a 16-electrode NWN multi-electrode array (MEA). Real-time voltage responses are read from other electrodes (e.g., channels 1, 2, 12, 13, 15). Readouts form dynamical features (M×784 per sample) fed to an external linear classifier. Online learning uses a recursive least squares (RLS) algorithm updating the weight matrix W ∈ R^{10×(M·784)} after each sample with the known label as target. For comparison, an offline batch linear classifier is trained via backpropagation with gradient descent (100 epochs, 500 mini-batches of size 100, learning rate η=0.1). Training uses 50,000 MNIST samples; testing uses 10,000 samples, with results averaged over 5 shuffles. Mutual information (MI) between digit classes and channel readouts is estimated per pixel position and averaged across 784 positions, tracking MI evolution over the training stream as well as static MI maps after training. Sequence memory task: a semi-repetitive 8-digit sequence (14751479) is streamed to the NWN similarly. In addition to voltage readouts (e.g., channels 7 and 13), network conductance time series (from measured current/voltage) is recorded, exhibiting delayed dynamics from memristive and recurrent effects. A sliding memory window of length L spans the sequence; the earliest digit in the window is the target to be reconstructed using a linear reconstructor trained online on features comprising voltage readout(s) and conductance-derived memory features from the subsequent L−1 digits. Reconstruction quality is quantified by the Structural Similarity Index Measure (SSIM). A memory exclusion experiment replaces columns of conductance features with voltage features from another channel to quantify the contribution of memory; exclusions are increased in 14-column increments (up to whole digits: 28, 56 columns, etc.). Device fabrication and measurement employ a 4×4 MEA with Ag₂Se nanowire networks and National Instruments instrumentation (data acquisition PXI-6368, source measurement PXI-4141, switch matrix TB-2642).

• Online MNIST classification accuracy (mean over 5 runs, 10,000 test images): 93.4% with 5 readout channels; 91.6% with 1 channel. Offline batch classifier: 91.4% (5 channels); 86.6% (1 channel). Online learning requires a single pass over 50,000 training samples, outperforming batch training despite far fewer epochs.
• Accuracy grows with number of readout channels; largest gain from 1→2 channels; convergence plateaus around ~92% after ~10,000 samples.
• Confusion matrix (5 channels): average 93.4% with s.d. ≈ 3%. Digit '1' highest accuracy 98.4%; lowest accuracies for '5' (89.6%) and '8' (89.5%).
• Learning dynamics: mean |ΔW| (change in weight matrix) peaks between ~10^2–10^3 samples and diminishes by ~10^4, coinciding with MI saturation, indicating learning aligns with information influx from the dataset. MI of input channel is substantially lower than MI of NWN readouts.
• Static MI maps (per class and channel) show distinctive class-dependent information distributions. Total MI per class correlates with per-class accuracy (e.g., highest MI for '1' aligns with highest accuracy; lowest MI for '5' and '8' aligns with lowest accuracies).
• Sequence memory: NWN conductance shows delayed dynamics with ≥2 orders of magnitude dynamic range; I–V phase-space trajectories indicate class- and position-dependent internal states. Reconstruction SSIM increases with memory window length L, saturating around L=5 (matching sequence repetition length). Repeated, simpler digits ('1','7') reconstruct best; digit '5' reconstructs worst, mirroring its classification difficulty. Digit '9' shows an SSIM jump from L=4 to L=5 due to unique subsequence context; '7' shows a jump from L=2 to L=3 linked to memory traces in simpler intervening digits.
• Memory exclusion: Replacing conductance features with memoryless voltage features degrades SSIM; plateaus observed when excluding whole digits (−28, −56 columns). Largest SSIM reductions around ~14, 42, 70 columns indicate central pixels carry most memory traces.

The study demonstrates that an NWN device can serve as a physical reservoir enabling online dynamical learning directly from spatiotemporal device responses. Online RLS training yields higher accuracy and faster convergence than batch gradient descent, leveraging the rich, nonlinear features generated by the recurrent, memristive NWN. MI analyses reveal that learning progress tracks the temporal evolution of information content in device readouts, and that class-wise MI correlates with class-wise accuracy, suggesting channel-specific information specialisation that could be exploited for adaptive channel selection or tuning. The sequence memory experiment further shows that NWN conductance dynamics embed memory patterns akin to attractor-like states, enabling reconstruction (recall) of earlier digits from subsequent inputs; performance scales with contextual window length and degrades when memory features are excised, evidencing that memory enhances learning. Compared to prior work, the achieved online accuracy (93.4%) surpasses several physical reservoir implementations and approaches simulated NWN systems that rely on additional preprocessing or deep architectures. The findings highlight the potential for end-to-end analogue implementations by pairing NWN reservoirs with hardware linear readouts, and suggest broader neuromorphic applications where continual, adaptive learning from non-stationary streams is essential.

This work provides a proof-of-concept that neuromorphic nanowire networks can support online learning from spatiotemporal dynamics for both classification and sequence memory recall. Key contributions include: (i) experimental demonstration of online MNIST classification with an NWN reservoir achieving 93.4% accuracy using five readout channels, outperforming a batch-trained baseline; (ii) information-theoretic characterisation linking learning progress and performance to mutual information in device readouts; and (iii) a novel sequence memory task showing that conductance-based memory patterns enable context-dependent reconstruction and that memory features materially enhance recall quality. Future directions include implementing analogue readout hardware for end-to-end systems, exploiting channel-wise information preferences for task-specific optimisation, scaling to richer sequence tasks (e.g., natural language processing), and developing training strategies that directly leverage and control NWN internal states for improved efficiency and continual learning.

Element-wise information-theoretic analysis within the NWN is constrained by the limited number of available MEA readout channels, precluding fine-grained internal state measurements. The linear readout/reconstructor is implemented externally in digital hardware rather than in-materia, so the system is not fully analogue end-to-end. Classification performance varies across digit classes (e.g., lower performance for '5' and '8'), reflecting variability in input distributions and sensitivity to device-channel dynamics. Sequence memory performance saturates with the repetition length and is influenced by overlap in subsequences and digit complexity.