Parallel Memristive-Friendly Reservoirs for Gradient-Free Long-Sequence Classification

Can a highly efficient sequence model remain competitive when none of its feature-producing weights are optimized? We introduce memristive-friendly parallelized reservoirs (MARS), a deep reservoir architecture whose dynamics are derived from a potentiation–depression model of memristive devices. MARS removes the dense recurrent matrix, reformulates the resulting input-dependent recurrence as an associative parallel scan, and stacks fixed, randomly initialized blocks through subtractive skip connections. All reservoir and encoder weights are sampled once and remain frozen; only a linear readout is trained with ridge regression. Training therefore requires neither gradient descent nor backpropagation through the reservoir. Despite this restriction, MARS is competitive with fully trained sequence models, including Mamba and LinOSS, on six long-sequence time-series classification datasets. It attains the highest mean accuracy on two datasets and a higher mean accuracy than Mamba on five of six. For fixed hyperparameters, MARS trains in $0.2$–$1.6$ seconds. Based on the reported times, this is approximately $54$–$390\times$ faster than the fastest gradient-trained baseline with reported timing on each dataset and $201$–$13,780\times$ faster than Mamba. MARS also provides an approximately $21\times$ forward-pass speedup over an already lightweight echo state network on long sequences. These results show that deep, partially random dynamical systems can achieve competitive accuracy with exceptionally fast model fitting. Because its local state update is derived from memristive potentiation and depression, MARS also offers a starting point for future implementations on memristive and in-memory hardware.