Positional Encoding in the Context of Memristor-Based Analog Computation for Automatic Speech Recognition

Reservoir computing (RC) is an emerging recurrent neural network architecture that has attracted growing attention for its low training cost and modest hardware requirements. Memristor-based circuits are particularly promising for RC, as their intrinsic dynamics can reduce network size and parameter overhead in tasks such as time-series prediction and image recognition. Although RC has been demonstrated with several memristive devices, a comprehensive evaluation of device-level requirements remains limited. In this paper, we analyze and explain the operation of a parallel delayed feedback network (PDFN) RC architecture with volatile memristors, focusing on how device characteristics -- such as decay rate, quantization, and variability -- affect reservoir performance. We further discuss strategies to improve data representation in the reservoir using preprocessing methods and suggest potential improvements. The proposed approach achieves 95.89% classification accuracy on MNIST, comparable with the best reported memristor-based RC implementations. Furthermore, the method maintains high robustness under 20% device variability, achieving an accuracy of up to 94.2%. These results demonstrate that volatile memristors can support reliable spatio-temporal information processing and reinforce their potential as key building blocks for compact, high-speed, and energy-efficient neuromorphic computing systems.

Standard positional encodings for transformers - sinusoidal and rotary (RoPE) - treat every position as equally local: they encode where a token is, but not how far its positional influence should extend. We propose that the Morlet wavelet, which simultaneously minimises uncertainty in position and frequency, is the natural basis for positional encoding, and introduce Morlet Positional Encoding (MoPE): each embedding dimension learns its own frequency and locality bandwidth from data. The main theoretical result is a unification: sinusoidal PE and the RoPE correlation kernel both emerge as limiting cases of MoPE when locality is switched off (sigma_i -> infinity). The phase of MoPE recovers the RoPE rotation angle exactly; the amplitude adds a learned Gaussian locality kernel that standard encodings lack. Empirically, MoPE combined with Energy-Gated Attention achieves +0.119 improvement over standard attention on TinyShakespeare, outperforming either component alone. Analysis of the learned parameters reveals that all 128 frequency-bandwidth pairs converge to the wavelet admissibility boundary - an empirical observation consistent with a companion result on energy gating, suggesting a reproducible property of character-level language signals that warrants further investigation.

The mismatch between continuous acoustic signals and discrete event-driven processing remains a fundamental bottleneck for neuromorphic speech processing. Current systems typically rely on fixed spike encoders, forcing downstream Spiking Neural Networks (SNNs) to compensate for non-adaptive input representations. To address this, we present a learnable residual speech-to-spike encoder jointly trained end-to-end with a Recurrent Leaky Integrate-and-Fire (R-LIF) backbone. We validate this approach on the Google Speech Commands v2 (GSC-v2) benchmark, achieving up to 94.97% accuracy. Notably, the learned encoder remains highly parameter-efficient with a compact 35k-parameter variant that reaches 89.8%, matching or exceeding prior baselines that require an order of magnitude more parameters. Our encoder-focused analysis, including linear probing and gradient-residual inspection, indicates that the encoder does not target faithful signal reconstruction but instead learns task-aligned spike representations that enhance class separability. Finally, we benchmark bio-inspired, hardware-friendly credit assignment by comparing Direct Feedback Alignment (DFA) with surrogate-gradient BPTT under identical architectures and training conditions. We find that DFA reaches 91.5% accuracy, quantifying the performance trade-off of bio-inspired learning rules for modern neuromorphic audio.