Polychronous Wave Computing: Timing-Native Address Selection in Spiking Networks

TL;DR

The operating envelope imposed by phase wrapping and mutual coherence, and collapse timing jitter, static phase mismatch, and dephasing are derived into a single effective phase-noise budget whose induced winner--runner-up margin predicts boundary-first failures and provides an intensity-only calibration target.

Abstract

Spike timing offers a combinatorial address space, suggesting that timing-based spiking inference can be executed as lookup and routing rather than as dense multiply--accumulate. Yet most neuromorphic and photonic systems still digitize events into timestamps, bins, or rates and then perform selection in clocked logic. We introduce Polychronous Wave Computing (PWC), a timing-native address-selection primitive that maps relative spike latencies directly to a discrete output route in the wave domain. Spike times are phase-encoded in a rotating frame and processed by a programmable multiport interferometer that evaluates K template correlations in parallel; a driven--dissipative winner-take-all stage then performs a physical argmax, emitting a one-hot output port. We derive the operating envelope imposed by phase wrapping and mutual coherence, and collapse timing jitter, static phase mismatch, and dephasing into a single effective phase-noise budget whose induced winner--runner-up margin predicts boundary-first failures and provides an intensity-only calibration target. Simulations show that nonlinear competition improves routing fidelity compared with noisy linear intensity readout, and that hardware-in-the-loop phase tuning rescues a temporal-order gate from 55.9% to 97.2% accuracy under strong static mismatch. PWC provides a fast routing coprocessor for LUT-style spiking networks and sparse top-1 gates (e.g., mixture-of-experts routing) across polaritonic, photonic, and oscillator platforms.

Figures (7)

• Figure 1: Polychronous wave computing for LUT-style spiking. (a) Computational abstraction: a LUT-SNN layer maps spike times $\{t_j\}_{j=1}^{N}$ (latency vector $x$) to discrete addresses $H_i(x)\in\{1,\ldots,K\}$, retrieves synaptic vectors $S_i[H_i(x)]\in\mathbb{R}^{D}$, and accumulates $y=\sum_i S_i[H_i(x)]$. (b) Physical realization: spike times are encoded as phases $\phi_j=\Omega t_j$ ($\Omega$ is an engineered reference (beat) frequency) within a wrap-free window $T_{\mathrm{wrap}}=2\pi/\Omega$; programmable complex couplings $J_{jk}=|J_{jk}|\mathrm{e}^{\mathrm{i}\theta_{jk}}$ evaluate all $K$ candidates by interference to produce amplitudes $\{\Psi_k\}$; driven--dissipative mode competition implements WTA selection, yielding a single discrete address $k^\ast$. (c) Device-system-level cartoon: temporally encoded inputs drive a programmable interference network whose outputs feed an output-node layer embedded in a shared reservoir (shaded red irregular region); nonlinear competition selects a single winning output, which is forwarded to a downstream switch (router) that activates one selected expert (hard MoE routing). Wave motifs indicate coherent pulses and relative phase accumulation; they are schematic and do not represent resolved optical oscillations.
• Figure 2: Robustness comparison of interferometric LUT discrimination. Linear log-margin $\Delta=\log\!(I_{\mathrm{true}}/I_{\mathrm{wrong}})$ versus timing jitter $\sigma_t$ for $K=8$ templates and $N=32$ input spikes; the gray band marks the decision boundary $\Delta=0$. Blue/orange points show Monte Carlo means $\pm$ SEM over $5$ independent template banks and $200$ trials per class (ideal interferometer $\sigma_\theta=0$; static per-coupling phase disorder $\sigma_\theta=0.2~\mathrm{rad}$). Solid black curves show a semi-analytic coherence-decay model for the log-margin under phase jitter $\sigma_\phi=\Omega\sigma_t$. Using $\mathbb{E}[I_{\rm true}]=N+N(N-1)e^{-\sigma_\phi^2}$ and absorbing the competitor baseline into a fitted offset, we plot $\Delta_{\rm th}(\sigma_t)=\log\!(1+(N-1)e^{-\alpha\sigma_\phi^2})-\log N+\Delta_0$, with $(\alpha,\Delta_0)$ fitted separately for the diverse and crowded regimes. (a) Diverse templates (i.i.d. uniform times; $K_{\mathrm{eff}}^{\mathrm{spec}}=7.25\pm0.11$): disorder has negligible effect and the zero-crossing remains near $\sigma_t\simeq 43~\mathrm{ps}$. (b) Crowded templates (sorted times within each pattern; $K_{\mathrm{eff}}^{\mathrm{spec}}=1.13\pm 0.03$): disorder shifts the zero-crossing from $\sim11.6~\mathrm{ps}$ to $\sim7.2~\mathrm{ps}$ (a $4.4~\mathrm{ps}$ operating-window reduction). Template diversity, quantified by $K_{\mathrm{eff}}^{\mathrm{spec}}$, acts as a robustness knob.
• Figure 3: Multi-port nonlinear selection: scoring $\rightarrow$ seeded competition $\rightarrow$ discrete address. (A) Time-to-phase encoding (wrap-free). A representative trial with $N=40$ input spikes mapped to phases $\phi_j=\Omega t_j$ within a wrap-free window $\Delta t_{\max}<T_{\mathrm{wrap}}$. (B) Interferometric template scores. Complex scores for all $K=6$ candidates, $\Psi_k=\sum_{j=1}^{N} J_{jk}e^{-i\Omega t_j}$ (with $J_{jk}=|J_{jk}|e^{i\theta_{jk}}$); the winner $k^\ast$ is highlighted. (C) Zoom on non-winners. Magnified view of the small-magnitude competing phasors near the origin. (D) Decision score after digitization. Bar plot of readout scores showing strong suppression of non-winners (inset: zoom of all candidates); the reported address is $\hat{k}=\arg\max_k I_k(t_{\mathrm{read}})$. (E) Early-time WTA dynamics. Seeded gain competition amplifies the leading mode and suppresses the others, showing the evolution of $I_k(t)=|\psi_k(t)|^2$ (inset: zoom of non-winner trajectories). (F) Operating envelope. Accuracy over timing jitter $\sigma_t/T_{\mathrm{wrap}}\in[0,0.5]$ and static phase disorder $\sigma_\theta\in[0,1.2]$ rad for $K=6$, $N=10$ on a $41\times41$ grid with $1000$ samples per pixel (trials $\times$ device realizations). Left: linear readout accuracy $P_{\mathrm{linear}}$ from the seed intensities $I_k^{(\mathrm{lin})}=|\Psi_k|^2$ (with multiplicative readout noise); middle: WTA readout accuracy $P_{\mathrm{WTA}}$ from the winner of the driven--dissipative competition model (Eq. \ref{['eq:dd_wta_revised']}); right: $\Delta P=P_{\mathrm{WTA}}-P_{\mathrm{linear}}$, with markers indicating pixels where WTA provides a statistically significant advantage (criterion in the Supplemental Material). The star marks the operating point used in (A--E).
• Figure 4: Temporal-order comparator as a one-bit primitive. Two input pulses $A$ and $B$ excite a four-mode junction at times $t_A$ and $t_B$, producing left/right output intensities $|\psi_{L,R}(t)|^2$. The junction routes energy predominantly left for $t_A<t_B$ (a) and right for $t_B<t_A$ (b). The decision uses integrated readout energies $E_{L,R}=\int_{t_0}^{t_0+T}|\psi_{L,R}(t)|^2\,dt$ (shaded window), yielding bit $b_{AB}=\mathbbm{1}[E_L>E_R]$ and margin $m_{AB}=\log(E_L/E_R)$. The simulations use the linear regime of the four-mode model ($U=0$). Parameters and disorder realizations are in Supplement Sec. S4.
• Figure 5: Interferometric polychrony: three-spike permutation decoding via pairwise comparators and cycle repair.(a) Column-normalized confusion matrix for classifying the $3!=6$ temporal permutations of three input pulses $(A,B,C)$ using three pairwise temporal-order comparators (AB, BC, AC). Each comparator simulates the four-mode junction primitive and integrates the readout intensities over a fixed window to obtain $E_{L,R}=\int_{t_0}^{t_0+T_w}\! I_{L,R}(t)\,dt$ (with $t_0=\max(t_X,t_Y)+2\sigma$ and $T_w=6\sigma$), returning a bit $b_{XY}=\mathbbm{1}[E_L>E_R]$ and signed margin $m_{XY}=\log\!\bigl[(E_L+\epsilon)/(E_R+\epsilon)\bigr]$ with $\epsilon=10^{-12}$. The three bits form a tournament code $(b_{AB},b_{BC},b_{AC})$; cyclic codes are repaired by flipping the weakest comparison, i.e. the bit associated with $\arg\min\{|m_{AB}|,|m_{BC}|,|m_{AC}|\}$, after which the repaired code is decoded to a permutation. Color scale uses symmetric logarithmic normalization to reveal small off-diagonal values. (b) Distribution of the minimum absolute margin $|m|_{\min}=\min(|m_{AB}|,|m_{BC}|,|m_{AC}|)$ for acyclic (valid) and cyclic (invalid) codes before repair. Cyclic codes concentrate at small $|m|_{\min}$, indicating that invalid codes predominantly occur near decision boundaries. Unless noted otherwise, $200$ trials are generated per permutation (seed $42$) by jittering the two inter-spike gaps as $g_{1,2}=\Delta t\,(1+0.10\,\mathcal{N}(0,1))$ with a minimum separation $\mathrm{min\_sep}=0.4$, forming ordered times $(t_1,t_2,t_3)=(t_{\mathrm{ref}},t_{\mathrm{ref}}+g_1,t_{\mathrm{ref}}+g_1+g_2)$, and assigning them to $(t_A,t_B,t_C)$ according to the target permutation. Comparator parameters are given in Supplement Sec. S4.