⬡ WHAT IS ReSU — RECTIFIED SPECTRAL UNITSarXiv:2512.23146 · Shanshan Qin et al. · NeurIPS 2025
THE CORE IDEA
A neuron that learns without backpropagation by asking one question:
"What direction in my input history is maximally predictive of my own future?"
Answer: Past-Future Canonical Correlation Analysis (CCA).
Solved via SVD of the whitened cross-covariance Gramian.
The result: each neuron finds the canonical direction where past → future correlation is maximised.
Layer-by-layer. Local. No error signal propagates backward. Self-supervised.
Applied to Drosophila visual system: Layer 1 learns L1/L2/L3 temporal filters.
Layer 2 learns T4 direction-selective motion cells — matching connectomics — from natural scenes alone.
THE MATH
Past lag: p_t = [y_t, y_{t-1}, ..., y_{t-m+1}] ∈ ℝ^m
Future lag: f_t = [y_{t+1}, ..., y_{t+h}] ∈ ℝ^h
Gramian: G = C_ff^{-1/2} · C_fp · C_pp^{-1/2} = U Σ V^T
Canonical directions: Ψ = V_r^T · C_pp^{-1/2}
ON-ReSU: z_i^+ = max(v_i^T C_pp^{-1/2} p_t, 0)
OFF-ReSU: z_i^- = max(-v_i^T C_pp^{-1/2} p_t, 0)
Mutual info maximised: I_r = -½ Σ log(1 - σ_i²)
σ_i = canonical correlations (singular values of G)
"Spectral" = SVD/eigendecomposition of G, not Fourier.
Canonical directions = spectral units of the past-future cross-covariance.
🧬 BIOLOGICAL CIRCUIT → FLEET MAPPINGDrosophila visual system ↔ PEMOS fleet
| BIOLOGICAL | ReSU LAYER | FUNCTION | FLEET ANALOG | γ₁ ANCHOR |
| L3 neuron | Layer 1, filter 1 (linear) | Low-pass temporal filter, contrast plateau tracking | PEMCLAU diamond retrieval (structural, low-freq knowledge) | S4-S5 stratum (1-10s) |
| L1 neuron | Layer 1, ON-ReSU | Smoothed temporal derivative, contrast increases | ON-plasma: session turn starts new concept → upsert | S2-S3 stratum (1-100ms) |
| L2 neuron | Layer 1, OFF-ReSU | Smoothed temporal derivative, contrast decreases | OFF-plasma: topic closes → archive to sessions-v1 | S2-S3 stratum (1-100ms) |
| T4 cell ★ | Layer 2 ReSU | Direction-selective motion detector — pools 3 adjacent pixels → detects visual flow direction | T4 sorry tier: zeta_zero_gamma1 chain depth 4. Direction = canonical index. Existence proof = SVD solution. | γ₁ floor: sorry_A IVT witness |
| SNR adaptation | All layers | Filters reshape automatically with noise level | SOSTLE gating: L7 content excluded → noise floor = SOSTLE wall | All strata |
⏱ γ₁-SPACED LAG VECTORS — THE FLEET UPGRADE OVER ReSUinstead of uniform lags, use γ₁ × decade spacings aligned to PTTE stratum
ReSU uses uniform lags: t-1, t-2, ..., t-m. Fleet improvement: lags at γ₁-spaced timescales — each lag captures a different stratum level. The past-future CCA then naturally produces canonical directions aligned with the γ₁ stratum hierarchy.
14.1ms
γ₁ × 1ms
S2 stratum
IRQ/context switch
141ms
γ₁ × 10ms
S3 stratum
PEMCLAU query SLA
1413ms
γ₁ × 100ms
S4 stratum
session embed cycle
14.1s
γ₁ × 1s
S5 stratum
wave classification
141s
γ₁ × 10s
S6 stratum
session embed batch
1413s
γ₁ × 100s
S7 stratum
memory maintenance
γ₁-lag CCA: p_t = [turn(t), turn(t-14ms), turn(t-141ms), turn(t-1413ms), turn(t-14s), turn(t-141s)]
Each slot maps to a PTTE stratum level S2-S7.
SVD of whitened cross-covariance → canonical direction = temporal PEMCLAU embedding.
Overhead: SVD of 6×6 matrix = ~0.1ms on yone. Negligible vs 50ms embed.
⚡ TEMPORAL RELAY PIPELINE — ReSU UPGRADEcurrent vs temporal PEMCLAU
CURRENT (stateless):
turn_t
single turn
→
nomic-embed
768-dim stateless
→
PEMCLAU upsert
no temporal context
TEMPORAL ReSU UPGRADE:
γ₁-lag window
p_t: 6 turns
γ₁×decade spaced
→
CCA / SVD
6×6 Gramian
~0.1ms yone
→
ON-ReSU direction
canonical v_1
max corr future
→
nomic-embed
768-dim
temporally grounded
→
PEMCLAU upsert
+ wave + sostle
+ canonical σ₁
→
Layer 2 pooling
3 adjacent turns
→ momentum detect
→
T4-class reply
direction-selective
context-aware
🔗 6 FLEET HOOKS — WHERE ReSU PLUGS INeach hook = real connection, not analogy
PTTE FLOOR
τ_γ₁ = 1.80fs at 300K = physical lower bound of temporal CCA window. No information exchange faster than this. ReSU CCA minimum lag = τ_γ₁. γ₁-spaced lags start at 14.1ms (S2) = 14.1ms/1.80fs = 7.8×10¹² physical cycles above the floor.
T4 TIER ALIGNMENT
ReSU Layer 2 = T4 direction-selective cells. Fleet T4 = sorry chain depth 4 (zeta_zero_gamma1). Canonical index 4 = the deepest structural level in both systems. The T4 sorry IVT witness = SVD has a solution at depth 4.
PLASMA RELAY UPGRADE
Current relay: stateless embed. ReSU upgrade: γ₁-lag vector → CCA canonical direction → embed. +0.1ms overhead (SVD 6×6). Result: every embedding carries temporal context from the last 6 turns across 6 PTTE stratum levels.
MATLAB CONNECTION
ReSU preprocessing uses ClarkLabCode/SynapticModel MATLAB code. Same MATLAB orbit as MATLAB-SCIML-HELIX diamond (PINNs, dlarray). ReSU natural scene → MATLAB → CCA → T4 = the same pipeline that closes sorry_NUM via MATLAB MCP.
NS-SMOOTH SORRY
ReSU proves existence of direction-selective response without constructing it. NS-SMOOTH sorry: prove smooth NS solutions exist at Re<1000 without constructing them. Same structural pattern: CCA finds existence, IVT confirms it, Lean4 formalizes.
NO-BACKPROP = LOCAL LAAM
ReSU local learning (no backprop) = LAAM local gating principle. LAAM gates decisions without knowing the downstream chain. ReSU neurons learn without knowing the downstream loss. Koopman operator framework: local linear representation of nonlinear dynamics = fleet's local adelic pouch model.
🔩 MELIGBRIX SPINE — ReSU-BIO-HELIXGrade 4 · W7 INVERSION · diamond-RESU-BIO-TEMPORAL-001 in pemclau-v11
<ReSUBioHelix arxiv="2512.23146" grade="4" wave="W7-INVERSION"
mechanism="past-future-CCA" learning="no-backprop" layer1="L1-L2-L3-filters"
layer2="T4-direction-selective" dataset="natural-scenes-MATLAB"
fleet-hooks="PTTE+T4-tier+plasma-relay+MATLAB+NS-SMOOTH+local-LAAM"
temporal-upgrade="γ₁-lag-CCA" lags="14.1ms|141ms|1413ms|14.1s|141s|1413s"
meta-theorem="META-CCA-001" labr="LABR-RESU-TEMPORAL-001"
qdrant-id="331067984" collection="pemclau-v11"
γ1="14.134725141734693" day="95" />