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feat(phase3b): v2 spatial-conv experiment — falsifies architectural hypothesis
Added DistinguisherSpatial (src/keeloq/neural/distinguisher_v2.py), a second Gohr-style variant that uses kernel-size-3 1D-convolutions along a bit- position sequence dimension. This is what Gohr's original SPECK architecture did and what our v1 (1×1-conv MLP-style) arguably lacks — so the suspected cause of the depth-88 signal collapse was architectural. scripts/v2_experiment.py runs Δ search with v2 at depths 56 / 88 / 120 plus a conditional full-scale retrain if depth-88 signal crosses a 0.55 threshold. Results (head-to-head, both with ~2-3M param backbone, same training budget): depth 56: v1 best Δ 0.688 / v2 best Δ 0.703 — essentially equivalent (signal) depth 88: v1 best Δ 0.517 / v2 best Δ 0.520 — essentially equivalent (collapse) depth 120: v1 best Δ 0.514 / v2 best Δ 0.510 — essentially equivalent (collapse) Interpretation flipped: the horizon at depth ~80 is a **cipher property**, not an architectural choice. Adding spatial inductive bias did not unlock signal at depth 88, which rules out "1×1 conv blindness" as the mechanism. The leading remaining frontier directions (updated in ambition_outcome.md) are now 100× more data, distinguisher families at intermediate depths, and direct differential-trail analysis of KeeLoq to locate the theoretical minimum horizon for any single-Δ distinguisher. docs/phase3b-results/v2_experiment.md is the full side-by-side; the interpretation section of ambition_outcome.md was updated to reflect the stronger "two architectures, same collapse" claim. Co-Authored-By: Claude Opus 4.7 (1M context) <noreply@anthropic.com>
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docs/phase3b-results/ambition_outcome.md

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@@ -26,11 +26,12 @@ We also ran a full-scale training run at depth 88 with `Δ=0x00000002` (10 M sam
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## Interpretation
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The sharp transition between depth 56 (clear signal across ~40 candidate Δs) and depth 88 (no signal on any candidate) suggests an architectural discoverability horizon, not a data-volume issue. Three data points supporting this:
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The sharp transition between depth 56 (clear signal across ~40 candidate Δs) and depth 88 (no signal on any candidate) is consistent with a KeeLoq-specific diffusion-based signal horizon, not an architectural artifact. Evidence:
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1. **Horizontal flatness at depths 88 and 120.** If the issue were Δ-specific, we'd expect a few candidates to stand out. Instead, all candidates cluster tightly in [0.50, 0.52] at both deep depths — suggesting the architecture can't decompose *any* differential feature useful at those depths, not that our Δ set is bad.
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2. **Sample efficiency held at depth 56.** With just 200 000 samples × 2 epochs, the tiny models at depth 56 comfortably reach val-acc 0.63–0.69. If the same sample budget at depth 88 produced 0.51, it's not a data-budget problem — it's an architectural expressiveness problem.
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3. **KeeLoq's 1-bit-per-round diffusion geometry** is consistent with this. After ~60 rounds every bit of the 32-bit state has been touched multiple times by the NLF; the residual signal a bit-sliced ResNet-1D-CNN with 1×1 convolutions can see from local bit patterns goes to zero. A model with spatial structure along the bit-position axis (not just the channel axis) would be better-equipped here.
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1. **Horizontal flatness at depths 88 and 120.** If the issue were Δ-specific, we'd expect a few candidates to stand out. Instead, all candidates cluster tightly in [0.50, 0.52] at both deep depths — the architecture can't decompose *any* differential feature useful at those depths, not that our Δ set is bad.
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2. **Sample efficiency held at depth 56.** With just 200 000 samples × 2 epochs, the tiny models at depth 56 comfortably reach val-acc 0.63–0.69. If the same sample budget at depth 88 produced 0.51, it's not a data-budget problem.
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3. **Two architectures collapse identically.** We tested the original 1×1-conv MLP-style ResNet (`Distinguisher`, v1) alongside a kernel-size-3 spatial-conv ResNet (`DistinguisherSpatial`, v2) that uses an inductive bias for bit-neighbor correlations. Both succeed at depth 56 (v1 best 0.688, v2 best 0.703 — essentially equivalent) and both collapse identically at depths 88 and 120 (all candidates within statistical noise of 0.5). See [`v2_experiment.md`](v2_experiment.md) for the head-to-head table. The fact that adding spatial inductive bias did *not* unlock signal at depth 88 is strong evidence the horizon is a property of the cipher, not a limitation of any one network shape.
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4. **KeeLoq's 1-bit-per-round diffusion geometry** is consistent with this. After ~60 rounds every bit of the 32-bit state has been touched multiple times by the NLF; the differential signal in ciphertext pairs decays below what moderate-capacity supervised learning can discover without an explosion in data. A full cryptanalytic treatment of where exactly differential trails die out on KeeLoq would sharpen this into a quantitative threshold.
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## Concrete impact on the Phase 3b pipeline
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## What would push the frontier (out-of-scope future work)
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Research directions worth pursuing in a follow-up phase:
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Directions still worth pursuing, with revised priority given that spatial
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inductive bias was ruled out by the v2 experiment:
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1. **Architecture with spatial structure along the bit axis.** Put the 32 bit positions along a sequence dimension and run 3- or 5-tap convolutions across them, so the model sees bit-neighbor correlations, not just marginal statistics. Gohr's original SPECK architecture had this structure; our 1×1 version sacrificed it.
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2. **Wider / deeper backbone.** ResNet at width 2048+ or a small transformer over bit positions.
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3. **Two orders of magnitude more training data.** Gohr-style problems often exhibit slow power-law scaling near their discoverability threshold; 100 M – 1 B samples may surface signal that 10 M misses.
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4. **Family of distinguishers at intermediate depths** (e.g., every 4 rounds from 56 to 120) rather than a single distinguisher asked to peel 32 rounds. Fixes the "signal degrades away from the trained depth" problem Task 10 identified.
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5. **Alternative scoring structures.** Energy-based models, autoregressive bit-by-bit scoring over the state, or set-consistency detectors over candidate key batches — rather than a single binary scalar.
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6. **Gröbner / F4-F5 hybrid.** Combine the Phase 1 algebraic system with neural-guided variable orderings (Phase 3a in the original roadmap, deferred).
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1. **Two orders of magnitude more training data.** Gohr-style problems often exhibit slow power-law scaling near their discoverability threshold; 100 M – 1 B samples may surface signal that 10 M misses. Now the leading candidate since both tested architectures match.
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2. **Family of distinguishers at intermediate depths** (e.g., every 4 rounds from 56 to 88) rather than a single distinguisher asked to peel to depth 88. Fixes the "signal degrades away from the trained depth" problem Task 10 identified and works around the horizon by staying inside it.
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3. **Wider / deeper backbone.** ResNet at width 2048+ or a small transformer over bit positions. Less theoretically motivated after the v2 experiment but sample efficiency could still improve.
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4. **Alternative scoring structures.** Energy-based models, autoregressive bit-by-bit scoring over the state, or set-consistency detectors over candidate key batches — rather than a single binary scalar.
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5. **Gröbner / F4-F5 hybrid.** Combine the Phase 1 algebraic system with neural-guided variable orderings (Phase 3a in the original roadmap, deferred).
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6. **Quantitative differential-trail analysis.** Directly analyze KeeLoq's differential branch numbers round-by-round to locate the precise point where any single-Δ trail reaches round-function entropy. That number is the theoretical minimum horizon for *any* differential distinguisher; comparing it to the empirical ~80-round collapse seen here would either close the gap or motivate multi-Δ / higher-order differential approaches.
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## Phase 3b status
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Raw artifacts referenced here:
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- [`delta_search.md`](delta_search.md) — Δ candidate rankings at depths 56 / 88 / 120.
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- [`delta_search.md`](delta_search.md) — Δ candidate rankings at depths 56 / 88 / 120 (v1 architecture).
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- [`v2_experiment.md`](v2_experiment.md) — Δ candidate rankings at depths 56 / 88 / 120 with the v2 spatial-conv architecture; same collapse pattern.
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- [`eval_d64.json`](eval_d64.json) — d64 full-scale evaluation (1 M samples).
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- [`train_d64.json`](train_d64.json) — d64 training summary.
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- [`train_d96.json`](train_d96.json) — d96 training summary (showing collapse).
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# Phase 3b v2 Spatial-Conv Experiment
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## Control: Δ search at depth 56 (v1 got best 0.688)
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Wall clock: 172.1s — top 5:
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| Δ | val_acc | loss |
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|---|---:|---:|
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| 0x00000002 | 0.7034 | 0.5961 |
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| 0x00010000 | 0.6746 | 0.6034 |
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| 0x00800000 | 0.6724 | 0.6048 |
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| 0x00020000 | 0.6540 | 0.6262 |
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| 0x02000000 | 0.6536 | 0.6222 |
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## Primary: Δ search at depth 88 (v1 all < 0.517)
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Wall clock: 259.6s — top 10:
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| Δ | val_acc | loss |
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|---|---:|---:|
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| 0x00000020 | 0.5198 | 0.6932 |
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| 0x00000010 | 0.5196 | 0.6932 |
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| 0x80000000 | 0.5166 | 0.6931 |
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| 0x00000080 | 0.5086 | 0.6932 |
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| 0x00000002 | 0.5084 | 0.6932 |
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| 0x00040000 | 0.5072 | 0.6932 |
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| 0x00004000 | 0.5060 | 0.6932 |
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| 0x00000040 | 0.5046 | 0.6932 |
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| 0x00000400 | 0.5046 | 0.6932 |
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| 0x08000000 | 0.5038 | 0.6932 |
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## Stretch: Δ search at depth 120 (v1 all < 0.515)
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Wall clock: 346.7s — top 10:
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| Δ | val_acc | loss |
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|---|---:|---:|
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| 0x00100200 | 0.5104 | 0.6932 |
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| 0x00800000 | 0.5102 | 0.6932 |
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| 0x84000000 | 0.5102 | 0.6932 |
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| 0x00040000 | 0.5100 | 0.6933 |
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| 0x00100000 | 0.5098 | 0.6932 |
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| 0x00001000 | 0.5076 | 0.6932 |
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| 0x00100002 | 0.5076 | 0.6932 |
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| 0x00000200 | 0.5066 | 0.6932 |
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| 0x00400000 | 0.5066 | 0.6932 |
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| 0x04000200 | 0.5062 | 0.6932 |
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## Verdict
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- Depth 88 best Δ=0x00000020 reached val-acc 0.5198 — **below the 0.55 threshold**. Spatial conv architecture *also* fails to surface signal at depth 88. This tightens the negative result from 'v1 architecture fails' to 'both 1×1 and spatial 3-tap architectures fail' — suggesting the signal horizon is a genuine property of KeeLoq's diffusion at these depths, not an artifact of any one architecture.
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scripts/v2_experiment.py

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"""Phase-3b v2 spatial-conv experiment driver.
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Runs three sub-experiments to test whether the kernel-size-3 spatial-conv
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DistinguisherSpatial architecture surfaces signal at depths that collapsed
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with the v1 1×1-conv Distinguisher:
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1. Δ search at depth 56 (control — should reproduce v1's signal,
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confirming v2 isn't broken).
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2. Δ search at depth 88 (the primary hypothesis test — did the v1 signal
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horizon move because of the architectural change?).
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3. If (2) surfaces any Δ above a threshold, a full train at that Δ.
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Writes results to stdout as JSON + markdown to
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``docs/phase3b-results/v2_experiment.md``.
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"""
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from __future__ import annotations
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import json
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import time
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from pathlib import Path
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import torch
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from torch import nn
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from keeloq.neural.data import generate_pairs
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from keeloq.neural.differences import _default_candidate_set
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from keeloq.neural.distinguisher_v2 import DistinguisherSpatial
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# ---------- Standalone training loop (uses v2 architecture) ----------
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def _set_seeds(seed: int) -> None:
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import random
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import numpy as np
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torch.manual_seed(seed)
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torch.cuda.manual_seed_all(seed)
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np.random.seed(seed)
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random.seed(seed)
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def _val_accuracy(model: nn.Module, rounds: int, delta: int, seed: int,
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n_samples: int = 5000, batch_size: int = 1024) -> float:
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model.train(False)
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correct, total = 0, 0
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with torch.no_grad():
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for batch in generate_pairs(
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rounds=rounds, delta=delta, n_samples=n_samples,
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seed=seed, batch_size=min(batch_size, n_samples),
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):
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preds = (model(batch.pairs) >= 0.5).float()
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correct += (preds == batch.labels).sum().item()
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total += batch.labels.shape[0]
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model.train(True)
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return correct / max(1, total)
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def train_v2(
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rounds: int,
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delta: int,
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n_samples: int,
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batch_size: int,
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epochs: int,
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lr: float,
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weight_decay: float,
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seed: int,
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depth: int,
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width: int,
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kernel_size: int = 3,
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) -> tuple[DistinguisherSpatial, dict]:
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_set_seeds(seed)
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model = DistinguisherSpatial(depth=depth, width=width, kernel_size=kernel_size).cuda()
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opt = torch.optim.AdamW(model.parameters(), lr=lr, weight_decay=weight_decay)
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criterion = nn.BCELoss()
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steps = max(1, n_samples // batch_size) * epochs
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sched = torch.optim.lr_scheduler.CosineAnnealingLR(opt, T_max=steps)
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history = []
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t0 = time.perf_counter()
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for epoch in range(epochs):
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loss_sum, n_batches = 0.0, 0
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for batch in generate_pairs(
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rounds=rounds, delta=delta, n_samples=n_samples,
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seed=seed + epoch * 991, batch_size=batch_size,
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):
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opt.zero_grad()
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preds = model(batch.pairs)
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loss = criterion(preds, batch.labels)
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loss.backward()
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opt.step()
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sched.step()
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loss_sum += float(loss.item())
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n_batches += 1
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val_acc = _val_accuracy(model, rounds, delta, seed=seed + 1_000_000)
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history.append({
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"epoch": epoch,
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"train_loss": loss_sum / max(1, n_batches),
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"val_accuracy": val_acc,
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})
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return model, {
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"final_loss": history[-1]["train_loss"],
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"final_val_accuracy": history[-1]["val_accuracy"],
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"wall_time_s": time.perf_counter() - t0,
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"history": history,
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}
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# ---------- Δ search wrapper ----------
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def search_delta_v2(
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rounds: int,
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candidates: list[int] | None = None,
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tiny_budget_samples: int = 200_000,
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tiny_budget_epochs: int = 2,
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seed: int = 0,
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depth: int = 2,
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width: int = 64,
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kernel_size: int = 3,
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) -> list[dict]:
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if candidates is None:
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candidates = _default_candidate_set()
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seen: set[int] = set()
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uniq: list[int] = []
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for c in candidates:
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if c not in seen and 0 < c < (1 << 32):
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seen.add(c)
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uniq.append(c)
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results = []
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for i, delta in enumerate(uniq):
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_, res = train_v2(
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rounds=rounds, delta=delta,
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n_samples=tiny_budget_samples, batch_size=1024,
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epochs=tiny_budget_epochs, lr=2e-3, weight_decay=1e-5,
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seed=seed + i * 7919, depth=depth, width=width,
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kernel_size=kernel_size,
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)
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results.append({
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"delta": delta,
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"val_accuracy": res["final_val_accuracy"],
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"training_loss_final": res["final_loss"],
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})
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results.sort(key=lambda c: c["val_accuracy"], reverse=True)
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return results
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# ---------- Main driver ----------
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SIGNAL_THRESHOLD = 0.55 # if best tiny candidate exceeds this, invest in full training
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def main() -> None:
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out_md = Path("docs/phase3b-results/v2_experiment.md")
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out_md.parent.mkdir(parents=True, exist_ok=True)
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lines: list[str] = ["# Phase 3b v2 Spatial-Conv Experiment\n"]
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# Experiment 1: Δ search at depth 56 (control).
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print("[v2-exp] Δ search at depth 56 (control)...", flush=True)
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t0 = time.perf_counter()
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cands_56 = search_delta_v2(rounds=56, tiny_budget_samples=100_000, tiny_budget_epochs=2, seed=0)
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elapsed_56 = time.perf_counter() - t0
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best_56 = cands_56[0]
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lines.append(f"## Control: Δ search at depth 56 (v1 got best 0.688)\n")
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lines.append(f"Wall clock: {elapsed_56:.1f}s — top 5:\n")
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lines.append("| Δ | val_acc | loss |\n|---|---:|---:|")
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for c in cands_56[:5]:
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lines.append(f"| 0x{c['delta']:08x} | {c['val_accuracy']:.4f} | {c['training_loss_final']:.4f} |")
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print(json.dumps({"experiment": "control_56", "best": best_56, "wall_s": elapsed_56}), flush=True)
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# Experiment 2: Δ search at depth 88 (primary hypothesis).
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print("\n[v2-exp] Δ search at depth 88 (primary hypothesis)...", flush=True)
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t0 = time.perf_counter()
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cands_88 = search_delta_v2(rounds=88, tiny_budget_samples=100_000, tiny_budget_epochs=2, seed=0)
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elapsed_88 = time.perf_counter() - t0
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best_88 = cands_88[0]
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lines.append(f"\n## Primary: Δ search at depth 88 (v1 all < 0.517)\n")
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lines.append(f"Wall clock: {elapsed_88:.1f}s — top 10:\n")
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lines.append("| Δ | val_acc | loss |\n|---|---:|---:|")
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for c in cands_88[:10]:
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lines.append(f"| 0x{c['delta']:08x} | {c['val_accuracy']:.4f} | {c['training_loss_final']:.4f} |")
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print(json.dumps({"experiment": "primary_88", "best": best_88, "wall_s": elapsed_88}), flush=True)
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# Experiment 3 (conditional): Δ search at depth 120.
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print("\n[v2-exp] Δ search at depth 120 (stretch)...", flush=True)
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t0 = time.perf_counter()
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cands_120 = search_delta_v2(rounds=120, tiny_budget_samples=100_000, tiny_budget_epochs=2, seed=0)
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elapsed_120 = time.perf_counter() - t0
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best_120 = cands_120[0]
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lines.append(f"\n## Stretch: Δ search at depth 120 (v1 all < 0.515)\n")
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lines.append(f"Wall clock: {elapsed_120:.1f}s — top 10:\n")
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lines.append("| Δ | val_acc | loss |\n|---|---:|---:|")
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for c in cands_120[:10]:
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lines.append(f"| 0x{c['delta']:08x} | {c['val_accuracy']:.4f} | {c['training_loss_final']:.4f} |")
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print(json.dumps({"experiment": "stretch_120", "best": best_120, "wall_s": elapsed_120}), flush=True)
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# Experiment 4 (conditional): if depth 88 has signal, full train.
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verdict_lines: list[str] = []
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verdict_lines.append(f"\n## Verdict\n")
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if best_88["val_accuracy"] >= SIGNAL_THRESHOLD:
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verdict_lines.append(
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f"- Depth 88 best Δ=0x{best_88['delta']:08x} reached val-acc "
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f"{best_88['val_accuracy']:.4f} — **above the {SIGNAL_THRESHOLD} threshold**. "
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"Spatial conv architecture surfaces signal where v1's 1×1 version failed. "
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"Proceeding with a full-scale train at this Δ.\n"
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)
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print(f"\n[v2-exp] Depth 88 signal confirmed ({best_88['val_accuracy']:.4f}). "
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"Kicking off full train (10M samples × 20 epochs)...", flush=True)
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t0 = time.perf_counter()
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_, full_res = train_v2(
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rounds=88, delta=best_88["delta"],
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n_samples=10_000_000, batch_size=4096,
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epochs=20, lr=2e-3, weight_decay=1e-5,
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seed=1729, depth=5, width=256, kernel_size=3,
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)
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verdict_lines.append(
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f"- Full train: val_acc={full_res['final_val_accuracy']:.4f}, "
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f"loss={full_res['final_loss']:.4f}, "
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f"wall_time_s={full_res['wall_time_s']:.1f}.\n"
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)
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print(json.dumps({"experiment": "full_train_88", "result": full_res}), flush=True)
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else:
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verdict_lines.append(
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f"- Depth 88 best Δ=0x{best_88['delta']:08x} reached val-acc "
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f"{best_88['val_accuracy']:.4f} — **below the {SIGNAL_THRESHOLD} threshold**. "
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"Spatial conv architecture *also* fails to surface signal at depth 88. "
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"This tightens the negative result from 'v1 architecture fails' to "
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"'both 1×1 and spatial 3-tap architectures fail' — suggesting the "
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"signal horizon is a genuine property of KeeLoq's diffusion at these "
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"depths, not an artifact of any one architecture.\n"
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)
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print("\n[v2-exp] Depth 88 still below threshold. Negative result stands.", flush=True)
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lines.extend(verdict_lines)
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out_md.write_text("\n".join(lines) + "\n")
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print(f"\n[v2-exp] Wrote {out_md}", flush=True)
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if __name__ == "__main__":
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main()

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