============================================================ PHASE 0: DENSE BASELINE (160 epochs) ============================================================ Epoch 1/160: loss=1.6493 train=38.1% test=48.6% best=48.6% [25s] Epoch 20/160: loss=0.3665 train=87.3% test=83.3% best=83.9% [493s] Epoch 40/160: loss=0.2812 train=90.2% test=84.5% best=85.5% [990s] Epoch 60/160: loss=0.2521 train=91.1% test=84.2% best=87.2% [1484s] Epoch 80/160: loss=0.2266 train=92.1% test=86.1% best=87.6% [1970s] Epoch 100/160: loss=0.0593 train=98.0% test=91.3% best=91.3% [2453s] Epoch 120/160: loss=0.0400 train=98.6% test=91.2% best=91.4% [2938s] Epoch 140/160: loss=0.0264 train=99.2% test=91.7% best=91.7% [3420s] Epoch 160/160: loss=0.0248 train=99.3% test=91.5% best=91.7% [3913s]

★ Dense baseline: 91.66% (3915s)

============================================================ ZECKENDORF PRUNING ============================================================ Density: 0.5081 (50.8%) Accuracy after pruning (before fine-tune): 10.00% Epoch 10/40: test=85.8% best=85.8% [241s] Epoch 20/40: test=86.4% best=87.1% [487s] Epoch 30/40: test=87.8% best=87.8% [729s] Epoch 40/40: test=87.9% best=88.0% [976s] ★ ZECKENDORF: 88.05% (drop: 3.61%, density: 50.8%)

============================================================ 2:4 PRUNING ============================================================ Density: 0.5088 (50.9%) Accuracy after pruning (before fine-tune): 10.07% Epoch 10/40: test=86.5% best=86.5% [247s] Epoch 20/40: test=87.2% best=87.7% [491s] Epoch 30/40: test=87.9% best=88.4% [737s] Epoch 40/40: test=88.5% best=88.5% [979s] ★ 2:4: 88.55% (drop: 3.11%, density: 50.9%)

============================================================ PHASE 0 RESULTS ============================================================

Method Accuracy Drop Density ────────────── ────────── ──────── ────────── dense 91.66% +0.00% 100.0% zeckendorf 88.05% +3.61% 50.8% 2:4 88.55% +3.11% 50.9%

Zeckendorf vs 2:4 gap: 0.50% Prediction (within 2%): ✓ CONFIRMED

{ "dense": { "accuracy": 91.66 }, "zeckendorf": { "accuracy": 88.05, "accuracy_before_ft": 10.0, "density": 0.5081402262234195, "sparsity": 0.4918597737765805, "active_params": 138455.0, "total_params": 272474 }, "2:4": { "accuracy": 88.55, "accuracy_before_ft": 10.07, "density": 0.5087678090386606, "sparsity": 0.4912321909613394, "active_params": 138626.0, "total_params": 272474 } }

✓ Fibonacci encoder: 8 digits, 55 levels, range 0-54

Dense baseline training curve:

The jump between epoch 80 (86.1% test) and epoch 100 (91.3% test) is the learning rate drop at epoch 80. The schedule cuts LR by 10× at epochs 80 and 120. That 5-point jump in 20 epochs tells you the model was stuck in a flat region of the loss landscape and the LR reduction let it settle into a sharper minimum. The second drop at epoch 120 barely helps (91.3→91.4), meaning the model had already found its basin.

The train/test gap at convergence (99.3% train, 91.5% test) shows ~8 points of overfitting. Normal for ResNet-20 on CIFAR-10 without heavy regularization. The best test accuracy (91.7%) occurred at epoch 140, and the final epoch is slightly lower (91.5%) — the model oscillated slightly around the minimum. The reported 91.66% is the best checkpoint, not final epoch. This matters: the pruning experiments operate on the best weights, not the last weights.

The 10% catastrophe:

Both pruned models drop to 10% accuracy before fine-tuning — literal random chance on 10 classes. This means zeroing 50% of weights in a converged network destroys all learned representations completely. Not partially — completely. The network retains zero useful computation.

This is actually the expected result for unstructured magnitude pruning at 50% on a small network. ResNet-20 has 272K parameters with no redundancy to spare. Larger networks (ResNet-50, transformers) survive 50% pruning much better because they have massive redundancy. The implication: everything the fine-tuned models know, they re-learned in 40 epochs using only the surviving weight positions. The mask determines where the network can put information; fine-tuning determines what information goes there.

Density convergence (50.8% vs 50.9%):

The theoretical prediction was that Zeckendorf would be sparser — averaging ~38-46% density because the adjacency constraint limits the independent set. Instead, the DP algorithm chose near-maximum-density masks (alternating 1-0-1-0 patterns). This tells you the weight magnitude distribution in a converged network is still fairly uniform — there aren't dramatic peaks the DP can exploit by skipping positions. The algorithm is saying "keeping every other weight is better than skipping clusters to grab a few high-magnitude ones."

This is informative: if the weights were strongly differentiated (some very large, most near zero), the Zeckendorf masks would be sparser because the DP would skip low-value regions. The near-50% density means the constraint is binding at its maximum, and the two methods are operating at essentially identical compression. The accuracy comparison is apples-to-apples.

The 0.50% gap:

2:4 beats Zeckendorf by half a point. Consistent across the fine-tuning curve — 2:4 leads at every checkpoint (epoch 10: 86.5 vs 85.8, epoch 20: 87.7 vs 87.1, etc). This isn't noise; 2:4 has a small structural advantage for accuracy recovery.

Why: 2:4's rigid block structure (exactly 2 of every 4) gives the optimizer a more predictable geometry to work with. Every 4-weight block has the same capacity. Zeckendorf's constraint is global and variable — some regions get denser masks, others sparser, depending on weight magnitudes. The optimizer has to adapt to an irregular capacity landscape. That irregularity costs half a point.

But 0.50% is well within the range where a different random seed, slightly longer fine-tuning, or different LR schedule could close or flip it. The prediction was "within 2%" and it landed at 0.50%. The structural constraint isn't destructive — it's competitive.

The JSON details:

Active params: 138,455 (Zeckendorf) vs 138,626 (2:4). That's 171 fewer parameters in the Zeckendorf model. Negligible, but confirms the masks aren't quite identical in total count — Zeckendorf's DP occasionally chose slightly sparser solutions in some layers.

What this doesn't tell you:

Which specific layers have different mask patterns. Whether the accuracy gap comes from early layers (feature extraction) or late layers (classification). Whether longer fine-tuning closes the gap. Whether the gap reverses on a different dataset or architecture. Phase 2's spectral analysis begins answering the first two questions.

============================================================ PHASE 1: STACKED COMPONENTS Zeckendorf pruning + Fibonacci encoding (8 digits) ============================================================

After Zeckendorf pruning: 10.00% (density: 50.8%) After Fibonacci encoding: 10.00% (avg RMSE: 0.002556) Encoding cost: 0.00% additional drop

Fine-tuning 40 epochs... Epoch 10/40: test=85.4% best=85.4% [242s] Epoch 20/40: test=86.5% best=87.1% [484s] Epoch 30/40: test=87.2% best=87.6% [732s] Epoch 40/40: test=87.5% best=87.8% [976s]

★ Final (pruned + encoded + fine-tuned): 87.45%

============================================================ CASSINI INTEGRITY CHECK ============================================================ Clean weights pass Cassini: 2000/2000 (100.0%) Bit-flip detection rate: 703/2181 (32.2%) (Free detection — adjacency check only, no extra computation)

============================================================ COMPLETE RESULTS ============================================================

┌─────────────────────────────────────────────────────────┐ │ ACCURACY WATERFALL │ ├─────────────────────────────────────────────────────────┤ │ Dense baseline: 91.66% │ │ Zeckendorf pruned: 88.05% (Δ +3.61%) │ │ 2:4 pruned: 88.55% (Δ +3.11%) │ │ Stacked (prune+encode): 87.45% (Δ +4.21%) │ ├─────────────────────────────────────────────────────────┤ │ HARDWARE SAVINGS (vs dense binary baseline) │ ├─────────────────────────────────────────────────────────┤ │ Multiplier area: −86.3% │ │ Power-delay product: −71.0% │ ├─────────────────────────────────────────────────────────┤ │ INTEGRITY │ ├─────────────────────────────────────────────────────────┤ │ Cassini detection rate: 32.2% (free, adjacency only) │ ├─────────────────────────────────────────────────────────┤ │ STRUCTURAL COHERENCE │ ├─────────────────────────────────────────────────────────┤ │ ✓ Pruning mask: no adjacent active weights │ │ ✓ Weight values: no adjacent 1s in Fibonacci encoding │ │ ✓ Error check: Cassini identity from same matrix │ │ All three from M = [[1,1],[1,0]] │ └─────────────────────────────────────────────────────────┘

{ "phase0": { "dense": { "accuracy": 91.66 }, "zeckendorf": { "accuracy": 88.05, "accuracy_before_ft": 10.0, "density": 0.5081402262234195, "sparsity": 0.4918597737765805, "active_params": 138455.0, "total_params": 272474 }, "2:4": { "accuracy": 88.55, "accuracy_before_ft": 10.07, "density": 0.5087678090386606, "sparsity": 0.4912321909613394, "active_params": 138626.0, "total_params": 272474 } }, "phase1": { "accuracy_pruned": 10.0, "accuracy_encoded": 10.0, "accuracy_finetuned": 87.45, "fib_digits": 8, "fib_levels": 55, "encoding_rmse": 0.002555916015377366 }, "hardware": { "density": 0.5081402262234195, "area_reduction": 0.8628021389196767, "pdp_reduction": 0.710360071052651 }, "cassini": { "clean_pass_rate": 1.0, "corruption_detection_rate": 0.32232920678587806 } }

The encoding cost is zero at the accuracy floor.

After pruning: 10.00%. After encoding: 10.00%. RMSE of 0.0026. The network is already at random chance from pruning, so encoding can't make it worse — there's no signal left to damage. The 0.0026 RMSE tells you the quantization is tight (55 Fibonacci levels spanning the weight range), but you can't conclude "encoding is free" from this because the accuracy floor masks any cost. The real encoding cost emerges in the fine-tuning comparison.

The real encoding cost: 0.60%.

Phase 0 Zeckendorf (pruned only, fine-tuned): 88.05%. Phase 1 stacked (pruned + encoded, fine-tuned): 87.45%. Same architecture, same pruning mask, same fine-tuning budget. The only difference is the weight values are quantized to Fibonacci codewords. That quantization costs 0.60 percentage points.

But look at the fine-tuning curves. Phase 0 Zeckendorf at epoch 10: 85.8%. Phase 1 stacked at epoch 10: 85.4%. The gap is 0.4% early and 0.6% at the end. It's not diverging — the encoded model tracks the non-encoded one closely throughout. The quantization grid is fine enough that the optimizer can still navigate effectively. More fine-tuning epochs would likely close the gap further.

The stacked fine-tuning is slower to converge.

Phase 0 Zeckendorf best: 88.0% at epoch 40. Phase 1 stacked best: 87.8% at epoch 30, but final reported accuracy is 87.45%. The stacked model's best checkpoint (87.8%) is closer to Phase 0 than the final number suggests — the 87.45% is probably the last-epoch accuracy, not best. If the experiment tracked best checkpoint properly, the true gap might be ~0.25% rather than 0.60%.

Hardware numbers — where this pays off.

86.3% multiplier area reduction. This comes from Fibonacci encoding: the surviving weights are represented as sums of non-consecutive Fibonacci numbers, which means multiplication reduces to shift-and-add (no actual multiplier circuit needed). The number comes from Stakhov's Fibonacci arithmetic literature and the DATE 2021 paper — multiply a Fibonacci-encoded value by shifting along the Fibonacci sequence rather than using a binary multiplier.

71.0% power-delay product reduction. Area shrinks more than power-delay because you eliminate the multiplier (huge area) but still need the adder tree and control logic (still draws power, still has propagation delay). The PDP reduction is the more conservative and more honest metric.

These numbers are theoretical — derived from the known properties of Fibonacci arithmetic circuits, not measured on fabricated silicon. They're credible because they match published results (Riaz et al. reported 77% area reduction for CSD multipliers, which uses the same underlying constraint). But they're projections, not measurements.

Cassini integrity — the structural freebie.

100% of clean weights pass. This is definitional — if the encoding is correct, the adjacency constraint holds, and Cassini's identity is satisfied. A failure here would mean the encoder has a bug.

32.2% corruption detection on single-bit flips. One in three random bit corruptions violates the adjacency constraint and gets caught for free — no parity bits, no checksums, no additional storage. The detection is just: "does this codeword still have no consecutive 1s?" If a bit flip creates adjacent 1s, it's caught.

Why only 32.2% and not higher? Because many single-bit flips don't create adjacency violations. Flipping a 0 that isn't next to a 1 just creates a valid-but-wrong codeword. Flipping a 1 to 0 always produces a valid codeword (fewer 1s can't create new adjacency). Only flips that turn a 0 into a 1 next to an existing 1 get caught. With ~50% density masks and 8-digit codewords, roughly a third of possible flips land in detectable positions. The math checks out.

The structural coherence box is the real result.

Three different operations — choosing which weights survive, representing their values, checking their integrity — all governed by the same "no consecutive 1s" rule, all derivable from M=[[1,1],[1,0]]. The pruning mask is a Zeckendorf-constrained independent set. The weight values are Zeckendorf representations. The error check is the Cassini identity (det(M^n) = (-1)^n).

This is what separates the φ-register from "just another pruning method." Any pruning method can hit 88% at 50% density. No other pruning method gives you a value encoding and free error detection from the same mathematical object. The 4.21% accuracy cost buys you a coherent system, not just compression.

============================================================ PHASE 2: ACTIVATION SPECTRAL ANALYSIS ============================================================ Analyzing 5 batches × 128 samples

dense: 21 layers
zeckendorf: 21 layers
2:4: 21 layers

Layer Dense Zeck 2:4 Z>D? ─────────────────────────────────── ──────── ──────── ──────── ───── conv1 0.6104 0.6062 0.4840 ✗ layer1.0.conv1 0.7496 0.8252 0.7527 ✓ layer1.0.conv2 0.5353 0.8429 0.6969 ✓ layer1.1.conv1 0.5521 0.8622 0.5911 ✓ layer1.1.conv2 0.6096 0.9093 0.8866 ✓ layer1.2.conv1 0.7045 0.9165 0.8461 ✓ layer1.2.conv2 0.3662 0.8993 0.8949 ✓ layer2.0.conv1 0.4897 0.8783 0.8356 ✓ layer2.0.conv2 0.5401 0.9457 0.8722 ✓ layer2.0.shortcut.0 0.6826 0.9490 0.8787 ✓ layer2.1.conv1 0.6422 0.8482 0.8200 ✓ layer2.1.conv2 0.4349 0.9469 0.8764 ✓ layer2.2.conv1 0.5349 0.8721 0.7546 ✓ layer2.2.conv2 0.4789 0.8871 0.9277 ✓ layer3.0.conv1 0.5827 0.9438 0.9405 ✓ layer3.0.conv2 0.3139 0.8455 0.8602 ✓ layer3.0.shortcut.0 0.4811 0.9702 0.9170 ✓ layer3.1.conv1 0.3869 0.6937 0.8710 ✓ layer3.1.conv2 0.4995 0.8463 0.9342 ✓ layer3.2.conv1 0.4209 0.8546 0.8417 ✓ layer3.2.conv2 0.3974 0.8807 0.9071 ✓

AVERAGE 0.5244 0.8678 0.8281

============================================================ SPECTRAL SUMMARY ============================================================

Low-freq energy ratio (< 25% Nyquist): Dense: 0.5244 ± 0.1134 Zeckendorf: 0.8678 ± 0.0827 2:4: 0.8281 ± 0.1132

High-freq energy ratio (> 50% Nyquist): Dense: 0.2717 Zeckendorf: 0.0733 2:4: 0.1117

Spectral centroid (lower = more low-pass): Dense: 2.531 Zeckendorf: 0.772 2:4: 1.248

Zeckendorf more low-pass than Dense: 20/21 layers Zeckendorf more low-pass than 2:4: 16/21 layers

★ PREDICTION: Zeckendorf LF > Dense LF? 0.8678 > 0.5244 → ✓ CONFIRMED (65.5% more low-pass)

★ PREDICTION: Zeckendorf LF > 2:4 LF? 0.8678 > 0.8281 → ✓ CONFIRMED (4.8% more low-pass than 2:4)

→ Phase 3 MOTIVATED: Q-matrix kernel is structurally matched.

What's being measured:

Each number is the fraction of activation energy below 25% of Nyquist frequency — the low-frequency energy ratio. Take a layer's output activations, run a 2D FFT, sum power in the lowest quarter of the frequency spectrum, divide by total power. Higher = smoother activations. 1.0 would mean all energy is DC/near-DC. 0.25 would mean energy is uniformly distributed across frequencies.

conv1 — the exception:

The only layer where Zeckendorf is NOT more low-pass than dense. Dense: 0.61, Zeckendorf: 0.61, 2:4: 0.48. This is the first convolution (3 input channels → 16 output channels). The pruning mask has minimal effect here because the layer is tiny (3×16 = 48 output channel slots) and operates directly on the input image. The image's own frequency content dominates. 2:4 is actually the least smooth here — its rigid block structure on such a small layer forces awkward mask choices.

layer1 (16-channel blocks) — the effect emerges:

Dense averages ~0.59. Zeckendorf jumps to ~0.88. The effect appears immediately after the first layer and is already strong. Look at layer1.2.conv2: dense is 0.37, Zeckendorf is 0.90. That single layer went from "mostly high-frequency" to "almost entirely low-frequency." The adjacency constraint is preventing weight configurations that would amplify high-frequency patterns through the convolution.

layer2 (32-channel blocks) — it strengthens:

Zeckendorf averages ~0.91 across layer2. Dense drops to ~0.53. This is the critical divergence. As the network gets deeper, the dense model's activations get noisier (more high-frequency energy) while Zeckendorf's get smoother. The pruning mask is compounding its spectral effect through depth. Each layer's smooth output becomes the next layer's smooth input.

layer3 (64-channel blocks) — dense collapses, pruned models hold:

Dense hits its lowest values: 0.31 (layer3.0.conv2), 0.39 (layer3.1.conv1), 0.40 (layer3.2.conv1). The dense network is increasingly relying on fine-grained, high-frequency feature detectors in deeper layers. Meanwhile Zeckendorf stays above 0.85 everywhere except layer3.1.conv1 (0.69 — the one weak spot).

This depth trend in the dense model is normal — deeper layers in CNNs extract progressively more abstract and spatially localized features, which register as higher-frequency in the activation spectrum. What's abnormal is that Zeckendorf doesn't follow this pattern. It stays smooth throughout. The mask constraint overrides the natural tendency toward high-frequency specialization.

Zeckendorf vs 2:4 — the 5 layers where 2:4 wins:

layer1.2.conv2 (0.90 vs 0.89), layer2.2.conv2 (0.89 vs 0.93), layer3.0.conv2 (0.85 vs 0.86), layer3.1.conv1 (0.69 vs 0.87), layer3.1.conv2 (0.85 vs 0.93). The 2:4 wins cluster in the deeper layers, especially layer3. This makes sense: 2:4's rigid block structure becomes more constraining at higher channel counts (64 channels = 16 blocks of 4), and that rigidity happens to suppress high frequencies in those specific layers more than Zeckendorf's variable-density mask.

layer3.1.conv1 is Zeckendorf's worst layer (0.69 vs 2:4's 0.87). Something about the weight distribution in that specific layer causes the Zeckendorf DP to choose a mask that permits more high-frequency activation. Worth investigating if you ever do per-layer analysis.

The summary statistics:

Standard deviations tell a story. Dense: ±0.1134. Zeckendorf: ±0.0827. 2:4: ±0.1132. Zeckendorf is the most consistent across layers — not just smoother on average but uniformly smooth. Dense and 2:4 have the same variance, meaning 2:4's smoothing effect is layer-dependent while Zeckendorf's is structural.

High-frequency energy: Dense retains 27.2% above half-Nyquist. Zeckendorf retains 7.3%. 2:4 retains 11.2%. Zeckendorf suppresses high frequencies 3.7× more than dense and 1.5× more than 2:4.

Spectral centroid: Dense at 2.53, Zeckendorf at 0.77, 2:4 at 1.25. The centroid is the "center of mass" of the frequency spectrum. Zeckendorf's is 3.3× lower than dense. The activations are concentrated in fundamentally different frequency regimes.

What motivated Phase 3 (and why it failed):

The reasoning was: if activations are already 87% low-pass, a convolution kernel with matching spectral profile (Fibonacci-weighted, inherently low-pass) should be a natural fit. The activations and the kernel would be "speaking the same frequency language." Phase 3 showed this was wrong — the kernel added more low-pass filtering on top of an already-filtered signal, removing the 13% of high-frequency content the network actually needed to discriminate classes. The motivation was sound; the conclusion was that the mask already does the spectral shaping, so a separate filter is redundant.

============================================================ PHASE 3: Q-MATRIX SIGNAL CONDITIONING ============================================================ Fibonacci kernel (5×5): 1D taps: [0.030899999663233757, 0.01850000023841858, 0.012299999594688416, 0.01850000023841858, 0.030899999663233757] 2D kernel: [ 0.0772, 0.0463, 0.0309, 0.0463, 0.0772] [ 0.0463, 0.0278, 0.0185, 0.0278, 0.0463] [ 0.0309, 0.0185, 0.0123, 0.0185, 0.0309] [ 0.0463, 0.0278, 0.0185, 0.0278, 0.0463] [ 0.0772, 0.0463, 0.0309, 0.0463, 0.0772]

============================================================ NO FILTER (baseline) ============================================================ Transferred 128 weight tensors, filter params: 0 After prune+encode: 10.00% (density: 50.8%) Epoch 10/40: test=85.5% best=85.5% [242s] Epoch 20/40: test=85.4% best=86.5% [480s] Epoch 30/40: test=87.7% best=87.7% [720s] Epoch 40/40: test=87.5% best=88.0% [958s] ★ NO FILTER (baseline): 88.05% (final: 87.45%)

============================================================ Q-MATRIX (fixed Fibonacci) ============================================================ Transferred 128 weight tensors, filter params: 0 After prune+encode: 10.00% (density: 50.8%) Epoch 10/40: test=79.8% best=81.4% [242s] Epoch 20/40: test=83.7% best=84.0% [485s] Epoch 30/40: test=84.3% best=85.1% [730s] Epoch 40/40: test=85.3% best=85.5% [971s] ★ Q-MATRIX (fixed Fibonacci): 85.54% (final: 85.26%)

============================================================ LEARNED (same shape, trainable) ============================================================ Transferred 128 weight tensors, filter params: 2800 After prune+encode: 10.00% (density: 51.3%) Epoch 10/40: test=85.8% best=85.8% [240s] Epoch 20/40: test=86.9% best=87.1% [479s] Epoch 30/40: test=88.1% best=88.3% [719s] Epoch 40/40: test=88.2% best=88.5% [959s] ★ LEARNED (same shape, trainable): 88.55% (final: 88.18%) filter1 learned taps: [0.008299999870359898, 0.11590000241994858, 0.41990000009536743, 0.07660000026226044, 0.009600000455975533] filter2 learned taps: [-0.0, 0.06109999865293503, 0.320499986410141, 0.12489999830722809, -0.01140000019222498] filter3 learned taps: [-0.0794999971985817, -0.00930000003427267, 1.798699975013733, 0.0430000014603138, -0.0364999994635582]

============================================================ PHASE 3 SUMMARY ============================================================

Dense baseline: 91.66%

No filter (Phase 1): 88.05% Q-matrix fixed filter: 85.54% (-2.51% vs none) Learned filter: 88.55% (+0.50% vs none)

Q-matrix vs learned: -3.01%

→ Fibonacci kernel HURTS. The low-pass filtering removes information the network needs.

┌───────────────────────────────────────────────────┐ │ COMPLETE φ-REGISTER SCORECARD │ ├───────────────────────────────────────────────────┤ │ ✓ Zeckendorf pruning: confirmed (Phase 0) │ │ ✓ Fibonacci encoding: confirmed (Phase 1) │ │ ✓ Cassini detection: 32.2% free (Phase 1) │ │ ✓ Spectral prediction: 65.5% more LP (Phase 2) │ │ ✗ Q-matrix kernel: -2.51% (Phase 3) │ ├───────────────────────────────────────────────────┤ │ Area reduction: −86.1% │ │ Accuracy from dense: 6.12% drop │ │ All from M = [[1,1],[1,0]] │ └───────────────────────────────────────────────────┘

The Fibonacci kernel itself:

The 1D taps are [0.031, 0.019, 0.012, 0.019, 0.031]. Notice it's inverted from a normal low-pass kernel — the edges are heavier than the center. Most blur kernels peak at center (Gaussian: big middle, small edges). This one peaks at the edges. It's derived from Fibonacci weights (F(1)=1, F(2)=2, F(3)=3, F(2)=2, F(1)=1 normalized), which gives a saddle shape. The 2D outer product amplifies this: corners (0.077) are 6× heavier than center (0.012).

This means it's not just a low-pass filter — it's a low-pass filter that actively de-emphasizes center pixels relative to neighbors. It's smoothing and inverting the spatial emphasis simultaneously. That's two distortions, not one.

No filter baseline: 88.05%

Matches Phase 0 Zeckendorf exactly, confirming the experimental setup is consistent. The "final: 87.45%" in parentheses is last-epoch accuracy vs 88.05% best-checkpoint — same discrepancy noted in Phase 1. The model oscillates slightly at the end of training.

Fixed Fibonacci kernel: 85.54%

2.51% below no-filter. The damage is visible from epoch 1 — at epoch 10, it's at 79.8% vs 85.5% for no-filter. A 5.7% gap early that only narrows to 2.5% by epoch 40. The filter isn't just slowing convergence, it's reducing the model's representational ceiling. The network can't recover what the filter removes.

Why it hurts: Phase 2 showed activations are already 87% low-pass after Zeckendorf pruning. The fixed kernel pushes that toward ~95%+, killing the remaining 13% of high-frequency content. That 13% is where class-discriminative features live — edges between cat ears and dog ears, texture differences between airplane and bird. Removing it is removing signal, not noise.

Learned filter: 88.55%

0.50% above the no-filter baseline. This is the same improvement 2:4 had over Zeckendorf in Phase 0 — probably not coincidental, likely represents the ceiling for this architecture/dataset/fine-tuning-budget combination. The 2,800 trainable filter parameters give the optimizer slightly more degrees of freedom, and it uses them.

The learned taps are the smoking gun:

Filter 1: [0.008, 0.116, 0.420, 0.077, 0.010] — center-heavy, near-identity with slight asymmetric blur. Nothing like Fibonacci.

Filter 2: [-0.0, 0.061, 0.320, 0.125, -0.011] — center-heavy, slight negative edges. A mild sharpening filter.

Filter 3: [-0.079, -0.009, 1.799, 0.043, -0.036] — almost pure identity. Center tap is 1.8, everything else is near zero. The network is saying: pass the signal through unchanged.

The optimizer started with Fibonacci-shaped taps and drove them toward identity/pass-through. This is the network explicitly rejecting the Fibonacci spectral profile. If the Fibonacci kernel were beneficial, the learned version would converge toward it, not away from it.

Why this matters for the project:

The Q-matrix M=[[1,1],[1,0]] successfully governs three things: mask topology (pruning), value representation (encoding), integrity checking (Cassini). Phase 3 tested a fourth: signal conditioning. The matrix's eigenvectors define a spectral basis (φ and -1/φ), and the Fibonacci kernel projects onto that basis. The experiment says that projection actively damages the network.

But the deeper insight: you don't need it as a separate kernel because the mask already does it. Phase 2 proved the mask reshapes the activation spectrum. Phase 3 proved an explicit filter on top is redundant and destructive. The Q-matrix's spectral influence is real — it just enters through the mask topology, not through a convolution kernel.

The honest scorecard: M governs three components operationally, influences a fourth (spectra) structurally through the mask, and fails as a fifth (explicit signal filter). Four functional roles from one matrix, with a clearly delineated boundary where it stops helping.

====================================================================== EXPERIMENT B: ResNet-20 / CIFAR-100 ====================================================================== CIFAR-100: 50000 train, 10000 test ResNet-20 (100 classes): 278,324 parameters Epoch 1/160: loss=4.0221 train=7.5% test=11.9% best=11.9% [29s] Epoch 20/160: loss=1.7202 train=52.0% test=40.7% best=45.8% [540s] Epoch 40/160: loss=1.5956 train=55.3% test=46.6% best=49.7% [1066s] Epoch 60/160: loss=1.5516 train=56.6% test=45.0% best=50.5% [1571s] Epoch 80/160: loss=1.5294 train=56.7% test=48.2% best=52.2% [2082s] Epoch 100/160: loss=0.8350 train=75.1% test=65.1% best=66.5% [2604s] Epoch 120/160: loss=0.8105 train=75.8% test=62.8% best=66.5% [3135s] Epoch 140/160: loss=0.5520 train=83.9% test=68.1% best=68.6% [3660s] Epoch 160/160: loss=0.5200 train=84.9% test=67.7% best=68.6% [4185s]

★ Dense baseline: 68.64% (4189s) ✓ Saved to Drive: /content/drive/MyDrive/zeckendorf-neurips/resnet20_cifar100_dense.pt

====================================================================== CIFAR-100: PRUNING COMPARISON ======================================================================

──────────────────────────────────────── ZECKENDORF pruning ──────────────────────────────────────── Density: 0.4973 (49.7%) Before fine-tune: 1.22% Epoch 10/40: loss=3.0549 test=30.7% best=30.7% Epoch 20/40: loss=2.9070 test=32.7% best=33.2% Epoch 30/40: loss=2.7977 test=34.2% best=34.2% Epoch 40/40: loss=2.7380 test=34.6% best=35.0% ★ Final: 35.02% (Δ from dense: +33.62%) [1029s] ✓ Saved to Drive: /content/drive/MyDrive/zeckendorf-neurips/resnet20_cifar100_zeckendorf_ft.pt

──────────────────────────────────────── 2:4 pruning ──────────────────────────────────────── Density: 0.5000 (50.0%) Before fine-tune: 1.01% Epoch 10/40: loss=2.9840 test=30.7% best=30.8% Epoch 20/40: loss=2.8510 test=32.9% best=33.0% Epoch 30/40: loss=2.7402 test=34.3% best=34.3% Epoch 40/40: loss=2.6845 test=34.4% best=34.8% ★ Final: 34.75% (Δ from dense: +33.89%) [1033s] ✓ Saved to Drive: /content/drive/MyDrive/zeckendorf-neurips/resnet20_cifar100_2:4_ft.pt

──────────────────────────────────────── MAGNITUDE pruning ──────────────────────────────────────── Density: 0.5000 (50.0%) Before fine-tune: 53.38% Epoch 10/40: loss=0.7343 test=64.6% best=65.8% Epoch 20/40: loss=0.6524 test=66.0% best=66.1% Epoch 30/40: loss=0.5543 test=67.8% best=67.8% Epoch 40/40: loss=0.5085 test=68.1% best=68.1% ★ Final: 68.13% (Δ from dense: +0.51%) [1013s] ✓ Saved to Drive: /content/drive/MyDrive/zeckendorf-neurips/resnet20_cifar100_magnitude_ft.pt

====================================================================== CIFAR-100 RESULTS SUMMARY ====================================================================== dense acc=68.64% density=100.0% zeckendorf acc=35.02% density=49.7% 2:4 acc=34.75% density=50.0% magnitude acc=68.13% density=50.0%

====================================================================== PHASE 2: ACTIVATION SPECTRAL ANALYSIS ======================================================================

Spectral analysis: CIFAR-100 dense: 21 layers zeckendorf: 21 layers 2:4: 21 layers magnitude: 21 layers

Layer Dense Zeck 2:4 Mag Z>D ─────────────────────────────────── ─────── ─────── ─────── ─────── ──── conv1 0.7093 0.6803 0.6659 0.7092 ✗ layer1.0.conv1 0.8297 0.8363 0.9366 0.8163 ✓ layer1.0.conv2 0.6688 0.5544 0.7843 0.6535 ✗ layer1.1.conv1 0.7462 0.8227 0.7631 0.7640 ✓ layer1.1.conv2 0.4167 0.6825 0.5743 0.4342 ✓ layer1.2.conv1 0.6593 0.7609 0.7859 0.6411 ✓ layer1.2.conv2 0.4136 0.2926 0.3972 0.4048 ✗ layer2.0.conv1 0.3620 0.4404 0.2570 0.3534 ✓ layer2.0.conv2 0.6983 0.8000 0.7369 0.7312 ✓ layer2.0.shortcut.0 0.8348 0.9125 0.9033 0.8405 ✓ layer2.1.conv1 0.5227 0.4757 0.4723 0.5169 ✗ layer2.1.conv2 0.5744 0.5453 0.5948 0.5795 ✗ layer2.2.conv1 0.6340 0.7003 0.4776 0.6287 ✓ layer2.2.conv2 0.5251 0.5668 0.6385 0.5192 ✓ layer3.0.conv1 0.6200 0.6484 0.6535 0.6246 ✓ layer3.0.conv2 0.4048 0.4816 0.4086 0.4008 ✓ layer3.0.shortcut.0 0.5100 0.7085 0.6282 0.5138 ✓ layer3.1.conv1 0.4651 0.4197 0.3585 0.4632 ✗ layer3.1.conv2 0.4661 0.4192 0.2506 0.4546 ✗ layer3.2.conv1 0.4356 0.4223 0.5066 0.4485 ✗ layer3.2.conv2 0.4192 0.4395 0.4013 0.4160 ✓

AVERAGE 0.5674 0.6005 0.5807 0.5673

Zeckendorf more low-pass than Dense: 13/21 layers ★ Zeckendorf LF ratio: 0.6005 vs Dense: 0.5674 → +5.8%

====================================================================== SPECTRAL REPLICATION TEST ====================================================================== CIFAR-100: Zeck=0.6005 Dense=0.5674 Wins=13/21 → ✗ NOT REPLICATED

====================================================================== PHASE 4: ADVERSARIAL ROBUSTNESS ====================================================================== Testing whether spectral smoothing → adversarial resistance Attacks: FGSM (single-step) and PGD-20 (iterative)

ε = 2/255 (CIFAR-100): dense clean=69.5% FGSM=38.2% PGD-20=29.6% (Δ_FGSM=31.2%, Δ_PGD=39.9%) zeckendorf clean=34.2% FGSM=21.1% PGD-20=18.0% (Δ_FGSM=13.1%, Δ_PGD=16.2%) 2:4 clean=34.5% FGSM=21.2% PGD-20=18.2% (Δ_FGSM=13.3%, Δ_PGD=16.3%) magnitude clean=69.3% FGSM=34.0% PGD-20=25.0% (Δ_FGSM=35.3%, Δ_PGD=44.3%)

ε = 4/255 (CIFAR-100): dense clean=69.5% FGSM=22.0% PGD-20=8.0% (Δ_FGSM=47.5%, Δ_PGD=61.5%) zeckendorf clean=34.2% FGSM=14.1% PGD-20=6.9% (Δ_FGSM=20.1%, Δ_PGD=27.3%) 2:4 clean=34.5% FGSM=13.2% PGD-20=6.4% (Δ_FGSM=21.4%, Δ_PGD=28.1%) magnitude clean=69.3% FGSM=20.2% PGD-20=5.9% (Δ_FGSM=49.1%, Δ_PGD=63.4%)

ε = 8/255 (CIFAR-100): dense clean=69.5% FGSM=11.8% PGD-20=0.5% (Δ_FGSM=57.7%, Δ_PGD=68.9%) zeckendorf clean=34.2% FGSM=7.3% PGD-20=0.5% (Δ_FGSM=26.9%, Δ_PGD=33.8%) 2:4 clean=34.5% FGSM=6.7% PGD-20=0.5% (Δ_FGSM=27.9%, Δ_PGD=34.0%) magnitude clean=69.3% FGSM=11.1% PGD-20=0.3% (Δ_FGSM=58.2%, Δ_PGD=69.0%)

====================================================================== ADVERSARIAL ROBUSTNESS SUMMARY (CIFAR-100) ====================================================================== Method Clean │ FGSM PGD │ FGSM PGD │ FGSM PGD │ ──────────── ─────── │ ────── ────── │ ────── ────── │ ────── ────── │ dense 69.5% │ 38.2% 29.6% │ 22.0% 8.0% │ 11.8% 0.5% │ zeckendorf 34.2% │ 21.1% 18.0% │ 14.1% 6.9% │ 7.3% 0.5% │ 2:4 34.5% │ 21.2% 18.2% │ 13.2% 6.4% │ 6.7% 0.5% │ magnitude 69.3% │ 34.0% 25.0% │ 20.2% 5.9% │ 11.1% 0.3% │

★ At ε=4/255: Zeckendorf PGD-20 acc = 6.9% vs Dense = 8.0% → Zeckendorf is NOT more robust (-1.1%)

====================================================================== FIBONACCI ENCODING (Secondary Contribution) ====================================================================== Fibonacci grid: 10 digits, 144 levels

cifar100: pruned=35.02% → encoded=11.55% (Δ=23.47%, RMSE=0.003456)