Iso-parameter verification
Budget matching across the plain CNN grid.
Fixed-budget frontier
The best plain CNN sits at intermediate depth.
The 1.0x column keeps the parameter budget near 5M while depth changes. D=14 is the strongest iso-parameter row on both CIFAR tasks, with D=20 close on CIFAR-10.
Width-ratio cells are local off-budget checks around each iso width. The fixed-budget claim comes from the 1.0x column.
Depth by width ratio
CIFAR-100 accuracyIso-budget line
1.0x width ratioInterpretation
Extra width helps within each row, but the iso-budget column answers a different question. At the same target budget, extra plain depth eventually trades away too much trainability.
Dataset comparison
CIFAR-100 makes the depth penalty sharper.
CIFAR-10 shows a D=14 and D=20 plateau above D=8 and D=26. CIFAR-100 shows a clearer peak at D=14 and a larger deep-plain drop.
The table reports three-seed means from the plain CNN iso row. Accuracy and gap are percentages.
CIFAR-10 and CIFAR-100 iso rows
test accuracy| Dataset | Depth | Width | Params | Accuracy | Gap |
|---|
Gradient and trainability diagnostics
Deep plain models slow down before residual paths repair them.
Convergence epoch rises monotonically with depth at the iso budget. The gradient-ratio proxy does not collapse in a simple way, so the diagnosis is broader than one vanishing-gradient symptom.
Convergence is the epoch where online train accuracy reaches 99% of its own final value.
Convergence epoch by depth
plain CNN iso budgetDeep-side signal
D=8 mean
111.5
D=26 mean
129.0
Depths
4
Seeds per plain cell
3
Readout
The deepest plain endpoint has the slowest convergence and the weakest CIFAR-100 accuracy at the matched parameter budget.
Mechanism checks
The two extremes fail differently.
Residual pathways recover the deep endpoint, which supports a trainability account. Extra width rescues the shallow endpoint, but the recovery is parameter-expensive.
ResNet controls are diagnostic interventions, not a fully powered architecture benchmark.
Plain versus ResNet
CIFAR-100 matched 150Shallow-wide compensation
CIFAR-100Fixed optimizer protocol
The gap varies while SGD noise scale is fixed.
All plain-grid runs share the same learning rate, batch size, momentum, data size, and scalar noise-scale value. Gap variation therefore cannot be reduced to the scalar g value alone.
Fixed value: g = eta N / B(1 - beta) = 390.625 for every plain-grid run.
Gap proxy by width ratio
CIFAR-100, fixed gWhy this matters
The fixed protocol blocks a common confound: different architectures are not being handed different optimizer noise states. Remaining variation points back to architecture, optimization dynamics, and their interaction.
Paper figure set
Static figures remain available for paper parity.
The interactive views above are generated from the same committed aggregate data used by the paper figures.
The report keeps only the six public figures used here.
CIFAR-100 accuracy
The clearest D=14 peak in the frontier.
Trainability diagnostics
Convergence slows as plain depth rises.
ResNet control
Residual pathways recover the deep endpoint.
Noise-scale check
Gap variation remains at fixed scalar g.
Gradient proxy
The deep penalty is broader than one simple collapse.
Audit trail
Built from checked-in research artifacts.
The report uses curated aggregate outputs and source text already present in the repository. No expensive experiments were regenerated.
Run `python scripts/build_report_data.py` after updating CSV summaries.