Live inference · accuracy vs interpretability

Draw a digit · CNN vs Pure KAN

Same input, two stories: the CNN is usually more accurate, but opaque. The Pure KAN is a bit less accurate — and every decision edge is a plottable function φ(x).

Loading models…

Drawing pad Write here

Write a digit here

Click or tap inside this box · 0–9

Start in the dashed box above. Thick strokes work best.

Preprocessed 28×28 input sent to both models

Higher accuracy · opaque

CNN

—

LeNet-style · 23.7k params
97.1% MNIST test

Weights mix features; you mostly explain after the fact (Grad-CAM).

Lower accuracy · readable

Pure KAN

—

Chebyshev KAN · 263k params
92.1% MNIST test

Each edge is a learned φ(x) you can plot, prune, and symbolize.

Write in the dashed box — then read the tradeoff below.

CNN wins accuracy

97.1%

Fast, local filters. The “why” of a prediction is buried in the weight tensor.

KAN wins interpretability

92.1%

~5 pp less accurate on MNIST — but decisions live on univariate edge functions you can inspect.

Live KAN edges

Inspect φ(x) — click an edge

These are the same Chebyshev edge functions inside Pure KAN. After you draw, we rank edges by contribution to the predicted digit. CNN has no equivalent view.

Draw a digit to list contributing edges — or browse strongest edges.

Select an edge to plot φ(x) = Σ cₖ Tₖ(tanh(x))

The point isn’t beating the CNN — it’s reading the model

Pure KAN trades a few accuracy points for intrinsic interpretability: edges are functions, not black-box weights.

Plot φ(x) ↑ Click edges above — active vs flat curves are the model itself.

Prune the graph Drop weak edges by ‖c‖₂; at 50% sparsity ~97% of accuracy is retained.

Symbolize ~6% of sampled edges fit closed forms (R² ≥ 0.95) — readable math, not just heatmaps.

CNN: post-hoc explanation KAN: intrinsic edge functions Static evidence ↓

Why accept lower accuracy?

Interpretability you can show

Below: the same Pure KAN behind the demo. Even when it disagrees with the CNN, you can inspect which edges mattered — something a standard CNN does not give you natively.

Learned KAN edge functions — **Learned edge functions φ(x)** Active curves vs near-flat edges — the model’s nonlinearities are literally plots.

KAN attribution vs Grad-CAM — **Attribution vs Grad-CAM** KAN relevance can follow edge magnitudes; CNN explanations stay approximate and post-hoc.

KAN graph before pruning — **Before prune** Dense edge graph — accurate but hard to read.

KAN graph after pruning — **After prune** Magnitude pruning collapses dead edges into a smaller, still-runnable subnetwork.

Results

Benchmarks

Accuracy still matters — Conv-KAN closes much of the CNN gap while keeping a readable KAN head.

Theory

Why KAN can be less accurate and still valuable

CNNs use fixed activations on nodes after linear/conv mixing. Decisions hide in large weight tensors; Grad-CAM approximates where mattered, not the functions computed.

KANs put learnable univariate φ(x) on edges: φ(x)=Σ cₖ Tₖ(tanh(x)). You can plot, prune by ‖c‖₂, symbolize, and attribute along paths — that is the product, not a side note.

Accuracy-first

CNN

Local filters, fixed σ, fast inference. Explainability is mostly post-hoc.

Interpretability-first

Pure KAN

Flattens the image; every edge is a Chebyshev polynomial — slower and a bit less accurate here, but the decision path is readable.

Dimension	CNN	Pure KAN
MNIST test (these checkpoints)	97.1%	92.1%
Nonlinearity	Fixed on nodes	Learnable φ on edges
Inspectability	Post-hoc (Grad-CAM)	Intrinsic edge curves
What you optimize for	Speed + accuracy	Readable decision path