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Examples

Every example in the examples/ directory is a single, runnable script that trains/evaluates on synthetic data and saves a publication-grade, brand-themed figure. Run any of them with:

uv run python examples/<name>.py

The q-Gaussian family

Compact support (q < 1), Gaussian (q = 1) and heavy tails (1 < q < 3), with samples overlaid on the analytic density.

Fitting q by maximum likelihood

Recovers a hidden generating q by gradient descent on the q-Gaussian log-likelihood — q is just a differentiable parameter.

Derivative-free optimization

An animated q-exponential-weighted search (contour + 3-D surface) whose heavy tails (q > 1) escape a decoy minimum that traps greedy q = 1.

Label-noise robustness

Bounded Tsallis cross-entropy (q < 1) vs. the Shannon baseline, and a learnable q that discovers the robust regime on its own.

Node classification under noise

A GCN with learnable Tsallis q stays robust to noisy training labels, while the Shannon baseline propagates the errors across the graph.

Exploration on a bandit

A tsallis_entmax policy whose learnable q anneals exploration into exploitation for the lowest cumulative regret.

Sparse self-attention

Attention pooling with tsallis_entmax; a learnable q recovers sparse, signal-focused attention as distractors grow.

Learning q in attention

Animated: watch the attention q being learned — as q rises toward sparsemax, the attention map sharpens onto the informative tokens.

The recurring theme: q as a learnable parameter

Six of the eight examples make q itself trainable, and the headline result is consistent: gradient descent reliably discovers a useful entropic index, with no grid search.

  • Classification — the learned loss q settles in the robust regime (q ≈ 0.3) and matches the best hand-tuned fixed q at every noise level.
  • Node classification — on a graph, the learned GCN loss q settles in the robust regime and stays accurate as label noise the Shannon baseline amplifies grows.
  • Attention — the learned attention q converges near sparsemax (q ≈ 2.0), zeroing out distractor tokens.
  • Reinforcement learning — the learned policy q rises over training, annealing exploration into exploitation.