tempo_classification

Tempo-as-classification: a softmax over BPM bins with a Gaussian soft target.

Instead of regressing a number, the model scores a discrete grid of BPM bins. The target is not one-hot but a Gaussian centred on the true tempo, which gives the bin grid back its ordinal structure — a neighbouring bin is a near miss, not an unrelated class. Selected by loss: classification and dispatched by TempoModule, which also supplies the bin grid and sigma.

Functions

classification_tempo_loss(logits, tempo, ...)

Cross-entropy between predicted softmax and Gaussian soft target.

gaussian_soft_target(tempo, bin_centers, sigma)

Soft target distribution over tempo bins.
classification_tempo_loss(logits, tempo, bin_centers, sigma)[source]

Cross-entropy between predicted softmax and Gaussian soft target.

\[\mathcal{L} = -\frac{1}{B} \sum_{i=1}^{B} \sum_{j=1}^{n_{\text{bins}}} p_{i,j} \log \hat{p}_{i,j}\]

where \(p_{i,j}\) is the Gaussian soft target from gaussian_soft_target() and \(\hat{p}_{i,j}\) is the model’s softmax probability for bin \(j\).

Parameters:

  • logits (Tensor) – Model logits over BPM bins, shape (B, n_bins).

  • tempo (Tensor) – True BPM values, shape (B,).

  • bin_centers (Tensor) – BPM at the centre of each bin, shape (n_bins,).

  • sigma (float) – Gaussian standard deviation in BPM units.

Returns:

Scalar mean loss, shape ().

Return type:

Tensor

gaussian_soft_target(tempo, bin_centers, sigma)[source]

Soft target distribution over tempo bins.

For each sample, places a Gaussian centred on the true tempo across the discrete bin grid, then normalises to a probability distribution. Bins near the true tempo receive non-zero target mass, which gives the model a smoother gradient than a one-hot target and bakes in the ordinal structure of the bin grid.

\[p_{i,j} = \frac{\exp\left(-\frac{1}{2}\left(\frac{c_j - y_i}{\sigma}\right)^2\right)} {\sum_{k=1}^{n_{\text{bins}}} \exp\left(-\frac{1}{2}\left(\frac{c_k - y_i}{\sigma}\right)^2\right)}\]

where \(c_j\) is the centre of bin \(j\) and \(y_i\) is the true tempo of sample \(i\).

Parameters:

  • tempo (Tensor) – True BPM values, shape (B,).

  • bin_centers (Tensor) – BPM at the centre of each bin, shape (n_bins,).

  • sigma (float) – Gaussian standard deviation in BPM units.

Returns:

Soft target distribution, shape (B, n_bins).

Return type:

Tensor