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Sm Attention Pool

torchmil.nn.attention.SmAttentionPool

Bases: Module

Attention-based pooling with the Sm operator, as proposed in Sm: enhanced localization in Multiple Instance Learning for medical imaging classification.

Given an input bag \(\mathbf{X} = \left[ \mathbf{x}_1, \ldots, \mathbf{x}_N \right]^\top \in \mathbb{R}^{N \times \texttt{in_dim}}\), this model aggregates the instance features into a bag representation \(\mathbf{z} \in \mathbb{R}^{\texttt{in_dim}}\) as,

\[\begin{gather} \mathbf{f} = \operatorname{SmMLP}(\mathbf{X}) \in \mathbb{R}^{N}, \\ \mathbf{z} = \mathbf{X}^\top \operatorname{Softmax}(\mathbf{f}) = \sum_{n=1}^N s_n \mathbf{x}_n, \end{gather}\]

where \(s_n\) is the normalized attention score for the \(n\)-th instance.

To compute the attention values, \(\operatorname{SmMLP}\) is defined as \(\operatorname{SmMLP}(\mathbf{X}) = \mathbf{Y}^L\) where

\[\begin{gather} \mathbf{Y}^0 = \mathbf{X}\mathbf{W^0}, \\ \mathbf{Y}^l = \operatorname{act}( \texttt{Sm}(\mathbf{Y}^{l-1}\mathbf{W}^l)), \quad \text{for } l = 1, \ldots, L-1, \\ \mathbf{Y}^L = \mathbf{Y}^{L-1}\mathbf{w}, \end{gather}\]

where \(\mathbf{W^0} \in \mathbb{R}^{\texttt{in_dim} \times \texttt{att_dim}}\), \(\mathbf{W}^l \in \mathbb{R}^{\texttt{att_dim} \times \texttt{att_dim}}\), \(\mathbf{w} \in \mathbb{R}^{\texttt{att_dim} \times 1}\), \(\operatorname{act} \ \colon \mathbb{R} \to \mathbb{R}\) is the activation function, and \(\texttt{Sm}\) is the Sm operator, see Sm for more details.

Note: If sm_pre=True, the Sm operator is applied before \(\operatorname{SmMLP}\). If sm_post=True, the Sm operator is applied after \(\operatorname{SmMLP}\).

__init__(in_dim, att_dim=128, act='gelu', sm_mode='approx', sm_alpha='trainable', sm_layers=1, sm_steps=10, sm_pre=False, sm_post=False, sm_spectral_norm=False)

Parameters:

  • in_dim (int) –

    Input dimension.

  • att_dim (int, default: 128 ) –

    Attention dimension.

  • act (str, default: 'gelu' ) –

    Activation function for attention. Possible values: 'tanh', 'relu', 'gelu'.

  • sm_mode (str, default: 'approx' ) –

    Mode for the Sm operator. Possible values: 'approx', 'exact'.

  • sm_alpha (Union[float, str], default: 'trainable' ) –

    Alpha value for the Sm operator. If 'trainable', alpha is trainable.

  • sm_layers (int, default: 1 ) –

    Number of layers that use the Sm operator.

  • sm_steps (int, default: 10 ) –

    Number of steps for the Sm operator.

  • sm_pre (bool, default: False ) –

    If True, apply Sm operator before the attention pooling.

  • sm_post (bool, default: False ) –

    If True, apply Sm operator after the attention pooling.

  • sm_spectral_norm (bool, default: False ) –

    If True, apply spectral normalization to all linear layers.

forward(X, adj, mask=None, return_att=False)

Forward pass.

Parameters:

  • X (Tensor) –

    Bag features of shape (batch_size, bag_size, in_dim).

  • adj (Tensor) –

    Adjacency matrix of shape (batch_size, bag_size, bag_size).

  • mask (Tensor, default: None ) –

    Mask of shape (batch_size, bag_size).

  • return_att (bool, default: False ) –

    If True, returns attention values (before normalization) in addition to z.

Returns:

  • z ( Tensor ) –

    Bag representation of shape (batch_size, in_dim).

  • f ( Tensor ) –

    Only returned when return_att=True. Attention values (before normalization) of shape (batch_size, bag_size).