如何编写Keras自定义二次层实现逐样本计算X.T*X多项式特征？

Got it, let's sort out this issue. The problem with your current QuadraticLayer is that it's calculating the matrix product for the entire batch as a single tensor, instead of handling each training sample independently. Here's how to adjust it properly:

Modified QuadraticLayer Code #

import tensorflow as tf
from tensorflow.keras.layers import Layer

class QuadraticLayer(Layer):
    def __init__(self, **kwargs):
        super(QuadraticLayer, self).__init__(**kwargs)
    
    def build(self, input_shape):
        assert isinstance(input_shape, tuple)
        self.in_shape = input_shape[1]
        # Output shape is the square of input features (each sample's outer product flattened)
        self.out_shape = self.in_shape ** 2
        super(QuadraticLayer, self).build(input_shape)  # Always call this at the end
    
    def call(self, x):
        # x has shape (batch_size, in_features)
        # Expand dimensions to (batch_size, in_features, 1) for per-sample outer product
        x_expanded = tf.expand_dims(x, axis=-1)
        # Compute outer product for each sample: (batch_size, in_features, in_features)
        # transpose_b=True makes this (in_features,1) * (1,in_features) = (in_features,in_features) per sample
        outer_product = tf.matmul(x_expanded, x_expanded, transpose_b=True)
        # Flatten each sample's outer product to (batch_size, in_features^2)
        return tf.reshape(outer_product, (-1, self.out_shape))
    
    def compute_output_shape(self, input_shape):
        return (input_shape[0], self.out_shape)

Key Changes Explained #

• Expanding Dimensions: We use tf.expand_dims(x, axis=-1) to turn each sample from a 1D tensor (in_features,) into a 2D tensor (in_features, 1). This lets us compute the outer product for each sample separately.
• Per-Sample Outer Product: The tf.matmul with transpose_b=True calculates the outer product for every sample in the batch in parallel, resulting in a tensor of shape (batch_size, in_features, in_features).
• Correct Reshaping: We flatten each sample's 2D outer product matrix into a 1D vector, giving us the final output shape (batch_size, in_features²).
• Explicit Output Shape: Updated compute_output_shape to use input_shape[0] (the batch size) instead of hardcoding None—this is more clear about preserving the batch dimension.

Why Your Original Code Failed #

Your original tf.reshape(x, (self.in_shape, 1, -1)) didn't assign the reshaped tensor back to x, and it was combining all samples into one large 3D tensor. This meant the matmul was computing a Gram matrix for the entire dataset, not generating quadratic features per individual sample.

内容的提问来源于stack exchange，提问作者quester