ArcFace Metric Learning

Overview

ArcFace adds an angular margin penalty to the softmax loss, pushing embeddings of the same class closer and different classes further apart in hyperspherical space. Train a CNN with an ArcMarginProduct head, then discard the head and use the penultimate layer as your embedding extractor. Produces highly discriminative features for retrieval tasks.

Quick Start

import tensorflow as tf
import math

class ArcMarginProduct(tf.keras.layers.Layer):
    def __init__(self, n_classes, s=30, m=0.50, **kwargs):
        super().__init__(**kwargs)
        self.n_classes = n_classes
        self.s = s
        self.cos_m = tf.math.cos(m)
        self.sin_m = tf.math.sin(m)
        self.th = tf.math.cos(math.pi - m)
        self.mm = tf.math.sin(math.pi - m) * m

    def build(self, input_shape):
        self.W = self.add_weight(shape=(input_shape[0][-1], self.n_classes),
                                 initializer='glorot_uniform', trainable=True)

    def call(self, inputs):
        X, y = inputs
        cosine = tf.matmul(tf.math.l2_normalize(X, axis=1),
                           tf.math.l2_normalize(self.W, axis=0))
        sine = tf.math.sqrt(1.0 - tf.math.pow(cosine, 2))
        phi = cosine * self.cos_m - sine * self.sin_m
        one_hot = tf.cast(tf.one_hot(y, depth=self.n_classes), dtype=phi.dtype)
        output = (one_hot * phi) + ((1.0 - one_hot) * cosine)
        return output * self.s

# Training
backbone = tf.keras.applications.EfficientNetB3(include_top=False, pooling='avg')
x = backbone.output
margin = ArcMarginProduct(n_classes=num_products, s=30, m=0.5)
output = margin([x, label_input])
model.fit(...)

# Inference: extract embeddings (discard ArcFace head)
embedder = tf.keras.Model(inputs=model.input[0], outputs=model.layers[-4].output)
embeddings = embedder.predict(test_data)

Key Decisions

• s (scale): 30 is standard; higher values sharpen the distribution
• m (margin): 0.5 radians; increase for harder separation, decrease if training diverges
• L2 normalize: both features and weights must be normalized for angular margin to work
• Discard head at inference: the classification head is only needed during training

References

• Source: unsupervised-baseline-arcface
• Competition: Shopee - Price Match Guarantee