Max margin loss in TensorFlow

Question

I'm trying to implement a max margin loss in TensorFlow. the idea is that I have some positive example and i sample some negative examples and want to compute something like

where B is the size of my batch and N is the number of negative samples I want to use.

I'm new to tensorflow and I'm finding it tricky to implement it. My model computes a vector of scores of dimension B * (N + 1) where I alternate positive samples and negative samples. For instance, for a batch size of 2 and 2 negative examples I have a vector of size 6 with scores for the first positive example at index 0 and for the second positive example at position 3 and scores for negative examples in position 1, 2, 4 and 5. The ideal would be to get values like [1, 0, 0, 1, 0, 0].

What I could came up with is the following, using while and conditions:

# Function for computing max margin inner loop
def max_margin_inner(i, batch_examples_t, j, scores, loss):
    idx_pos = tf.mul(i, batch_examples_t)
    score_pos = tf.gather(scores, idx_pos)
    idx_neg = tf.add_n([tf.mul(i, batch_examples_t), j, 1])
    score_neg = tf.gather(scores, idx_neg)
    loss = tf.add(loss, tf.maximum(0.0, 1.0 - score_pos + score_neg))
    tf.add(j, 1)
    return [i, batch_examples_t, j, scores, loss]

# Function for computing max margin outer loop
def max_margin_outer(i, batch_examples_t, scores, loss):
    j = tf.constant(0)
    pos_idx = tf.mul(i, batch_examples_t)
    length = tf.gather(tf.shape(scores), 0)
    neg_smp_t = tf.constant(num_negative_samples)
    cond = lambda i, b, j, bi, lo: tf.logical_and(
        tf.less(j, neg_smp_t),
        tf.less(pos_idx, length))
    tf.while_loop(cond, max_margin_inner, [i, batch_examples_t, j, scores, loss])
    tf.add(i, 1)
    return [i, batch_examples_t, scores, loss]

# compute the loss
with tf.name_scope('max_margin'):
    loss = tf.Variable(0.0, name="loss")
    i = tf.constant(0)
    batch_examples_t = tf.constant(batch_examples)
    condition = lambda i, b, bi, lo: tf.less(i, b)
    max_margin = tf.while_loop(
        condition,
        max_margin_outer,
        [i, batch_examples_t, scores, loss])

The code has two loops, one for the outer sum and the other for the inner one. The problem I'm facing is that the loss variable keeps accumulating errors at each iteration without being reset after each iteration. So it actually doesn't work at all.

Moreover, it seems really not in line with tensorflow way of implementing things. I guess there could be better ways, more vectorized ways to implement it, hope someone will suggest options or point me to examples.

Answer 1

First we need to clean the input:

• we want an array of positive scores, of shape [B, 1]
• we want a matrix of negative scores, of shape [B, N]

import tensorflow as tf

B = 2
N = 2
scores = tf.constant([0.5, 0.2, -0.1, 1., -0.5, 0.3])  # shape B * (N+1)

scores = tf.reshape(scores, [B, N+1])

scores_pos = tf.slice(scores, [0, 0], [B, 1])

scores_neg = tf.slice(scores, [0, 1], [B, N])

---

Now we only have to compute the matrix of the loss, i.e. all the individual loss for every pair (positive, negative), and compute its sum.

loss_matrix = tf.maximum(0., 1. - scores_pos + scores_neg)  # we could also use tf.nn.relu here
loss = tf.reduce_sum(loss_matrix)