tf.math.approx_min_k

Returns min k values and their indices of the input operand in an approximate manner.

tf.math.approx_min_k(
    operand,
    k,
    reduction_dimension=-1,
    recall_target=0.95,
    reduction_input_size_override=-1,
    aggregate_to_topk=True,
    name=None
)

See https://arxiv.org/abs/2206.14286 for the algorithm details. This op is only optimized on TPU currently.

operand Array to search for min-k. Must be a floating number type.
k Specifies the number of min-k.
reduction_dimension Integer dimension along which to search. Default: -1.
recall_target Recall target for the approximation.
reduction_input_size_override When set to a positive value, it overrides the size determined by operand[reduction_dim] for evaluating the recall. This option is useful when the given operand is only a subset of the overall computation in SPMD or distributed pipelines, where the true input size cannot be deferred by the operand shape.
aggregate_to_topk When true, aggregates approximate results to top-k. When false, returns the approximate results. The number of the approximate results is implementation defined and is greater equals to the specified k.
name Optional name for the operation.

Tuple of two arrays. The arrays are the least k values and the corresponding indices along the reduction_dimension of the input operand. The arrays' dimensions are the same as the input operand except for the reduction_dimension: when aggregate_to_topk is true, the reduction dimension is k; otherwise, it is greater equals to k where the size is implementation-defined.

We encourage users to wrap approx_min_k with jit. See the following example for nearest neighbor search over the squared l2 distance:

import tensorflow as tf
@tf.function(jit_compile=True)
def l2_ann(qy, db, half_db_norms, k=10, recall_target=0.95):
  dists = half_db_norms - tf.einsum('ik,jk->ij', qy, db)
  return tf.nn.approx_min_k(dists, k=k, recall_target=recall_target)

qy = tf.random.uniform((256,128))
db = tf.random.uniform((2048,128))
half_db_norms = tf.norm(db, axis=1) / 2
dists, neighbors = l2_ann(qy, db, half_db_norms)

In the example above, we compute db_norms/2 - dot(qy, db^T) instead of qy^2 - 2 dot(qy, db^T) + db^2 for performance reason. The former uses less arithmetics and produces the same set of neighbors.