jax.lax.approx_min_k(operand, k, reduction_dimension=-1, recall_target=0.95, reduction_input_size_override=-1, aggregate_to_topk=True)[source]#

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

See https://arxiv.org/abs/2206.14286 for the algorithm details.

  • operand (Array) – Array to search for min-k. Must be a floating number type.

  • k (int) – Specifies the number of min-k.

  • reduction_dimension (int) – Integer dimension along which to search. Default: -1.

  • recall_target (float) – Recall target for the approximation.

  • reduction_input_size_override (int) – 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 (bool) – When true, aggregates approximate results to the top-k in sorted order. When false, returns the approximate results unsorted. In this case, the number of the approximate results is implementation defined and is greater or equal to the specified k.


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.

Return type:

tuple[Array, Array]

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

>>> import functools
>>> import jax
>>> import numpy as np
>>> @functools.partial(jax.jit, static_argnames=["k", "recall_target"])
... def l2_ann(qy, db, half_db_norms, k=10, recall_target=0.95):
...   dists = half_db_norms - jax.lax.dot(qy, db.transpose())
...   return jax.lax.approx_min_k(dists, k=k, recall_target=recall_target)
>>> qy = jax.numpy.array(np.random.rand(50, 64))
>>> db = jax.numpy.array(np.random.rand(1024, 64))
>>> half_db_norm_sq = jax.numpy.linalg.norm(db, axis=1)**2 / 2
>>> dists, neighbors = l2_ann(qy, db, half_db_norm_sq, k=10)

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