MSA and pair representations

ESMFold Relative Position Buckets

EasyRaw PyTorchAbout 10 min1 public example plus private tests

Free account with email, Google or GitHub. Your code runs in an isolated PyTorch sandbox.

Your task

Turn each ordered residue pair’s signed offset into a clipped category and look up its supplied embedding. ESMFold uses residue_index[j] − residue_index[i]; invalid pairs use the learned padding bucket 0, whose embedding may be nonzero.

Function signature

esmfold_relative_position_buckets(
    residue_index: torch.Tensor,
    mask: torch.Tensor,
    weight: torch.Tensor,
    residue_radius: int = 32,
) -> dict[str, torch.Tensor]

Worked example

Offsets use j minus i. The valid 2-by-2 bucket block is [[2, 3], [1, 2]]. Token 2 is invalid, so every touching pair uses padding bucket 0. Its embedding is the supplied nonzero weight[0]=10; padding embeddings must not be zeroed.

import torch

residue_index = torch.tensor([[2, 3, 9]], dtype=torch.int64)
mask = torch.tensor([[True, True, False]], dtype=torch.bool)
weight = torch.tensor([[10.0], [20.0], [30.0], [40.0]], dtype=torch.float64, requires_grad=True)
residue_radius = 1

result = esmfold_relative_position_buckets(residue_index=residue_index, mask=mask, weight=weight, residue_radius=residue_radius)

Expected return

{
    'indices': torch.tensor([[[[2], [3], [0]], [[1], [2], [0]], [[0], [0], [0]]]], dtype=torch.int64),
    'features': torch.tensor([[[[0.0, 0.0, 1.0, 0.0], [0.0, 0.0, 0.0, 1.0], [1.0, 0.0, 0.0, 0.0]], [[0.0, 1.0, 0.0, 0.0], [0.0, 0.0, 1.0, 0.0], [1.0, 0.0, 0.0, 0.0]], [[1.0, 0.0, 0.0, 0.0], [1.0, 0.0, 0.0, 0.0], [1.0, 0.0, 0.0, 0.0]]]], dtype=torch.float64),
    'embedding': torch.tensor([[[[30.0], [40.0], [10.0]], [[20.0], [30.0], [10.0]], [[10.0], [10.0], [10.0]]]], dtype=torch.float64),
}

Parameters

Parameter	Shape and meaning
`residue_index`torch.Tensor	$[B, N]$ Supplied residue numbering, not required to start at zero.
`mask`torch.Tensor	$[B, N]$ True for valid tokens.
`weight`torch.Tensor	$[2r+2,C]$ Learned projection from the ordered one-hot feature blocks to output channels.
`residue_radius`intDefault `32`	Clipping radius for residue-index differences.

Return

dict[str, torch.Tensor]

Return exactly the named fields applicable to this operation.

Required behavior

For pair(i,j), bucket = clamp(residue_index[j] − residue_index[i], −r, r) + r +1. Invalid pairs use bucket0, a REAL learned padding category. Return its one-hot vector and weight lookup even for invalid pairs; do not zero the padding embedding.
Return indices $[B,N,N,1]$ , one-hot features (B,N,N,2r+2), and embedding. Valid offsets occupy categories 1 through2r+1.
Use CPU float32/float64 tensors with one shared floating dtype/device. Preserve strided layouts and do not mutate supplied tensors.
Use raw tensor operations, not a ready-made implementation of the requested primitive. Supplied parameters and random variates must not be reinitialized.

Why this matters

ESMFold uses a learned lookup for clipped residue offsets and reserves a real embedding row for padding.

Starter code

You write the body of this function in the BioTorch workspace. Your code runs in an isolated PyTorch sandbox; Run checks the public examples and Submit grades the full test suite, including gradients.

import torch


def esmfold_relative_position_buckets(
    residue_index: torch.Tensor,  # (B, N)
    mask: torch.Tensor,  # (B, N)
    weight: torch.Tensor,  # (2r+2,C)
    residue_radius: int = 32,
) -> dict[str, torch.Tensor]:
    """Return dict[str, torch.Tensor]:
    
    indices: (B,N,N,1).
    features: (B,N,N,2r+2).
    embedding: (B, N, N, C)."""
    # Implement the operation. Inputs and test setup are supplied by BioTorch.
    raise NotImplementedError("Implement esmfold_relative_position_buckets")

Ready to implement it?

3 progressive hints, a solution walkthrough, and grading that checks values, shapes and gradients are waiting in the workspace.

Write and run your solution Sign in

Free account with email, Google or GitHub. Your code runs in an isolated PyTorch sandbox.

Related exercises

Sources and further reading

A primitive exercise, not an end-to-end reproduction of the named models. No affiliation or endorsement is implied.