Dense 1-D dilated convolution

Your task

Function signature

dilated_conv1d(
    x: torch.Tensor,
    weight: torch.Tensor,
    bias: torch.Tensor,
    padding: list[int] | tuple[int, int] = [0, 0],
    dilation: int = 1,
    stride: int = 1,
) -> torch.Tensor

Worked example

Cross-correlation keeps kernel order

import torch

x = torch.tensor([[[1.0], [2.0], [3.0], [4.0]]], dtype=torch.float64, requires_grad=True)
weight = torch.tensor([[[1.0]], [[10.0]]], dtype=torch.float64, requires_grad=True)
bias = torch.tensor([0.0], dtype=torch.float64, requires_grad=True)
padding = [0, 0]
dilation = 1
stride = 1

result = dilated_conv1d(x=x, weight=weight, bias=bias, padding=padding, dilation=dilation, stride=stride)

Expected return

torch.tensor([[[21.0], [32.0], [43.0]]], dtype=torch.float64)

Parameters

Return

torch.Tensor · [B, \mathrm{Lout}, \mathrm{Cout}]

Required behavior

• Implement dense 1-D cross-correlation using raw tensor operations, without convolution helpers. x is [B,L,\mathrm{Cin}], weight is [K,\mathrm{Cin},\mathrm{Cout}], and bias is [\mathrm{Cout}], all the same floating dtype/device. B,L,Cin,Cout,K are positive.
• options are dilation (positive int, default 1), stride (positive int, default 1), and padding (two nonnegative ints (\mathrm{left},\mathrm{right}), default (0,0)). No groups/depthwise variant or implicit same-padding rule is included at launch.
• Let \mathrm{effective\_size}=\mathrm{dilation}\cdot (K-1)+1 and \mathrm{Lout}=\operatorname{max}(0, \operatorname{floor}((L+\mathrm{left}+\mathrm{right}-\mathrm{effective\_size})/\mathrm{stride})+1).
• Return y [B,\mathrm{Lout},\mathrm{Cout}] with y[b,t,o]=\mathrm{bias}[o]+\sum_{k=0..K-1,c=0..\mathrm{Cin}-1} x_{\mathrm{zero}}[b,t\cdot \mathrm{stride}+k\cdot \mathrm{dilation}-\mathrm{left},c] \cdot \mathrm{weight}[k,c,o], where x_zero is zero outside 0\le \mathrm{position}<L. This is cross-correlation: DO NOT reverse the K axis.
• The output includes bias but no activation or input residual. Use explicit asymmetric padding, including even kernels.
• For causal alignment set \mathrm{left}=\mathrm{dilation}\cdot (K-1), \mathrm{right}=0; output t then sees input positions no later than t\cdot \mathrm{stride}. Padding may exceed the input length, as may dilation. Settings with no valid output windows return shape [B,0,\mathrm{Cout}] and zero parameter/input VJPs.
• No normalization or numerical \epsilon is used.

Why this matters

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 dilated_conv1d(
    x: torch.Tensor,  # (B, L, Cin)
    weight: torch.Tensor,  # (K, Cin, Cout)
    bias: torch.Tensor,  # (Cout,)
    padding: list[int] | tuple[int, int] = [0, 0],
    dilation: int = 1,
    stride: int = 1,
) -> torch.Tensor:
    """Return a tensor with shape (B, Lout, Cout)."""
    # Implement the operation. Inputs and test setup are supplied by BioTorch.
    raise NotImplementedError("Implement dilated_conv1d")

Sources and further reading

• calico/basenji · blocks.py
• HazyResearch/hyena-dna · standalone_hyenadna.py