Conv3d

Quantization-aware 3-D convolution — trainable float kernel, fake-quant per forward.

The training-time stand-in that lucid.quantization.prepare_qat installs in place of a float lucid.nn.Conv3d (volumetric / video backbones). It keeps a trainable float kernel but routes both the weight and the layer output through a lucid.quantization.FakeQuantize on every forward, so the network feels the int8 rounding error as it learns and adapts its kernel to the eventual int8 grid. This closes the train / inference accuracy gap: a network trained with the rounding baked in barely moves when its weights are finally frozen to int8, whereas plain post-training quantization perturbs a kernel that never saw rounding.

Straight-through estimator (STE). Rounding is a step function whose derivative is zero almost everywhere, so a literal round would block all gradient flow. The fake-quant rounds in the forward pass but, in the backward pass, pretends it was the identity — the incoming gradient passes straight through to the float kernel (clipped to the quantization range). The kernel thus stays fully trainable while every forward value it produces is the dequantized number an int8 conv kernel would have computed.

Where it sits. lucid.quantization.prepare_qat deep-copies the float model and swaps each lucid.nn.Conv3d for this class, attaching the weight and activation FakeQuantize modules from the layer's qconfig. After training, lucid.quantization.convert reads the trained kernel together with the activation observer's final (scale, zero_point) and bakes them into an inference lucid.nn.quantized.Conv3d whose weight is stored as (typically per-output-channel) int8 codes.

On each forward the kernel is fake-quantized, the ordinary F.conv3d runs, and the result is fake-quantized onto the observed activation grid:

where $\star$ is the 3-D cross-correlation, $s, z$ are the scale / zero-point the enclosing FakeQuantize derives from its observer (per-output-channel for the weight), and $q_{\min}, q_{\max}$ are the grid bounds. The straight-through unit derivative is what keeps the layer differentiable despite the non-differentiable round.