Conv3d

Quantized 3-D convolution — int8 kernel, dequantize-to-float compute.

The volumetric member of the quantized conv family (video, 3-D medical imaging), and the inference-time replacement that lucid.quantization.convert installs for a calibrated float lucid.nn.Conv3d. Volumetric kernels are the largest weights in a 3-D net, so the int8 checkpoint / working-set savings matter most here.

Representation (sidecar design B). The learned float kernel is quantized once, at from_float time, into an int8 code tensor plus a per-output-channel scale / zero_point; the float kernel is then dropped. Only the int8 codes, the qparams, and the (still-float) bias live in the module, so the checkpoint is far smaller than the float layer's. Each forward dequantizes the kernel back to float, runs the ordinary F.conv3d, and finally fake-quantizes the output onto the activation grid that calibration observed. Keeping the convolution itself in float means the result matches a genuine int8 kernel to within a rounding step and the layer runs unchanged on any device, with no int8 conv kernel required.

Per-channel weights. The kernel (out_channels, in_channels/groups, kd, kh, kw) is quantized independently for every output channel (axis 0): each filter carries its own scale and zero-point. Because different output filters often span very different dynamic ranges, per-channel quantization tracks them far more tightly than a single per-tensor scale, and is the standard accuracy-preserving choice for convolution kernels. The bias is small and precision-sensitive, so it is left in float.

Encoding happens once (at from_float); decode + convolve run on every forward:

where $s_o, z_o$ are the per-output-channel weight scale / zero-point (index $o$ runs over out_channels) and $S, Z$ the scalar calibrated output (scale, zero_point) with grid bounds $q_{\min}, q_{\max}$ (0, 255 for the default quint8). The decode → float-conv → re-quantize round-trip is what makes the output bit-equivalent to a true int8 kernel without needing one.