Implement and vectorize NumPy Conv2D

You are given an image tensor and a convolution kernel stored in relational tables. The input tensor follows an NCHW layout (batch, channel, height, width), flattened into rows, and the kernel follows a (C_out, C_in, k_h, k_w) layout. Tables: - input_tensor: one row per pixel of the input tensor. - kernel_weights: one row per weight in the convolution kernel. - conv_config: convolution hyperparameters (stride and padding). For this data set, there is a single batch (batch_id = 1) and a single configuration (config_id = 1) with stride_h = 1, stride_w = 1, pad_h = 0, pad_w = 0. Define the 2D convolution as a cross-correlation (no kernel flipping): output[batch_id, out_channel, out_row, out_col] = sum over in_channel, k_row, k_col of input[batch_id, in_channel, out_row * stride_h + k_row - pad_h, out_col * stride_w + k_col - pad_w] * kernel[out_channel, in_channel, k_row, k_col] Assume padding is chosen so that the kernel never goes out of bounds for this sample (i.e., only valid positions are produced). Pixels outside the input tensor are treated as zero (but for this configuration, no such positions are needed). Write a single SQL query that returns the convolution result as one row per output element, with the following columns: - batch_id - out_channel - out_row (0-based) - out_col (0-based) - value (the convolution result at that position) Your solution should: - Join input_tensor with kernel_weights and use the stride/padding values from conv_config (config_id = 1). - Derive the output spatial indices (out_row, out_col) from the input and kernel coordinates. - Use set-based SQL (joins and aggregations) rather than procedural loops or cursors.