Modify this PyTorch pseudo-code to perform negative sampling if the pos_ids are known: label #shape=[batch_s, pos_ids] hidden #shape=[batch_s, ch] logits #shape=[ch, C] out=np.dot(logits, hidden(X)) #shape=[batch_s, C] loss=cross_entropy(out, label)

To implement negative sampling, we first need to generate negative sample IDs. Assuming C is the total number of classes, we can randomly sample k negative IDs from the range [0, C-1], ensuring they are distinct from the positive IDs. Then, we compute the logits for both positive and negative samples by selecting the appropriate columns from the logits matrix using their respective IDs. The outputs for positive and negative samples are then concatenated. Finally, the loss is calculated using a suitable objective function, such as binary cross-entropy, comparing the model's predictions for positive samples against a label of 1 and for negative samples against a label of 0.