Implement CLIP-Style Symmetric Contrastive Loss (Image-Text)

Problem Given a batch of image and text embeddings paired one-to-one as positives, implement the CLIP-style symmetric contrastive loss. Let batch size be B. Image embeddings I ∈ R^{B×D} and text embeddings T ∈ R^{B×D}. Compute the similarity matrix: S = I @ T^T, where S[i][j] is the similarity between image i and text j. Build labels: labels = [0, 1, 2, ..., B-1] (image i matches text i). Compute bidirectional cross-entropy and average: loss_i = cross_entropy(S, labels) (image→text) loss_t = cross_entropy(S^T, labels) (text→image) loss = (loss_i + loss_t) / 2 Implement this loss (PyTorch or NumPy-style pseudocode is fine). cross_entropy(logits, labels) should apply softmax row-wise, take the negative log-likelihood at the given label per row, and average over the batch. I/O (for implementation/self-test) Input: I (float matrix B×D), T (float matrix B×D) Output: scalar float loss Constraints 1 ≤ B ≤ 2048 1 ≤ D ≤ 4096 Must be numerically stable (e.g., subtract row-wise max before softmax). Example test cases (illustrative) Case 1 Input: B=1, any I,T Expected: labels=[0], loss=0.0 (single class => prob 1). Case 2 Input: B=2, D=2 I = [[1,0],[0,1]] T = [[1,0],[0,1]] Expected: diagonal similarities are highest, loss should be small. Case 3 Input: B=2, D=2 I = [[1,0],[0,1]] T = [[0,1],[1,0]] Expected: diagonal similarities are lowest, loss should be large. Case 4 Input: B=3, D=3 I = identity(3) T = identity(3) Expected: loss_i == loss_t, and loss should be small. Case 5 Input: random I,T (e.g., standard normal) Expected: finite loss (no NaN/Inf). Example Input B=1, D=3 I=[[0.2, -0.1, 0.5]] T=[[0.4, 0.0, -0.3]] Output 0.0