ViT Classification Forward

Implement the full Vision Transformer (ViT) forward pass for image classification — patch embedding → N transformer blocks → classifier head on the [CLS] token.

This problem composes the two preceding building blocks end-to-end:

1. Patch embedding with [CLS] token (Task 11) — converts an image batch (N, C, H, W) into a sequence (N, num_patches + 1, d_model) by extracting non-overlapping patches, projecting them, prepending a [CLS] token, and adding position embeddings.

2. Pre-LN ViT encoder blocks (Task 12) — each block applies x = x + MHA(LN(x)) then x = x + FFN(LN(x)) with manual layer norm, multi-head self-attention, and GELU activation; no library shortcuts.

3. Classifier head — project the final [CLS] representation to logits: logits = seq[:, 0, :] @ w_head.

Pipeline

seq = patch_embed_with_cls(x, w_proj, cls_token, pos_embed)
for i in range(num_blocks):
    seq = vit_block(seq, w_q_i, w_k_i, w_v_i, w_o_i, w_mlp1_i, w_mlp2_i, num_heads)
cls_repr = seq[:, 0, :]
logits   = cls_repr @ w_head
return logits

Weight packing convention

blocks_weights has shape (num_blocks, 6, d_model, d_model). For block i, blocks_weights[i, 0..5] are: [w_q, w_k, w_v, w_o, w_mlp1, w_mlp2].

Simplification: d_ff = d_model so all six weight matrices are (d_model, d_model).

Implementation constraints

• No nn.MultiheadAttention, no F.scaled_dot_product_attention, no nn.LayerNorm — implement everything from scratch.
• Manual layer norm: (x - mean) / sqrt(var + eps), eps=1e-5.
• Manual softmax for attention scores.
• Manual GELU: 0.5 * x * (1 + tanh(sqrt(2/π) * (x + 0.044715 * x³))).

References

• Dosovitskiy et al., “An Image Is Worth 16x16 Words: Transformers for Image Recognition at Scale”, ICLR 2021.

Inputs / Output

• x: (N, C, H, W) — image batch.
• w_proj: (C*P*P, d_model) — patch projection.
• cls_token: (d_model,) — learnable [CLS] token.
• pos_embed: (num_patches + 1, d_model) — position embeddings.
• blocks_weights: (num_blocks, 6, d_model, d_model) — packed block weights.
• w_head: (d_model, num_classes) — classifier head.
• num_heads: int — number of attention heads.
• Output: (N, num_classes) — classification logits.