Full forward pass (tokens to embeddings to blocks to logits)

The problem, from first principles

Every previous question in this curriculum's [04-seq-modeling] and [05-transformers-llm] sections built exactly ONE piece of a language model in isolation: [04-seq-modeling/02-embeddings/01-token-embedding-lookup] turns ids into vectors, [04-seq-modeling/02-embeddings/03-sinusoidal-positional-encoding] injects position, [01-transformer-block/07-stack-blocks] refines those vectors through many Transformer blocks, and [02-weight-tying]'s compute_output_logits turns the result into vocabulary scores. This question's entire content is WIRING, connecting five already-independently-verified pieces into one genuine, working, end-to-end forward pass, from raw integer token ids all the way to next-token logits, with no new mathematics introduced anywhere.

From theory to code

Implement full_lm_forward(token_ids, token_embedding_table, blocks_params, num_heads, tied, output_weight, mask), chaining: token embedding lookup, adding sinusoidal positional encoding, running the result through [07-stack-blocks]'s stack of Transformer blocks, and finally [02-weight-tying]'s output projection.

Constraints

• token_ids includes a leading batch dimension, (batch, seq_len): every downstream piece (attention's head-splitting, specifically) requires one.
• Positional encoding is computed for exactly token_ids's sequence length and ADDED to the token embeddings ([05-combine-token-positional-embeddings]'s pattern), before any Transformer block runs.
• blocks_params and num_heads pass straight through to [07-stack-blocks]'s stack_transformer_blocks, unchanged.
• tied/output_weight pass straight through to [02-weight-tying]'s compute_output_logits, unchanged.

Hints

token_embeddings = embedding_forward(token_ids, token_embedding_table)
positional_embeddings = sinusoidal_positional_encoding(seq_len, d_model)
x = combine_embeddings(token_embeddings, positional_embeddings)

x = stack_transformer_blocks(x, num_heads, blocks_params, mask=mask)
return compute_output_logits(x, token_embedding_table, tied, output_weight)