can you explain in bullet points the PositionalEncoding in hw7_sol.py


hw7_sol.py (line 343) wraps sinusoidal positional encodings in a module so embeddings inherit temporal order information that self-attention alone can’t infer.
hw7_sol.py (lines 345-349) precomputes a [1, max_len, num_hiddens] table where the even channels store sin(pos / 10000^(i/num_hiddens)) and the odd channels store the matching cosine terms; this matches the original Transformer formulation.
hw7_sol.py (line 350) registers that table as a persistent buffer (self.pe), so it moves with the model across devices but isn’t treated as a learnable parameter.
hw7_sol.py (lines 353-354) simply slices the precomputed table to the current sequence length, adds it to the token embeddings (broadcast across the batch), and keeps everything on the same device as X.
hw7_sol.py (line 355) applies dropout after the addition, meaning both token embeddings and positional signals are jointly regularized before entering the rest of the Transformer stack.



also how is that being used in the blocks/attention


hw7_sol.py (lines 414-415) wires a shared PositionalEncoding into every Transformer decoder instance so the embeddings carry fixed absolute position patterns before any attention happens.
hw7_sol.py (line 432) multiplies the raw token embeddings by sqrt(num_hiddens) (matching the original Transformer scaling), then immediately passes them through self.pos_encoding(...); the sine/cosine table is added elementwise so each position now has a unique phase shift mixed with its lexical embedding.
Once enriched with position info, those tensors flow through every decoder block (hw7_sol.py (lines 433-441)). Block 1’s causal self-attention (attention1) therefore gets both content and position cues, letting the attention logits distinguish “token A at step t” from “token A at step t+1; the stored weights (_attention_weights[0][i]`) you inspect later already incorporate that positional bias.
The same decorated representations also serve as the queries for cross-attention (attention2), so when the decoder attends over encoder outputs, each timestep’s query remains uniquely anchored in absolute time, preventing different decoder steps from collapsing onto identical query vectors.
The encoder mirrors this setup: hw7_sol.py (lines 476-485) builds its own PositionalEncoding and adds it to the input embeddings before any self-attention. Every encoder block then consumes position-aware inputs, so its multi-head attention can reason about relative order even though the mechanism itself is permutation-invariant.



is it overall correctly implemented?


hw7_sol.py (lines 343-355) matches the standard Transformer sinusoidal positional encoding: it precomputes sin/cos waves at log-spaced frequencies, stores them as a non-trainable buffer, and adds them to embeddings followed by dropout.
Encoder path (hw7_sol.py (lines 476-485)) scales embeddings by sqrt(num_hiddens) before calling PositionalEncoding, then feeds them through stacked self-attention blocks—exactly what Vaswani et al. describe.
Decoder path (hw7_sol.py (lines 414-441)) does the same scaling/positional addition and then runs causal self-attention, cross-attention, and FFN layers, keeping per-layer caches so autoregressive decoding works.
Nothing stands out as incorrect: timestep masks are applied, positional info is injected once per forward call, the buffer rides along with the model on device moves, and both encoder/decoder blocks consume the enriched tensors. So yes—implementation looks correct.

any details that can be improved?


hw7_sol.py (lines 345-352) hardcodes max_len=5000; guarding against sequences longer than that (e.g., grow buffer lazily when X.size(1) exceeds cached length) would prevent subtle runtime errors if you experiment with much longer sequences.
hw7_sol.py (line 432) and hw7_sol.py (line 485) both multiply embeddings by math.sqrt(self.num_hiddens) before adding positions; consider wrapping embedding + scale + positional add in a helper so the encoder and decoder can’t accidentally diverge (also simplifies future changes such as learnable positional encodings).
hw7_sol.py (lines 353-354) re-slices self.pe each call; you could store the slice in a local and reuse it when populating attention caches to avoid repeated .to(X.device) calls inside the decode loop. Not a bottleneck today, but noticeable when decoding token-by-token on large batches.


conceptually how the positional embedding works inside the blokcs? I mean how order in the sequence is being preserved


Transformer self-attention treats its inputs as an unordered set: each token projects to queries/keys/values and interacts purely via similarity. Without extra information, the mechanism can’t tell “token A at position 3” from “token A at position 7.”
The positional encoding injected before the blocks solves this. Each timestep gets a deterministic sin/cos pattern where every dimension has a different wavelength (hw7_sol.py (lines 343-355)). Add this vector to the token embedding and you give the attention layers a phase “fingerprint” tied to absolute position.
In practice, the Q/K projections now see two components: lexical content (from the embedding) and phase offsets (from the position signal). When attention computes Q·Kᵀ, those sinusoidal channels cause relative phase differences to affect the dot product, meaning queries naturally prefer keys whose position offset matches the pattern learned for “look one token back,” “look three tokens ahead,” etc.
Because the encoding is added once up front, every block in the stack receives tensors already annotated with position. Residual connections keep that signal alive as it flows through multi-head attention and feed-forward layers, so later blocks can still reason about order even after several transformations.



i need more intuition on how to explain the transforme blocks + attention + positional_encoding , thus removing recursion


Transformer Intuition

PositionalEncoding injects order: each token embedding gets a fixed sinusoidal “timestamp,” so even though attention is permutation-invariant, queries/keys carry phase info that encodes “I’m the 5th token,” “I’m the 7th,” etc. Relative offsets show up as predictable phase differences, letting attention reason about sequence order.

Multi-Head Self-Attention replaces recurrence by letting every token look at every other token in one shot. Each head projects the sequence into a different subspace, scores all pairs (Q·K) using those position-aware vectors, and mixes values accordingly. The network learns patterns like “pay attention to the previous verb” or “attend to the subject two tokens back” without stepping through time sequentially.

Transformer Block stacks two ideas: (1) multi-head self-attention + residual + normalization contextualizes each token with information pulled from the whole sequence; (2) a position-wise feed-forward network (same MLP applied to every position) lets the model rewrite each token’s representation with non-linear combinations of the aggregated context. Residual paths keep gradients stable and preserve the positional signals throughout the stack.

Removing Recursion: in RNNs, temporal order is preserved by iterative hidden-state updates; attention instead processes all positions in parallel. Because positional encodings tag each timestep and attention can connect any pair directly, the model no longer needs to step through the sequence. Context flows instantly across tokens, enabling much deeper, more parallel architectures.

Decoder Blocks mirror the encoder but add two constraints: masked self-attention enforces autoregressive order (only attend to past positions), and cross-attention uses the decoder’s position-tagged queries against the encoder’s outputs to fuse source and target streams. Caches store accumulated keys/values so inference still runs one token at a time without recomputing the whole past.