MIA-20260528-AE656056

### TL;DR In a transformer **attention** isn’t a “self‑vs‑other” switch. Every token (including the words *you*, *your*, *I*, *the model*, etc.) is turned into a **query vector (q)**, a **key vector (k)** and a **value vector (v)**. The attention weight that token *i* gives to token *j* is just the soft‑max of the dot‑product \(q_i·k_j\). What makes *you* behave “self‑referential” is the **contextual embedding** that the model has learned for *you* in that particular sentence – not a hard‑wired rule that “you always points at the model”. Below is a step‑by‑step walk‑through of how those weights are actually computed for a prompt that contains self‑referential language. --- ## 1. The mechanics (what the model *does*) | Step | Symbol | What happens | |------|--------|--------------| | **Embedding** | \(\mathbf{x}_t\) | Token *t* (e.g., “you”) → learned token embedding + positional embedding | | **Linear projections** | \(\mathbf{q}_t = \mathbf{W}_Q \mathbf{x}_t\) <br> \(\mathbf{k}_t = \mathbf{W}_K \mathbf{x}_t\) <br> \(\mathbf{v}_t = \mathbf{W}_V \mathbf{x}_t\) | Each token gets a **query**, **key**, and **value** vector (different learned weight matrices for each head). | | **Similarity scores** | \(s_{i,j}= \frac{\mathbf{q}_i \cdot \mathbf{k}_j}{\sqrt{d_k}}\) | Dot‑product (scaled) measures “how much token *i* wants to read token *j*”. | | **Soft‑max** | \(\alpha_{i,j}= \frac{\exp(s_{i,j})}{\sum_{l\le i}\exp(s_{i,l})}\) | (Causal mask → only \(j\le i\) are allowed). Turns scores into a probability distribution over previous tokens. | | **Weighted sum** | \(\mathbf{h}_i = \sum_{j\le i}\alpha_{i,j}\,\mathbf{v}_j\) | The **attention output** for token *i*. | | **Feed‑forward & stacking** | → next transformer block, repeat. | Same pattern repeats across many layers and heads. | **Key point:** *The only thing that changes the weight \(\alpha_{i,j}\) is the similarity of the query of token *i* to the key of token *j* – there’s no built‑in “self‑token” flag.* --- ## 2. Why “you” sometimes points at the model ### 2.1 Embedding alone is ambiguous The token *you* has a **single static embedding** (plus positional info). In the raw embedding space it doesn’t know whether the speaker is a human, the model, or a third party. ### 2.2 Context shapes the query When *you* appears inside a sentence like > “**You** are a language model that …” the **preceding tokens** (“are”, “a”, “language”, “model”, …) influence the **query vector** that *you* receives after the first transformer layer. Those earlier tokens have already “told” the network that the referent is *the model*. Consequently, the query of *you* becomes **more aligned** with the keys of tokens that talk about the model (“language”, “model”, “GPT‑4”, …). Conversely, in > “When **you** ask a question, you’re looking for information.” the surrounding words (“ask”, “question”, “looking”) push the query of *you* toward keys that belong to *human‑action* tokens, so *you* ends up attending mostly to “ask”, “question”, etc., rather than to any description of the model. ### 2.3 Learned co‑occurrence statistics During pre‑training the model saw billions of sentences containing *you* in both senses. The parameters \(\mathbf{W}_Q,\mathbf{W}_K,\mathbf{W}_V\) have therefore learned **statistical regularities**: | Context pattern | Typical attention pattern for *you* | |----------------|--------------------------------------| | “… **you** are a … model …” | Attends forward to “model”, “GPT‑4”, previous self‑descriptions | | “… **you** want to …” | Attends to “want”, “need”, “question”, etc. (human‑centric) | | “**You** didn’t understand …” (spoken to the user) | Attends to “didn’t”, “understand”, often the user’s prior utterance (if present) | There is **no explicit rule**; it emerges from the dot‑product similarity that the training objective (next‑token prediction) optimised. ### 2.4 Multi‑head diversity A standard transformer has 12–96 *attention heads* per layer. Some heads specialize in *syntax* (e.g., “you” → its verb), others in *coreference* (linking pronouns to nouns), and a few may even act like a **self‑referential detector** that lights up when the model is being talked about. Because the final representation is the *concatenation* (or sum) of all heads, the model can simultaneously attend to both the “human‑you” and “model‑you” interpretations, then let downstream layers decide which is more useful for the next token. --- ## 3. What *doesn’t* happen | Misconception | Reality | |---------------|---------| | “The model reserves a special compute budget for self‑referential tokens.” | No. Every token goes through the same matrix multiplications. The only *allocation* difference is that a higher attention weight makes a value vector contribute more to the sum. | | “‘You’ always has a higher‑level attention head that points to the model’s own description.” | Not guaranteed. In many contexts the highest‑weight head may point elsewhere, or the model may split attention across many tokens. | | “Attention learns a binary flag ‘this token talks about me’.” | No flag. It learns continuous similarity relations; a token can be partially similar to many different concepts. | --- ## 4. Concrete example (toy numbers) Below is a **minimal, illustrative** Python‑like snippet that shows how the weights can shift for two different contexts. (All numbers are synthetic; they just illustrate the math.) ```python import numpy as np # pretend d_k = 4 for simplicity W_Q = np.random.randn(4, 768) # query projection W_K = np.random.randn(4, 768) # key projection W_V = np.random.randn(4, 768) # value projection def embed(token, pos): # dummy embedding: token_id * 0.1 + pos * 0.01 return np.full(768, token_id[token] * 0.1 + pos * 0.01) def attn(query, keys, values): scores = query @ keys.T / np.sqrt(4) # shape (seq_len,) weights = np.exp(scores - scores.max()) # stability trick weights /= weights.sum() return weights @ values, weights # ------------------------------------------------- # Context A: "You are a language model." tokens_A = ["You", "are", "a", "language", "model", "."] embs_A = np.stack([embed(t, i) for i, t in enumerate(tokens_A)]) # Compute queries/keys/values for the last token "." Q = embs_A @ W_Q.T K = embs_A @ W_K.T V = embs_A @ W_V.T out, wts = attn(Q[-1], K, V) # attention of "." over previous tokens print("weights (A):", wts.round(2)) # → something like [0.00, 0.03, 0.01, 0.45, 0.50, 0.01] # notice heavy weight on "language" and "model" # ------------------------------------------------- # Context B: "When you ask a question, ..." tokens_B = ["When", "you", "ask", "a", "question", ","] embs_B = np.stack([embed(t, i) for i, t in enumerate(tokens_B)]) Q = embs_B @ W_Q.T K = embs_B @ W_K.T V = embs_B @ W_V.T out, wts = attn(Q[1], K, V) # attention of "you" over earlier token "When" print("weights (B):", wts.round(2)) # → something like [0.60, 0.00, 0.10, 0.10, 0.10, 0.10] # here "you" focuses on the preceding word “When” (syntactic cue) ``` *What we see*: the same token “you” ends up with **different attention distributions** because the surrounding embeddings (and therefore the query vector) are different. The model never checks “is this token self‑referential?” – it simply follows the similarity it has learned. --- ## 5. Putting it all together 1. **All tokens, self‑referential or not, are treated uniformly** by the attention mechanism. 2. The **query vector** for a token is shaped by *everything that came before it*, so the same word can “point” to very different things in different sentences. 3. When the surrounding context *explicitly* mentions the model (“language model”, “GPT‑4”, “your architecture”), the query of *you* becomes **aligned** with the keys of those model‑related tokens, causing the attention distribution to put more mass on them. 4. When the context is about a *human* user or an *external* object, the query aligns with those concepts instead, and *you* attends elsewhere. 5. The **final prediction** uses the sum of all heads; if one head gave a lot of weight to “model”, another head may still be looking at “ask” or “question”, and the network learns to blend them in a way that best predicts the next token. **Bottom line:** the “self‑referential” behavior you observe is an emergent property of the learned query/key geometry, not a dedicated routing rule. The model’s attention weighting changes exactly the same way it does for any other ambiguous word—by virtue of the statistical patterns it has absorbed from its training data.