In-context learning mechanisms — Hinglish notes

4.4.9 · AI-ML › Alignment, Prompting & RAG

In-context learning KIYA hai?

YEH EXIST KYUN KARTA HAI? Pretraining ke dauran model itna zyada text dekhta hai jahan document mein pehle establish hua pattern baad ke tokens ko predict karta hai (lists, tables, translations, Q&A threads). Next-token loss minimize karne ke liye usse majburan "context mein pattern dhundho, phir use continue karo" mein achha banna padta hai. ICL wahi skill hai jo inference time pe reuse hoti hai.

YEH KAAM KAISE KARTA HAI? Do mechanistic stories

Dono stories compatible hain: model ke andar already algorithm hai; context use select aur steer karta hai.

Derivation: zyada demos kyun madad karte hain (Bayesian task inference)

Formula Latent task ke upar posterior

$k$ ke saath concentrate hoti hai Maano $c$ hidden concept hai (true task). Pretraining se prior $p (c)$ . Har demo $(x_{i}, y_{i})$ (approximately) true concept $c^{*}$ se generate hota hai.

Step 1 — Demos pe Bayes. $k$ demos ke baad posterior: $p (c ∣ D_{k}) = \frac{p ( c ) \prod _{i = 1}^{k} p ( x _{i} , y _{i} ∣ c )}{\sum _{c^{'}} p ( c ^{'} ) \prod _{i = 1}^{k} p ( x _{i} , y _{i} ∣ c ^{'} )}$ Yeh step kyun? Demos evidence hain; Bayes hamara belief update karta hai ki konsa concept inhe generate kiya.

Step 2 — Marginalizing karke query predict karo. $p (y ∣ x_{k + 1}, D_{k}) = \sum_{c} p (y ∣ x_{k + 1}, c) p (c ∣ D_{k})$ Yeh step kyun? Model kisi ek task pe commit nahi karta; woh predictions ko average karta hai, weighted by ki har task kitni likely hai.

Step 3 — Concentration. True $c^{*}$ aur kisi bhi galat $c^{'}$ ke ratio ka log lo: $lo g \frac{p ( c ^{*} ∣ D _{k} )}{p ( c ^{'} ∣ D _{k} )} = lo g \frac{p ( c ^{*} )}{p ( c ^{'} )} + \sum_{i = 1}^{k} lo g \frac{p ( x _{i} , y _{i} ∣ c ^{*} )}{p ( x _{i} , y _{i} ∣ c ^{'} )}$ Sum ka har term average pe $+ KL (p (\cdot ∣ c^{*}) ∥ p (\cdot ∣ c^{'})) \geq 0$ hai. Yeh step kyun? Expected per-demo log-likelihood gap ek KL divergence hi hai, jo non-negative hai aur distinguishable tasks ke liye strictly positive hai.

Conclusion. Log-ratio $\approx k \cdot KL$ badhta hai, isliye $p (c^{*} ∣ D_{k}) \to 1 exponentially in k .$ Posterior true task pe collapse hoti hai — yahi reason hai ki zyada shots ke saath accuracy badhti hai aur phir saturate ho jaati hai.

Toy mechanism: attention as one gradient step

Formula Linear-attention ↔ gradient descent (sketch)

Ek linear model $\overset{y}{^} = W x$ consider karo. Demos ${(x_{i}, y_{i})}$ pe $W_{0} = 0$ se ordinary least-squares gradient step, loss $\frac{1}{2} \sum_{i} ∥ y_{i} - W x_{i} ∥^{2}$ ke saath: $W_{1} = W_{0} - η \nabla_{W} L = η \sum_{i = 1}^{k} y_{i} x_{i}^{⊤}$ Yeh step kyun? $\nabla_{W} \frac{1}{2} ∥ y_{i} - W x_{i} ∥^{2} = - (y_{i} - W_{0} x_{i}) x_{i}^{⊤} = - y_{i} x_{i}^{⊤}$ at $W_{0} = 0$ .

Query $x_{k + 1}$ pe prediction: $\overset{y}{^} = W_{1} x_{k + 1} = η \sum_{i = 1}^{k} y_{i} (x_{i}^{⊤} x_{k + 1})$ Ab attention se compare karo. Ek single (linear) attention head output karta hai $\sum_{i} value_{i} \cdot sim (key_{i}, query)$ . Set karo $value_{i} = y_{i}$ , $key_{i} = x_{i}$ , $query = x_{k + 1}$ , similarity $=$ dot product: $Attn = \sum_{i = 1}^{k} y_{i} (x_{i}^{⊤} x_{k + 1})$ Identical form. Toh demos pe attention ka forward pass ek GD step reproduce karta hai — network apne activations mein ek virtual model "train" karta hai. Yahi "weight updates ke bina learning" ka mechanistic matlab hai.

Worked examples

Worked example Example 1 — Sentiment (few-shot)

Review: "Loved every minute." → Positive
Review: "Total waste of money." → Negative
Review: "The plot dragged on." → ???

Kyun kaam karta hai: do demos $p (c = sentiment classification)$ badhate hain; label format ("→ Positive/Negative") model ko output space batata hai. Model marginalizes → Negative predict karta hai.

Worked example Example 3 — Recency & ordering

A→1, B→2, C→3, then B→?

Models recent demos aur majority label ki taraf biased hote hain. Demos ko reorder karna predictions flip kar sakta hai — yeh symptom hai ki ICL conditioning hai, clean learning nahi.

Common mistakes

Recall Feynman: ek 12-saal ke bachhe ko explain karo

Socho ek bahut smart tota hai jisne poora internet padha hai. Tum usse dobara train nahi karte. Bas pehle kuch examples dikhate ho: "cat→animal, rose→plant, dog→?" Kyunki usne pehle lakho chhote lists aise dekhe hain, woh samajh jaata hai ki tum konsa game khel rahe ho aur pattern complete karta hai: "animal". Usne koi test ke liye padhaa nahi — usne bas woh rule notice kiya jo tum usके saamne hint kar rahe the. Yahi noticing-and-continuing in-context learning hai.

Active recall

In-context learning kya hai?

Ek frozen LLM jo prompt mein demonstrations pe condition karke ek naya task perform karta hai, bina kisi weight update ke; "learning" forward pass mein hoti hai.

ICL mein model ke parameters mein kya badlta hai?

Kuch nahi —

θ

fixed rehta hai; sirf transient activations context pe depend karti hain.

k-shot ICL objective state karo.

\overset{y}{^} = ar g max_{y} P_{θ} (y ∣ x_{1}, y_{1}, \dots, x_{k}, y_{k}, x_{k + 1})

Bayesian view: demonstrations kya karte hain?

Woh latent tasks ke upar posterior

p (c ∣ D_{k})

shift karte hain, use true task pe concentrate karte hue.

Zyada shots ke saath accuracy saturate kyun hoti hai?

Log-posterior-ratio

\approx k \cdot KL

badhta hai, isliye

p (c^{*} ∣ D_{k}) \to 1

exponentially; extra demos diminishing returns dete hain.

Ek GD step linear attention ke barabar kyun hai?

W_{0} = 0

se GD deta hai

\overset{y}{^} = η \sum_{i} y_{i} (x_{i}^{⊤} x_{k + 1})

, same form jaise attention with keys

x_{i}

, values

y_{i}

, query

x_{k + 1}

Flipped labels ke baad bhi ICL accuracy achhi kyun ho sakti hai?

Demos mainly input distribution, label space, aur format convey karte hain (task location); pretraining priors mapping supply karti hai — jab tak task novel/hard na ho.

Zero-shot vs one-shot vs few-shot?

k=0,1,kai demonstrations respectively.

Do biases jo batate hain ki ICL conditioning hai clean learning nahi?

Recency bias (baad ke demos zyada weighted) aur majority-label bias.

ICL vs fine-tuning ek line mein?

Fine-tuning permanently weights edit karta hai; ICL per-prompt, reversible conditioning hai.

Connections

Transformers and Attention — attention woh substrate hai jo ICL implement karta hai.
Prompt Engineering — demo count, order, aur format ICL ke levers hain.
Chain-of-Thought Prompting — ICL extended with reasoning steps in the demos.
Retrieval-Augmented Generation (RAG) — retrieved passages context ki tarah act karte hain jo same conditioning mechanism ko steer karta hai.
Bayesian Inference — task-posterior derivation.
Gradient Descent — implicit-optimization interpretation.
Fine-tuning vs Prompting — kab weights change karein vs context se steer karein.