llm workflow

vik ✓ @vikhyatk · Dec 18 2026 interview questions: - you are in the middle of a refactor and the model says 8% context left before auto-compaction. what do you do? - how do you decide which tasks to give to claude, codex gpt 5.2 xhigh, and chatgpt pro? - tell me about a time you disagreed with an LLM

@GSalafatinos: The way I did it was progressively asking it to breakdown the problem into self-contained sub-questions that could be used to make a determination. I'd feed each one to a fresh context gemini and report back. This particular subquestion produced the counter example in response. [Embedded image, mathematical text document:] Question: Behavior of TV Distance for Specific α-Bounded Structures Let Ω be a finite set, |Ω| = d. Let α ∈ (0,1/d]. Let Pi, Qi (i = 1,...,n) be α-bounded distributions on Ω, meaning ∀x ∈ Ω, α ≤ Pi(x) ≤ 1 − α and α ≤ Qi(x) ≤ 1 − α. Let δi = ||Pi − Qi||TV and TVn = ||P⊗n − Q⊗n||TV. We are investigating the conjecture TVn ≤ √(Σδi²) · max{1, log(1/α)}. The binary symmetric case (d = 2, Pi = (1−α, α), Qi = (α, 1−α)) appears not to violate the conjecture. We seek to understand if other structures can lead to a violation, particularly for small α (large d) where the gap between potential χ²-based bounds (~√(n/α)) and the conjecture's log(1/α) factor is largest, but perhaps avoiding the rapid saturation seen in the binary case. Consider the following specific structures (or similar ones designed to probe the interaction of small δi, small α, and tensorization): Structure 1: Uniform Background with Small Perturbation Let α = 1/d. Let Qi = Q = (1/d, 1/d, ..., 1/d) be the uniform distribution (which is α-bounded). Let ε be a small positive value such that α − ε ≥ α is NOT required, but P must still be α-bounded. This requires careful construction. * Example Construction: Let d ≥ 3. Define P by moving mass ε from coordinate 2 to coordinate 1. P = (α+ε, α−ε, α, ..., α). For P to be α-bounded, we need α−ε ≥ α, implying ε ≤ 0. Let's try moving mass from d−1 coordinates to one coordinate. Let P(1) = α + (d−1)ε, P(x) = α − ε for x = 2,...,d. * Check α-bounds: We need α − ε ≥ α ⟹ ε ≤ 0. * This seems difficult. Alternative: Let P be only slightly different from Q. Let P(1) = α+ε', P(2) = α+ε'', ..., ΣP(x) = 1. How small must ε', ε'' be to maintain α ≤ P(x), Q(x) ≤ 1−α? * Consider d = 3, α = 0.1. Q = (0.1, 0.4, 0.5) (Assume non-uniform Q to allow more flexibility). Let P = (0.15, 0.4, 0.45). Here δ = 0.05. α ≤ P(x), Q(x) ≤ 1−α. Structure 2: Non-Uniform Background, Difference at Low Probability Let d ≥ 3. Choose a non-uniform Qi = Q such that Q(1) = α but Q(x) > α for x > 1. Let Pi = P be constructed by modifying Q slightly, primarily changing Q(1) and perhaps one other coordinate Q(j) where Q(j) is large, such that P remains α-bounded and δ = ||P−Q||TV is small. * Example Construction (d = 4, α = 0.1): Q = (0.1, 0.25, 0.3, 0.35). This is α-bounded. Let P = (0.15, 0.25, 0.3, 0.30). P is α-bounded. Here δ = 0.05. The difference is concentrated at x = 1 (where Q is small) and x = 4. Question: For structures like those proposed above (or variations): 1. Can TVn = ||P⊗n − Q⊗n||TV be calculated exactly or tightly bounded (upper and lower) for small values of n (e.g., n = 2,3,4,...) and representative small values of α?