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中文题目At launch there were twice as many regional funds as global funds. Today, 18 regional funds and 18 global funds remain live. If the regional-fund survival rate was 45%, what was the global-fund survival rate?
打开 →A gradient vector g has norm ||g|| greater than clip threshold c. Derive the clipped gradient under standard global-norm clipping.
打开 →Why does global-norm clipping change the magnitude of a gradient vector but not its direction whenever clipping is active?
打开 →A prediction problem used to depend on short motifs, but after a product change the label now depends on matching information from the first and last quarter of each sequence. Which architecture family should move up the ranking?
打开 →A desk uses the same per-bucket cutoff 0.0045 across 20 independent event buckets. What family-wise false-positive probability does that imply?
打开 →If every sample weight in a node is multiplied by the same constant c>0, how does each candidate split's weighted impurity decrease change?
打开 →A gradient vector is g=(6,8), whose norm is 10. If the clip threshold is 5, what clipped gradient is produced?
打开 →A sequence problem has mostly local structure, but a small fraction of labels flips because of interactions between positions hundreds of steps apart. Missing those interactions is very costly. Which architecture family should you favor?
打开 →A parameter vector is w_t=(3,4). Its gradient is g=(6,8), whose norm is 10. Apply global-norm clipping with threshold 5, then a decoupled weight-decay step with learning rate eta=0.1 and lambda=0.1. What is the new parameter vector?
打开 →You test 40 independent noise strategies. A strategy is launched only if it passes an in-sample screen at level 1/20 and then passes a second independent validation at level 1/10. Under the global null, what is the probability that at least one noise strategy still gets launched?
打开 →A local approximation is even more non-convex, so the repair parameter must rise accordingly. A local PnL model is h(q)=q^4-10q^2+lambda q^2. What is the smallest lambda that makes h globally convex?
打开 →Why is a portfolio that is locally riskless over dt not automatically globally riskless over the whole life of the option?
打开 →A research model has a locally non-convex quartic approximation, and risk wants the smallest ridge that fixes it everywhere. A local PnL model is h(q)=q^4-6q^2+lambda q^2. What is the smallest lambda that makes h globally convex?
打开 →Give one reason why solving the KKT equations in a nonconvex problem may fail to identify the global optimum.
打开 →Why can a market be globally incomplete yet still assign a unique arbitrage-free price to one particular claim?
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