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Please email info@easterncompute.com with whatever you feel will help us best understand you and your abilities.

We have a set of bonus questions that we rotate at semi-regular intervals. You will get brownie points if you can answer any two of the following questions in your email:

1. Suppose you want to estimate 4 parameters: the means of 4 independent Gaussian random variables (so, say, the weight of a randomly chosen bag of Lays chips, the IQ of a high schooler in Texas, the height of a Korean male, and the height of a Finnish female). You have a limited data collection budget, so you only managed to collect one data point for each of these parameters, resulting in a 4-element data vector \(X = [X_1, X_2, X_3, X_4]\) from which you want to estimate a 4-element vector of \(\theta_i\)s under the assumption that each data point collected follows the distribution \(X_i \sim N(\theta_i, 1)\). Provide a good estimator for \(\theta = [\theta_1, ..., \theta_4]\) subject to a mean (i.e. expected) squared error loss function.

2. Here’s a fairly recent paper in which the authors leverage recent innovations in large language model representation engineering to devise an approach for preventing LLM jailbreaking. What aspect of their evaluation methodology confounds their conclusion that their circuit breaker is effective when it comes to stymying RepE attacks? Elaborate.

3. How many iterations will the for loop for (int i = 0; i < Random(1, 100); i++) run for? Explain. (Please note that the for loop generates a new random number at every iteration and checks the condition, as opposed to saving ~50 (in expectation) at the beginning and running that many times.)