We provide a computational complexity lens to understand the power of machine learning models, particularly their ability to model complex systems.

Machine learning models are often trained on data drawn from sampleable or more complex distributions, a far wider range of distributions than just computable ones. By focusing ... more >>>

It is a long-standing open question whether the average-case hardness of NP implies the existence of a one-way function. The hypothetical world in which this does not hold is called Pessiland, which is the most pessimistic among Impagliazzo's five possible worlds. In this paper, we present the first "sharp" characterization ... more >>>

We consider the worst-case hardness of the gap version of the classic time-bounded Kolmogorov complexity problem—$Gap_pMK^tP[s_1,s_2]$—where the goal is to determine whether for a given string x, $K^t(x) ?s_1(n)$ or $K^{p(t)}(x) > s_2(n)$, where $K^t(x)$ denotes the t-bounded Kolmogorov complexity of x. As shown by Hirahara (STOC’18), if $Gap_pMK^tP[s_1,s_2] \notin ... more >>>