This paper proves a new lower bound of $ ildeΩ(n^2)$ for read-once parity branching programs on boolean functions, improving upon the previous bound of $ ildeΩ(n^{1.5})$.

This paper proves space lower bounds for entropy-efficient random sampling using i.i.d. uniform bits.

This paper unconditionally proves the Orthogonal Vectors and Monotone Orthogonal Vectors conjectures in concrete computational models, and provides stronger lower bounds for Boolean formulas and branc…

This paper establishes an unconditional barrier for AC0-natural proofs, showing that they cannot prove lower bounds greater than $2^{n^{7/(d-5)}}$ against depth-$d$ circuits.

The paper establishes information-theoretic lower bounds for stochastic optimization using low-bit gradients by reducing the problem to compressed Gaussian mean estimation, yielding sharp bounds on co…

This paper settles the complexity of three sketching problems in graphs and distributions.

This paper proves lower bounds for the size of multiplicative graph spanners in the $f$-degree fault tolerant model, matching previous conditional lower bounds and current upper bounds.

This paper measures the lower bound for the shortest program generating a sequence, proving a conservation law and providing a deterministic engine to recover generating programs for certain sequences…

This paper improves the theoretical bounds for estimating discrete probability distributions using the $\ell_\infty$ norm, resolving several open questions in the field.

This paper shows that shallow circuits cannot prepare near-optimal states for random quantum $p$-spin glasses, and proves depth lower bounds for such preparations.

The paper improves Banaszczyk's inequality, providing a significantly better tail estimate for the discrete Gaussian measure on a lattice, which has applications in analyzing dual attacks against the…

The polynomial-time low-degree conjecture, which predicts that low-degree indistinguishability, a uniform null distribution, permutation invariance, and independent resampling imply polynomial-time ha…

The paper develops a new framework for proving lower bounds for the maximum matching problem in the semi-streaming model, improving upon the previous best known bounds.

The paper presents an adaptive scaling algorithm with a competitive ratio of 1.373 for incremental submodular maximization under increasing cardinality constraint, improving upon the previous best res…

This paper proves the conjecture that Local SGD outperforms Mini-batch SGD under bounded second-order heterogeneity for general convex objectives, improving the convergence guarantee and lower bounds.