Xinyue Xiang | Searcharxiv

arXiv2026

Generalized Balls into Bins

Consider a set of bins and two-choice balls arriving by a Poisson process. We must allocate each incoming ball immediately to one of two incident bins. For a given function $f$ and every bin, we aim to bound the expectation of $f(L)$---where $L$ is the bin's final load---based on the arrival rate of balls incident to that bin. We call this problem Generalized Balls into Bins, capturing many problems as special cases including the original Balls into Bins by Azar et al. (1994) and Online Stochastic Matching by Feldman et al. (2009). We show that Greedy provides optimal amortized bounds for all convex and concave functions $f$. Further, we propose another algorithm that achieves non-trivial bounds without amortization. As an application, we design a competitive algorithm for a stochastic model of completion time minimization on unrelated machines.

cs.DS↗

arXiv2026

Disentangling Language Roles in Multilingual LLM Task Execution

Multilingual LLMs are increasingly used when instruction, source content, and required response languages do not coincide. Existing benchmarks have expanded multilingual instruction-following evaluation, but they rarely isolate these three roles within a fully crossed design. We introduce MTM-Bench, a controlled benchmark for language-conditioned task execution in which each instance is defined by a triplet $(L_{\text{instr}}, L_{\text{content}}, L_{\text{resp}})$. Across English, Spanish, and Chinese, MTM-Bench enumerates all 27 triplets and contains 2{,}430 instances per model across semantic reversal, final-state extraction, and language purity with update realization. We evaluate 20 frontier and open-weight LLMs using decomposed metrics for semantic correctness, target-language adherence, constraint satisfaction, contamination ratio, and joint success, with scoring validated by a targeted human audit. The fully crossed design reveals that degradation is organized by the role a language occupies in the task structure, not merely by mismatch count. The response-language role is the dominant axis of variation, and a single response-slot mismatch accounts for most degradation. The response-only and full-mismatch comparison suggests that mismatch count is not a monotonic predictor of difficulty, with model-level ordering varying across systems. Task families fail through distinct channels, showing that semantic correctness alone does not capture reliable multilingual task execution.

cs.CL↗