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Evaluation has been central to advances in AI, and it is equally critical to autonomous discovery. Yet scaling autonomous discovery to real-world engineering challenges faces a fundamental bottleneck: the cost of evaluating progress. In real settings, a single true evaluation, such as a full benchmark or serving trace,...
We study strong coresets for $\ell_p$ subspace approximation. Given a matrix $A\in\mathbb{R}^{n\times d}$, the goal is to sample and rescale a small number of its rows to obtain $SA$ such that $\left\|SA(I-P_F)\right\|_{p,2}^p=(1\pm\varepsilon)\left\|A(I-P_F)\right\|_{p,2}^p$ simultaneously for every subspace $F\subset...
In online inverse linear optimization, a learner recommends an action and then observes the choice of an expert who maximizes a fixed, unknown linear objective on $\mathbb{R}^{d}$; the goal is to learn to optimize this objective without observing it. Sakaue recently obtained the optimal regret $O(\sqrt d)$ with a rando...
Mixture-of-experts (MoE) layers increase model capacity without a proportional increase in per-example computation. However, conventional flat routers can yield imbalanced expert utilization and treat experts as an unstructured collection, whose indices carry no topological meaning. We introduce {\bf BRANCH-MoE}, a rou...
DLB, the Distributed Load Balancer is introduced, a novel system designed to minimize end-to-end user latency for large-scale, heterogeneous workloads and its design choices and practical experiences gained from the system in production are detailed.
The present work builds on the differential-equation method, itself a limiting form of the auxiliary-receiver approach in network information theory using a continuum of degraded receivers, and gives a computer-assisted proof of the Courtade--Kumar conjecture.
In [AS21], Axiotis and Sviridenko conjectured that the linear dependence on the restricted condition number in sparse convex optimization cannot be improved by a polynomial-time algorithm. We establish their conjectured lower bound for least-squares objectives, conditional on the randomized exact-volume Small-Set Expan...
Stellar Colosseum is introduced, a model-agnostic harness for allocating inference across research in mathematics and theoretical computer science that demonstrates the capabilities of Colosseum through open-ended research and evaluations on theorem-proving and competitive programming benchmarks.
This work proposes Subsampled Stochastic TurboQuant (SSTQ), a framework that combines overcomplete equal-norm tight frames, coordinate subsampling, and privacy-aware one-dimensional quantization and empirically evaluates SSTQ against established baselines on federated learning tasks using CIFAR-10 and Fashion-MNIST, de...
For the $n\times n$ lower-triangular all-ones matrix $Q$, we prove a near-optimal lower bound \[ \gamma_{2,1}(Q) := \inf_{Q=AB} \|A\|_{2\to\infty}\|B\|_{1\to1} = \Omega\!\left( \frac{\log^{3/2}n}{(\log\log n)^{3/2}} \right), \] where the infimum ranges over real factorizations of arbitrary finite inner dimension. This...
This work introduces TCS-Bench, a benchmark for evaluating Large Language Models (LLMs) on research-level Theoretical Computer Science (TCS) proof generation, and benchmarks the verifier against human-expert proof judgements on a set of target statements and generated proofs pairs.
This work instantiates a new paradigm of incremental memory activation, where the effective capacity of memory is progressively expanded as the context grows, and applies this paradigm to state-of-the-art models, observing consistent improvements on standard language modeling and reasoning, as well as on long-context r...
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