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Code LLMs have shown promising results with converting tasks in natural language to programs that can be executed by service robots. We are interested in finetuning small, specialized LLMs for this purpose, but collecting datasets of…
RL with Verifiable Rewards (RLVR) has emerged as a promising paradigm for improving the reasoning abilities of large language models (LLMs). Current methods rely primarily on policy optimization frameworks like PPO and GRPO, which follow…
We consider the problem of approximating all real roots of a square-free polynomial $f$. Given isolating intervals, our algorithm refines each of them to a width of $2^{-L}$ or less, that is, each of the roots is approximated to $L$ bits…
In this paper, we present the first outer approximation algorithm for multi-objective mixed-integer linear programming problems with any number of objectives. The algorithm also works for certain classes of non-linear programming problems.…
The LC method described in this work seeks to approximate the roots of polynomial equations in one variable. This book allows you to explore the LC method, which uses geometric structures of Lines L and Circumferences C in the plane of…
In this paper, an exact algorithm in polynomial time is developed to solve unrestricted binary quadratic programs. The computational complexity is $O\left( n^{\frac{15}{2}}\right) $, although very conservative, it is sufficient to prove…
In this paper, we analyze the convergence %semi-convergence properties of projected non-stationary block iterative methods (P-BIM) aiming to find a constrained solution to large linear, usually both noisy and ill-conditioned, systems of…
We describe an approximate rational arithmetic with round-off errors (both absolute and relative) controlled by the user. The rounding procedure is based on the continued fraction expansion of real numbers. Results of computer experiments…
We introduce a new iterative rounding technique to round a point in a matroid polytope subject to further matroid constraints. This technique returns an independent set in one matroid with limited violations of the other ones. On top of the…
Designing models that are both expressive and preserve known invariances of tasks is an increasingly hard problem. Existing solutions tradeoff invariance for computational or memory resources. In this work, we show how to leverage…
Packing rings into a minimum number of rectangles is an optimization problem which appears naturally in the logistics operations of the tube industry. It encompasses two major difficulties, namely the positioning of rings in rectangles and…
Recently, rubrics have been used to guide LLM judges in capturing subjective, nuanced, multi-dimensional human preferences, and have been extended from evaluation to reward signals for reinforcement fine-tuning (RFT). However, rubric…
Modeling of microlensing events poses computational challenges for the resolution of the lens equation and the high dimensionality of the parameter space. In particular, numerical noise represents a severe limitation to fast and efficient…
This paper presents a novel outer approximation algorithm for nonsmooth mixed-integer nonlinear programming (MINLP) problems. The method proceeds by fixing the integer variables and solving the resulting nonlinear convex subproblem. When…
Convex quadratic programs (QPs) constitute a fundamental computational primitive across diverse domains including financial optimization, control systems, and machine learning. The alternating direction method of multipliers (ADMM) has…
Motivated by limitations on the depth of near-term quantum devices, we study the depth-computation trade-off in the query model, where the depth corresponds to the number of adaptive query rounds and the computation per layer corresponds to…
In Directed Multiway Cut(Dir-MC) the input is an edge-weighted directed graph $G=(V,E)$ and a set of $k$ terminal nodes $\{s_1,s_2,\ldots,s_k\} \subseteq V$; the goal is to find a min-weight subset of edges whose removal ensures that there…
Scientific computing applications, such as computational fluid dynamics and climate modeling, typically rely on 64-bit double-precision floating-point operations, which are extremely costly in terms of computation, memory, and energy. While…
Post-training quantization is an effective method for reducing the serving cost of large language models, where the standard approach is to use a round-to-nearest quantization level scheme. However, this often introduces large errors due to…
Model merging aims to combine multiple fine-tuned models into a single set of weights that performs well across all source tasks. While prior work has shown that merging can approximate the performance of individual fine-tuned models for…