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Siddharth Prasad

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Machine Learning Artificial Intelligence Data Structures and Algorithms math.OC Computer Science and Game Theory math.NT

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preprint2026arXiv

In-Context Credit Assignment via the Core

We propose incentive-aligned mechanisms for in-context credit assignment: the task of assigning credit for AI-generated content (e.g. code, news articles, short-form videos) among creators whose intellectual property appears in the context window. Our approach is based on the least core solution concept from cooperative game theory, which distributes value in a way that is as stable as possible by ensuring that no subset of creators is significantly under-compensated relative to the value they could generate on their own. We develop algorithms for approximating the least core, which leverage novel routines for constraint seeding and constraint separation. On a web retrieval credit assignment task, we find that our approaches are capable of approximating the least core using orders of magnitude fewer LLM calls compared to alternative methods.

preprint2022arXiv

Improved Sample Complexity Bounds for Branch-and-Cut

Branch-and-cut is the most widely used algorithm for solving integer programs, employed by commercial solvers like CPLEX and Gurobi. Branch-and-cut has a wide variety of tunable parameters that have a huge impact on the size of the search tree that it builds, but are challenging to tune by hand. An increasingly popular approach is to use machine learning to tune these parameters: using a training set of integer programs from the application domain at hand, the goal is to find a configuration with strong predicted performance on future, unseen integer programs from the same domain. If the training set is too small, a configuration may have good performance over the training set but poor performance on future integer programs. In this paper, we prove sample complexity guarantees for this procedure, which bound how large the training set should be to ensure that for any configuration, its average performance over the training set is close to its expected future performance. Our guarantees apply to parameters that control the most important aspects of branch-and-cut: node selection, branching constraint selection, and cutting plane selection, and are sharper and more general than those found in prior research.

preprint2022arXiv

Structural Analysis of Branch-and-Cut and the Learnability of Gomory Mixed Integer Cuts

The incorporation of cutting planes within the branch-and-bound algorithm, known as branch-and-cut, forms the backbone of modern integer programming solvers. These solvers are the foremost method for solving discrete optimization problems and thus have a vast array of applications in machine learning, operations research, and many other fields. Choosing cutting planes effectively is a major research topic in the theory and practice of integer programming. We conduct a novel structural analysis of branch-and-cut that pins down how every step of the algorithm is affected by changes in the parameters defining the cutting planes added to the input integer program. Our main application of this analysis is to derive sample complexity guarantees for using machine learning to determine which cutting planes to apply during branch-and-cut. These guarantees apply to infinite families of cutting planes, such as the family of Gomory mixed integer cuts, which are responsible for the main breakthrough speedups of integer programming solvers. We exploit geometric and combinatorial structure of branch-and-cut in our analysis, which provides a key missing piece for the recent generalization theory of branch-and-cut.

preprint2014arXiv

Walks on Primes in Imaginary Quadratic Fields

We generalize the Gaussian moat problem to the finitely many imaginary quadratic fields exhibiting unique factorization in their integers. We map this problem to the Euclidean minimum spanning tree problem and use Delaunay triangulation and Kruskal's algorithm to find moats in these fields in $O(|\mathbf{P}| \log |\mathbf{P}|)$ time, where $\mathbf{P}$ denotes the set of primes we are searching through. Our algorithm uses symmetry and boundaries to correctly and efficiently identify all moats, in order of increasing length, along with the farthest prime reached for each moat, in an underlying unbounded graph of infinite primes. We also derive asymptotic estimates on the density of primes in certain imaginary quadratic fields. Based on this and symmetry arguments, we conjecture that for a given step bound $k$, we can travel farther away from the origin in $\mathbb{Z}[i]$ and $\mathbb{Z}\left[\frac{-1+\sqrt{-3}}{2}\right]$ than in $\mathbb{Z}[\sqrt{-2}]$. This conjecture is corroborated by our computational results.