arXiv subjects

Adam Jozefiak

Publications and source records attributed to Adam Jozefiak.

3 recordsLinked to original sources

arXiv2026

OS-Pruner: Pruning Chains-of-Thought of Reasoning Models via Optimal Stopping

Large Language Models (LLMs) have achieved remarkable success in complex reasoning tasks through Chain-of-Thought (CoT) prompting. However, these models often exhibit "computational overthinking," generating redundant reasoning steps that increase latency and cost without improving accuracy. Recent studies suggest that CoT trajectories can be significantly pruned, yet existing methods often rely on forcing a static thinking budget, heuristic filtering, sub-optimal early exit via classification, or expensive re-training. In this paper, we introduce OS-Pruner, a lightweight plug-in framework that formulates chain-of-thought pruning as an optimal stopping problem. Given a reasoning prefix, OS-Pruner learns whether further reasoning is worth its token cost by optimizing an explicit utility that trades off final-answer accuracy against generated length. Our novel formulation enables the model to dynamically assess the sufficient point of termination for a reasoning chain. OS-Pruner is designed to be lightweight during both training and inference, and to provide users with fine-grained control over the reasoning-effort vs. accuracy trade-off. On diverse reasoning benchmarks and base models, OS-Pruner achieves 20-60\% reduction in generation length with minimal accuracy sacrifice.

cs.AI↗

arXiv2022

A Knapsack Intersection Hierarchy Applied to All-or-Nothing Flow in Trees

We introduce a natural knapsack intersection hierarchy for strengthening linear programming relaxations of packing integer programs, i.e., $\max\{w^Tx:x\in P\cap\{0,1\}^n\}$ where $P=\{x\in[0,1]^n:Ax \leq b\}$ and $A,b,w\ge0$. The $t^{th}$ level $P^{t}$ corresponds to adding cuts associated with the integer hull of the intersection of any $t$ knapsack constraints (rows of the constraint matrix). This model captures the maximum possible strength of "$t$-row cuts", an approach often used by solvers for small $t$. If $A$ is $m \times n$, then $P^m$ is the integer hull of $P$ and $P^1$ corresponds to adding cuts for each associated single-row knapsack problem. Thus, even separating over $P^1$ is NP-hard. However, for fixed $t$ and any $\epsilon>0$, results of Pritchard imply there is a polytime $(1+\epsilon)$-approximation for $P^{t}$. We then investigate the hierarchy's strength in the context of the well-studied all-or-nothing flow problem in trees (also called unsplittable flow on trees). For this problem, we show that the integrality gap of $P^t$ is $O(n/t)$ and give examples where the gap is $\Omega(n/t)$. We then examine the stronger formulation $P_{\text{rank}}$ where all rank constraints are added. For $P_{\text{rank}}^t$, our best lower bound drops to $\Omega(1/c)$ at level $t=n^c$ for any $c>0$. Moreover, on a well-known class of "bad instances" due to Friggstad and Gao, we show that we can achieve this gap; hence a constant integrality gap for these instances is obtained at level $n^c$.

cs.DS↗

arXiv2020

Eigenvalues and Eigenvectors of Tau Matrices with Applications to Markov Processes and Economics

In the context of matrix displacement decomposition, Bozzo and Di Fiore introduced the so-called $\tau_{\varepsilon,\varphi}$ algebra, a generalization of the more known $\tau$ algebra originally proposed by Bini and Capovani. We study the properties of eigenvalues and eigenvectors of the generator $T_{n,\varepsilon,\varphi}$ of the $\tau_{\varepsilon,\varphi}$ algebra. In particular, we derive the asymptotics for the outliers of $T_{n,\varepsilon,\varphi}$ and the associated eigenvectors; we obtain equations for the eigenvalues of $T_{n,\varepsilon,\varphi}$, which provide also the eigenvectors of $T_{n,\varepsilon,\varphi}$; and we compute the full eigendecomposition of $T_{n,\varepsilon,\varphi}$ in the specific case $\varepsilon\varphi=1$. We also present applications of our results in the context of queuing models, random walks, and diffusion processes, with a special attention to their implications in the study of wealth/income inequality and portfolio dynamics.

math.NA↗