arXiv subjects

Jenny Kaufmann

Publications and source records attributed to Jenny Kaufmann.

4 recordsLinked to original sources

arXiv2025

Can Interpretation Predict Behavior on Unseen Data?

Interpretability research often predicts model responses to targeted mechanistic interventions. But can we predict responses to unseen input data? We propose and demonstrate this alternate objective by using model internals to predict their out-of-distribution (OOD) behavior. We train hundreds of Transformers on simple synthetic tasks, where perfect in-distribution accuracy is compatible with multiple OOD generalization rules. We successfully use attention patterns -- observed only on in-distribution data -- to predict which rule each model follows on OOD data. Our experiments decouple the mechanistic faithfulness of our interpretation from its predictive value; ablations reveal such internal patterns can suppress rather than support the rule they predict, showing observational analysis can forecast behavior even when causal analysis fails to support a simple cause-effect link. Our findings are a proof-of-concept for a new interpretability objective: understanding model internals to predict behavior and assess reliability under distribution shift.

cs.LG↗

arXiv2023

Approximating Min-Diameter: Standard and Bichromatic

The min-diameter of a directed graph $G$ is a measure of the largest distance between nodes. It is equal to the maximum min-distance $d_{min}(u,v)$ across all pairs $u,v \in V(G)$, where $d_{min}(u,v) = \min(d(u,v), d(v,u))$. Our work provides a $O(m^{1.426}n^{0.288})$-time $3/2$-approximation algorithm for min-diameter in DAGs, and a faster $O(m^{0.713}n)$-time almost-$3/2$-approximation variant. (An almost-$α$-approximation algorithm determines the min-diameter to within a multiplicative factor of $α$ plus constant additive error.) By a conditional lower bound result of [Abboud et al, SODA 2016], a better than $3/2$-approximation can't be achieved in truly subquadratic time under the Strong Exponential Time Hypothesis (SETH), so our result is conditionally tight. We additionally obtain a new conditional lower bound for min-diameter approximation in general directed graphs, showing that under SETH, one cannot achieve an approximation factor below 2 in truly subquadratic time. We also present the first study of approximating bichromatic min-diameter, which is the maximum min-distance between oppositely colored vertices in a 2-colored graph.

cs.DS↗

arXiv2022

Approximation Algorithms for Min-Distance Problems in DAGs

The min-distance between two nodes $u, v$ is defined as the minimum of the distance from $v$ to $u$ or from $u$ to $v$, and is a natural distance metric in DAGs. As with the standard distance problems, the Strong Exponential Time Hypothesis [Impagliazzo-Paturi-Zane 2001, Calabro-Impagliazzo-Paturi 2009] leaves little hope for computing min-distance problems faster than computing All Pairs Shortest Paths, which can be solved in $\tilde{O}(mn)$ time. So it is natural to resort to approximation algorithms in $\tilde{O}(mn^{1-ε})$ time for some positive $ε$. Abboud, Vassilevska W., and Wang [SODA 2016] first studied min-distance problems achieving constant factor approximation algorithms on DAGs, obtaining a $3$-approximation algorithm for min-radius on DAGs which works in $\tilde{O}(m\sqrt{n})$ time, and showing that any $(2-δ)$-approximation requires $n^{2-o(1)}$ time for any $δ>0$, under the Hitting Set Conjecture. We close the gap, obtaining a $2$-approximation algorithm which runs in $\tilde{O}(m\sqrt{n})$ time. As the lower bound of Abboud et al only works for sparse DAGs, we further show that our algorithm is conditionally tight for dense DAGs using a reduction from Boolean matrix multiplication. Moreover, Abboud et al obtained a linear time $2$-approximation algorithm for min-diameter along with a lower bound stating that any $(3/2-δ)$-approximation algorithm for sparse DAGs requires $n^{2-o(1)}$ time under SETH. We close this gap for dense DAGs by obtaining a near-$3/2$-approximation algorithm which works in $O(n^{2.350})$ time and showing that the approximation factor is unlikely to be improved within $O(n^{ω- o(1)})$ time under the high dimensional Orthogonal Vectors Conjecture, where $ω$ is the matrix multiplication exponent.

cs.DS↗

arXiv2021

Coloring graph classes with no induced fork via perfect divisibility

For a graph $G$, $χ(G)$ will denote its chromatic number, and $ω(G)$ its clique number. A graph $G$ is said to be perfectly divisible if for all induced subgraphs $H$ of $G$, $V(H)$ can be partitioned into two sets $A$, $B$ such that $H[A]$ is perfect and $ω(H[B]) < ω(H)$. An integer-valued function $f$ is called a $χ$-binding function for a hereditary class of graphs $\cal C$ if $χ(G) \leq f(ω(G))$ for every graph $G\in \cal C$. The fork is the graph obtained from the complete bipartite graph $K_{1,3}$ by subdividing an edge once. The problem of finding a polynomial $χ$-binding function for the class of fork-free graphs is open. In this paper, we study the structure of some classes of fork-free graphs; in particular, we study the class of (fork,$F$)-free graphs $\cal G$ in the context of perfect divisibility, where $F$ is a graph on five vertices with a stable set of size three, and show that every $G\in \cal G$ satisfies $χ(G)\leq ω(G)^2$. We also note that the class $\cal G$ does not admit a linear $χ$-binding function.

math.CO↗