arXiv subjects

Duncan Soiffer

Publications and source records attributed to Duncan Soiffer.

4 recordsLinked to original sources

arXiv2026

Catastrophic Compositional Generation: Why Vanilla Diffusion Models Fail to Extrapolate

The task of compositional generation involves using a conditional generative model, trained only on a subset of the possible conditions, to produce samples from compositionally-defined target distributions such as a geometric combination of the source distributions. In this work, we argue that this task is often infeasible for vanilla conditional diffusion models: we conjecture that no inference-time technique can efficiently produce samples from the target distribution in certain well-motivated settings. This idea is supported by theory-guided generalization arguments and carefully-designed experiments on both synthetic and realistic data. In particular, while recent methods such as Feynman-Kac correction reduce inference-time approximation error, our results show that score estimation error has a more catastrophic effect on performance when the target distribution is out-of-distribution with respect to the sources, highlighting the need for a different approach to this task.

cs.LG↗

arXiv2026

Improved Upper Bounds for Slicing the Hypercube

A collection of hyperplanes $\mathcal{H}$ slices all edges of the $n$-dimensional hypercube $Q_n$ with vertex set $\{-1,1\}^n$ if, for every edge $e$ in the hypercube, there exists a hyperplane in $\mathcal{H}$ intersecting $e$ in its interior. Let $S(n)$ be the minimum number of hyperplanes needed to slice $Q_n$. We prove that $S(n) \leq \lceil \frac{4n}{5} \rceil$, except when $n$ is an odd multiple of $5$, in which case $S(n) \leq \frac{4n}{5} +1$. This improves upon the previously known upper bound of $S(n) \leq \lceil\frac{5n}{6} \rceil$ due to Paterson reported in 1971. We also obtain new lower bounds on the maximum number of edges in $Q_n$ that can be sliced using $k<n$ hyperplanes. We prove the improved upper bound on $S(n)$ by constructing $8$ hyperplanes slicing $Q_{10}$ aided by the recently introduced CPro1: an automatic tool that uses reasoning LLMs coupled with automated hyperparameter tuning to create search algorithms for the discovery of mathematical constructions.

cs.AI↗

arXiv2025

Semantic Agreement Enables Efficient Open-Ended LLM Cascades

Cascade systems route computational requests to smaller models when possible and defer to larger models only when necessary, offering a promising approach to balance cost and quality in LLM deployment. However, they face a fundamental challenge in open-ended text generation: determining output reliability when generation quality lies on a continuous spectrum, often with multiple valid responses. To address this, we propose semantic agreement -- meaning-level consensus between ensemble outputs -- as a training-free signal for reliable deferral. We show that when diverse model outputs agree semantically, their consensus is a stronger reliability signal than token-level confidence. Evaluated from 500M to 70B-parameter models, we find that semantic cascades match or surpass target-model quality at 40% of the cost and reduce latency by up to 60%. Our method requires no model internals, works across black-box APIs, and remains robust to model updates, making it a practical baseline for real-world LLM deployment.

cs.CL↗

arXiv2024

Improved Lower Bounds on the Expected Length of Longest Common Subsequences

It has been proven that, when normalized by $n$, the expected length of a longest common subsequence of $d$ random strings of length $n$ over an alphabet of size $σ$ converges to some constant that depends only on $d$ and $σ$. These values are known as the Chvátal-Sankoff constants, and determining their exact values is a well-known open problem. Upper and lower bounds are known for some combinations of $σ$ and $d$, with the best lower and upper bounds for the most studied case, $σ=2, d=2$, at $0.788071$ and $0.826280$, respectively. Building off previous algorithms for lower-bounding the constants, we implement runtime optimizations, parallelization, and an efficient memory reading and writing scheme to obtain an improved lower bound of $0.792665992$ for $σ=2, d=2$. We additionally improve upon almost all previously reported lower bounds for the Chvátal-Sankoff constants when either the size of alphabet, the number of strings, or both are larger than 2.

cs.DS↗