Eric Ma

Nima Anari, Alireza Haqi, Eric Ma

We study correlated rounding on the hypersimplex, the base polytope of the uniform matroid. For each point $x$ in the hypersimplex, the goal is to sample a $k$-subset $A(x)$ with marginals $x$, while coupling the samples for all choices of $x$ so that nearby inputs produce nearby sets. We give a constant-stretch scheme. Our scheme samples the maximum-entropy $k$-subset distribution with prescribed marginals using a common random ordering and common uniform thresholds. For every $x,y\in[0,1]^n$ with $\sum_i x_i=\sum_i y_i=k$, it satisfies $\mathbb{E}[|A(x)\triangle A(y)|]\le 6\|x-y\|_1$. This improves the previous $O(\log k)$ bound for hypersimplex correlated rounding and answers an open question raised by Naor, Raju, Shetty, Srinivasan, Valieva, and Wajc. By adding dummy coordinates, the same result gives stretch at most $12$ for the at-most-$k$ polytope. The proof was found in a GPT 5.5 Pro Extended conversation prompted by the authors, and Codex was used to help assemble the manuscript under the authors' supervision.

Spencer L. Gordon, Manav Kant, Eric Ma et al.

Product of experts (PoE) are layered networks in which the value at each node is an AND (or product) of the values (possibly negated) at its inputs. These were introduced as a neural network architecture that can efficiently learn to generate high-dimensional data which satisfy many low-dimensional constraints -- thereby allowing each individual expert to perform a simple task. PoEs have found a variety of applications in learning. We study the problem of identifiability of a product of experts model having a layer of binary latent variables, and a layer of binary observables that are iid conditional on the latents. The previous best upper bound on the number of observables needed to identify the model was exponential in the number of parameters. We show: (a) When the latents are uniformly distributed, the model is identifiable with a number of observables equal to the number of parameters (and hence best possible). (b) In the more general case of arbitrarily distributed latents, the model is identifiable for a number of observables that is still linear in the number of parameters (and within a factor of two of best-possible). The proofs rely on root interlacing phenomena for some special three-term recurrences.

Hang Jiang, Xiajie Zhang, Robert Mahari et al. · allen-ai

Making legal knowledge accessible to non-experts is crucial for enhancing general legal literacy and encouraging civic participation in democracy. However, legal documents are often challenging to understand for people without legal backgrounds. In this paper, we present a novel application of large language models (LLMs) in legal education to help non-experts learn intricate legal concepts through storytelling, an effective pedagogical tool in conveying complex and abstract concepts. We also introduce a new dataset LegalStories, which consists of 294 complex legal doctrines, each accompanied by a story and a set of multiple-choice questions generated by LLMs. To construct the dataset, we experiment with various LLMs to generate legal stories explaining these concepts. Furthermore, we use an expert-in-the-loop approach to iteratively design multiple-choice questions. Then, we evaluate the effectiveness of storytelling with LLMs through randomized controlled trials (RCTs) with legal novices on 10 samples from the dataset. We find that LLM-generated stories enhance comprehension of legal concepts and interest in law among non-native speakers compared to only definitions. Moreover, stories consistently help participants relate legal concepts to their lives. Finally, we find that learning with stories shows a higher retention rate for non-native speakers in the follow-up assessment. Our work has strong implications for using LLMs in promoting teaching and learning in the legal field and beyond.

Sejoon Oh, Yiqiao Jin, Megha Sharma et al. · gatech

Multimodal large language models (MLLMs) have revolutionized vision-language understanding but remain vulnerable to multimodal jailbreak attacks, where adversarial inputs are meticulously crafted to elicit harmful or inappropriate responses. We propose UniGuard, a novel multimodal safety guardrail that jointly considers the unimodal and cross-modal harmful signals. UniGuard trains a multimodal guardrail to minimize the likelihood of generating harmful responses in a toxic corpus. The guardrail can be seamlessly applied to any input prompt during inference with minimal computational costs. Extensive experiments demonstrate the generalizability of UniGuard across multiple modalities, attack strategies, and multiple state-of-the-art MLLMs, including LLaVA, Gemini Pro, GPT-4o, MiniGPT-4, and InstructBLIP. Notably, this robust defense mechanism maintains the models' overall vision-language understanding capabilities.