Environment Animals Wildlife'Attack squirrel' sends two people to the ER A friendly reminder to not feed wildlife. Breakthroughs, discoveries, and DIY tips sent every weekday. The residents of San Rafael, California, have been traumatized by some vicious wildlife . While cougars, coyotes, or great white sharks would be viable guesses for the culprit, this time it was a less formidable predator. The aggressor is a squirrel .

In this paper, we present non-asymptotic optimization guarantees of gradient descent methods for estimating structured transition matrices in high-dimensional vector autoregressive (V AR) models.

The emergence of generative AI, particularly large language models (LLMs), has opened the door for student-centered and active learning methods like project-based learning (PBL). However, PBL poses practical implementation challenges for educators around project design and management, assessment, and balancing student guidance with student autonomy. The following research documents a co-design process with interdisciplinary K-12 teachers to explore and address the current PBL challenges they face. Through teacher-driven interviews, collaborative workshops, and iterative design of wireframes, we gathered evidence for ways LLMs can support teachers in implementing high-quality PBL pedagogy by automating routine tasks and enhancing personalized learning. Teachers in the study advocated for supporting their professional growth and augmenting their current roles without replacing them. They also identified affordances and challenges around classroom integration, including resource requirements and constraints, ethical concerns, and potential immediate and long-term impacts. Drawing on these, we propose design guidelines for future deployment of LLM tools in PBL.

In recent years, neural network-based models have achieved state-of-the-art performance across a wide array of tasks. These models effectively capture relevant features or concepts from samples, tailored to the specific prediction tasks they address (Yang and Hu, 2021b; Bordelon and Pehlevan, 2022a; Ba et al., 2022b). A fundamental challenge lies in understanding how these models learn such features and determining whether these features can be interpreted or even retrieved directly (Radhakrishnan et al., 2024). Recent advancements in mechanistic interpretability have opened multiple avenues for elucidating how transformerbased models, including Large Language Models (LLMs), acquire and represent features (Bricken et al., 2023; Doshi-Velez and Kim, 2017). These advances include uncovering neural circuits that encode specific concepts (Marks et al., 2024b; Olah et al., 2020), understanding feature composition across attention layers (Yang and Hu, 2021b), and revealing how models develop structured representations (Elhage et al., 2022). One line of research posits that features are encoded linearly within the latent representation space through sparse activations, a concept known as the linear representation hypothesis (LRH) (Mikolov et al., 2013; Arora et al., 2016). However, this hypothesis faces challenges in explaining how neural networks function, as models often need to represent more distinct features than their layer dimensions would theoretically allow under purely linear encoding. This phenomenon has been studied extensively in the context of large language models through the lens of superposition (Elhage et al., 2022), where multiple features share the same dimensional space in structured ways.

Markov Logic Networks (MLNs) are weighted first-order logic templates for generating large (ground) Markov networks. Lifted inference algorithms for them bring the power of logical inference to probabilistic inference. These algorithms operate as much as possible at the compact first-order level, grounding or propositionalizing the MLN only as necessary. As a result, lifted inference algorithms can be much more scalable than propositional algorithms that operate directly on the much larger ground network. Unfortunately, existing lifted inference algorithms suffer from two interrelated problems, which severely affects their scalability in practice. First, for most real-world MLNs having complex structure, they are unable to exploit symmetries and end up grounding most atoms (the grounding problem).

In this paper, we present a new approach for lifted MAP inference in Markov logic networks (MLNs). The key idea in our approach is to compactly encode the MAP inference problem as an Integer Polynomial Program (IPP) by schematically applying three lifted inference steps to the MLN: lifted decomposition, lifted conditioning, and partial grounding. Our IPP encoding is lifted in the sense that an integer assignment to a variable in the IPP may represent a truth-assignment to multiple indistinguishable ground atoms in the MLN. We show how to solve the IPP by first converting it to an Integer Linear Program (ILP) and then solving the latter using state-of-the-art ILP techniques. Experiments on several benchmark MLNs show that our new algorithm is substantially superior to ground inference and existing methods in terms of computational efficiency and solution quality.

In this work, we investigate the problem of learning distance functions within the query-based learning framework, where a learner is able to pose triplet queries of the form: ``Is $x_i$ closer to $x_j$ or $x_k$?'' We establish formal guarantees on the query complexity required to learn smooth, but otherwise general, distance functions under two notions of approximation: $\omega$-additive approximation and $(1 + \omega)$-multiplicative approximation. For the additive approximation, we propose a global method whose query complexity is quadratic in the size of a finite cover of the sample space. For the (stronger) multiplicative approximation, we introduce a method that combines global and local approaches, utilizing multiple Mahalanobis distance functions to capture local geometry. This method has a query complexity that scales quadratically with both the size of the cover and the ambient space dimension of the sample space.