Deep network models are often purely inductive during both training and inference on unseen data. When these models are used for prediction, but they may fail to capture important semantic information and implicit dependencies within datasets. Recent advancements have shown that combining multiple modalities in large-scale vision and language settings can improve understanding and generalization performance. However, as the model size increases, fine-tuning and deployment become computationally expensive, even for a small number of downstream tasks. Moreover, it is still unclear how domain or prior modal knowledge can be specified in a backpropagation friendly manner, especially in large-scale and noisy settings.

In the design and operation of complex dynamical systems, it is essential to ensure that all state trajectories of the dynamical system converge to a desired equilibrium within a guaranteed stability region. Yet, for many practical systems -- especially in aerospace -- this region cannot be determined a priori and is often challenging to compute. One of the most common methods for computing the stability region is to identify a Lyapunov function. A Lyapunov function is a positive function whose time derivative along system trajectories is non-positive, which provides a sufficient condition for stability and characterizes an estimated stability region. However, existing methods of characterizing a stability region via a Lyapunov function often rely on explicit knowledge of the system governing equations. In this work, we present a new physics-informed machine learning method of characterizing an estimated stability region by inferring a Lyapunov function from system trajectory data that treats the dynamical system as a black box and does not require explicit knowledge of the system governing equations. In our presented Lyapunov function Inference method (LyapInf), we propose a quadratic form for the unknown Lyapunov function and fit the unknown quadratic operator to system trajectory data by minimizing the average residual of the Zubov equation, a first-order partial differential equation whose solution yields a Lyapunov function. The inferred quadratic Lyapunov function can then characterize an ellipsoidal estimate of the stability region. Numerical results on benchmark examples demonstrate that our physics-informed stability analysis method successfully characterizes a near-maximal ellipsoid of the system stability region associated with the inferred Lyapunov function without requiring knowledge of the system governing equations.

Detecting Alzheimer's Disease (AD) from narrative transcripts remains a challenging task for large language models (LLMs), particularly under out-of-distribution (OOD) and data-scarce conditions. While in-context learning (ICL) provides a parameter-efficient alternative to fine-tuning, existing ICL approaches often suffer from task recognition failure, suboptimal demonstration selection, and misalignment between label words and task objectives, issues that are amplified in clinical domains like AD detection. We propose Explicit Knowledge In-Context Learners (EK-ICL), a novel framework that integrates structured explicit knowledge to enhance reasoning stability and task alignment in ICL. EK-ICL incorporates three knowledge components: confidence scores derived from small language models (SLMs) to ground predictions in task-relevant patterns, parsing feature scores to capture structural differences and improve demo selection, and label word replacement to resolve semantic misalignment with LLM priors. In addition, EK-ICL employs a parsing-based retrieval strategy and ensemble prediction to mitigate the effects of semantic homogeneity in AD transcripts. Extensive experiments across three AD datasets demonstrate that EK-ICL significantly outperforms state-of-the-art fine-tuning and ICL baselines. Further analysis reveals that ICL performance in AD detection is highly sensitive to the alignment of label semantics and task-specific context, underscoring the importance of explicit knowledge in clinical reasoning under low-resource conditions.

Evidence suggests that large pre-trained language models (LMs) acquire some reasoning capacity, but this ability is difficult to control.

Large Language Models (LLMs) define probability measures on text. By considering the implicit knowledge question of what it means for an LLM to know such a measure and what it entails algorithmically, we are naturally led to formulate a series of tasks that go beyond generative sampling, involving forms of summarization, counterfactual thinking, anomaly detection, originality search, reverse prompting, debating, creative solving, etc. These tasks can be formulated as games based on LLM measures, which we call Cross-Entropy (Xent) Games . Xent Games can be single-player or multi-player. They involve cross-entropy scores and cross-entropy constraints, and can be expressed as simple computational graphs and programs. We show the Xent Game space is large enough to contain a wealth of interesting examples, while being constructible from basic game-theoretic consistency axioms. We then discuss how the Xent Game space can be used to measure the abilities of LLMs. This leads to the construction of Xent Game measures: finite families of Xent Games that can be used as capability benchmarks, built from a given scope, by extracting a covering measure. To address the unbounded scope problem associated with the challenge of measuring general abilities, we propose to explore the space of Xent Games in a coherent fashion, using ideas inspired by evolutionary dynamics.

It is sometimes assumed that Large Language Models (LLMs) know language, or for example that they know that Paris is the capital of France. But what -- if anything -- do LLMs actually know? In this paper, I argue that LLMs can acquire tacit knowledge as defined by Martin Davies (1990). Whereas Davies himself denies that neural networks can acquire tacit knowledge, I demonstrate that certain architectural features of LLMs satisfy the constraints of semantic description, syntactic structure, and causal systematicity. Thus, tacit knowledge may serve as a conceptual framework for describing, explaining, and intervening on LLMs and their behavior.