Modeling continuous-time dynamics from sparse and irregularly-sampled time series remains a fundamental challenge. Neural controlled differential equations provide a principled framework for such tasks, yet their performance is highly sensitive to the choice of control path constructed from discrete observations. Existing methods commonly employ fixed interpolation schemes, which impose simplistic geometric assumptions that often misrepresent the underlying data manifold, particularly under high missingness. We propose FlowPath, a novel approach that learns the geometry of the control path via an invertible neural flow. Rather than merely connecting observations, FlowPath constructs a continuous and data-adaptive manifold, guided by invertibility constraints that enforce information-preserving and well-behaved transformations. This inductive bias distinguishes FlowPath from prior unconstrained learnable path models. Empirical evaluations on 18 benchmark datasets and a real-world case study demonstrate that FlowPath consistently achieves statistically significant improvements in classification accuracy over baselines using fixed interpolants or non-invertible architectures. These results highlight the importance of modeling not only the dynamics along the path but also the geometry of the path itself, offering a robust and generalizable solution for learning from irregular time series.

Equation discovery from data is a core challenge in machine learning for science, requiring the recovery of concise symbolic expressions that govern complex physical and geometric phenomena. Recent approaches with large language models (LLMs) show promise in symbolic regression, but their success often hinges on memorized formulas or overly simplified functional forms. Existing benchmarks exacerbate this limitation: they focus on scalar functions, ignore domain grounding, and rely on brittle string-matching based metrics that fail to capture scientific equivalence. We introduce SurfaceBench, first comprehensive benchmark for symbolic surface discovery. SurfaceBench comprises 183 tasks across 15 categories of symbolic complexity, spanning explicit, implicit, and parametric equation representation forms. Each task includes ground-truth equations, variable semantics, and synthetically sampled three dimensional data. Unlike prior SR datasets, our tasks reflect surface-level structure, resist LLM memorization through novel symbolic compositions, and are grounded in scientific domains such as fluid dynamics, robotics, electromagnetics, and geometry. To evaluate equation discovery quality, we pair symbolic checks with geometry-aware metrics such as Chamfer and Hausdorff distances, capturing both algebraic fidelity and spatial reconstruction accuracy. Our experiments reveal that state-of-the-art frameworks, while occasionally successful on specific families, struggle to generalize across representation types and surface complexities. SurfaceBench thus establishes a challenging and diagnostic testbed that bridges symbolic reasoning with geometric reconstruction, enabling principled benchmarking of progress in compositional generalization, data-driven scientific induction, and geometry-aware reasoning with LLMs. We release the code here: https://github.com/Sanchit-404/surfacebench

Although neural operators are widely used in data-driven physical simulations, their training remains computationally expensive. Recent advances address this issue via downstream learning, where a model pretrained on simpler problems is fine-tuned on more complex ones. In this research, we investigate transformer-based neural operators, which have previously been applied only to specific problems, in a more general transfer learning setting. We evaluate their performance across diverse PDE problems, including extrapolation to unseen parameters, incorporation of new variables, and transfer from multi-equation datasets. Our results demonstrate that advanced neural operator architectures can effectively transfer knowledge across PDE problems.

We investigate transformer prediction of long Collatz steps, a complex arithmetic function that maps odd integers to their distant successors in the Collatz sequence ( $u_{n+1}=u_n/2$ if $u_n$ is even, $u_{n+1}=(3u_n+1)/2$ if $u_n$ is odd). Model accuracy varies with the base used to encode input and output. It can be as high as $99.7\%$ for bases $24$ and $32$, and as low as $37$ and $25\%$ for bases $11$ and $3$. Yet, all models, no matter the base, follow a common learning pattern. As training proceeds, they learn a sequence of classes of inputs that share the same residual modulo $2^p$. Models achieve near-perfect accuracy on these classes, and less than $1\%$ for all other inputs. This maps to a mathematical property of Collatz sequences: the length of the loops involved in the computation of a long Collatz step can be deduced from the binary representation of its input. The learning pattern reflects the model learning to predict inputs associated with increasing loop lengths. An analysis of failure cases reveals that almost all model errors follow predictable patterns. Hallucination, a common feature of large language models, almost never happens. In over $90\%$ of failures, the model performs the correct calculation, but wrongly estimates loop lengths. Our observations give a full account of the algorithms learned by the models. They suggest that the difficulty of learning such complex arithmetic function lies in figuring the control structure of the computation -- the length of the loops. We believe that the approach outlined here, using mathematical problems as tools for understanding, explaining, and perhaps improving language models, can be applied to a broad range of problems and bear fruitful results.

Operational safety at mission-critical work sites is a top priority given the complex and hazardous nature of daily tasks. This paper presents the Human-Agent Risk Navigation and Event Safety System (HARNESS), a modular AI framework designed to forecast hazardous events and analyze operational risks in U.S. Department of Energy (DOE) environments. HARNESS integrates Large Language Models (LLMs) with structured work data, historical event retrieval, and risk analysis to proactively identify potential hazards. A human-in-the-loop mechanism allows subject matter experts (SMEs) to refine predictions, creating an adaptive learning loop that enhances performance over time. By combining SME collaboration with iterative agentic reasoning, HARNESS improves the reliability and efficiency of predictive safety systems. Preliminary deployment shows promising results, with future work focusing on quantitative evaluation of accuracy, SME agreement, and decision latency reduction.

The Neural Tangent Kernel (NTK) characterizes how a model's state evolves over Gradient Descent. Computing the full NTK matrix is often infeasible, especially for recurrent architectures. Here, we introduce a matrix-free perspective, using trace estimation to rapidly analyze the empirical, finite-width NTK. This enables fast computation of the NTK's trace, Frobenius norm, effective rank, and alignment. We provide numerical recipes based on the Hutch++ trace estimator with provably fast convergence guarantees. In addition, we show that, due to the structure of the NTK, one can compute the trace using only forward- or reverse-mode automatic differentiation, not requiring both modes. We show these so-called one-sided estimators can outperform Hutch++ in the low-sample regime, especially when the gap between the model state and parameter count is large. In total, our results demonstrate that matrix-free randomized approaches can yield speedups of many orders of magnitude, leading to faster analysis and applications of the NTK.

Students often report difficulties in accessing day-to-day academic information, which is usually spread across numerous institutional documents and websites. This fragmentation results in a lack of clarity and causes confusion about routine university information. This project proposes the development of a chatbot using Generative Artificial Intelligence (GenAI) and Retrieval-Augmented Generation (RAG) to simplify access to such information. Several GenAI models were tested and evaluated based on quality metrics and the LLM-as-a-Judge approach. Among them, Gemini 2.0 Flash stood out for its quality and speed, and Gemma 3n for its good performance and open-source nature.

Summarizing consumer health questions (CHQs) can ease communication in healthcare, but unfaithful summaries that misrepresent medical details pose serious risks. We propose a framework that combines TextRank-based sentence extraction and medical named entity recognition with large language models (LLMs) to enhance faithfulness in medical text summarization. In our experiments, we fine-tuned the LLaMA-2-7B model on the MeQSum (English) and BanglaCHQ-Summ (Bangla) datasets, achieving consistent improvements across quality (ROUGE, BERTScore, readability) and faithfulness (SummaC, AlignScore) metrics, and outperforming zero-shot baselines and prior systems. Human evaluation further shows that over 80\% of generated summaries preserve critical medical information. These results highlight faithfulness as an essential dimension for reliable medical summarization and demonstrate the potential of our approach for safer deployment of LLMs in healthcare contexts.

Data attribution for text-to-image models aims to identify the training images that most significantly influenced a generated output. Existing attribution methods involve considerable computational resources for each query, making them impractical for real-world applications. We propose a novel approach for scalable and efficient data attribution. Our key idea is to distill a slow, unlearning-based attribution method to a feature embedding space for efficient retrieval of highly influential training images. During deployment, combined with efficient indexing and search methods, our method successfully finds highly influential images without running expensive attribution algorithms. We show extensive results on both medium-scale models trained on MSCOCO and large-scale Stable Diffusion models trained on LAION, demonstrating that our method can achieve better or competitive performance in a few seconds, faster than existing methods by 2,500x - 400,000x. Our work represents a meaningful step towards the large-scale application of data attribution methods on real-world models such as Stable Diffusion.

Long context LLMs are vulnerable to prompt injection, where an attacker can inject an instruction in a long context to induce an LLM to generate an attacker-desired output. Existing prompt injection defenses are designed for short contexts. When extended to long-context scenarios, they have limited effectiveness. The reason is that an injected instruction constitutes only a very small portion of a long context, making the defense very challenging. In this work, we propose PISanitizer, which first pinpoints and sanitizes potential injected tokens (if any) in a context before letting a backend LLM generate a response, thereby eliminating the influence of the injected instruction. To sanitize injected tokens, PISanitizer builds on two observations: (1) prompt injection attacks essentially craft an instruction that compels an LLM to follow it, and (2) LLMs intrinsically leverage the attention mechanism to focus on crucial input tokens for output generation. Guided by these two observations, we first intentionally let an LLM follow arbitrary instructions in a context and then sanitize tokens receiving high attention that drive the instruction-following behavior of the LLM. By design, PISanitizer presents a dilemma for an attacker: the more effectively an injected instruction compels an LLM to follow it, the more likely it is to be sanitized by PISanitizer. Our extensive evaluation shows that PISanitizer can successfully prevent prompt injection, maintain utility, outperform existing defenses, is efficient, and is robust to optimization-based and strong adaptive attacks. The code is available at https://github.com/sleeepeer/PISanitizer.