Time Series, Vision, and Language: Exploring the Limits of Alignment in Contrastive Representation Spaces

The Platonic Representation Hypothesis posits that learned representations from models trained on different modalities converge to a shared latent structure of the world. However, this hypothesis has largely been examined in vision and language, and it remains unclear whether time series participate in such convergence. We first examine this in a trimodal setting and find that independently pretrained time series, vision, and language encoders exhibit near-orthogonal geometry in the absence of explicit coupling. We then apply post-hoc alignment by training projection heads over frozen encoders using contrastive learning, and analyze the resulting representations with respect to geometry, scaling behavior, and dependence on information density and input modality characteristics. Our investigation reveals that overall alignment in contrastive representation spaces improves with model size, but this alignment is asymmetric: time series align more strongly with visual representations than with text, and images can act as effective intermediaries between time series and language. We further see that richer textual descriptions improve alignment only up to a threshold; training on denser captions does not lead to further improvement. Analogous effects are observed for visual representations. Our findings shed light on considerations for building multimodal systems involving non-conventional data modalities beyond vision and language.

Rethinking Diffusion Models with Symmetries through Canonicalization with Applications to Molecular Graph Generation

Many generative tasks in chemistry and science involve distributions invariant to group symmetries (e.g., permutation and rotation). A common strategy enforces invariance and equivariance through architectural constraints such as equivariant denoisers and invariant priors. In this paper, we challenge this tradition through the alternative canonicalization perspective: first map each sample to an orbit representative with a canonical pose or order, train an unconstrained (non-equivariant) diffusion or flow model on the canonical slice, and finally recover the invariant distribution by sampling a random symmetry transform at generation time. Building on a formal quotient-space perspective, our work provides a comprehensive theory of canonical diffusion by proving: (i) the correctness, universality and superior expressivity of canonical generative models over invariant targets; (ii) canonicalization accelerates training by removing diffusion score complexity induced by group mixtures and reducing conditional variance in flow matching. We then show that aligned priors and optimal transport act complementarily with canonicalization and further improves training efficiency. We instantiate the framework for molecular graph generation under $S_n \times SE(3)$ symmetries. By leveraging geometric spectra-based canonicalization and mild positional encodings, canonical diffusion significantly outperforms equivariant baselines in 3D molecule generation tasks, with similar or even less computation. Moreover, with a novel architecture Canon, CanonFlow achieves state-of-the-art performance on the challenging GEOM-DRUG dataset, and the advantage remains large in few-step generation.

Assessing Low Back Movement with Motion Tape Sensor Data Through Deep Learning

Back pain is a pervasive issue affecting a significant portion of the population, often worsened by certain movements of the lower back. Assessing these movements is important for helping clinicians prescribe appropriate physical therapy. However, it can be difficult to monitor patients' movements remotely outside the clinic. High-fidelity data from motion capture sensors can be used to classify different movements, but these sensors are costly and impractical for use in free-living environments. Motion Tape (MT), a new fabric-based wearable sensor, addresses these issues by being low cost and portable. Despite these advantages, novelty and variability in sensor stability make the MT dataset small scale and inherent to noise. In this work, we propose the Motion-Tape Augmentation Inference Model (MT-AIM), a deep learning classification pipeline trained on MT data. In order to address the challenges of limited sample size and noise present within the MT dataset, MT-AIM leverages conditional generative models to generate synthetic MT data of a desired movement, as well as predicting joint kinematics as additional features. This combination of synthetic data generation and feature augmentation enables MT-AIM to achieve state-of-the-art accuracy in classifying lower back movements, bridging the gap between physiological sensing and movement analysis.

Think like a Scientist: Physics-guided LLM Agent for Equation Discovery

Explaining observed phenomena through symbolic, interpretable formulas is a fundamental goal of science. Recently, large language models (LLMs) have emerged as promising tools for symbolic equation discovery, owing to their broad domain knowledge and strong reasoning capabilities. However, most existing LLM-based systems try to guess equations directly from data, without modeling the multi-step reasoning process that scientists often follow: first inferring physical properties such as symmetries, then using these as priors to restrict the space of candidate equations. We introduce KeplerAgent, an agentic framework that explicitly follows this scientific reasoning process. The agent coordinates physics-based tools to extract intermediate structure and uses these results to configure symbolic regression engines such as PySINDy and PySR, including their function libraries and structural constraints. Across a suite of physical equation benchmarks, KeplerAgent achieves substantially higher symbolic accuracy and greater robustness to noisy data than both LLM and traditional baselines.

Divide and Learn: Multi-Objective Combinatorial Optimization at Scale

Multi-objective combinatorial optimization seeks Pareto-optimal solutions over exponentially large discrete spaces, yet existing methods sacrifice generality, scalability, or theoretical guarantees. We reformulate it as an online learning problem over a decomposed decision space, solving position-wise bandit subproblems via adaptive expert-guided sequential construction. This formulation admits regret bounds of $O(d\sqrt{T \log T})$ depending on subproblem dimensionality \(d\) rather than combinatorial space size. On standard benchmarks, our method achieves 80--98\% of specialized solvers performance while achieving two to three orders of magnitude improvement in sample and computational efficiency over Bayesian optimization methods. On real-world hardware-software co-design for AI accelerators with expensive simulations, we outperform competing methods under fixed evaluation budgets. The advantage grows with problem scale and objective count, establishing bandit optimization over decomposed decision spaces as a principled alternative to surrogate modeling or offline training for multi-objective optimization.

Demystifying Mergeability: Interpretable Properties to Predict Model Merging Success

Model merging combines knowledge from separately fine-tuned models, yet success factors remain poorly understood. While recent work treats mergeability as an intrinsic property, we show with an architecture-agnostic framework that it fundamentally depends on both the merging method and the partner tasks. Using linear optimization over a set of interpretable pairwise metrics (e.g., gradient L2 distance), we uncover properties correlating with post-merge performance across four merging methods. We find substantial variation in success drivers (46.7% metric overlap; 55.3% sign agreement), revealing method-specific "fingerprints". Crucially, however, subspace overlap and gradient alignment metrics consistently emerge as foundational, method-agnostic prerequisites for compatibility. These findings provide a diagnostic foundation for understanding mergeability and motivate future fine-tuning strategies that explicitly encourage these properties.

Guardian-regularized Safe Offline Reinforcement Learning for Smart Weaning of Mechanical Circulatory Devices

We study the sequential decision-making problem for automated weaning of mechanical circulatory support (MCS) devices in cardiogenic shock patients. MCS devices are percutaneous micro-axial flow pumps that provide left ventricular unloading and forward blood flow, but current weaning strategies vary significantly across care teams and lack data-driven approaches. Offline reinforcement learning (RL) has proven to be successful in sequential decision-making tasks, but our setting presents challenges for training and evaluating traditional offline RL methods: prohibition of online patient interaction, highly uncertain circulatory dynamics due to concurrent treatments, and limited data availability. We developed an end-to-end machine learning framework with two key contributions (1) Clinically-aware OOD-regularized Model-based Policy Optimization (CORMPO), a density-regularized offline RL algorithm for out-of-distribution suppression that also incorporates clinically-informed reward shaping and (2) a Transformer-based probabilistic digital twin that models MCS circulatory dynamics for policy evaluation with rich physiological and clinical metrics. We prove that \textsf{CORMPO} achieves theoretical performance guarantees under mild assumptions. CORMPO attains a higher reward than the offline RL baselines by 28% and higher scores in clinical metrics by 82.6% on real and synthetic datasets. Our approach offers a principled framework for safe offline policy learning in high-stakes medical applications where domain expertise and safety constraints are essential.

Symmetry in Neural Network Parameter Spaces

Modern deep learning models are highly overparameterized, resulting in large sets of parameter configurations that yield the same outputs. A significant portion of this redundancy is explained by symmetries in the parameter space--transformations that leave the network function unchanged. These symmetries shape the loss landscape and constrain learning dynamics, offering a new lens for understanding optimization, generalization, and model complexity that complements existing theory of deep learning. This survey provides an overview of parameter space symmetry. We summarize existing literature, uncover connections between symmetry and learning theory, and identify gaps and opportunities in this emerging field.

Understanding Mode Connectivity via Parameter Space Symmetry

Neural network minima are often connected by curves along which train and test loss remain nearly constant, a phenomenon known as mode connectivity. While this property has enabled applications such as model merging and fine-tuning, its theoretical explanation remains unclear. We propose a new approach to exploring the connectedness of minima using parameter space symmetry. By linking the topology of symmetry groups to that of the minima, we derive the number of connected components of the minima of linear networks and show that skip connections reduce this number. We then examine when mode connectivity and linear mode connectivity hold or fail, using parameter symmetries which account for a significant part of the minimum. Finally, we provide explicit expressions for connecting curves in the minima induced by symmetry. Using the curvature of these curves, we derive conditions under which linear mode connectivity approximately holds. Our findings highlight the role of continuous symmetries in understanding the neural network loss landscape.

Discovering Symbolic Differential Equations with Symmetry Invariants

Discovering symbolic differential equations from data uncovers fundamental dynamical laws underlying complex systems. However, existing methods often struggle with the vast search space of equations and may produce equations that violate known physical laws. In this work, we address these problems by introducing the concept of \textit{symmetry invariants} in equation discovery. We leverage the fact that differential equations admitting a symmetry group can be expressed in terms of differential invariants of symmetry transformations. Thus, we propose to use these invariants as atomic entities in equation discovery, ensuring the discovered equations satisfy the specified symmetry. Our approach integrates seamlessly with existing equation discovery methods such as sparse regression and genetic programming, improving their accuracy and efficiency. We validate the proposed method through applications to various physical systems, such as fluid and reaction-diffusion, demonstrating its ability to recover parsimonious and interpretable equations that respect the laws of physics.