#01Nov 5, 2026
cs.LG
Data-driven discovery of intrinsic Lie point symmetries of differential equation systems
Ilker Gurcan, Kadir Ustun, Ramazan Gokberk Cinbis
Discovering continuous symmetries directly from differential-equation data can reveal geometric structure for model reduction and scientific machine learning without symbolic determining equations or a closed-form representation of the governing system. We formulate intrinsic Lie point-symmetry discovery as an operator-theoretic problem on sampled jet-space data. Admissible generators are identified from a sampled determining operator and separated from redundant, solution-dependent, and geometrically trivial directions. The framework combines prolongation, sequential subspace restrictions, and a fixed nonlinear dictionary linear in trainable coefficients. A rank-stabilization preflight test diagnoses systems whose represented intrinsic symmetry algebra does not stabilize under dictionary refinement. On a controlled differential-equation benchmark with an analytically known 11-dimensional represented intrinsic symmetry algebra, the method recovers the complete represented generator set, reproduces its Lie-bracket structure to numerical precision, and approximates a known generator beyond the training domain. Here we show that explicit intrinsic continuous-symmetry generators can be recovered from data obtained from exact or approximate differential systems.
#02Nov 5, 2026
cs.LG
On the limitations of molecular representations
Acer Blake, Fergus Imrie, Charlotte M. Deane
Molecular representations such as fingerprints and learned embeddings play a central role in cheminformatics and small-molecule machine learning. They serve as the primary input for a diverse array of tasks, including clustering, dataset splitting, and virtual screening, yet their evaluation is often limited to downstream model performance on narrow benchmark tasks. We carried out a systematic investigation of the quality of molecular representations, finding that none of the state-of-the-art molecular embedding models capture graph structure, 3D shape, or ADMET endpoint similarity better than fingerprints or physicochemical descriptors. However, classical fingerprints also revealed their own material limitations. For example, we show that depending on the representation, between 225M and $\sim$4B molecules have non-unique representations in the 10.8B Enamine REAL database, with implications for virtual screening. Our findings provide an insight into the current limitations of molecular representations, outlining future research directions for the development of more robust encodings of small molecules.
#03Nov 5, 2026
cs.AI
RM-VLM: From Natural-Language Task Descriptions to Vision-Grounded Reward Machines
Roko Parac, Christos Ziakas, Leo Ardon and 1 more
Reward machines (RMs) have been proposed as a reward formulation in reinforcement learning (RL) to capture non-Markovian tasks where credit assignment depends on history. By representing reward functions as automata, RMs expose the task's temporal structure and allow such rewards to be handled within a Markovian framework. However, they assume a labelling function, a proposition-grounding oracle for observations, which must be manually engineered for each environment, limiting their wider applicability. In this work, we address this limitation by proposing RM-VLM, a novel approach in which a large language model (LLM) generates an RM from a natural-language task description, and a vision-language model (VLM) acts as the labelling function, grounding the RM's propositions over image-based observations during RM-guided policy learning. A VLM-based value function estimator is used to assess the agent's progress towards each RM transition and derive a dense reward signal. We evaluate RM-VLM on three domains covering non-Markovian grid-world navigation, robotic manipulation, and 3D object collection. Our experimental results show that RM-VLM consistently achieves higher task success rates than existing VLM-based reward methods across all tested domains.
#04Nov 5, 2026
cs.LG
Conformal Prediction for Time-Dependent PDEs
Joshua Stiller, Annika Schneider, Eyke Hüllermeier
Uncertainty quantification is crucial in scientific machine learning, where models inform safety-critical tasks such as flood forecasting, financial risk management, and thermal control in machines. Conformal prediction provides distribution-free coverage guarantees, but in time-dependent settings common to physics and engineering, these guarantees can break down, leading to systematic undercoverage. We study this problem in the context of surrogate models for time-dependent physical systems described by partial differential equations. We prove that in a function space setting, distributions at arbitrarily close times can be mutually singular, making exact coverage guarantees impossible. We further show that in discretized settings, the total variation distance between distributions often saturates exponentially fast with the grid resolution, mandating restrictions on the spatial discretization to ensure coverage. Finally, for certain settings, we show how to use principled weighted conformal prediction to obtain finite-sample coverage guarantees over growing time horizons.
#05Nov 5, 2026
cs.CL
Label-Wording Augmentation in a Typed-Decision Encoder: Gains on Unfamiliar Words, Not on Abbreviations or Codes
Vladimir Beskorovainyi
Typed-decision models score options that the caller supplies at request time, so their accuracy depends on label wording that the model's developer does not control. We compare two releases of a 307M-parameter multilingual cross-encoder, Ru-Jev, trained on thirteen Russian-language tasks; the later release adds an augmentation that presents labels in several surface forms. Holding questions fixed and varying only how eighteen routing labels are worded, we evaluate ten label vocabularies, produced by three separate processes and checked for overlap with the training data, with five candidates per question and, for eight of them, also with eighteen. On held-out vocabularies made of ordinary or borrowed words (English-derived jargon, office slang, department names), the augmented release is more accurate in every setting, by up to 0.24. Eleven of these fourteen gains survive a Holm correction (slang with eighteen candidates and descriptive sentences with five do not), and for jargon on all labels the label-level interval excludes zero in both settings. On abbreviations and opaque codes it gives no usable gain: on abbreviations it is not better, and worse on the clean slice, and on opaque codes both releases stay at or below chance once labels related to training options are removed. In most cells where accuracy rises, the risk-coverage area falls, but with eighteen candidates confident errors rise on jargon and slang. On two datasets neither release saw, accuracy moves by -8.4 and +5.6 points. We also report four evaluation hazards from comparing the two releases.