Kalyan Ramakrishnan

Erik Y. Wang, Sumeet Motwani, James V. Roggeveen et al.

Can AI make progress on important, unsolved mathematical problems? Large language models are now capable of sophisticated mathematical and scientific reasoning, but whether they can perform novel research is still widely debated and underexplored. We introduce HorizonMath, a benchmark of over 100 predominantly unsolved problems spanning 8 domains in computational and applied mathematics, paired with an open-source evaluation framework for automated verification. Our benchmark targets a class of problems where discovery is hard, requiring meaningful mathematical insight, but verification is computationally efficient and simple. Because these solutions are unknown, HorizonMath is immune to data contamination, and most state-of-the-art models score near 0%. Existing research-level benchmarks instead rely on formal proof verification or manual review, both of which are expensive to scale. Using this platform, we find two problems for which GPT 5.4 Pro proposes solutions that improve on the best-known published results, representing potential novel contributions (pending expert review). We release HorizonMath as an open challenge and a growing community resource, where correct solutions to problems in the unsolved problem classes could constitute novel results in the mathematical literature.

Kalyan Ramakrishnan

Audio-Visual Event Localization (AVEL) is the task of temporally localizing and classifying \emph{audio-visual events}, i.e., events simultaneously visible and audible in a video. In this paper, we solve AVEL in a weakly-supervised setting, where only video-level event labels (their presence/absence, but not their locations in time) are available as supervision for training. Our idea is to use a base model to estimate labels on the training data at a finer temporal resolution than at the video level and re-train the model with these labels. I.e., we determine the subset of labels for each \emph{slice} of frames in a training video by (i) replacing the frames outside the slice with those from a second video having no overlap in video-level labels, and (ii) feeding this synthetic video into the base model to extract labels for just the slice in question. To handle the out-of-distribution nature of our synthetic videos, we propose an auxiliary objective for the base model that induces more reliable predictions of the localized event labels as desired. Our three-stage pipeline outperforms several existing AVEL methods with no architectural changes and improves performance on a related weakly-supervised task as well.

Kalyan Ramakrishnan, Lars L. Schaaf, Chen Lin et al.

We show that neural networks can be optimized to represent minimum energy paths as continuous functions, offering a flexible alternative to discrete path-search methods such as Nudged Elastic Band (NEB). Our approach parameterizes reaction paths with a network trained on a loss function that discards tangential energy gradients and enables instant estimation of the transition state. We first validate the method on two-dimensional potentials and then demonstrate its advantages over NEB on challenging atomistic systems where (i) poor initial guesses yield unphysical paths, (ii) multiple competing paths exist, or (iii) the reaction follows a complex multi-step mechanism. Results highlight the versatility of the method: for instance, a simple adjustment to the sampling strategy during optimization can help escape local-minimum solutions. Finally, in a low-dimensional setting, we demonstrate that a single neural network can learn from existing paths and generalize to unseen systems, showing promise for a universal reaction path representation.