arXiv subjects

Kalyan Ramakrishnan

Publications and source records attributed to Kalyan Ramakrishnan.

4 recordsLinked to original sources

arXiv2026

Measuring Progress in Reasoning Toward Mathematical Discovery with Automatic Verification

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 113 predominantly unsolved problems spanning eight domains in mathematics and the mathematical sciences, paired with an open-source evaluation framework for automated verification. Our benchmark targets the generator-verifier gap: problems where discovery is hard and requires meaningful mathematical insight, but verification is computationally straightforward. This contrasts with most existing research-level benchmarks, which instead rely on formal proof verification or manual review, both of which are expensive to scale. Because these solutions are unknown, HorizonMath is resistant to data contamination, and most state-of-the-art models score under 10%. Using this framework, we identify six novel solutions to research problems that either resolve previously open questions or improve on the best-known published results, with GPT-5.4 Pro and GPT-5.6 Sol each discovering three of these solutions. Across seven frontier model families, reasoning efficiency and behavior also vary substantially. We release HorizonMath as an open challenge and a growing community resource, where each verified solution is a candidate contribution to the mathematical literature.

cs.LG↗

arXiv2025

Implicit Neural Representations for Chemical Reaction Paths

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.

cs.LG↗

arXiv2025

Modeling Gene Expression Distributional Shifts for Unseen Genetic Perturbations

We train a neural network to predict distributional responses in gene expression following genetic perturbations. This is an essential task in early-stage drug discovery, where such responses can offer insights into gene function and inform target identification. Existing methods only predict changes in the mean expression, overlooking stochasticity inherent in single-cell data. In contrast, we offer a more realistic view of cellular responses by modeling expression distributions. Our model predicts gene-level histograms conditioned on perturbations and outperforms baselines in capturing higher-order statistics, such as variance, skewness, and kurtosis, at a fraction of the training cost. To generalize to unseen perturbations, we incorporate prior knowledge via gene embeddings from large language models (LLMs). While modeling a richer output space, the method remains competitive in predicting mean expression changes. This work offers a practical step towards more expressive and biologically informative models of perturbation effects.

q-bio.GN↗

arXiv2023

Temporal Label-Refinement for Weakly-Supervised Audio-Visual Event Localization

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.

cs.CV↗