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Shaul Druckmann

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3 published item(s)

preprint2026arXiv

Unlocking LLM Creativity in Science through Analogical Reasoning

Autonomous science promises to augment scientific discovery, particularly in complex fields like biomedicine. However, this requires AI systems that can consistently generate novel and diverse solutions to open-ended problems. We evaluate LLMs on the task of open-ended solution generation and quantify their tendency to mode collapse into low-diversity generations. To mitigate this mode collapse, we introduce analogical reasoning (AR) as a new approach to solution generation. AR generates analogies to cross-domain problems based on shared relational structure, then uses those analogies to search for novel solutions. Compared to baselines, AR discovers significantly more diverse generations (improving solution diversity metrics by 90-173%), generates novel solutions over 50% of the time (compared to as little as 1.6% for baselines), and produces high-quality analogies. To validate the real-world feasibility of AR, we implement AR-generated solutions across four biomedical problems, yielding consistent quantitative gains. AR-generated approaches achieve a nearly 13-fold improvement on distributional metrics for perturbation effect prediction, outperform all baselines on AUPRC when predicting cell-cell communication, infer brain region interactions with a high Spearman correlation ($ρ$=0.729) to published methods, and establish state-of-the-art performance on 2 datasets for oligonucleotide property prediction. The novel and diverse solutions produced by AR can be used to augment the search space of existing solution generation methods.

preprint2020arXiv

Avoiding Spurious Local Minima in Deep Quadratic Networks

Despite their practical success, a theoretical understanding of the loss landscape of neural networks has proven challenging due to the high-dimensional, non-convex, and highly nonlinear structure of such models. In this paper, we characterize the training landscape of the mean squared error loss for neural networks with quadratic activation functions. We prove existence of spurious local minima and saddle points which can be escaped easily with probability one when the number of neurons is greater than or equal to the input dimension and the norm of the training samples is used as a regressor. We prove that deep overparameterized neural networks with quadratic activations benefit from similar nice landscape properties. Our theoretical results are independent of data distribution and fill the existing gap in theory for two-layer quadratic neural networks. Finally, we empirically demonstrate convergence to a global minimum for these problems.

preprint2015arXiv

Spectrum density of large sparse random matrices associated to neural networks

The eigendecomposition of the coupling matrix of large biological networks is central to the study of the dynamics of these networks. For neural networks, this matrix should reflect the topology of the network and conform with Dale's law which states that a neuron can have only all excitatory or only all inhibitory output connections, i.e., coefficients of one column of the coupling matrix must all have the same sign. The eigenspectrum density has been determined before for dense matrices $J_{ij}$, when several populations are considered. However, the expressions were derived under the assumption of dense connectivity, whereas neural circuits have sparse connections. Here, we followed mean-field approaches in order to come up with exact self-consistent expressions for the spectrum density in the limit of sparse matrices for both symmetric and neural network matrices. Furthermore we introduced approximations that allow for good numerical evaluation of the density. Finally, we studied the phenomenology of localization properties of the eigenvectors.