The successful training of neural networks hinges on the use of first order optimization methods, yet the theoretical characterization of these methods remains incomplete. This is especially true in settings with mild overparameterization. In this work, we study the gradient flow dynamics of two-layer ReLU networks from small initialization with orthogonal training data. We prove the limiting flow converges to a saddle-to-saddle jump process as the initialization scale tends to zero, revealing an incremental learning phenomenon in which a new neuron activates at each saddle. This analysis recovers the known result of Dana et al. (2025, arXiv:2502.16977) that the network interpolates the training data with high probability as soon as $m \gtrsim \log(n)$, where $m$ is the network width and $n$ is the number of training samples. This incremental process characterization also allows us to derive a novel implicit bias result: the learned interpolator has a squared $\ell_2$-norm scaling as $\sqrt{n}$, which is within a constant factor of the minimal $\ell_2$-norm interpolator. More broadly, our work provides the first rigorous proof of an incremental learning process for ReLU networks, whilst suggesting mildly overparameterized networks can converge to interpolating solutions whose complexity is of the same order as that of the optimal interpolator.

Understanding the consequences of mutation for molecular fitness and function is a fundamental problem in biology. Recently, generative probabilistic models have emerged as a powerful tool for estimating fitness from evolutionary sequence data, with accuracy sufficient to predict both laboratory measurements of function and disease risk in humans, and to design novel functional proteins. Existing techniques rest on an assumed relationship between density estimation and fitness estimation, a relationship that we interrogate in this article. We prove that fitness is not identifiable from observational sequence data alone, placing fundamental limits on our ability to disentangle fitness landscapes from phylogenetic history. We show on real datasets that perfect density estimation in the limit of infinite data would, with high confidence, result in poor fitness estimation; current models perform accurate fitness estimation because of, not despite, misspecification. Our results challenge the conventional wisdom that bigger models trained on bigger datasets will inevitably lead to better fitness estimation, and suggest novel estimation strategies going forward.

Asynchronous Bayesian optimization is widely used for gradient-free optimization in domains with independent parallel experiments and varying evaluation times. Existing methods posit that standard acquisitions lead to redundant and repeated queries, proposing complex solutions to enforce diversity in queries. Challenging this fundamental premise, we show that methods, like the Upper Confidence Bound, can in fact achieve theoretical guarantees essentially equivalent to those of sequential Thompson sampling. A conceptual analysis of asynchronous Bayesian optimization reveals that existing works neglect intermediate posterior updates, which we find to be generally sufficient to avoid redundant queries. Further investigation shows that by penalizing busy locations, diversity-enforcing methods can over-explore in asynchronous settings, reducing their performance. Our extensive experiments demonstrate that simple standard acquisition functions match or outperform purpose-built asynchronous methods across synthetic and real-world tasks.

Project lead, main contributor, correspondence to alexandre.rame@isir.upmc.fr. Equal experimental contribution, order determined at random. Further information and resources related to this project can be found on this website.

Neural Information Processing Systems http://nips.cc/

Agentic AI "scientists" now use language models to search the literature, run analyses, and generate hypotheses. We evaluate KOSMOS, an autonomous AI scientist, on three problems in radiation biology using simple random-gene null benchmarks. Hypothesis 1: baseline DNA damage response (DDR) capacity across cell lines predicts the p53 transcriptional response after irradiation (GSE30240). Hypothesis 2: baseline expression of OGT and CDO1 predicts the strength of repressed and induced radiation-response modules in breast cancer cells (GSE59732). Hypothesis 3: a 12-gene expression signature predicts biochemical recurrence-free survival after prostate radiotherapy plus androgen deprivation therapy (GSE116918). The DDR-p53 hypothesis was not supported: DDR score and p53 response were weakly negatively correlated (Spearman rho = -0.40, p = 0.76), indistinguishable from random five-gene scores. OGT showed only a weak association (r = 0.23, p = 0.34), whereas CDO1 was a clear outlier (r = 0.70, empirical p = 0.0039). The 12-gene signature achieved a concordance index of 0.61 (p = 0.017) but a non-unique effect size. Overall, KOSMOS produced one well-supported discovery, one plausible but uncertain result, and one false hypothesis, illustrating that AI scientists can generate useful ideas but require rigorous auditing against appropriate null models.

Discovering the antecedents of individuals' influence in collaborative environments is an important, practical, and challenging problem. In this paper, we study interpersonal influence in small groups of individuals who collectively execute a sequence of intellective tasks. We observe that along an issue sequence with feedback, individuals with higher expertise and social confidence are accorded higher interpersonal influence. We also observe that low-performing individuals tend to underestimate their high-performing teammate's expertise. Based on these observations, we introduce three hypotheses and present empirical and theoretical support for their validity. We report empirical evidence on longstanding theories of transactive memory systems, social comparison, and confidence heuristics on the origins of social influence. We propose a cognitive dynamical model inspired by these theories to describe the process by which individuals adjust interpersonal influences over time. We demonstrate the model's accuracy in predicting individuals' influence and provide analytical results on its asymptotic behavior for the case with identically performing individuals. Lastly, we propose a novel approach using deep neural networks on a pre-trained text embedding model for predicting the influence of individuals. Using message contents, message times, and individual correctness collected during tasks, we are able to accurately predict individuals' self-reported influence over time. Extensive experiments verify the accuracy of the proposed models compared to baselines such as structural balance and reflected appraisal model. While the neural networks model is the most accurate, the dynamical model is the most interpretable for influence prediction.

Neural Information Processing Systems http://nips.cc/

This paper investigates the asymmetric low-rank matrix completion problem, which can be formulated as an unconstrained non-convex optimization problem with a nonlinear least-squares objective function, and is solved via gradient descent methods. Previous gradient descent approaches typically incorporate regularization terms into the objective function to guarantee convergence. However, numerical experiments and theoretical analysis of the gradient flow both demonstrate that the elimination of regularization terms in gradient descent algorithms does not adversely affect convergence performance. By introducing the leave-one-out technique, we inductively prove that the vanilla gradient descent with spectral initialization achieves a linear convergence rate with high probability. Besides, we demonstrate that the balancing regularization term exhibits a small norm during iterations, which reveals the implicit regularization property of gradient descent. Empirical results show that our algorithm has a lower computational cost while maintaining comparable completion performance compared to other gradient descent algorithms.