We propose Equivariance by Contrast (EbC) to learn equivariant embeddings from observation pairs $(\mathbf{y}, g \cdot \mathbf{y})$, where $g$ is drawn from a finite group acting on the data. Our method jointly learns a latent space and a group representation in which group actions correspond to invertible linear maps -- without relying on group-specific inductive biases. We validate our approach on the infinite dSprites dataset with structured transformations defined by the finite group $G:= (R_m \times \mathbb{Z}_n \times \mathbb{Z}_n)$, combining discrete rotations and periodic translations. The resulting embeddings exhibit high-fidelity equivariance, with group operations faithfully reproduced in latent space. On synthetic data, we further validate the approach on the non-abelian orthogonal group $O(n)$ and the general linear group $GL(n)$. We also provide a theoretical proof for identifiability. While broad evaluation across diverse group types on real-world data remains future work, our results constitute the first successful demonstration of general-purpose encoder-only equivariant learning from group action observations alone, including non-trivial non-abelian groups and a product group motivated by modeling affine equivariances in computer vision.

As future superhuman models become increasingly complex, accurately supervising their behavior may exceed human capabilities. Recent works have demonstrated that in such scenarios, weak models can effectively supervise strong models, a phenomenon known as weak-to-strong generalization. However, we find that naive weak-to-strong generalization fails under distribution shifts, often leading to worse performance of the strong model than its weak supervisors. To address this, we propose RAVEN, a robust weak-to-strong generalization framework that dynamically learns the optimal combinations of weak models in addition to parameters of the strong model. We demonstrate the effectiveness of RAVEN on image classification, text classification, and preference alignment tasks. RAVEN outperforms alternative baselines by over 30% on out-of-distribution tasks while matching or surpassing existing methods on in-distribution tasks. Moreover, our results show that RAVEN assigns higher weights to more accurate weak models, demonstrating its ability to automatically identify trustworthy supervision.

Adversarial training has emerged as a key technique to enhance model robustness against adversarial input perturbations. Many of the existing methods rely on computationally expensive min-max problems that limit their application in practice. We propose a novel formulation of adversarial training in reproducing kernel Hilbert spaces, shifting from input to feature-space perturbations. This reformu-lation enables the exact solution of inner maximization and efficient optimization. It also provides a regularized estimator that naturally adapts to the noise level and the smoothness of the underlying function. We establish conditions under which the feature-perturbed formulation is a relaxation of the original problem and propose an efficient optimization algorithm based on iterative kernel ridge regression. We provide generalization bounds that help to understand the properties of the method. We also extend the formulation to multiple kernel learning. Empirical evaluation shows good performance in both clean and adversarial settings.

Large Language Models (LLMs) enable a new form of digital experimentation where treatments combine human and model-generated content in increasingly sophisticated ways. The main methodological challenge in this setting is representing these high-dimensional treatments without losing their semantic meaning or rendering analysis intractable. Here, we address this problem by focusing on learning low-dimensional representations that capture the underlying structure of such treatments. These representations enable downstream applications such as guiding generative models to produce meaningful treatment variants and facilitating adaptive assignment in online experiments. We propose double kernel representation learning, which models the causal effect through the inner product of kernel-based representations of treatments and user covariates. We develop an alternating-minimization algorithm that learns these representations efficiently from data and provides convergence guarantees under a low-rank factor model. As an application of this framework, we introduce an adaptive design strategy for online experimentation and demonstrate the method's effectiveness through numerical experiments.

Algorithmic fairness is a socially crucial topic in real-world applications of AI. Among many notions of fairness, subgroup fairness is widely studied when multiple sensitive attributes (e.g., gender, race, age) are present. However, as the number of sensitive attributes grows, the number of subgroups increases accordingly, creating heavy computational burdens and data sparsity problem (subgroups with too small sizes). In this paper, we develop a novel learning algorithm for subgroup fairness which resolves these issues by focusing on subgroups with sufficient sample sizes as well as marginal fairness (fairness for each sensitive attribute). To this end, we formalize a notion of subgroup-subset fairness and introduce a corresponding distributional fairness measure called the supremum Integral Probability Metric (supIPM). Building on this formulation, we propose the Doubly Regressing Adversarial learning for subgroup Fairness (DRAF) algorithm, which reduces a surrogate fairness gap for supIPM with much less computation than directly reducing supIPM. Theoretically, we prove that the proposed surrogate fairness gap is an upper bound of supIPM. Empirically, we show that the DRAF algorithm outperforms baseline methods in benchmark datasets, specifically when the number of sensitive attributes is large so that many subgroups are very small.

Flow and diffusion-based models have emerged as powerful tools for scientific applications, particularly for sampling non-normalized probability distributions, as exemplified by Boltzmann Generators (BGs). A critical challenge in deploying these models is their reliance on sample likelihood computations, which scale prohibitively with system size $n$, often rendering them infeasible for large-scale problems. To address this, we introduce $\textit{HollowFlow}$, a flow-based generative model leveraging a novel non-backtracking graph neural network (NoBGNN). By enforcing a block-diagonal Jacobian structure, HollowFlow likelihoods are evaluated with a constant number of backward passes in $n$, yielding speed-ups of up to $\mathcal{O}(n^2)$: a significant step towards scaling BGs to larger systems. Crucially, our framework generalizes: $\textbf{any equivariant GNN or attention-based architecture}$ can be adapted into a NoBGNN. We validate HollowFlow by training BGs on two different systems of increasing size. For both systems, the sampling and likelihood evaluation time decreases dramatically, following our theoretical scaling laws. For the larger system we obtain a $10^2\times$ speed-up, clearly illustrating the potential of HollowFlow-based approaches for high-dimensional scientific problems previously hindered by computational bottlenecks.

Performative predictions are forecasts which influence the outcomes they aim to predict, undermining the existence of correct forecasts and standard methods of elicitation and estimation. We show that conditioning forecasts on covariates that separate them from the outcome renders the target distribution forecast-invariant, guaranteeing well-posedness of the forecasting problem. However, even under this condition, classical proper scoring rules fail to elicit correct forecasts. We prove a general impossibility result and identify two solutions: (i) in decision-theoretic settings, elicitation of correct and incentive-compatible forecasts is possible if forecasts are separating; (ii) scoring with unbiased estimates of the divergence between the forecast and the induced distribution of the target variable yields correct forecasts. Applying these insights to parameter estimation, conditional forecasts and proper scoring rules enable performatively stable estimation of performatively correct parameters, resolving the issues raised by Perdomo et al. (2020). Our results expose fundamental limits of classical forecast evaluation and offer new tools for reliable and accurate forecasting in performative settings.

The Poisson Generalized Linear Model (GLM) is a foundational tool for analyzing neural spike train data. However, standard implementations rely on discretizing spike times into binned count data, limiting temporal resolution and scalability. Here, we develop Monte Carlo (MC) methods and polynomial approximations (PA) to the continuous-time analog of these models, and show them to be advantageous over their discrete-time counterparts. Further, we propose using a set of exponentially scaled Laguerre polynomials as an orthogonal temporal basis, which improves filter identification and yields closed-form integral solutions under the polynomial approximation. Applied to both synthetic and real spike-time data from rodent hippocampus, our methods demonstrate superior accuracy and scalability compared to traditional binned GLMs, enabling functional connectivity inference in large-scale neural recordings that are temporally precise on the order of synaptic dynamical timescales and in agreement with known anatomical properties of hippocampal subregions. We provide open-source implementations of both MC and PA estimators, optimized for GPU acceleration, to facilitate adoption in the neuroscience community.

This work addresses the finite-time analysis of nonsmooth nonconvex stochastic optimization under Riemannian manifold constraints. We adapt the notion of Goldstein stationarity to the Riemannian setting as a performance metric for nonsmooth optimization on manifolds. We then propose a Riemannian Online to NonConvex (RO2NC) algorithm, for which we establish the sample complexity of $O(ε^{-3}δ^{-1})$ in finding $(δ,ε)$-stationary points. This result is the first-ever finite-time guarantee for fully nonsmooth, nonconvex optimization on manifolds and matches the optimal complexity in the Euclidean setting. When gradient information is unavailable, we develop a zeroth order version of RO2NC algorithm (ZO-RO2NC), for which we establish the same sample complexity. The numerical results support the theory and demonstrate the practical effectiveness of the algorithms.

Traditional models of climate change use complex systems of coupled equations to simulate physical processes across the Earth system. These simulations are highly computationally expensive, limiting our predictions of climate change and analyses of its causes and effects. Machine learning has the potential to quickly emulate data from climate models, but current approaches are not able to incorporate physically-based causal relationships. Here, we develop an interpretable climate model emulator based on causal representation learning. We derive a novel approach including a Bayesian filter for stable long-term autoregressive emulation. We demonstrate that our emulator learns accurate climate dynamics, and we show the importance of each one of its components on a realistic synthetic dataset and data from two widely deployed climate models.