DirMoE: Dirichlet-routed Mixture of Experts

Mixture-of-Experts (MoE) models have demonstrated exceptional performance in large-scale language models. Existing routers typically rely on non-differentiable Top-$k$+Softmax, limiting their performance and scalability. We argue that two distinct decisions, which experts to activate and how to distribute expert contributions among them, are conflated in standard Top-$k$+Softmax. We introduce Dirichlet-Routed MoE (DirMoE), a novel end-to-end differentiable routing mechanism built on a Dirichlet variational autoencoder framework. This design fundamentally disentangles the core routing problems: expert selection, modeled by a Bernoulli component, and expert contribution among chosen experts, handled by a Dirichlet component. The entire forward pass remains fully differentiable through the use of Gumbel-Sigmoid relaxation for the expert selection and implicit reparameterization for the Dirichlet distribution. Our training objective, a variational ELBO, includes a direct sparsity penalty that precisely controls the number of active experts in expectation, alongside a schedule for key hyperparameters that guides the model from an exploratory to a definitive routing state. Moreover, our DirMoE router matches or exceeds other methods while improving expert specialization.

MixFlow: Mixture-Conditioned Flow Matching for Out-of-Distribution Generalization

Achieving robust generalization under distribution shift remains a central challenge in conditional generative modeling, as existing conditional flow-based methods often struggle to extrapolate beyond the training conditions. We introduce MixFlow, a conditional flow-matching framework for descriptor-controlled generation that directly targets this limitation by jointly learning a descriptor-conditioned base distribution and a descriptor-conditioned flow field via shortest-path flow matching. By modeling the base distribution as a learnable, descriptor-dependent mixture, MixFlow enables smooth interpolation and extrapolation to unseen conditions, leading to substantially improved out-of-distribution generalization. We provide analytical insights into the behavior of the proposed framework and empirically demonstrate its effectiveness across multiple domains, including prediction of responses to unseen perturbations in single-cell transcriptomic data and high-content microscopy-based drug screening tasks. Across these diverse settings, MixFlow consistently outperforms standard conditional flow-matching baselines. Overall, MixFlow offers a simple yet powerful approach for achieving robust, generalizable, and controllable generative modeling across heterogeneous domains.

Trained Models Tell Us How to Make Them Robust to Spurious Correlation without Group Annotation

Classifiers trained with Empirical Risk Minimization (ERM) tend to rely on attributes that have high spurious correlation with the target. This can degrade the performance on underrepresented (or 'minority') groups that lack these attributes, posing significant challenges for both out-of-distribution generalization and fairness objectives. Many studies aim to enhance robustness to spurious correlation, but they sometimes depend on group annotations for training. Additionally, a common limitation in previous research is the reliance on group-annotated validation datasets for model selection. This constrains their applicability in situations where the nature of the spurious correlation is not known, or when group labels for certain spurious attributes are not available. To enhance model robustness with minimal group annotation assumptions, we propose Environment-based Validation and Loss-based Sampling (EVaLS). It uses the losses from an ERM-trained model to construct a balanced dataset of high-loss and low-loss samples, mitigating group imbalance in data. This significantly enhances robustness to group shifts when equipped with a simple post-training last layer retraining. By using environment inference methods to create diverse environments with correlation shifts, EVaLS can potentially eliminate the need for group annotation in validation data. In this context, the worst environment accuracy acts as a reliable surrogate throughout the retraining process for tuning hyperparameters and finding a model that performs well across diverse group shifts. EVaLS effectively achieves group robustness, showing that group annotation is not necessary even for validation. It is a fast, straightforward, and effective approach that reaches near-optimal worst group accuracy without needing group annotations, marking a new chapter in the robustness of trained models against spurious correlation.

Annotation-Free Group Robustness via Loss-Based Resampling

It is well-known that training neural networks for image classification with empirical risk minimization (ERM) makes them vulnerable to relying on spurious attributes instead of causal ones for prediction. Previously, deep feature re-weighting (DFR) has proposed retraining the last layer of a pre-trained network on balanced data concerning spurious attributes, making it robust to spurious correlation. However, spurious attribute annotations are not always available. In order to provide group robustness without such annotations, we propose a new method, called loss-based feature re-weighting (LFR), in which we infer a grouping of the data by evaluating an ERM-pre-trained model on a small left-out split of the training data. Then, a balanced number of samples is chosen by selecting high-loss samples from misclassified data points and low-loss samples from correctly-classified ones. Finally, we retrain the last layer on the selected balanced groups to make the model robust to spurious correlation. For a complete assessment, we evaluate LFR on various versions of Waterbirds and CelebA datasets with different spurious correlations, which is a novel technique for observing the model's performance in a wide range of spuriosity rates. While LFR is extremely fast and straightforward, it outperforms the previous methods that do not assume group label availability, as well as the DFR with group annotations provided, in cases of high spurious correlation in the training data.