Recently, equivariant neural networks for policy learning have shown promising improvements in sample efficiency and generalization, however, their wide adoption faces substantial barriers due to implementation complexity. Equivariant architectures typically require specialized mathematical formulations and custom network design, posing significant challenges when integrating with modern policy frameworks like diffusion-based models. In this paper, we explore a number of straightforward and practical approaches to incorporate symmetry benefits into diffusion policies without the overhead of full equivariant designs. Specifically, we investigate (i) invariant representations via relative trajectory actions and eye-in-hand perception, (ii) integrating equivariant vision encoders, and (iii) symmetric feature extraction with pretrained encoders using Frame Averaging. We first prove that combining eye-in-hand perception with relative or delta action parameterization yields inherent SE(3)-invariance, thus improving policy generalization. We then perform a systematic experimental study on those design choices for integrating symmetry in diffusion policies, and conclude that an invariant representation with equivariant feature extraction significantly improves the policy performance. Our method achieves performance on par with or exceeding fully equivariant architectures while greatly simplifying implementation.

Unlike reasoning, which often entails a deep sequence of deductive steps, complex real-world planning is characterized by the need to synthesize a broad spectrum of parallel and potentially conflicting information and constraints. For example, in travel planning scenarios, it requires the integration of diverse real-world information and user preferences.

Optimal transport between graphs, based on Gromov-Wasserstein and other extensions, is a powerful tool for comparing and aligning graph structures. However, solving the associated non-convex optimization problems is computationally expensive, which limits the scalability of these methods to large graphs. In this work, we present Unbalanced Learning of Optimal Transport (ULOT), a deep learning method that predicts optimal transport plans between two graphs. Our method is trained by minimizing the fused unbalanced Gromov-Wasserstein (FUGW) loss. We propose a novel neural architecture with cross-attention that is conditioned on the FUGW tradeoff hyperparameters. We evaluate ULOT on synthetic stochastic block model (SBM) graphs and on real cortical surface data obtained from fMRI. ULOT predicts transport plans with competitive loss up to two orders of magnitude faster than classical solvers. Furthermore, the predicted plan can be used as a warm start for classical solvers to accelerate their convergence. Finally, the predicted transport plan is fully differentiable with respect to the graph inputs and FUGW hyperparameters, enabling the optimization of functionals of the ULOT plan.

We present a theoretical framework showing that popular LLM alignment methods--including RLHF and its variants--can be understood as divergence estimators between aligned (safe or preferred) and unaligned (harmful or less-preferred) distributions. This perspective explains the emergence of separation in the latent space between safe and harmful prompts after alignment. As an application of our general divergence framework, we propose KLDO, a novel KL divergence-based alignment method, and empirically validate its effectiveness. We further show that using compliance-refusal datasets, rather than standard preference-based datasets, leads to stronger separation and improved safety alignment. Finally, to quantify the separation effect, we propose a distance-based metric in the prompt representation space, which also acts as a statistically significant indicator for model safety.

Tokenization imposes a fixed granularity on the input text, freezing how a language model operates on data and how far in the future it predicts. Byte Pair Encoding (BPE) and similar schemes split text once, build a static vocabulary, and leave the model stuck with that choice. We relax this rigidity by introducing an autoregressive U-Net that learns to embed its own tokens as it trains. The network reads raw bytes, pools them into words, then pairs of words, then up to 4 words, giving it a multi-scale view of the sequence. At deeper stages, the model must predict further into the future -- anticipating the next few words rather than the next byte -- so deeper stages focus on broader semantic patterns while earlier stages handle fine details. When carefully tuning and controlling pretraining compute, shallow hierarchies tie strong BPE baselines, and deeper hierarchies have a promising trend. Because tokenization now lives inside the model, the same system can handle character-level tasks and carry knowledge across low-resource languages.

We argue that in addition to training signals, enhancing the expressiveness of the policy class is crucial for the performance gains in RL. Flow-based generative models offer such potential, excelling at capturing complex, multimodal action distributions. However, their direct application in online RL is challenging due to a fundamental objective mismatch: standard flow training optimizes for static data imitation, while RL requires value-based policy optimization through a dynamic buffer, leading to difficult optimization landscapes.

We propose efficient methods for solving stochastic simple bilevel optimization problems with convex inner levels, where the goal is to minimize an outer stochastic objective function subject to the solution set of an inner stochastic optimization problem. Existing methods often rely on costly projection or linear optimization oracles over complex sets, limiting their scalability. To overcome this, we propose an iteratively regularized conditional gradient approach that leverages linear optimization oracles exclusively over the base feasible set. Our proposed methods employ a vanishing regularization sequence that progressively emphasizes the inner problem while biasing towards desirable minimal outer objective solutions. In the one-sample stochastic setting and under standard convexity assumptions, we establish non-asymptotic convergence rates of $O(t^{-1/4})$ for both the outer and inner objectives. In the finite-sum setting with a mini-batch scheme, the corresponding rates become $O(t^{-1/2})$. When the outer objective is nonconvex, we prove non-asymptotic convergence rates of $O(t^{-1/7})$ for both the outer and inner objectives in the one-sample stochastic setting, and $O(t^{-1/4})$ in the finite-sum setting. Experimental results on over-parametrized regression and dictionary learning tasks demonstrate the practical advantages of our approach over existing methods, confirming our theoretical findings.

Concept Bottleneck Models (CBMs) have been proposed as a compromise between white-box and black-box models, aiming to achieve interpretability without sacrificing accuracy. The standard training procedure for CBMs is to predefine a candidate set of human-interpretable concepts, extract their values from the training data, and identify a sparse subset as inputs to a transparent prediction model. However, such approaches are often hampered by the tradeoff between exploring a sufficiently large set of concepts versus controlling the cost of obtaining concept extractions, resulting in a large interpretability-accuracy tradeoff. This work investigates a novel approach that sidesteps these challenges: BC-LLM iteratively searches over a potentially infinite set of concepts within a Bayesian framework, in which Large Language Models (LLMs) serve as both a concept extraction mechanism and prior. Even though LLMs can be miscalibrated and hallucinate, we prove that BC-LLM can provide rigorous statistical inference and uncertainty quantification. Across image, text, and tabular datasets, BC-LLM outperforms interpretable baselines and even black-box models in certain settings, converges more rapidly towards relevant concepts, and is more robust to out-of-distribution samples.

Algorithm unrolling methods have proven powerful for solving the regularized least squares problem in computational magnetic resonance imaging (MRI). These approaches unfold an iterative algorithm with a fixed number of iterations, typically alternating between a neural network-based proximal operator for regularization, a data fidelity operation and auxiliary updates with learnable parameters. While the connection to optimization methods dictate that the proximal operator network should be shared across unrolls, this can introduce artifacts or blurring. Heuristically, practitioners have shown that using distinct networks may be beneficial, but this significantly increases the number of learnable parameters, making it challenging to prevent overfitting. To address these shortcomings, by taking inspirations from proximal operators with varying thresholds in approximate message passing (AMP) and the success of time-embedding in diffusion models, we propose a time-embedded algorithm unrolling scheme for inverse problems. Specifically, we introduce a novel perspective on the iteration-dependent proximal operation in vector AMP (VAMP) and the subsequent Onsager correction in the context of algorithm unrolling, framing them as a time-embedded neural network. Similarly, the scalar weights in the data fidelity operation and its associated Onsager correction are cast as time-dependent learnable parameters. Our extensive experiments on the fastMRI dataset, spanning various acceleration rates and datasets, demonstrate that our method effectively reduces aliasing artifacts and mitigates noise amplification, achieving state-of-the-art performance. Furthermore, we show that our time-embedding strategy extends to existing algorithm unrolling approaches, enhancing reconstruction quality without increasing the computational complexity significantly.

Neural solvers for the Vehicle Routing Problem (VRP) have typically relied on either node or edge inputs, limiting their flexibility and generalization in real-world scenarios. We propose UniteFormer, a unified neural solver that supports node-only, edge-only, and hybrid input types through a single model trained via joint edge-node modalities. UniteFormer introduces: (1) a mixed encoder that integrates graph convolutional networks and attention mechanisms to collaboratively process node and edge features, capturing cross-modal interactions between them; and (2) a parallel decoder enhanced with query mapping and a feed-forward layer for improved representation. The model is trained with REINFORCE by randomly sampling input types across batches. Experiments on the Traveling Salesman Problem (TSP) and Capacitated Vehicle Routing Problem (CVRP) demonstrate that UniteFormer achieves state-of-the-art performance and generalizes effectively to TSPLib and CVRPLib instances. These results underscore UniteFormer's ability to handle diverse input modalities and its strong potential to improve performance across various VRP tasks.