This survey systematises the sprawling literature at the intersection of optimal transport and reinforcement learning through a four-question taxonomy: what role OT plays, which distributions are compared, which formulation is used, and how temporal structure is handled. By foregrounding the geometry-aware nature of transport-based discrepancies, the authors explain why OT can outperform $f$-divergences when learner and expert distributions overlap weakly—a common scenario in imitation learning, offline RL and robust control. The result is a broad methodological map spanning occupancy matching, trust regions, world-model learning and multi-agent settings.

The paper argues that attributing model behavior to synthetic training data requires first recording how each item was generated, because a waveform-label pair alone erases upstream history. The authors introduce a structured provenance substrate that binds scenario seeds, generated content, audio waveforms, fact checklists, quality signals, and review lineage into an immutable manifest. They instantiate this in a five-pass audit of 113 synthetic Japanese care-handoff speech assets totaling 1.552 hours, finding that while versioned, seed-disjoint manifests support some downstream attribution research, exact upstream tracing is blocked by floating generator aliases and missing per-item TTS stamps. The work reframes data attribution as a two-stage problem: establish a typed, versioned generation path $z \longrightarrow x \longrightarrow m \longrightarrow r \longrightarrow b$ before attempting causal or contributive claims.

This paper studies causal logistic bandits with counterfactual fairness constraints, where the learner observes only factual rewards and must infer counterfactual effects through shared logistic parameters. The core contribution is establishing minimax optimal regret-violation tradeoffs under a weak pooled coverage condition, showing that a target-specific information scale $V_\star$ governs the estimation difficulty and yielding matching $\widetilde{\Theta}(T^{2/3})$ upper and lower bounds.

Flow Matching (FM) suffers from trajectory crossings that create high-frequency velocity targets and amplify numerical integration errors during few-step sampling. This paper proposes CoFlow, a framework that injects a repulsive contrastive drift into the forward SDE to push training trajectories away from negative samples, thereby smoothing the learned velocity field. The authors derive a simulation-free stochastic interpolant, prove that the transformation preserves the endpoint distributions when boundary terms vanish, and show consistent improvements on ImageNet 256x256 at 20 sampling steps without extra training cost.

PPO is the workhorse of on-policy deep RL, yet it discards collected data after just a few updates, leaving substantial sample efficiency on the table. This paper asks whether reusing recent off-policy samples within a multiple importance weighting framework can improve PPO without changing its core mechanics. The authors propose two variants—uniform ($\omega$PPO-U) and balance-heuristic-corrected ($\omega$PPO-BH)—derive policy improvement bounds that account for stale advantages, and empirically show that moderate windowed reuse boosts final performance while excessive reuse can backfire.

User interactions across movies, news, and dialogue all supply evidence that can update a user model, even though their native vocabularies differ. This paper proposes an action-on-item schema that maps heterogeneous behaviors into a shared event interface, enabling one history encoder — PerTIDE — to learn reusable state updates for both predictive ranking and personalized headline generation. The authors support the idea with invariance and stability theory, plus controlled transfer experiments showing that a frozen source-trained core retains a $15.23$ MRR advantage over a random core, suggesting that compatible histories can share a single update mechanism.

This work tackles decentralized learning in multi-player stochastic games where each agent's state transitions depend only on its own state and action, but rewards are arbitrarily coupled. The core idea is to run independent online mirror descent in the dual space of local occupancy measures, using asynchronous dyadic confidence sets to handle unknown transition kernels without synchronized episodes. This matters because the guarantees scale with local state-action dimensions and mixing times rather than the joint product space, offering the first fully online, uncoordinated framework for this setting.

Diffusion language models generate text through iterative denoising rather than left-to-right prediction, making attribution a spatiotemporal problem: support for any output token is distributed across both network depth and timesteps. This paper introduces Diffusion Layer Integrated Gradients (DLIG), which extends Integrated Gradients to score a DLM's commitment to its completion at any chosen layer and denoising step, decomposing it into per-token contributions. It matters because existing token-attribution tools ignore the denoising trajectory entirely, while interventional alternatives are computationally expensive.

The paper tackles the problem of learning task-agnostic world models for planning in latent space. It introduces CTWM, a reconstruction-free method that combines residual prediction with a log-determinant regularizer to recover the scaled Laplacian representation, so that latent L2 distances correspond to environment commute-time distances. This matters because it enables zero-shot goal-reaching without reward, and empirically CTWM matches or beats the LeWM baseline while using half the parameters.

We study non-clairvoyant single-machine scheduling to minimize the sum of completion times, a problem for which no constant-competitive algorithm is possible in the pure setting. The authors introduce a robustness framework that leverages a classifier's confusion matrix to partition jobs into predicted classes, characterizing uncertainty as internal permutations rather than numerical scenarios. This structural information yields an oblivious non-adaptive Min-Cost algorithm that is simultaneously optimal for multiple criteria, alongside new adaptive and randomized extensions.

This paper addresses the challenge of learning minimal, interpretable piecewise-linear representations of unknown nonlinear dynamical systems from time-series data. The authors propose training a higher-capacity almost-linear RNN first, then hierarchically reducing it via a fixed-point-guided procedure that linearizes redundant ReLU units while preserving distinct fixed-point symbols, and finally retraining the compact model from the parent initialization. The central insight is that redundant nonlinear capacity can act as a structural and optimization scaffold for discovering reliable minimal models, which matters because directly training at the theoretical minimal capacity often fails catastrophically.

Kamiya and Nicholls introduce the Clifford Sheaf Neural Network (CSNN), a geometric-graph architecture that places Clifford-algebra stalks on cellular sheaves and transports multivector features with learned restriction maps. The core advance is replacing versor conjugation with a normalized reversion sandwich $s_c(x)=c x \tilde{c}/q(c)$, yielding a sheaf Laplacian that stays positive semidefinite by construction while mixing feature grades. Despite a careful theoretical map of the design space, the paper contains no empirical experiments, leaving its practical value for graph-level regression entirely unproven.

This paper tackles community detection in multilayer networks where connectivity patterns and node degrees vary across layers. The proposed method, mFROST, jointly factorizes each layer via orthogonal symmetric nonnegative matrix trifactorization $A_l \approx D_l V \theta_l (D_l V)^\top$, enforcing shared community assignments $V$ while allowing layer-specific degree corrections $D_l$ and community interactions $\theta_l$. This flexibility matters because real-world multiplex networks often exhibit heterogeneous node sociability and diverse block structures that simpler shared-factor models miss.

This paper studies model collapse in diffusion models under a fixed-budget data regime, where synthetic data accumulates but each generation trains on a constant-size subsample from the growing pool. Unlike prior work on total replacement (rapid collapse) or unbounded accumulation (collapse avoided), the authors argue that fixed budgets yield partial, feature-selective collapse: "fragile" features with large eigenvalues in a linearized parameter dynamics model decay quickly, while "robust" features with small eigenvalues persist for exponentially many generations. They support this with theory (stochastic recursion giving per-feature halving times) and experiments on 2D spirals, MNIST, Fashion-MNIST, and CIFAR-10.

Neural architecture search is bottlenecked by the cost of obtaining ground-truth performance labels. ppNAS addresses this by fusing a small set of labeled architectures with a large set of zero-cost proxies via prediction-powered inference. The core insight is to construct pairwise ranking supervision from both sources and debias systematic discrepancies using a rectified PPI objective, yielding state-of-the-art results under tight evaluation budgets.

Standard stable port-Hamiltonian neural networks (s-PHNNs) enforce a single global minimum in the learned Hamiltonian, limiting them to systems with exactly one attractor. The authors overcome this by parametrizing the Hamiltonian as a product of Bregman divergences generated by a single fully input-convex neural network (FICNN), yielding a model---the ms-PHNN---that can represent multiple asymptotically stable equilibria while retaining local stability certificates by construction. This matters because many physical systems, from buckled beams to magnetic pendulums, exhibit multi-stable energy landscapes that existing guaranteed-stable neural ODEs cannot capture.

Standard variational information bottleneck (VIB) regularizes representations by penalizing a single global mutual information $I(Z;X)$, which inherently treats all encoded information as equally valuable. This paper identifies a structural limitation: under a label-induced partition $C=\pi(Y)$, the chain rule gives $I(Z;X)=I(Z;C)+I(Z;X\mid C)$, so scalar compression conflates condition-level structure with residual within-condition variation. The authors propose a dual-bottleneck objective combining a standard KL term for global capacity and a conditional KL term that targets within-condition information, instantiated with a simplex-structured conditional prior. The result is a principled regularizer that integrates into existing pipelines and shows the clearest empirical benefits in low-data classification and medical-image segmentation, exactly where nuisance-like residual variation can dominate.

Disorder is ubiquitous in functional crystals—nearly half of ICSD entries show some form of disorder—yet most generative models assume perfectly ordered lattices with deterministic site occupations. EP-Flow attacks formula-conditioned disordered crystal structure prediction without site-level annotations by representing occupancies as an Occupancy Distribution Matrix (ODM) that lives on a formula-dependent transportation polytope. It proposes a flow-matching model that canonicalizes heterogeneous polytopes into a shared double-centered space via log-domain double centering, learns a marginal-preserving velocity field, and recovers valid occupancies with a differentiable Sinkhorn inverse map, jointly generating fractional coordinates and lattice parameters. If the absolute performance can be scaled, this formalism could become a standard way to handle substitutional, vacancy, and interstitial disorder in generative materials design.

Neural scaling laws favor ever-larger models, but deciding when a network actually needs more capacity remains ad hoc. CAGE-NAS proposes a theoretically grounded rule: keep the architecture fixed only while the current parameter space can certify a valid functional gradient descent step; otherwise, expand the structure in a function-preserving way. By coupling growth decisions to the geometry of the empirical tangent space, the method unifies training and architecture adaptation under a single convergence certificate. On a controlled synthetic regression task, it discovers compact three-layer MLPs that sit in the extreme top tail of an exhaustive post-hoc search, though the evaluation remains limited to a toy benchmark.

Standard grasp synthesis systems freeze their parameters after offline training and struggle with unfamiliar objects. This paper presents a continual-learning framework that replaces the fixed parametric scorer with a memory-based non-parametric model in a learned embedding space, augmented by recalling and transferring user demonstrations to new scenes via geometric registration. Instead of gradient-based finetuning, the robot adapts by adding grasp outcomes and demonstrations to structured memories, which enables fast, lightweight updates during real-world deployment with limited forgetting.