This paper studies nonlinear in-context learning via single-index models, comparing a kernel learner (fixed spherical-harmonic features followed by linear attention) against a feature learner (linear attention on raw inputs followed by a learned nonlinear readout). Using the replica method, the authors derive predictions for memorization and generalization errors across varying pretraining data, task diversity, and context lengths, and validate them numerically over a broad parameter range. The analysis reveals phase diagrams for architectural advantage and qualitatively different context-length scalings: the kernel learner needs $L = \Theta(d^k)$ to recover degree-$k$ harmonics, while the feature learner exploits all teacher components at $L = \Theta(d)$.

This paper asks whether a fixed offline corpus generated by a behaviour policy can ever distinguish two candidate Regular Decision Processes (RDPs). It proves that when two candidates are $\pi$-observationally equivalent, their posterior odds remain frozen at the prior for any sample size (Theorem 6), gives an exact measure-zero characterization via the product-automaton blame language (Theorem 12), and derives PEC, a linear-time algorithm that certifies equivalence and names the missing experiment. The work matters because existing PAC offline guarantees for RDPs assume a distinguishability condition that was previously impossible to verify.

This paper develops a high-dimensional theory for why masked autoencoders learn better representations than standard autoencoders. In a spiked model with heterogeneous noise, the authors prove that a linear masked autoencoder recovers the latent feature at linear sample complexity $n=O(d)$ where PCA fails. They further quantify how dynamic mask resampling lowers sample complexity compared to static masking, and validate the qualitative predictions in CNNs, vision transformers, and a BERT pilot.

This paper proves worst-case lower bounds for stochastic first-order algorithms in nonconvex--concave minimax optimization, explicitly permitting variance-reduction via same-sample oracle queries. Its main result shows that the stochastic barrier remains $\Omega(L^3 D_Y^2 \Delta \sigma^2 \varepsilon^{-6})$ even with mean-square smoothness. Complementary nonconvex--strongly-concave bounds are also provided. Together the results establish that variance reduction does not improve the fundamental accuracy exponent in the minimax setting.

LITL addresses the problem of recovering target Langevin dynamics when only biased or static source samples are available, complemented by black-box evaluative feedback. The core idea is to learn the dominant spectral subspace of the target infinitesimal generator and its projected drift via importance-weighted Dirichlet representation learning, explicitly avoiding target trajectories, gradients, or retraining. This matters for molecular dynamics, auditing generative models, and post-hoc steering of learned representations under distribution shift.

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.

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.

Counterfactual generation aims to sample the distribution of outcomes that would occur if a treatment were applied to an entire population, but observational data suffer from selection bias because treated individuals differ systematically from the target population. This paper develops a flow-matching method that learns to transport observed outcomes to counterfactual targets using a learned source-target coupling, a doubly robust training objective, and a score-corrected stochastic sampler with Gaussian smoothing. The core theoretical result is a finite-step KL bound governed by the coupling displacement moment $D_5$ rather than worst-case regularity, yielding near-linear dimension scaling and an end-to-end nonparametric sample-complexity guarantee; experiments on synthetic and semi-synthetic image data support the predicted coupling dependence and show that stochastic sampling can outperform deterministic counterparts at limited discretization budgets.

Most fairness tests ask whether a model treats groups exactly equally, but real audits often need to decide whether a disparity exceeds a legally or practically meaningful tolerance. This paper formalizes tolerance-based fairness auditing as two distinct statistical objectives—formal violation certification and early-warning sensitivity screening—and develops empirical-likelihood procedures calibrated to each. Constrained empirical likelihood (CEL) controls false violation declarations over a tolerance region, while split empirical likelihood (SEL) and an adjusted variant (ASEL) use an adaptive boundary-proxy principle to increase detection near the boundary. The work matters because it translates abstract fairness requirements into actionable, objective-dependent statistical guarantees.

Treating model release as a design problem rather than a convention, this paper asks how many of $k$ automated tests a model should pass before deployment to guarantee a stated reliability target while retaining as many good models as possible. Using a two-class Gaussian latent-factor model with common within-class correlation $\rho$, the author proves that precision rises strictly with the required pass count $r$, so the optimal gate is the most lenient $r$-of-$k$ rule that meets the target. This matters because teams often default to pass-all gating, which can decimate the pool of acceptable models when tests are even modestly correlated; the paper shows that misjudging dependence by a factor of two can hurt more than shifting the gate by one test.

This paper tackles endogenous nonstationary stochastic bandits where actions drive an unobserved latent linear system and rewards are bilinear in the action and latent state. Prior work achieved only $\widetilde{\mathcal{O}}(T^{2/3})$ regret via explore-then-commit (ETC) because the infinite-memory reward process couples learning and planning. The authors show that under stable dynamics the memory can be truncated geometrically, reduce the problem to a block-level linear bandit via cyclic approximation, and propose an optimistic block-UCB algorithm (Block-OFUL) that achieves $\widetilde{\mathcal{O}}(\sqrt{T})$ regret. The result is theoretically appealing but leans heavily on an exact block-maximization oracle and on knowing the dynamical stability constant $\rho$.

Many Bayesian inference problems involve implicit priors known only through samples, such as generative model outputs or historical ensembles. This paper proposes performing posterior sampling in the Gaussian source space of an improved MeanFlow (iMF) transport map, using parallel tempering with pCN or hybrid split-HMC updates. Its central theoretical advance is proving Wasserstein stability bounds for the implemented few-step posterior in terms of the joint population training loss, removing the need for vanishing ODE discretization error.

Offline goal-conditioned RL (GCRL) struggles with long-horizon tasks because discounting shrinks value differences between distant states until they fall below function approximation error. This work introduces GITA, which learns a single value network conditioned on a temporal abstraction stride $k$ and trains one high-level policy by aggregating advantage-weighted regression updates across multiple scales. By implicitly letting the best-suited scale dominate per state-goal pair, GITA raises average success rate on OGBench by 25 percentage points over HIQL without requiring a problem-specific fixed $k$.

Diffusion models with classifier-free guidance (CFG) compute paired conditional and unconditional activations at each denoising step, yet existing post-training quantizers treat those branches as independent sources. This paper identifies the CFG branch space as a structured coding axis—matched activations are strongly correlated and jointly shaped by the guidance direction—and proposes Guidance-Correlation Branch Transform (GCBT), a lightweight $2\times 2$ orthogonal rotation applied per layer before activation quantization. It admits a closed-form per-layer solution, plugs into existing PTQ pipelines with negligible overhead, and offers a complementary, easy-to-adopt lever for low-bit generation fidelity.

The paper solves the problem that weight-space task arithmetic is trapped in one architecture because parameter updates share no common coordinate system. Its core idea is the platonic task vector—a model-agnostic object beneath per-model task vectors—and the Universal Task Descriptor (UTD), an architecture-independent matrix of fine-tuning-induced affinity shifts that can be added or negated directly. A closed-form operator folds into the target's last layer, while a low-rank adapter fits the same objective across all layers. The work matters because it enables label-free, weight-free composition of task knowledge across six heterogeneous vision–language and audio–text families.

This paper addresses the static nature of Large Language Models that prevents dynamic adaptation to streaming contexts. The authors introduce In-Place Test-Time Training, which repurposes existing MLP down-projection matrices as “fast weights” that update during inference via a Next-Token Prediction (NTP)-aligned objective. Unlike prior TTT methods that require architectural changes, this approach enables “drop-in” enhancement of pretrained models without retraining from scratch.

Neyman–Pearson multiclass classification (NPMC) handles asymmetric error costs by constraining class-specific misclassification rates, yet existing methods fail when training labels are corrupted. This paper proposes an empirical likelihood (EL) framework that recovers true class proportions and posterior probabilities from noisy labels via an exponential tilting density ratio model, enabling valid error control without prior knowledge of the noise transition matrix. The approach combines semiparametric estimation theory with a practical EM algorithm, yielding classifiers that satisfy NP oracle inequalities asymptotically.

This paper addresses the critical challenge of detecting occult hemorrhage (internal bleeding) in intensive care units, where delayed diagnosis leads to preventable physiological shock and death. The authors develop a Bayesian regime switching model (RSM) that tracks five latent physiological states—including stable, hemorrhage, and recovery—using longitudinal vital signs (heart rate, MAP, hemoglobin, lactate) and medication history. Applied to 33,924 Mayo Clinic ICU encounters, the model aims to provide interpretable, probabilistic early warnings that outperform standard vital sign monitoring by accounting for autoregressive trends and pre-admission physiological changes.

Job recommender systems deployed by public employment services are typically optimized for predictive metrics like clicks, applications, or hires rather than job seeker welfare. This paper develops a structural job-search model where vacancy value depends on utility $U$ and hiring probability $p$, deriving a welfare-optimal ranking based on an expected-surplus index $\Gamma(p, U) = p \sigma \log(1 + e^{\Delta(p,U)/\sigma})$. Through two randomized field experiments with the French public employment service, the authors demonstrate that algorithms approximating this theoretical benchmark substantially outperform existing approaches, while formalizing the "inversion problem" where behavior-based rankings diverge from welfare-maximizing ones.

This paper proposes a fundamental shift in evaluating probabilistic time series forecasting by replacing passive observation of historical trajectories with an interventionist "noise titration" protocol. By injecting calibrated Gaussian noise into known chaotic and stochastic dynamical systems, the authors transform forecasting into an exact distributional inference task where statistical calibration can be verified against ground-truth likelihoods. They extend the Fern architecture to output full covariance structures via SPD cone parameterization, then use the framework to expose severe failures in zero-shot foundation models under non-stationarity.