This paper studies online convex optimization against comparators that switch $k$ times among only $m$ distinct points, generalizing the classic experts tracking problem to continuous domains. While discretizing the domain and applying the Bousquet–Warmuth long-term-memory algorithm yields information-theoretic regret $\widetilde O(md+k)$, this is computationally inefficient. The authors prove that, under the hypergraphic planted-clique conjecture, no polynomial-time algorithm can achieve $\widetilde O(k^a d^b)$ regret whenever the exponents violate $\theta a + b < \theta + 1/2$, establishing a fundamental computational barrier for exp-concave losses even when $m=2$.

Gaussian diffusion models poorly cover extreme regions for heavy-tailed data because their light-tailed corruption kernels yield exponentially sparse tail samples. This paper introduces Annealed Lévy Diffusion (ALD), which specifies time-dependent $\alpha(t)$-stable perturbation marginals via a Gaussian scale-mixture representation, enabling a two-phase schedule that transitions from heavy-tailed exploration to Gaussian refinement. The construction retains conditional-Gaussian score matching with only one added scalar input, making it compatible with standard diffusion training while targeting distributions with polynomial tails.

Contextual partial monitoring is a sequential learning problem where the learner observes only partial feedback instead of incurred losses. The paper proposes E2D.PMSide, a computationally efficient instantiation of the Estimation-to-Decisions (E2D) meta-algorithm that reduces contextual partial monitoring to online regression. Its core contribution is replacing E2D's intractable per-round minimax exploration rule with tractable surrogates—epsilon-greedy for globally observable games and inverse gap weighting for locally observable ones—thereby achieving optimal $O(T^{2/3})$ and $O(\sqrt{T})$ regret rates. The work matters because it provides the first oracle-efficient algorithms for this setting with general function approximation and demonstrates practical benefits on LLM routing and label-efficient prediction.

Feldman (2021) gave an influential lower bound linking the cost of not fitting training labels to excess population risk via frequency-dependent coefficients $\tau_{n,\ell}$. This paper demonstrates that Feldman's central conditioning identity fails because the counts of other points convey information about the sampling distribution, and it provides an exact three-point counterexample together with an exponentially large multiplicative gap. The authors recover a valid bound within the same model by replacing the count-only coefficient with the exact full-sample posterior mean, which depends on both multiplicity and the complete frequency profile.

Class-incremental graph learning suffers from catastrophic forgetting because models are repeatedly fine-tuned on new classes, causing severe recency bias where earlier sessions are misclassified as recent ones. MAEM addresses this by freezing a dedicated Mixture-of-Experts expert per session and routing test nodes via the reconstruction error of session-specific masked autoencoders, eliminating the need for task identities or a shared trainable router. To prevent unbounded model growth, it merges least-used experts via Git Re-Basin alignment followed by topology-aware pseudo-data distillation, achieving strong replay-free performance across four benchmarks.

Fine-tuning pretrained diffusion and flow matching models for reward maximization tends to collapse modes or shift mass between distant regions. This paper introduces Weighted Adjoint Matching, which modifies the stochastic optimal control formulation of Adjoint Matching by placing a time-dependent weight $w(t)$ on the quadratic control cost---expensive early to preserve coarse semantics, cheap late to refine details and increase reward. The authors prove equivalence to maximizing reward under pathwise KL regularization, and demonstrate improved reward-diversity tradeoffs on Gaussian mixtures and MNIST.

Mixed-precision quantization for sparse MoE models needs more than expert rankings: NatScale introduces contrast calibration, a principled way to control how strongly sensitivity scores compete for storage. It applies a model-specific power transformation $w_i = g_i^{\beta_\tau}$ so that normalized squared weights achieve a target Jeffreys divergence $\mathcal{J}(q(\beta_\tau), u) = \tau$, preserving rank order while setting a common information-theoretic scale. Combined with joint gate/up/down error measurement and spectral structural priors, it allocates bit-widths under a global byte budget via LP relaxation and rounding.

What is the least width required for a deep neural network to universally approximate continuous functions from $\mathbb{R}^n$ to $\mathbb{R}^m$? This paper attacks the minimal-width problem by importing tools from differential topology, proving that whenever real projective space $\mathbb{RP}^{n-1}$ smoothly immerses into $\mathbb{R}^n$, any network with a continuous monotone activation must have width at least $n+\min\{n,m\}$ to approximate arbitrary maps. This yields the exact ReLU minimal width $n+m$ for the special dimensions $n\in\{2,3,4,7,8\}$ with $m\le n$, and exposes a surprising link between universal approximation and the immersibility of projective spaces.

Rotation-based post-training quantization for LLMs currently forces a choice between cheap data-agnostic transforms like Hadamard and costly learned rotations that require iterative optimization. SpectrumQuant introduces a closed-form, covariance-aware orthogonal transform derived from a first-principles objective on the Stiefel manifold: by aligning activations with their eigenbasis and applying a Hadamard or butterfly mixing component, it equalizes per-coordinate variances to minimize quantization error. The result is a method that cuts calibration costs by more than $20\times$ relative to learned baselines while preserving competitive accuracy on Llama and Mistral models.

Standard diffusion models rely on additive Gaussian noise, yet many imaging modalities---including PET and astronomical photon counting---produce discrete Poisson observations. This paper introduces Mixed Poisson Diffusion Models (MPDMs), a generative framework in which the forward corruption is driven by multivariate counting processes rather than Brownian motion. The core payoff is a family of posterior samplers structurally matched to Poisson inverse problems, featuring exact sampling for Poisson denoising and principled adaptations of DPS, PnP-DM, and DAPS.

Negative guidance in diffusion models aims to steer generation away from undesired conditions, but existing methods rely on local repulsive terms that do not target an explicit density and whose bias cannot be reduced by more computation. This paper recasts the problem as sampling from the explicit avoidance density $p_{\text{target}}(x) \propto p(x)(1-p(c \mid x))^{\lambda}$, estimates the per-timestep posterior $p_t(c \mid x_t)$ via online Positive-Unlabeled learning, and corrects particle drift with Sequential Monte Carlo. The result is a principled sampler that is asymptotically exact in the particle limit and empirically Pareto-dominates existing methods on avoidance-quality trade-offs across Gaussian mixtures, CIFAR-10, and Stable Diffusion.

The paper studies minimax estimation of the pseudo-spectral gap $\gamma_{ps}$ of a continuous-state Markov chain on $[0,1]^d$ from a single trajectory. The core idea is to discretize the state space into a regular grid, approximate the transition density by a histogram, and adapt finite-state estimators to this compressed chain. The result matters because it yields fully empirical concentration inequalities for non-iid data, enabling UCB bandit algorithms and PAC-Bayes bounds without prior knowledge of mixing coefficients.

This paper studies the nonconvex optimisation landscape of finite-particle maximum mean discrepancy (MMD) quantisation, where a target probability measure is approximated by a weighted atomic measure. For the one-dimensional Gaussian kernel, the authors prove that beyond explicit particle thresholds every local minimum has arbitrarily small MMD and every high-MMD stationary point is unstable under unweighted gradient flow. These are the first finite-particle overparameterisation guarantees for weighted MMD, though the analysis is currently limited to one dimension.

SNACK addresses the challenge of generating attributed graphs using standard sequence models without sacrificing structural validity or probabilistic correctness. Its core idea is a bijective string encoding of the lower-triangular adjacency matrix that, when paired with BFS ordering and invalid logit masking, guarantees 100% valid outputs and enables exact computation of the sequence-to-graph distribution $q(\mathbf{x}|G)$. This matters because it bridges the efficiency of autoregressive Transformers with the principled reward-matching guarantees of GFlowNets, a combination that prior non-injective string representations like SMILES could not support.

Score-based generative models with heavy-tailed $\alpha$-stable Lévy noise have shown empirical promise for extreme-event modeling, yet theoretical guarantees remain scarce. This paper develops a non-asymptotic $W_p$ convergence framework for scale-preserving $\alpha$-stable dynamics and proves that global Wasserstein convergence alone does not separate stable from Brownian models on heavy-tailed targets. A sharp distinction emerges instead in the tails: stable dynamics inherit power-law tails with index $\alpha$, while Brownian outputs stay light-tailed, and asymptotically correct extreme-quantile scaling requires matching the target tail index $\nu$ to the noise index $\alpha$. These results establish tail-index matching as a principled design mechanism for capturing heavy-tailed phenomena.

Conflicting studies on whether neural networks converge to a shared representation have used different alignment metrics and reached opposite conclusions. This paper proposes the Lattice Representation Hypothesis (LRH), which formalizes alignment criteria into a lattice ordered by strength, and argues that disagreements arise because prior work evaluates criteria at different points on this lattice. It also proves in idealized models that the training procedure and objective determine which criteria are met reliably across independent runs, supported by experiments on dozens of pretrained vision and language models.

This paper studies noiseless efficient global optimization via Gaussian Process Thompson Sampling (GP-TS) in the frequentist RKHS setting. It proves that standard GP-TS suffers an intrinsic $\sqrt{\log N}$ simple-regret penalty for Mat\'ern kernels, yielding $O(N^{-\nu/d}\sqrt{\log N})$, and proposes Capped Thompson Sampling (GP-CTS), which achieves the minimax-optimal $\Theta(N^{-\nu/d})$ rate using a known RKHS norm bound. The analysis covers both discrete and continuous domains and is notable for matching upper and lower bounds in a non-bandit setting.

The paper studies how to learn interpretable binary classifiers as sparse Boolean rules by optimizing the weights of a fixed-structure DNF network. It proposes mixed integer linear programming (MILP) formulations that trade off training misclassification against rule sparsity, with an advanced formulation that dramatically reduces integer variables and redundant constraints while preserving exact Boolean semantics. A combined warm-start and dropout strategy is introduced to break symmetries and push scalability to larger datasets.

The paper studies the personalization–collaboration trade-off in federated learning via Generalized Total Variation Minimization (GTVMin) with least-squares models on an arbitrary communication graph. Using random matrix theory in the proportional high-dimensional limit, it derives exact asymptotic test-error formulas under Gaussian-mixture data and proves that the GTVMin solution concentrates at rate $1/\sqrt{p}$, independently of the graph structure or regularization strength $\alpha$. If the modeling assumptions hold, the results provide a principled way to tune $\alpha$ from training data alone.

Population dynamics are often observed only as unpaired snapshots, leaving the evolution between measurements fundamentally underdetermined. This paper introduces Neural Wasserstein Splines (NWSP), a method that learns a continuous curve of distributions by penalizing the intrinsic Wasserstein acceleration rather than the acceleration of individual particles, which is representation-dependent. It couples a neural spline generator with a finite-dictionary projection of velocity and its time derivative, achieving competitive results on synthetic and single-cell benchmarks.