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.

This tutorial reframes model validation as the design of a performance estimator rather than a mere software setting. It surveys splits from hold-out to nested group cross-validation, links geometric fold choices to the correct independent unit (record, subject, center), and provides eight controlled leakage scenarios grounded in biomedical examples such as EEG epochs and paired-eye OCT. The core argument is that an elaborate fold structure is scientifically invalid if applied to the wrong unit, and that even a simple hold-out can be rigorous when the unit, size, and isolation constraints are correct.

Technical documentation preserves collaborative context, but sentence-level specificity predictors were trained on general-domain prose. This paper audits whether two such predictors—SpeciTeller and a pinned post-publication implementation of Ko et al.'s domain-adapted model—produce stable, useful signals when applied to technical corpora (GitHub, Ansible, Python docs) and used to rank LLM-generated revisions. Using a three-stage evidence structure, the authors separate score interpretation, local correspondence with humans and controlled edits, and bounded decision value for post-generation candidate selection.

Coordinated multi-humanoid loco-manipulation is notoriously difficult because it couples high-dimensional whole-body control with decentralized decision making and scalability. MASkillBlender addresses this by learning a shared decentralized high-level multi-agent RL policy that blends frozen, pre-trained single-humanoid primitive skills, eliminating the need for task-specific motion references or painstaking per-task reward engineering. The authors further introduce a permutation-based data augmentation strategy and prove, under a homogeneous Markov game formulation, that it preserves the policy-gradient direction. Simulated experiments across cooperative manipulation and locomotion tasks suggest broad versatility across robot embodiments and simulators, though the work stops short of real-world validation and is limited to small, homogeneous teams.

Training hybrid Transformer-SSM models requires expensive per-scale learning rate (LR) tuning. This paper empirically shows that "naïve" Maximal Update Parameterization (μP) — as originally prescribed for pure Transformers, with no SSM-specific modifications — combined with AdamW achieves near-zero LR transfer gap across hybrid architectures from width 256 to 2048 (8×) and depth 4 to 32 (8×), up to billion parameters and on a production Nemotron-H model. The authors propose a two-condition decomposition (global update-to-weight invariance from μP, local per-component balance from AdamW's g/√v normalization) to explain why coordinate checks fail while transfer still succeeds.

Model merging for LLMs typically requires expensive benchmark evaluations to tune combination coefficients. This paper proposes SLIM, which treats coefficient selection as a classical mixture experiment on the simplex. It builds a quadratic surrogate of aggregate performance using only $T(T+1)/2$ evaluations—individual experts and equal-weight pairs—then optimizes the surrogate without further measurements. The core finding is that this minimal structured design predicts unseen mixtures accurately and yields competitive merges at a fraction of the cost of evolutionary or surrogate baselines, though restricting coefficients to the simplex may limit absolute performance.

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.

Time series anomaly detection benchmarks traditionally optimize for detection accuracy while neglecting explainability and interpretability. This paper introduces SHAD, a real-world benchmark comprising 215 high-dimensional multivariate time series collected from distributed cloud storage systems, complete with per-dimension labels and rich semantic annotations. The authors evaluate 18 detection algorithms, probe spatial attribution for explainability, and test frozen LLMs for interpretability, demonstrating that accurate detection does not guarantee diagnostic utility and that zero-shot semantic interpretation remains largely unresolved.

Most interpretability studies ablate or probe a single training checkpoint, leaving it unclear whether observed depth-dependent sensitivities are stable or transient. This paper tracks whole-block identity bypass across five released pretraining trajectories and eleven model-domain combinations to ask what persists and what shifts. The core finding is that the relative depth ordering of block sensitivities remains recognizable even as the magnitudes redistribute, and that the intervention pathway itself evolves differently across models and perturbation scales. The work matters because it cautions against treating single-checkpoint ablation profiles as static descriptions of a model's internal organization.

The nonparametric maximum likelihood estimator (NPMLE) of a Gaussian mixture is a convex program over an infinite-dimensional space, yet its maximizers can be nonunique and are only known to have at most $n$ atoms. This paper shows that a vanishingly small random reweighting of the likelihood---using independent Gamma weights that concentrate around one---selects a unique maximizer with polylogarithmically many atoms in any fixed dimension $d$. The resulting estimator retains a Hellinger rate that is parametric up to logarithmic factors, solving the open problem of exact sparsity for multivariate Gaussian NPMLEs without any support penalty.

Looped Transformers reuse shared blocks to scale depth without adding parameters, but MoE variants degrade beyond two loops. This paper diagnoses two bottlenecks—hidden-state drift and expert selection collapse—and proposes LOOM, combining residual scaling, embedding re-injection, per-loop routers, and a Looping Residual. It matters because it attempts to establish recurrent depth as a genuine, compute-efficient scaling axis for sparse LLMs.