Papers

Before a machine learning model ships, it often has to pass a suite of automated tests. Requiring every test to pass looks safe, yet it can reject many models that would have served users well, and it does not say how trustworthy a passing model actually is. We treat the release gate as a design problem: choose how many tests a model must pass so that cleared models meet a stated reliability target, while keeping as many good models as possible. A two-class latent-factor model makes both costs explicit and reduces each calculation to a one-dimensional integral. We prove that when both classes share the same latent correlation, a stricter gate always raises reliability, so the gate that keeps the most good models is the most lenient one that still meets the target. Under pass-all gating, any reliability target short of perfection is attainable within the model, but the share of good models kept tends to zero as the suite grows. Correlation between tests sets the price. In one configuration, a 99 percent target needs 8 independent tests, but 74 tests at a latent correlation of 0.3 and 5,182 at 0.5, where the gate keeps fewer than one good model in ten. We also give a validation procedure, built on exact binomial bounds, that certifies a gate from labelled data even when the gate is chosen from a fixed shortlist.

Post-training quantization for diffusion models increasingly exploits timestep, feature, and layer structure. While recent work has begun incorporating CFG structure into diffusion quantization, activation quantization still operates independently across conditional and unconditional coordinates, leaving cross-activation structure unexploited. We show that matched CFG activations form a strongly correlated two-dimensional source and that, under a fixed bit budget, the choice of branch coding basis materially affects quantization fidelity. Motivated by this observation, we introduce branch-space transform coding, which rotates matched CFG branches via an offline derived 2x2 orthogonal matrix, requiring minimal modifications to model parameters or the quantization pipeline. We further derive the Guidance-Correlation Branch Transform (GCBT), which jointly incorporates the CFG guidance direction and cross-branch second moments. Under an equal-rate quantization-noise surrogate, GCBT admits a closed-form per-layer solution without gradient optimization or angle search. Applied on top of existing diffusion PTQ methods, GCBT yields statistically significant fidelity gains in most evaluated comparisons with no statistically significant degradation, while leaving the underlying host quantization pipeline unchanged.

Distinct pre-trained models specialized for the same task converge to closely similar behavior, yet the parameter updates that produce it share no common coordinate system. Weight-space task arithmetic is therefore confined to a single model, and transporting an update between models requires a structural correspondence. Drawing on Plato's allegory of the cave, we hypothesize that these model-specific updates are shadows cast by one shared, model-agnostic object, the platonic task vector. To make it operational across models of different architectures, we introduce Universal Task Descriptors, matrices whose shape is independent of architecture and embedding dimension, which record a task's functional effect and admit addition and negation as ordinary matrix operations, and we transfer a descriptor into a target in two ways. A single least-squares solve returns a linear operator folded into the target's last layer, and a bank of such operators, one per source and task, realizes any composition as a signed sum of its entries. Alternatively, a low-rank adapter of the target's encoder is trained on the same objective at the price of one optimization per edit. Despite a model-specific residual comparable in norm to the shared component, transfer from another model retains 74 to 80 percent of the gain the target's own descriptors attain. Experiments across six model families, eight tasks and audio-text models confirm both realizations.

We study an endogenous nonstationary stochastic bandit problem with latent linear dynamics, where actions affect both immediate rewards and the future evolution of an unobserved latent state. Rewards are bilinear in the current action and latent state, inducing history-dependent rewards and a nontrivial long-horizon planning problem. The existing explore-then-commit approach achieves $\tilde{O}(T^{2/3})$ regret by uniformly exploring to estimate the latent dynamics and then committing to an optimized open-loop action sequence. We show that this rate can be improved via adaptive block-level optimism. Our key step is a cyclic approximation: under stable dynamics, the infinite-memory reward process can be truncated, and the open-loop benchmark can be approximated by optimizing a finite-memory block-level proxy. Building on this reduction, we propose a UCB-based block algorithm that maintains confidence sets for the truncated dynamics parameters and selects blocks optimistically. We prove a regret bound of order $\tilde{O}(\sqrt T)$, significantly improving over the previous $\tilde{O}(T^{2/3})$ guarantee for the same model. To the best of our knowledge, this is the first $\tilde{O}(\sqrt T)$ regret guarantee for latent linear-dynamics bandits with bilinear reward observations and an open-loop action-sequence benchmark.

Existing approaches to offline goal-conditioned reinforcement learning (GCRL) struggle with long-horizon tasks. Discounting shrinks value differences between distant states until they fall below the function approximation error, leaving the agent with no signal for ranking states. Temporal abstraction, which treats k environment steps as a single transition, restores this signal at long range, but no single fixed k suits all state-goal distances: large k preserves value differences across long temporal distances while collapsing distinctions between nearby states, and small k does the reverse. We make this trade-off explicit and introduce Generalized Implicit Temporal Abstraction (GITA), which conditions a single value function on k. GITA trains one policy by aggregating advantage-weighted supervision across multiple k values, so scales assigning larger positive advantages to a state-goal pair contribute more strongly to its update. GITA does not need to choose between local resolution and long-range signal; it retains both without committing to a single k. On OGBench, GITA outperforms a broad range of offline GCRL baselines, raising average success rate across all tasks by 25 percentage points (73% relative improvement) over HIQL. It also improves over the strongest fixed-k method, OTA, by 7 percentage points (14% relative).

Modern data pipelines increasingly combine human-created and human-curated data with AI-generated data for model training and evaluation. As datasets grow, they often add semantically redundant samples rather than expanding semantic coverage, which deteriorates the quality of the whole dataset. Existing diversity metrics primarily summarize lexical variation, entropy, or pairwise similarity, but provide limited characterization of the shape of the underlying data distribution. In this paper, we propose PLDiv, a diversity metric derived from persistence landscapes that quantifies the structural organization of a dataset from its geometric representation. PLDiv summarizes how data neighborhoods evolve as nearby samples progressively connect, producing an interpretable scalar measure of structural diversity without requiring task-specific supervision. Whether measuring intrinsic diversity in text generations or image embeddings, or detecting semantic collapse in instruction datasets and reasoning trajectories, PLDiv performs competitively against evaluated baselines and aligns strongly with diversity labels during semantic collapse. Consequently, it effectively supports applications in synthetic data monitoring, dataset construction, data augmentation, and generative model evaluation.

Looped transformers reuse one shared block across many recurrent steps, so depth becomes a quantity that can be spent at runtime rather than a stack of distinct layers. Those extra steps help only if a write made on one recurrent step is still readable on later ones, and that depends on the linear map applied to the residual between recurrent steps. We show that whether the loop learns to track state is a geometric question about the form of this map, and we propose blockwise conformal injections: the residual splits into coordinate-aligned groups and rotates inside each one, so every group has its own timescale while the geometry stays exact within it. Our experiments show a performance increase on a demanding form of state tracking - last-token accuracy when the rest of the prefix is already correct - and on language modelling, where a signal written earlier has to be retrieved at the end of the sequence.

LLM-as-a-judge evaluation commonly aggregates multiple judges' decisions into a majority vote, yet this panel decision process does not guarantee that the evaluation of an individual item is reliable. We propose Structured Cross-fitted Uncertainty Risk (SCUR), a label-free approach for estimating instance-level evaluation reliability based on the judge panel's behavior. A latent measurement model serves as the backbone for measurement system analysis, from which SCUR derives three complementary signals capturing panel uncertainty, measurement cross-entropy, and perturbation sensitivity. These three sources of evidence are combined into a risk score. We evaluate the SCUR approach on five real-world benchmarks using majority-vote error ranking, selective trust, and risk stratification. Furthermore, we show our approach to be more effective at detecting high-consensus risk items, which are the blind spots for many other LLM-as-a-judge evaluation methods.

Electricity price forecasting (EPF) supports scheduling, bidding, and risk management in electricity markets, yet existing benchmarks focus mainly on numerical inputs, leaving the forecasting value of forecast-time textual context insufficiently evaluated. We introduce TRACE, a reproducible benchmark of 7,300 zone–day instances pairing prices from five zones in a major U.S. market with official operational text available at the forecast cutoff. TRACE reconstructs official operational text at each cutoff, preventing post-cutoff information leakage. We evaluate TRACE for semantic alignment and forecasting value. Semantic assessments align with central movement and both tail risks in ground-truth prices, most consistently for upper-tail price risk. Forecasting value is reflected in a median 7.4% reduction in upper-tail pinball loss across time-series foundation models. A controlled cross-day text-mismatch ablation reverses the gains, falling below the no-text baseline.

Many scientific questions require reasoning about what was never observed: What if the conditions, interventions, or history had been different? Models can predict accurately on observed data yet fail on such what-if queries when correlated inputs are varied independently. A common remedy is to add controlled simulation data in which these factors are explicitly disentangled, but this requires access to a simulator, can be computationally expensive, and inherits the simulator's modeling assumptions. We introduce ReRoute, a framework for targeted scientific what-if prediction that combines factual data with partial mechanistic knowledge, without requiring controlled intervention data for adaptation. ReRoute fixes the queried input of a pretrained backbone to a reference value, reintroduces its variation through a known mechanistic pathway, and fine-tunes on the original factual data, while leaving downstream effects to the learned dynamics. We provide a causal identification result for this construction under explicit structural assumptions, with the core argument machine-checked in Lean. After showing that ReRoute achieves highly accurate counterfactual predictions in a controlled advection-diffusion system where exact responses are available, we turn to state-of-the-art climate emulation. On held-out coupled-climate interventions, ReRoute reduces aggregate climate error by 18.2-31.8% under severe CO$_2$ distribution shifts while preserving skill under standard conditions, at a small fraction of the cost of retraining on additional controlled simulations, without even accounting for the substantial expense of generating such data. Finally, on an emulator trained from historical ERA5 reanalysis, where no counterfactual reference exists, ReRoute preserves substantially more of the surface warming implied by the observed boundary conditions under a fixed-CO$_2$ counterfactual.

It has recently been shown that nearest-neighbour retrieval provides a strong baseline for molecular fingerprint prediction from MS/MS spectra, with several variants matching or outperforming current deep learning models (Khoo and Barzilay, 2026; Liu et al., 2026; Gupta et al., 2026). Importantly, "nearest neighbour" encompasses a family of retrieval methods that differ in the information assumed to be available at inference. In this report, we systematically compare several nearest-neighbour variants and show how these differing assumptions affect performance. Our goal is to establish stricter baselines that enable more rigorous benchmarking and better measure progress in this area.

We consider the estimation of drift, diffusion, and noise covariance from discrete observations of stochastic differential equations driven by Gaussian processes. For a fixed observation horizon $T>0$ and a known initial state $x_0\in\mathbb R$, we study \begin{equation*} dX_t=a(X_t)\,dt+\sigma(X_t)\,dZ_t^{\beta,f}, \qquad X_0=x_0,\quad 0\leq t\leq T. \end{equation*} \smallskip\noindent Here $a:\mathbb R\to\mathbb R$ is the drift coefficient, $\sigma:\mathbb R\to(0,\infty)$ is the diffusion coefficient, and $Z^{\beta,f}$ is a centered Gaussian process from the weighted sub-fractional Brownian family, with covariance \begin{equation*} \operatorname{Cov}(Z_s^{\beta,f},Z_t^{\beta,f}) =\int_0^{s\wedge t} f(r)q_\beta(s-r,t-r)\,dr, \qquad 0\leq s,t\leq T. \end{equation*} \smallskip\noindent Here $s\wedge t=\min\{s,t\}$. The temporal weight $f:[0,T]\to[0,\infty)$ is measurable, bounded, and positive almost everywhere, and $\beta\in(0,2)$ is the covariance exponent. For $u,v\geq0$, the kernel is $q_\beta(u,v)=[u^\beta+v^\beta-(u+v)^\beta]/(1-\beta)$ when $\beta\ne1$. Its continuous extension at $\beta=1$ is $q_1(u,v)=(u+v)\log(u+v)-u\log u-v\log v$, with $0\log0=0$. Using the Euler approximation, we reconstruct the Gaussian driving increments from observed transitions and use their joint density to obtain a trajectory likelihood. Neural and radial-basis representations model the drift, diffusion, and normalized temporal weight, while a likelihood profile estimates the covariance exponent and diffusion scale. We compare the method with two neural alternatives on the same simulated trajectories in twenty coefficient settings.

By learning transferable rewards, inverse reinforcement learning (IRL) enables counterfactual evaluation of agents under modified environments. Such transfer places strict requirements on coverage since target environments affect agents' state occupancy. We propose a multi-task IRL method that pools data across multiple agents with different rewards in the same environment under a low-rank assumption. In addition to alleviating coverage requirements, so each task need not visit every state as long as others do, the method offers scalable evaluation of multiple tasks under new environments as computationally intensive planning scales with rank rather than the number of tasks. We provide finite sample guarantees on reward recovery and on policy learning in new environments. Experiments show our method is robust to limited coverage, recovers rewards on and off of each task's support, transfers to target environments at lower regret than baselines, with its computational advantage over per-task methods widening as tasks grow.

There is considerable interest in using time-varying electricity prices to shape consumer demand response, and better align energy demand with renewable production. However, optimal prices generally vary over time in response to complex signals such as weather forecasts, sunrise/sunset times, and day-of-week patterns; and existing methods are not able to make efficient use of such rich contextual information. Here, we propose a neural-network-based algorithm for contextual energy pricing, modeling pricing as a Stackelberg game and leveraging a mean-field solution representation from Mehrabi et al.(2024). The approach learns constrained mappings from contextual features to feasible price signals. We validate our approach by simulating the energy grid in several US cities, and show that incorporating contextual information can considerably increase the value of the demand response programs.

Recent theoretical work identified fundamental properties of representation geometry that shape inference ability of deep neural networks. These include signal-noise factorization (SNF), the ability to segregate signal from noise, and signal-signal factorization (SSF), the ability to segregate task-specific and task-irrelevant signals. Here, we built regularizers that reinforce these two properties during training. We compared networks trained with these regularizers to $L_2$-regularized baseline networks on the CIFAR-100 classification task to understand how our regularizers shape representation geometry and impact performance on a well-known computer vision baseline. Enhancing SNF via regularization improved model performance but enhancing SSF did not. Motivated by biomedical applications, we investigated how our regularizers affected performance on the BloodMNIST dataset treated with MedMNIST-C corruptions at five severity levels, and found even larger performance gains using the SNF regularizer. To understand the mechanism by which SNF-regularization produces improved performance, we analyzed the nuisance subspaces across regularization regimes, finding that the SNF-regularized models represent noise in distinct subspaces, separate from class-relevant signal. Because this geometry is explicit, the dominant corruption-induced directions can be estimated on held-out data and projected out of the representations. This manipulation led to a substantial gain in accuracy. These results show that regularizers that enforce signal-noise factorization can produce substantial improvements on computer vision tasks that contain out-of-distribution image distortions at inference time. They also highlight how shaping representations affects model performance: isolating nuisance variables from categorical ones is more important than maintaining factorized representations of categorical variables.

Post-training compression of LLM attention is often formulated as independent matrix approximation, ignoring both the shared structure among attention projections and the representation shift introduced by earlier compression. We propose FTC, a sequential structured compression framework that adapts the approximation to the current compressed model while jointly exploiting the native Q/K/V head structure under a fixed storage budget. The output projection is handled separately to account for the changed post-attention representation. FTC requires neither fine-tuning nor gradient-based recovery. Across seven decoder-only LLMs from 6B to 32B parameters, FTC achieves the lowest WikiText-2 perplexity among the compared methods at every tested keep ratio on five modern GQA models, with the largest gains under aggressive compression. The improvements transfer to downstream tasks and remain substantial at the 32B scale.

We develop multifidelity methods for constructing triangular transport maps from samples, when high-fidelity data are scarce but lower-fidelity data are more abundant. Using this set of multifidelity data, we approximate a triangular transport map that bijectively maps between a tractable reference density and the high-fidelity target distribution. We introduce two strategies to leverage low-fidelity data: a hierarchical approach that composes maps between adjacent fidelity levels, and a non-hierarchical method that incorporates low-fidelity information through monotonicity-preserving corrections to the map parameterization. Numerical experiments compare these strategies with single-fidelity transport and demonstrate how the proposed multifidelity approaches can improve map estimation from limited high-fidelity data. To illustrate the broader utility of the learned maps, we also deploy them in a downstream amortized simulation-based inference task. This example shows that multifidelity improvements in map estimation can translate to improved conditional sampling and uncertainty quantification when high-fidelity data are scarce.

Compression reports summarize how far a compressed language model moved from the dense one, usually by a KL divergence; a deployment that relies on the dense model's outputs needs to know how many of its decisions changed. We show that total variation, not KL, answers this directly. Across 802 compressed and perturbed copies of 19 open models on five corpora and nine mechanically unrelated perturbation families, the rate at which the arg-max token changes (the flip rate) tracks total variation at a ratio with median $1.05$, with no fitted constant. KL converts into flips only through its square root and a factor that varies fourfold across models and corpora, because KL averages over tokens before the root is taken; first-order statistics averaged per token, such as Hellinger distance, avoid this, but reports rarely give them. As a result, of two compressors reported on different models and corpora whose flip rates differ by at least $10%$, KL assigns the smaller divergence to the one that changes more decisions in $11%$ of cases, total variation in $1%$. Two pre-registered tests mark the limits: on a held-out code corpus the ratio held for all eight models while three predictions about KL each failed for half of them or more, and on three new models with real kernels it stayed in its band for 37 of 38 checkpoints but fell below one on code for two models. In vLLM speculative decoding, total variation measured under teacher forcing predicts greedy draft acceptance with a mean relative error of $1.1$–$2.4%$, without the task-specific calibration that KL needs.

We introduce Grand Canonical Generators (GCG), a generative framework that extends Boltzmann generators to the grand canonical ensemble. We present two designs. The first conditions a variable-size generative model on the chemical potential, sampling particle number and configuration jointly. The second factorizes the grand canonical distribution into a particle-number distribution and the corresponding canonical Boltzmann density. This factorized formulation can use any existing Boltzmann generator for the canonical component, encodes the known linear chemical-potential dependence analytically, and yields a tractable likelihood that supports self-normalized importance sampling (SNIS). Empirically, GCG accurately reproduces grand canonical observables on a Lennard–Jones fluid and methane adsorption in a zeolite, demonstrating generalization across chemical potentials and correction via SNIS and grand canonical Monte Carlo.

Uncertainty quantification is critical in scientific machine learning, where black-box, image-based models are increasingly deployed in high-stakes settings. In many such applications, model outputs inform costly decisions, yet most methods provide only point estimates without quantifying predictive uncertainty. This challenge is compounded by the limited accessibility and interpretability of model internals, making it difficult to assess reliability across different regions of the input space. As a result, there is a growing need for methods that can provide input-dependent uncertainty estimates to guide both model development and downstream experimentation. To address this need, we propose Adaptive Conformal Prediction using Nearest Neighbors (ACPNN), an input-adaptive conformal framework for image regression. ACPNN leverages information from neighboring samples to produce locally adaptive uncertainty estimates while maintaining low computational cost. The neighborhood structure is defined using a scaled distance metric learned via a Gaussian Process with an automatic relevance determination (ARD) kernel. We demonstrate the effectiveness of ACPNN on a diffusion model for emulating inertial confinement fusion (ICF) simulations, showing that it achieves reliable and adaptive uncertainty quantification.

Neural operators learn maps between function spaces, while hereditary network dynamics are described by Volterra resolvents with non-rational Laplace symbols. We introduce a fractional Laplace neural operator (fLNO) that embeds this structure in the learned map. For commuting excitation–Laplacian pairs, one block graph-spectral layer represents the full linear Volterra solution operator exactly. We establish an expressivity frontier for finite rational realizations: they approximate fractional memory geometrically on compact frequency windows, but cannot reproduce the non-integer critical asymptotics generated by a branch point, and on the half-line the best rational rate is root-exponential. The same theory yields trainable parametrizations that enforce a prescribed stability margin by construction, and a graphon-transfer theorem separates genuine operator consistency from parameter sharing. In a common-data benchmark, positive rational operators can match or exceed fLNO accuracy on finite horizons, whereas in controlled near-critical experiments fLNO recovers the branching coordinate more faithfully with far fewer parameters; unconstrained rational fits can cross the stability boundary, while certified parametrizations cannot. A four-parameter spectral law transfers without retraining from graphs of size 48 to 192 with 0.51–0.62% relative error. Applications to Chilean aftershock sequences and to renewal models for Chile and 21 Italian regions illustrate structured inference with explicit uncertainty. The contribution is an operator-learning architecture in which exact memory structure, physical coordinates and stability guarantees coexist with competitive accuracy.

When minimizing the squared-error loss, the popular CP decomposition can be interpreted as parameter inference in a Gaussian model with a low-rank mean tensor and constant variance across the tensor entries. We introduce heteroskedastic-CP (HCP), which models entrywise variability with a non-constant, low-rank precision tensor, and develop an alternating block-coordinate ascent method to recover both the low-rank mean and precision tensors from noisy observations. Our procedure is computationally competitive, with the same leading-order factor-update complexity as CP-ALS. We demonstrate HCP on synthetic experiments and an EEG application.

As an alternative to the standard geometric analyses, we give an exact, information-theoretic analysis of stochastic gradient descent (SGD) and its variants. We show that a preconditioned SGD step is the posterior-mean update of a Gaussian Bayes model, and that its one-step regret splits into an intrinsic-time cost and a change in comparator information. The split extends to an identity for the objective itself. Convex convergence, strict-saddle-point escape, the link between flatness and generalization, the standard learning-rate schedules, adaptive optimizers, and the noisy, momentum, heavy-tailed, and gradient-free variants of SGD each correspond to a term or a special case of this identity. We measure its terms on synthetic and real training runs. On real networks it attributes the slack of classical convergence bounds to the terms their derivations drop and separates optimizers that reach the same training loss. That separation follows the number and consistency of their steps. Its relation to which of them generalizes better differs between networks. For gradient-free SGD the identity determines how a curvature preconditioner should enter the update. The sharpness-based generalization certificate it yields, with a data-independent isotropic prior, is vacuous at network scale unless the curvature spectrum is nearly flat across all parameters.

Continual parameter-efficient fine-tuning for large language models (LLMs) must balance retention of previously acquired knowledge, adaptation to new tasks, and strict parameter budgets. We present ChainLoRA, a replay-free continual merging framework built on chain-updated task-vector geometry. From a parameter-merging perspective, we formulate a geometric view of forgetting through a measurable interaction between task updates, separating directional overlap from coefficient coupling. Building on this view, ChainLoRA combines chain-updated training with post-stream adaptive SVD merging. During training, initialization and a one-sided orthogonality proxy use only the last carrier, keeping their historical-state footprint and regularization overhead constant as the task stream grows. At merging time, Adaptive SVD extracts a shared carrier and aligns it to the latest task through Procrustes adaptation. Our theoretical analysis shows that Procrustes adaptation facilitates geometric approximate separation of shared and task-specific components. The one-sided proxy further bounds inter-task interference. An effective-rank penalty additionally promotes efficient utilization of the task subspace during continual learning. Experiments show that ChainLoRA achieves state-of-the-art performance among the evaluated replay-free methods on the Large and SuperNI benchmarks, while remaining competitive on Standard CL and attaining almost the closest average scores to the evaluated replay-based method across all three benchmarks.

We introduce IrekoGPT, a post-hoc method for converting pretrained LLMs into slimmable models whose width can be adjusted at inference time. Building on SliceGPT, we retain its projection matrices without pruning them, allowing a single model to expose nested subnetworks at different widths. We improve robustness by calibrating each layer across multiple compression ratios, and correct downstream linear layers through gradient-free ridge regression. Across Llama and Qwen models, preliminary results show improvements over naive PCA-based slimming, with the largest gains at high compression. Code is available at https://github.com/aimagelab/IrekoGPT

Knowing how much a causal predictor could improve need not reveal the gain of the repair actually learned. We quantify this gap in a scalar Gaussian causal experiment with known intervention geometry: auxiliary data identify effect magnitude up to bounded contamination, while diagnostics identify direction. The target is the squared-loss gain of the realized trained repair relative to a fitted reference. Jointly optimizing the learner and assessor under uniform learning MSE $\eta$ avoids the trivial solution of making no repair. At the usual $1/k$ learning scale, every feasible learner incurs a $k^{-2}$ assessment floor, even when oracle potential is estimable at a faster rate. In the magnitude-rich regime, we characterize a sharp leading-log frontier: the assessment exponent is $\min{\ell_k,2k\eta_k/U}$ to first relative order, where $\ell_k=\log(1/(k^2E_k))$ and $E_k$ is auxiliary precision. A diagnostic-abstention rule attains this exponent with unknown nuisance parameters. We also bound the critical allowance window and transfer the frontier to adaptive sampling by exact Gaussian simulation. Finite-grid experiments distinguish sign-tail suppression from total MSE and expose conservative finite-budget behavior. The result isolates how the assessment target changes information requirements in this experiment; it is not a general causal identifiability claim.

Neural combinatorial optimization typically assumes a centralized solver that reads the whole instance. We study the opposite: combinatorial optimization under a hard information horizon, where every node commits to its share of a global solution seeing only its $k$-hop neighborhood, and those commitments must compose into a globally feasible solution. We formalize this as local set cover and instantiate it on weighted multipoint relay (MPR) selection, the NP-hard 2-hop covering problem of the Optimized Link State Routing Protocol version 2 (OLSRv2) routing protocol (RFC~7181), whose horizon is imposed by the protocol, not chosen by the modeler. We prove two results. Any deterministic selector whose horizon is one hop short must either fail coverage or land a factor $\Delta$ from optimal, and an $L$-layer graph neural network (GNN) read out at the deciding node is exactly an $L$-hop selector, so capacity cannot buy back radius. Conversely, at the horizon a \ac{GNN} of depth $O(\Delta)$ reproduces the RFC~7181 covering greedy, and at width $O(c_{\max}\Delta)$ its metric-aware weighted analogue, inheriting the $(1+\ln\Delta_2)$-approximation in both cases. Empirically, a 3-layer \ac{GATv2} with a coverage-completing decoder, behavior-cloned from the CP-SAT optimum, reaches $\text{cost}/\text{opt}=1.030\pm0.001$ against greedy's $1.138$, closing $79.1\%$ of the gap at $100\%$ coverage. Restricting the same learner to one hop, on identical instances with the same decoder and demonstrations, collapses it to $1.344$, far worse than greedy. Two transfer checks target real-world networks. OLSRv2's unmodified selection code matches our cardinality greedy on $200/200$ unit-cost instances, and on $40{,}308$ instances of real battalion mobility the frozen model closes $48\%$ of the gap at full coverage. The information horizon, not the model capacity, is the most significant variable.

A weight space network (or metanetwork) takes the weights of another neural network as input and predicts properties of it. Most prior work trains such models on input networks of one or a few fixed sizes and evaluates them in-distribution. The few attempts at out-of-distribution size generalization remain limited in scope and have achieved only modest success. Consequently, the potential efficiency gains of training on small networks and evaluating on much larger ones remain largely unrealized. We propose Transferable Graph Metanetworks, which extend the graph metanetwork paradigm with a set of modifications that make performance transferable across input networks of different widths. The modifications follow two principles: invariance to the ways in which networks of different widths represent the same function, and continuity, such that weights representing similar functions receive similar predictions. We further study whether size generalization is possible for input networks trained independently from random initialization. Empirically, our modifications significantly improve size generalization on every task we consider. Performance is strongest on input networks trained under the maximal-update parameterization ($\mu$P), where it remains robust up to $42\times$ the training width. Theoretically, we explain these observations with infinite-width limit theory: we prove size-generalization guarantees for our model on $\mu$P-trained inputs, and explain why it can fail under other parameterizations.

Contemporary Genomic Foundation Models (GFMs) rely on a DNA-as-a-string paradigm that employs masked token prediction objectives for pretraining. However, this abstraction does not explicitly model the biochemical, structural, and physical properties essential to biological function. Many molecular properties can be estimated from sequence using established biophysical models, so their utility lies not in providing an independent modality, but in introducing priors that training objectives can explicitly exploit. We introduce VANDAM, a framework that extends the training of GFMs with DNA molecular priors. In self-supervised training, VANDAM predicts regional molecular properties from pooled representations. When functional labels are available and can reward retaining molecular priors, local features are additionally injected at the input. VANDAM consistently improves downstream performance across four architecture families and nine held-out genomic tasks by complementing token-based objectives. Probing experiments further demonstrate that the use of molecular priors generalizes to other unseen molecular properties.

Time-series foundation models (TSFMs) perform strongly across forecasting tasks, but their per-series inference is ill-suited to neighbor-rich forecasting, where each query has access to related but nonidentical historical series. Continuous glucose monitoring (CGM) and Web/cloud workloads exemplify this setting: CGM trajectories share physiological patterns but vary across individuals, devices, and conditions, while Web/cloud workloads combine common operating regimes with non-stationarity, heavy tails, and bursts. These histories share useful structure, yet neighbors are not equally relevant. Existing methods either fine-tune TSFMs for each target domain, incurring additional costs and offering limited transferability across backbones, or append retrieved series without verifying whether they support the current forecast. The key challenges are conflicting residual evidence from neighboring series and residual patterns that vary across TSFMs and forecasting tasks. We formulate test-time neighborhood scaling: using same-domain neighbor evidence without modifying the backbone. We propose RACE (Residual-Aware Correction of Forecasting Errors), a two-stage framework for using historical neighbors. We first retrieve query-compatible neighbors, align their residuals to the query scale, and aggregate coherent evidence into the training-free RACE-TF correction. Full RACE then uses a lightweight, domain-specific Gate to determine when applying the correction is beneficial, with a reusable training workflow across TSFM backbones. Across four TSFMs, RACE improves all three domain-aggregate metrics on both primary domains, with the largest gains on high-error queries. Within each domain, a Gate trained on one TSFM transfers to other backbones without adaptation, and the resulting pipeline improves all 72 cross-backbone metric comparisons over the matched frozen targets.