Papers

World models are typically trained and evaluated by prediction error, assuming that more accurate predictions lead to better decisions. We show that this assumption can fail because models with similar total error can differ substantially in planning performance when their errors occur on different state dimensions. We introduce Decision-Relevant Prediction Error (DRPE), which measures prediction error on the state dimensions that affect decisions. We also develop an iso-error evaluation protocol that varies error allocation while keeping total error fixed. In a factored gridworld with known state relevance and a standardized planner, we evaluate 55 controlled and learned models across different error levels and allocations. Total prediction error is weakly related to planning success (Spearman $\rho=-0.25$), whereas DRPE is strongly predictive ($\rho=-0.84$; $-0.98$ within the controlled family). Models with only a 1% difference in total error can differ by 60 percentage points in planning success (97% vs 37%). The relevant error also depends on the task, with model rankings reversing across tasks at the same total error. Deeper imagination further amplifies decision-relevant errors, while learned models exhibit systematic bias on rare but decision-critical events. We formalize sufficient conditions under which DRPE correctly ranks models and total prediction error cannot.

Hyperdimensional computing (HDC) is attractive for efficient and robust learning, but conventional inference still encodes every query independently, repeatedly paying the cost of high-dimensional projection. We introduce SupHDC, a new inference paradigm that processes multiple queries through a shared encoding computation. SupHDC assigns lightweight random slot keys, superposes the keyed queries before encoding, and uses slot-specific classifiers to recover their individual predictions. A random-feature kernel view explains why exact recovery of each hypervector is unnecessary: inference only needs to preserve the class evidence that determines the prediction. Across ten datasets, SupHDC achieves 1.39x analytical speedup with no average accuracy loss, and up to 2.08x speedup with only a 2.67 percentage-point mean accuracy loss. On a Raspberry Pi~5, it delivers 2.01x measured wall-clock speedup with a 2.26 percentage-point loss in mean prediction accuracy. SupHDC shows that high-dimensional redundancy can be used not only for robustness, but also as capacity for shared inference.

We circumvent the Sanford-Hsu-Telgarsky (SHT) single-layer induction obstruction within a linear, one-step, causal, bilinear, symplectically consistent design class on the post-RoPE substrate, by lifting attention onto a symplectic phase space, mirroring Hairer's lift of Stormer-Verlet. The lift exits the premise of the SHT counting argument rather than the bound itself. The reframing exhibits the obstruction as a filter-order gap: a one-layer bilinear score realises a $z$-transform of joint order $(0,0)$, whereas the induction discriminator requires key-side order $\geq 1$. Applying the symplectic upper shear $M_\gamma:(q,p)\mapsto(q+\gamma p,p)$ to the post-RoPE query and key streams closes it. We prove this lift is unique within the factorised subclass, exactly symplectic at operator level, and requires post-RoPE placement; and in an explicit $T_4$-only Gaussian reduction we derive a closed-form two-branch induction phase transition, held out at $r=0.9876$ with zero fitted parameters. That law is an analytically solvable limit, not a robust prediction: restoring the $T_3$ channel moves $\gamma_c$ at $d_k=64$ from 1.030 to 0.569 and removes the crossover. Deployability follows by exact derivation: the KV cache is unchanged, prefix reuse and speculative decoding are preserved, overhead is $6d$ FLOPs per token per layer, INT8 headroom grows by at most $\log_2(1+2\gamma)$ bits, fused kernels are unmodified, and no parameters are added. At 91.3M parameters a supercritical sweep locates an emergence band: induction forms 3/3 seeds at $\gamma=0.80$ in a mean of 717 steps, against 2/3 seeds and 2700 steps at $\gamma=0$. Adverse results are reported as directly: a key-only half-lift reaches 0.949 against 0.811 for the symmetric operator, so if induction accuracy is the objective, the half-lift is the better construction. Forty-one notebooks and result files ship as ancillary material.

Leaderboards rank long-horizon agents by their final outputs. Yet a higher score alone does not establish whether two systems are comparable or which stage accounts for the difference. Unequal evidence, inputs, or budgets can affect scores, and statistical corrections do not remove this mismatch. We introduce compositional controllability to address these questions. A comparison window covers one stage, several stages, or the whole agent. Our central result bounds the gap between observed and controlled score differences using only nuisance outside the window. This yields an admissibility test applied before scores are inspected. Inadmissible comparisons are refused. For admissible pairs, an ordering is certified only when the score gap exceeds the combined sampling and nuisance radii; otherwise, it remains undecided. These decisions give each system a rank interval. We introduce BioLitBench, a benchmark of 2,042 biomedical articles represented as structured claim graphs. Among seven published pipelines, a conventional statistical analysis declares a winner in 14 of 21 pairwise comparisons. Yet the top-ranked system alone received the target review's bibliography. To isolate pipeline performance, our test requires matched inputs and a fixed backbone model. It refuses 11 of the 21 comparisons, including every comparison involving the top-ranked system. Seven of the 14 conventional conclusions fall within these refused pairs. The same comparison windows support stage-level training. We train SCRIBE on Qwen3.8-27B using rewards measured at each stage's exit. Under matched evidence, SCRIBE achieves a certified rank interval of [1,2], with certified advantages over all evaluated published pipelines and the evaluated Claude and OpenAI agents. Under same pool, SCRIBE matches the strongest published retriever and is certified above three published pipelines.

As AI models grow in size and usage, their energy demands increase dramatically, raising sustainability and economic concerns. Neuromorphic hardware, inspired by the energy efficiency of the brain, seeks to address this challenge by offering low-power, fast-processing alternatives to conventional computing. Such hardware is particularly well-suited to control systems deployed in resource-constrained environments, which are best trained via reinforcement learning (RL). This contribution presents the design and implementation of a fully on-chip, closed-loop Loihi 2 RL agent. Our neuromorphic circuit consists of a fully embedded Q-learning algorithm and an on-chip simulation of the CartPole-v0 environment on Loihi 2. Our Q-learning algorithm trained the same number of successful agents as the CPU implementation in only half the execution time and with two orders of magnitude less dynamic power. These findings demonstrate the viability of RL on neuromorphic hardware and highlight its promise for building energy-efficient, real-time, embedded AI systems.

Domain experts trained from a shared checkpoint can transfer their specialized capabilities to a single student through on-policy distillation (OPD). Existing research primarily focuses on improving this merging process, while the algorithms used to train the experts have received limited systematic comparison. We investigate which training algorithm produces teachers better suited to OPD through controlled single-teacher comparisons of supervised fine-tuning (SFT) and reinforcement learning (RL) across Agentic, Reasoning, and Perception. Teachers and students share the same Qwen3.5-9B initialization, and the two teacher types are compared at similar task performance. Our experiments show that RL teachers yield stronger students and higher recovery of teacher performance gains across all three domains. At their best checkpoints, RL-guided students outperform SFT-guided students by 4.27, 1.50, and 0.86 percentage points, respectively. In Agentic, the best SFT-guided student recovers only 44.44% of its teacher's performance gain over the base model, whereas the best RL-guided student recovers 115.00%, surpassing its teacher. Our further analysis shows that RL teachers undergo smaller parameter displacements from the shared initialization than SFT teachers. These findings support the hypothesis that RL teachers' smaller departures from the student's starting point facilitate learning through OPD, resulting in stronger students.

Prompt engineering has become an indispensable tool for using large language models (LLMs), turning LLMs into task-specific experts without changing their weights. Despite notable theoretical advances in prompt engineering, the theory for the more practical hard or discrete prompts is largely open. In this paper, we try to fill this gap either by providing a complete solution or by making substantial progress on the three core theoretical questions regarding hard prompts. First, we show that determining the existence of a hard prompt for a transformer to solve a downstream task is NP-complete and that finding an optimal hard prompt is NP-hard, which is the first computational complexity result for hard prompting, as far as we know. Second, we show that, unlike soft or continuous prompts, hard prompts have essential limitations: hard prompts are not complete; short hard prompts do not significantly enhance the ability of transformers; and long hard prompts exhibit the "prompt dominating answer phenomenon," meaning that, with high probability, the same answer is given for all queries of the same length. On the other hand, linear hard prompts do not have the limitations of short or long prompts. Third, we provide a tight bound on the size of the task in terms of the prompt length for the performance of prompts on the finite task to generalize to the entire data distribution, leading to a necessary and sufficient condition for generalizability. This is the first result on generalization for prompting, as far as we know. Our findings not only offer the first theoretical insights into hard prompts but also provide provably reliable practical guidance for real-world LLM usage.

Active feature acquisition (AFA) sequentially selects informative features under budget constraints. However, existing policies rarely distinguish whether information contributed by interacting features is redundant, unique, or synergistic. We introduce SynAFA, a state-dependent AFA policy that combines pairwise joint information and conditional information, with Partial Information Decomposition (PID) characterizing its information structure. Across five tabular datasets and MNIST-loop, performance is heterogeneous. SynAFA shows its strongest gains at low budgets on PhysioNet, where synergistic and redundant feature pairs are supported by permutation tests, but its advantage diminishes as budgets increase and does not depend on pair proposals. SynAFA performs significantly worse than nearly all baselines on MiniBooNE, and than CAE on MNIST-loop. Controlled synthetic experiments further show that, within budget, SynAFA's advantage rises as joint information becomes more synergy-dominated, including when total joint information is held approximately constant. Further analyses show that the budget-dependent erosion is not resolved by non-greedy local search, which improves a diagnostic set-level objective but leaves predictive performance no better, often significantly worse, and that improvements in this objective are weakly aligned with the fixed classifier's predictive utility. These findings characterize when pairwise synergy can benefit AFA while exposing a persistent challenge in translating local information into effective acquisition objectives.

Drifting Models train a one-step generator by recomputing a finite-sample drift field at every iteration and taking an optimizer step toward the drifted target. The field says how generated samples should move, but the step is taken in parameters shared by all samples, so the motion the network actually makes need not match the motion it was given. This leaves a basic training question open: should extra compute go into fitting the current target more closely, or into recomputing the field? We study it on ImageNet 256x256. Holding the target fixed for k optimizer steps and measuring the realized displacement, we find that deeper fitting does bring the network closer to the frozen target, and that the number of steps needed before it makes any net progress drops from about sixteen early in training to one later on. When the extra steps come for free, k=2 also lowers FID. Once they are paid for, the result flips: at approximately matched measured wall-clock, spending the budget on fresh fields gives lower FID than deeper fitting, on both training seeds. The target itself shows why a fresh field is worth so much. Redrawing the finite support rotates its direction far more than a parameter update does (cosine ~0.3-0.6 against ~0.95), and a correction that is optimal in field space is not reliably better in FID than a parameter-free one. For Drifting, fitting each target well and spending compute well are different goals.

Efficient sampling from Boltzmann distributions is central to modelling complex physical systems. Markov Chain Monte Carlo (MCMC) methods suffer from critical slowing down, high autocorrelation, and poor mode-mixing, limiting their scalability. Recent advances, like Boltzmann Generators, offer a promising alternative but remain constrained by costly MCMC-based training, inefficient sampling, and poor ergodicity. We introduce an algorithm for learning Boltzmann distributions that does not require any true samples for training. Our approach draws inspiration from flow matching but departs fundamentally from sample-trajectory matching to distribution-trajectory matching. The algorithm iteratively reshapes the target distribution, using model generated samples to guide learning and ensure comprehensive mode coverage. We validate our method on standard benchmarks, including a 2D Gaussian mixture, Many-Well distributions, and high-dimensional scalar $\phi^4$ theory. The proposed approach not only improves sampling performance and accuracy over traditional MCMC and flow-based baselines but also establishes a new method for sample-free learning of complex physical distributions.

Fine-tuning a language model on sensitive records can leave it able to reproduce them. We ask when this memorization arises and how to prevent it without knowing in advance which spans are sensitive. Our starting point is that most memorization scores and attacks share one statistical core: whether the model assigns a token more probability than some reference would. Taking as the reference a model trained on the complementary half of the same corpus gives the Target Reference Advantage (TRA), a per-token signal that separates what a model fit to a particular record from what it learned across records, and is cheap and differentiable. We then study what drives memorization during fine-tuning: it keeps growing well past the validation minimum, is larger on small datasets and at higher learning rates, and higher when the underlying task is harder. Early stopping removes much of it, but because it is chosen by aggregate validation loss it helps least for rare, hard-to-predict spans embedded in otherwise learnable text, which is exactly what sensitive information tends to be. We therefore introduce TRAP, a one-sided penalty on tokenwise TRA that acts only where the target model pulls ahead of its reference. On student essays with annotated personal information and clinical cases with patient identifiers, TRAP brings memorization near the level of an untrained model at little utility cost, where generic regularizers barely move and differential privacy gives up most of what fine-tuning bought.

It has recently been found that deep learning often occurs at the "edge of stability (EoS)," where the maximum Hessian eigenvalue of the model is stabilized at a value reciprocal to the learning rate. However, what happens before we reach that regime? We fix a deep learning problem and vary first order optimization methods with dense learning rate sweeps. We then track the characterizing quantities of a learning trajectory: the loss, the sharpness, and the alignment between consecutive gradients. To our surprise, if we scale the learning rate by the dc gain of the optimizer, these traces from the sweeps from different optimizers almost perfectly overlap across a large range of learning rates. The dc-normalized optimizers have another role that only becomes apparent in high learning rates: they select when the sharpness value detaches from this universal curve and enters the edge of stability. Upon this discovery, we specify three distinct regimes with respect to the dc-adjusted learning rate: the low-LR regime where the trajectory is nearly insensitive to the optimizer, the high-LR regime, where the optimizer governs the sharpness according to the EoS reciprocal rule, and the in-between mid-LR regime where so-called progressive sharpening originates independently of the optimizer. This distinguishes the role of the optimizer, the learning rate, and the model in shaping the learning progress.

Neural ODEs learn dynamics from trajectory losses, but their adjoint gradients lack the regressor-times-parameter-error structure on which Lyapunov analyses of online adaptation rest, so training on streaming data comes without stability guarantees. We show that this structure is in fact present: the adjoint gradient decomposes exactly into a positive semi-definite trajectory operator acting on the parameter error plus a nonlinear perturbation with explicit, horizon-dependent bounds. A quadratic Lyapunov function then certifies online Neural ODE training over sliding windows under computable gain and horizon conditions, and the same certificate extends to stored data: its drift branch recovers concurrent learning, and its trajectory branch yields NODE-CL, a stored-segment Gauss-Newton method built on batched forward sensitivities that needs no state-derivative estimates. On four DeepMind Control Suite domains, NODE-CL attains the lowest median prediction error on three under velocity measurement noise, where observer-based concurrent learning degrades by up to 8x; with clean measurements it is best on the pendulum and within a factor of 1.6 of the best stored-data baseline on the cartpole and reacher.

Pre-training data poisoning of large language models is usually studied using targeted backdoors and their survival through safety post-training, which leaves open a more basic question: how does a model's clean data performance degrade as the poison rate $\varepsilon$ grows? Motivated by our controlled pre-training runs of OLMo-style models, in which the relative clean data validation perplexity increase $\Delta$ between poisoned and clean models matched in architecture, token budget, and optimization schedule is well fit by a power law $\Delta\approx C\varepsilon^{a}$ with a non-integer exponent, we ask what such a law requires theoretically. We first prove an analyticity barrier: whenever the contaminated objective depends analytically on $\varepsilon$ around a nondegenerate clean data optimum, $\Delta$ is generically quadratic in $\varepsilon$, so a generic non-integer exponent is a signature of genuinely singular structure. We then supply that structure in solvable truncated ridge regression with heavy-tailed covariates, controlled by $q_\star$, and a label-shift poisoning. Our central result is that the excess risk scaling exponent depending on the order of limits: in the higher dimensional proportional regime it is $\epsilon^{q_\star/(q_\star+2)}$, whereas taking the ample-data limit first gives $\epsilon^{2-2/q_\star}$, and the limits do not commute. We confirm this prediction through several numerical simulations. Finally, we argue that finite training time plays the role of truncation on the curvature spectrum in local LLM pre-training, deriving the observed scaling law under heavy tailed inverse curvature spectrum as a modeling hypothesis.

Efficiently learning and sampling from high dimensional, multimodal unnormalized distributions without target samples remains a challenging problem. Although normalizing flows can generate samples efficiently, training based on the reverse KL divergence using only the unnormalized target density may suffer from mode collapse. We introduce SIMANF, a sample free framework that integrates simulated annealing with normalizing flows. SIMANF progressively transforms the target distribution from a smooth initial form to the original target distribution and trains the flow sequentially across these stages. By transferring the learned representation between stages, the method promotes mode coverage while progressively capturing finer features of the target distribution. Following annealing, a final refinement stage combines the reverse KL divergence with an importance weighted forward KL objective using samples generated by the flow. SIMANF requires no target samples during training and uses only the unnormalized density. We demonstrate its effectiveness on Many-Well distributions and high dimensional Scalar Phi4 lattice field theory distribution.

Multi-label classification (MLC) requires predicting multiple relevant labels for each instance, where a central challenge is modeling complex label dependencies arising from co-occurrence patterns. Existing approaches are limited in capturing high-order label correlations, relying on implicit learning through contrastive objectives or pairwise attention mechanisms without structural guidance. We propose HyperLabel, an encoder-decoder framework that explicitly models label dependencies through hypergraph neural networks. Our contributions are twofold: (i) We construct a label hypergraph where sample-defined hyperedges naturally encode multi-way co-occurrence patterns, providing explicit structural prior knowledge that captures relationships beyond pairwise interactions. (ii) We propose a unified cross-modal learning approach where HGNN+ performs bidirectional message passing to integrate feature information with label structure, and a shared cross-attention decoder processes both modalities through complementary learning objectives. Extensive experiments on seven benchmark datasets demonstrate that HyperLabel achieves state-of-the-art performance, with particularly significant improvements on macro-F1 scores (+10.3% on Delicious, +8.2% on Bibtex), validating that explicit hypergraph structure effectively captures complex label relationships. The code is available at https://github.com/iZHpy/Multi-label_hypergraph .

Hyperbolic geometry has emerged as a principled space for representing hierarchical graphs. However, existing hyperbolic graph neural networks typically rely on shared curvature configurations and feature-driven attention, failing to explicitly exploit local hierarchical topological patterns. To bridge this gap, we introduce the Hyperbolic Sombor Index (HSO) as a lightweight structural prior for capturing hierarchy-indicative degree stratification. Building on this, we propose HSO-GAT, a topology-adaptive hyperbolic graph attention network that unifies geometric adaptation and message propagation. Specifically, it comprises two complementary modules: HSO-Guided Local Curvature Adaptation, which performs adaptive node-wise geometric scaling from aggregated node-level HSO signals, and HSO-Gated Hyperbolic Graph Attention, which enables structure-aware message passing through feature-conditioned gating. Theoretically, we establish the monotonic sensitivity of edge-level HSO to degree imbalance and analyze the validity and radial scaling properties of node-adaptive hyperbolic mappings. Extensive experiments on eight benchmark datasets demonstrate that HSO-GAT consistently achieves state-of-the-art performance in both node classification and link prediction tasks.

Multimodal tabular-image learning is gaining growing attention, yet it faces challenges due to tabular data unavailable at test time. A practical solution involves transferring tabular knowledge to images during training to enhance the performance of image models at inference. However, the overlooked yet important challenges lie in the modality imbalance between images and tables, as well as their asymmetric modality relationship in cross-modal transfer, which limits the auxiliary role of tabular data. To address these issues, we propose Skewed Knowledge Transfer (SKT), which asymmetrically transfers tabular knowledge to improve the image model by adaptive integration of modality gradients in a shared parameter space. Specifically, we first introduce a multimodal shared head, which allows the model to benefit from cross-modal structure without adding additional parameters. We then design a two-step Nash Bargaining strategy to effectively leverage tabular gradients. In the first step, SKT seeks a point of modality balance and uses preference awareness in the second step to steer combined gradients toward image-beneficial directions. Furthermore, we theoretically analyze the Pareto improvement and convergence of SKT. To this end, tabular knowledge is explicitly transferred to enhance image models. Empirical experiments on widely used tabular-image datasets reveal that SKT consistently improves image unimodal performance by using tabular data as auxiliary information.

Post-hoc Bayesian fine-tuning places Gaussians around trained low-rank adapters, yet a calibrated posterior does not by itself yield a useful generalization certificate. Such a posterior admits an informative PAC-Bayes certificate only when both the loss of its sampled predictors and its KL divergence from an admissible prior are small. In this research, we characterize this certification frontier for Gaussian LoRA posteriors and separate three interventions: changing the prior, changing the stochastic predictor, and changing only how its complexity is counted. First, an exact isotropic KL envelope eliminates the prior scale and yields a width threshold that excludes posterior widths before sampling, while a zero-KL floor identifies targets that no complexity reduction can reach at a measured risk bound. Second, we minimize KL in closed form over the full $GL(r)$ symmetry of the low-rank factors, leaving every sampled adapter product unchanged, and derive the noncentral objective required when the prior center is trained on an independent split. On a small-pool RoBERTa audit of 567 configurations, the recorded 64-draw summaries imply a certificate floor of $0.7298$ even with zero KL and Chernoff accounting, so reducing complexity alone cannot certify these posteriors at the recorded budgets. For a stable posterior in a controlled Gaussian-factor task, Chernoff accounting certifies risk below $0.1$ on 20 of 20 datasets with 1024 draws, whereas Hoeffding certifies none. On deliberately deformed synthetic rank-four factors, matrix balancing reduces KL by $29.3\%$ on average beyond scalar balancing without changing any prediction. Numerical split-prior scenarios make the remaining risk and complexity budgets explicit.

We study the generalization of spectral gradient descent (SpecGD) in overparameterized matrix classification with corrupted labels. Each input combines a shared low-rank signal with a rank-one sample-specific perturbation, referred to as a shortcut, that enables memorization but does not generalize. We contrast collapsed shortcuts, which share a singular direction, with dispersed shortcuts, which occupy distinct singular directions. Changing only this geometry can reverse the relative generalization of GD and SpecGD: collapsed shortcuts can favor SpecGD, while dispersed shortcuts can favor GD. In the dispersed regime, exact shortcut orthogonality eliminates the signal from the late-stage SpecGD direction, while vanishing random correlations collectively generate a small but generalization-relevant signal through a second-order effect. To identify the direction selected by SpecGD, which the spectral max-margin problem alone does not determine, we combine a refined analysis of its dual with the exponentiated-gradient dynamics of normalized loss weights. Finally, we show that a single SpecGD step can already interpolate and generalize well, while continued training converges to a direction with substantially worse generalization.

Agents that answer questions from compressed or retrieved memory must recognize when the evidence a query needs is no longer in memory. Benchmarks for this task usually create insufficient-evidence examples by deleting supporting passages. We show that this construction leaks the label through memory size: on MuSiQue, a classifier that only counts paragraphs reaches an area under the ROC curve (AUROC) of $0.979$ for detecting unsafe memory, higher than the lexical estimator we initially evaluated. We propose a size-matched construction that provably removes this shortcut, and use it to study MemSafe, an estimator that cross-encodes the query with each memory unit and aggregates the units with a set transformer. Across three multi-hop question answering datasets and five seeds, MemSafe reaches $0.968$ and $0.983$ AUROC on MuSiQue and HotpotQA, $0.26$ to $0.39$ above a lexical baseline, while the third dataset, 2WikiMultiHopQA, is saturated. A frozen pretrained cross-encoder with a logistic head already closes $41\%$ of the MuSiQue gap between the lexical baseline and MemSafe. At the same time, MemSafe degrades more than a weak baseline on the unanswerable questions released with MuSiQue, reaches only $0.639$ AUROC on SQuAD~2.0, and needs several thousand clinical training examples before it outperforms a feature-based estimator. Used as a gate for a 7B reader, it reduces the error rate on answered questions from $0.850$ to $0.631$ at $5\%$ coverage, outperforming both reader confidence and, on average, the ground-truth integrity label, although a 7B LLM judge is the better gate at $10\%$ coverage. These results indicate that the way insufficient evidence is constructed matters as much as the estimator that detects it.

Standard autoencoder (AE) inference uses a single encoder-decoder pass, though the latent may not be optimal for each sample under a fixed decoder. We ask whether a trained AE can reveal information for improving its own reconstruction. Repeated application of a frozen AE to its reconstruction produces transient image- and latent-space trajectories, termed Self-Reconstruction Dynamics (SRD). Although this degrades fidelity in the AEs studied here, SRD contains sample-specific information for correcting the reconstruction. We propose SRD-guided Reconstruction Refinement (SRD-RR), which predicts a latent correction from a short SRD with the AE frozen and no per-sample test-time optimization. We also introduce MSE-recov, an MSE recovery ratio relative to an empirical decoder-optimized reference. Across six datasets, SRD-RR recovers 38.6% of the empirically recoverable MSE gap with one transition and 45.3% with two. A two-transition variant trained without direct access to original images, using an SRD-derived pseudo-target, achieves 40.7% recovery and a 1.74 dB average PSNR gain. Removing trajectory information reduces the gain, while cross-sample trajectory assignment causes severe degradation, confirming strong sample specificity. Nonlinear SRD-conditioned refinement consistently outperforms fixed and trained linear latent correction. On a pretrained DINOv2-based representation autoencoder (RAE) with substantially different latent dynamics, SRD conditioning again improves a matched trajectory-free predictor. However, pixel-MSE latent refinement reveals a strong mismatch between pixel fidelity and perceptual quality, while the SRD-derived pseudo-target mitigates this degradation. Overall, SRD is a useful sample-specific refinement signal, while the objective determines how it translates into pixel and perceptual quality.

Releasing a model update requires certifying that its current-population risk stays below a threshold. Trusted labels are expensive, while a cheap evaluator, such as an LLM judge, scores every example. Reusing evaluator errors from earlier audits is tempting, but when may such evidence replace current labels? It depends on the status of history. If the errors can change invisibly, no label-free test detects the change, and every valid, useful certifier must keep buying labels at a rate we characterize; if a bound on the change is assumed, label-free certification is valid at an explicit error cost. For the middle ground, where history is informative but untrusted, we propose portfolio vigilance, a sequential certifier mixing a betting expert guided by history with one that learns only from current labels; history affects only how it bets, so validity holds for any history. The contribution is not prior-informed betting or expert mixtures, but separating history that may enter validity from history that may only guide label collection. In a canonical model, accurate history shortens decisions but never raises the evidence growth rate; stale history can destroy it. On held-out CIFAR-10N and DICES-990 data, portfolio vigilance needs 0.465 (95% CI $[0.327,0.575]$) and 0.740 ($[0.618,0.877]$) times the labels of a matched prediction-powered monitor, with no observed false certification, and fewer labels on all six external blocks. Under corrupted advice it stays within 8.0% of its better component, while trusting history alone costs up to 1.66 times as much. In post-confirmatory repeated-judge experiments on DICES-990 and ToxicChat, changing a fixed LLM judge's rubric moves its scores beyond run-to-run variation; the portfolio then needs 0.790 ($[0.667,0.909]$) and 0.631 ($[0.520,0.770]$) times the labels of the matched monitor, and fewer than trusting history alone.

Multimodal test-time adaptation (TTA) aims to adapt a pretrained multimodal model online to distribution shift across modalities using unlabeled test data, showing broad potential in real-world applications. However, existing methods primarily focus on adjusting fused features to bridge the source-target gap, lacking explicit control over intermediate representation misalignment, which is a key driver of performance drop under distribution shift. In this work, we tackle this challenge from the perspective of representation engineering. Unlike previous TTA methods that update fusion weights in place, we propose FourIer Representation Editor (FIRE), a novel multimodal TTA approach that directly edits semantically rich intermediate representations. Specifically, we first adopt representation editors into each intermediate layer of the unimodal encoders, enabling layer-wise calibration of unimodal representations. To further enhance the diversity and stability of the low-rank editing subspaces, each representation editor performs frequency domain mixing via the fast Fourier transform to construct structured bases. Moreover, we introduce multi-level adaptation objectives to optimize these editors, jointly promoting cross-modal semantic alignment, source-target statistical alignment, and asymmetric prediction consistency. In this way, FIRE yields aligned unimodal representations for fusion and further improves prediction reliability. Extensive experiments on two widely used multimodal benchmarks under various corruption types demonstrate the superiority of FIRE over existing multimodal TTA methods.

Recent multi-agent LLM systems increasingly combine heterogeneous models for specialized agent roles. However, text-based communication requires each receiver to prefill shared context already processed by the sender. Reusing the sender's key-value (KV) cache avoids this redundancy, but prefill-free transfer across model families must handle differences in tokenization, model depth, and KV representations. To address these issues, we propose HeteroFold, a prefill-free cross-family KV cache transfer method that keeps both the sender and receiver frozen. HeteroFold aligns model structures, maps the sender cache into the receiver space, and calibrates it to preserve receiver behavior. Across six transfer directions, HeteroFold achieves the best cache-transfer performance on all four long-context benchmarks and most short-context settings. It also matches text-based communication on the multi-agent benchmark. At 32K context length, Llama-3.1-8B$\rightarrow$Ministral-3-14B transfer is $10.7\times$ faster than Native Prefill and $1.18$–$1.47\times$ faster than the state-of-the-art prefill-free baselines, Dense Latent and KV Ridge. These results show that HeteroFold enables efficient cross-family KV reuse without receiver prefill.

Tool-using LLM agents must decide not only whether additional information is needed, but also which source can resolve the uncertainty. Existing proactive approaches often specialize in either user clarification or environment verification, without explicitly determining the appropriate information source for each decision. We formulate this problem as uncertainty routing among ACT, CLARIFY, and VERIFY, and propose PROUR, a proactive uncertainty routing framework. PROUR decomposes action uncertainty into disagreement across plausible user-goal interpretations, which signals user-side ambiguity, and the entropy remaining within each interpretation, which signals missing world-side evidence. To acquire information from the routed source, a query generator is trained with a mode-conditioned information-gain reward, targeting user-goal identification under CLARIFY and next-action identification under VERIFY. On $\tau$-bench, PROUR achieves 28.17% average success rate across retail and airline, outperforming the strongest prior method by 4.57% while using 2.17 fewer interaction steps. The learned policy further generalizes to stronger task agents and transactional domains of $\tau^3$-bench without retraining, demonstrating the benefit of source-aligned uncertainty resolution for proactive agents.

Acquiring data is costly: higher measurement fidelity costs power and storage and risks collecting irrelevant content, while aggressive cost reduction can discard information that later analysis needs. We address this trade-off with an information-theoretic framework that acquires data relevant to a broad set of tasks rather than to one model. A mask policy, conditioned on side information, chooses which pixels to measure so as to maximize the mutual information between a discrete image and its partial observation under a budget; since the image entropy does not depend on the mask, this is equivalent to minimizing the conditional entropy. A frozen discrete denoising diffusion model (D3PM) supplies the posterior, and we use it in two ways: as an entropy surrogate for training a one-shot mask generator, and as the criterion for sequential greedy acquisition. The one-shot generator outperforms random masks only with care, including an unbiased gradient estimator for binary masks. With sequential acquisition, on MNIST the prior makes $8\times$ fewer errors than random at a $10\%$ budget, and on CIFAR-10 it gains $0.9$–$3.4$~dB. On fastMRI, our proposed technique using a static mask outperforms the well-known methods such as variable density and LOUPE.

Large language model (LLM) leaderboards compare model capabilities by ranking models according to their mean performance on fixed benchmarks. However, variability in evaluation outcomes across runs may produce unsupported claims of model superiority on the benchmark, a risk compounded by leaderboard updates. In this paper, we propose BB-EDGE (Benchmark-Weighted and Block-Factorized e-processes for Directed Graph Evaluation), a principled framework that represents an LLM leaderboard as a directed graph whose edges certify pairwise mean-performance advantages, with anytime-valid family-wise error rate (FWER) control. Concretely, for each direction, BB-EDGE constructs an empirical-Bernstein e-process by factorizing evidence over protocol-defined blocks and assigning stakes proportional to the corresponding block weights, then applies direct e-Holm across these $e$-processes to certify directional advantages as edges. Theoretically, we characterize weight-proportional linear stakes under heterogeneous benchmark-average nulls and prove anytime FWER control under arbitrary within-block and cross-pair dependence. BB-EDGE further supports anytime-valid Top-$k$ certification and simultaneous rank intervals. Extensive experiments on synthetic data and four real-world benchmarks demonstrate that BB-EDGE maintains anytime FWER control while achieving high efficiency.

Observationally equivalent causal models can still disagree about what happens under intervention, because interventions create inputs that never occur in observational data. We introduce Interventional Separation Selection (ISS), which repeatedly queries the true system with an admissible intervention on which the surviving candidate models disagree, discards the candidates the outcome contradicts, and stops once no intervention within a cost bound separates the survivors. If the true system is among the candidates, this stopping condition certifies that every survivor agrees with it on every admissible intervention within the bound, a guarantee that no observational learner can give, however much data it sees. The stopping condition depends only on the survivors, so it can be checked without knowing the truth. For continuous variables the candidates form an infinite version space, and mixed-integer linear programs decide the stopping condition exactly over all of it, with agreement holding up to a tolerance. On a three-digit colored MNIST causal abstraction task in which ink hue tracks digit size, plain convolutional networks trained on examples reach zero held-out error, yet disagree with shape-based labels on 26% of single-digit edits, as often as hue-based labels do. Auditing the causal abstractions of networks observed only on such images, ISS certifies what each network perceives with 13.6 interventions per image on average, and each certificate, checked against every admissible intervention, holds whenever the network's true abstraction is among the candidates. When a network bypasses a unit that every candidate abstraction relies on, certificates covering interventions on that unit can be silently void, and twenty random validation interventions refute 69% of them.

A gradient descent method is arithmetically simple if the operations are limited to $+,-, \times$, and division $x/2^t$ with integer $t$. An arthmetically simple gradient method is easy to implement in chip design. We show how to transform AdaGrad, Adam, and AdamW into arithmetically simple. AdamW is based on the recursion $x_{t+1}=(1-\lambda\eta)x_t-\frac{\eta }{s}m_t$ and Adam is the special case of AdamW with $\lambda=0$. We transform them into a static case with $s=S(T)$, where $T$ is the number of iterations, and $S(T)$ is a fixed function. The convergence analysis is given for a static Adam, which is also arithmetically simple.