Resting-state functional magnetic resonance imaging (rs-fMRI) functional connectivity (FC) matrices are widely used for individual-level prediction, but strong performance within one cohort may not generalize to a new cohort. We ask whether within-dataset performance remains when the test data come from an entirely held-out rs-fMRI dataset. Each scan is represented as a regularized symmetric positive definite (SPD) correlation connectome, which allows methods to use the geometry of the SPD manifold. We introduce a reproducible age-prediction benchmark across six rs-fMRI datasets: COBRE, ADNIDOD, Cam-CAN, ABIDE, OASIS-3, and ADNI. The benchmark compares a vectorized correlation baseline, Tangent-Space Ridge, SPDNet, and split-wise Riemannian harmonization under within-dataset GroupKFold, pooled GroupKFold, and leave-one-dataset-out (LODO) evaluation. Within-dataset and pooled GroupKFold results are substantially more favorable than LODO results. When an entire dataset is held out, prediction error increases, differences among methods narrow, and performance is strongly affected by age-range mismatch and cohort heterogeneity. The benchmark provides common inputs, model settings, data splits, and analysis scripts so that future SPD matrix learning methods can be evaluated under the same external-validation protocol.
Ce Ju, Antoine Collas, Florent Bouchard et al.· 0 citations
Recurrent, attention-free sequence models share a structural weakness: a fading state cannot perform exact recall of something seen once, far in the past. We add to the Kathleen trunk a second memory layer -- a "notebook": a fixed-key holographic (HRR) associative store with a learned local write gate, a self-gating raw read, and write-triggered forgetting -- 25K parameters that attach to the logits of any trunk. (1) Mechanism: on a controlled needle-in-haystack task the notebook reaches 80-82% one-shot recall at 4x the training length, where the bare trunk scores ~4% and a parameter-matched attention head scores 100% inside its training length and 0% beyond it. Addressing is length-invariant by construction; the untrained memory alone recalls at 90% accuracy identically at 512, 2048 and 4096 bytes. Because the store is a linear superposition, two capabilities follow from arithmetic alone: selective unlearning (one subtraction erases one fact to chance, retained facts unharmed) and per-token attribution (counterfactual erasure names the source fact of every correct byte, 100% provenance). (2) Real text: on WikiText-2 bytes the notebook improves prediction of repeated rare words by +0.15-0.27 bits/byte, the gain growing with the distance between mentions and holding zero-shot at 4x training length; write-triggered forgetting eliminates memory pollution at 8x length (first-mention cost +0.33 -> -0.004). (3) Scope and scale: a parameter-matched attention head does generalize on natural-text repetition, so the notebook's claim is exact recall at O(L); on a WikiText-103 ladder (8 to 512 MB) the zero-shot repeat gain rises monotonically. All experiments are pre-registered, seeds reported, and reproducible on a single free-tier GPU.
We study null-space estimation from a noisy matrix. For a simple left null space, we first derive an exact compact expression for the error of the smallest left singular vector. We then give an all-order series for the SVD vector and projector, followed by compact and consistently truncated series forms for the fixed-realization empirical risk and conditional population generalization risk. The recursion extends to a multiple-dimensional null space by following the complete invariant subspace. The convergence radius is not inferred from an error plot: it is computed independently from the nearest complex exceptional point that joins a retained eigenvalue branch to its complement. A reduced-nullity experiment shows that moving this spectral boundary can increase the radius, although the improvement is not monotone in the retained nullity. For individually ordered null directions under Gaussian training with \(\tau\geq m\), we prove that the Wishart splitting matrix \(W\) gives a strict second-order empirical ranking. Gaussian averaging equalizes the leading generalization risks at both small and very large noise, while a column-swap theorem proves strict expected generalization ranking for an isotropic signal subspace. For unequal spikes, an exact population-overlap criterion and a simultaneous \(99\%\) Monte Carlo confidence certificate explain the observed intermediate ranking. A sixth-order risk correction improves the lower-crossover estimate in the reported experiment. This equal--ranked--equal phenomenon is a finite-sample diagnostic related to spectral mixing, but its tolerance crossings, the exceptional-point radius, and the asymptotic BBP threshold are three distinct quantities.
Large language models (LLMs) finetuned for specialized domains represent crucial high-impact applications. Inference-time alignment improves safety degraded from specialization finetuning without requiring substantial computational resources, complementing finetuning-based methods with an easy-to-use, plug-and-play solution. However, existing inference-time methods fail to reliably improve safety without disrupting domain capability. We identify the root cause as complementary expertise orthogonality: specialized base models and general-domain guidance models have orthogonal competencies, making the guidance signal unreliable for specialized generation. This primarily manifests as stop token interference, where the guidance model's tendency toward continuation overrides the base model's decision to stop, burying correct answers under guidance-induced continuation. To address this problem, we propose CREST, an inference-time alignment method that steers base model hidden representations using safety directions extracted from a guidance model of any family, avoiding token-level structural limitations entirely. CREST improves safety where specialization has weakened it while preserving both domain-specific capability and the safety of already well-aligned models, outperforming baselines by up to 22.2\% on safety benchmarks. Our code is available at: https://github.com/DecayingSeart/CREST.
Jin Gan, Xin Li, Jun Luo· 0 citations
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The exact Shannon capacity is unknown for every odd cycle beyond the five-cycle $C_5$, making odd cycles a central open problem in zero-error information theory. Improving the known lower bounds requires constructing large independent sets in strong powers of these graphs. Recent AI-assisted work has produced a rapid sequence of improvements: building on the construction of Itty et al., Gao developed a recursive product construction for combining structured independent sets, and Buys, Polak, and Zuiddam (BPZ) subsequently strengthened this through a richer recursion framework.
We continue this line of AI-assisted exploration and introduce a heterogeneous refinement of these constructions. The central observation is that the usefulness of an intermediate construction depends not only on the size of its current main independent set, but also on the auxiliary structure it carries into subsequent recursion. Consequently, different parts of that auxiliary structure need not use the same independent set, and different occurrences in a recursion need not use the same intermediate representation. We formalize this for Gao's binary product and derive explicit propagation rules showing how heterogeneous choices strengthen the resulting gadget while leaving its current code size unchanged, then extend the principle to the more general BPZ framework, tailoring constructions to the distinct roles they play within the recursion.
Applying these refinements to the seven-cycle $C_7$, we obtain an independent set in $C_7^{\boxtimes 500}$ yielding $\Theta(C_7)\ge 3.25883262\ldots$, improving the best known lower bound. Beyond the numerical gain, the results illustrate a general principle for recursive zero-error constructions: intermediate structures with the same dimension and current code size can have different downstream value depending on where and how they are used in the recursion.
We study decentralized online optimization of upper-linearizable payoffs over an action set under efficient separation access, with applications to online continuous diminishing-return (DR) submodular maximization. We propose Decentralized Barrier Follow-the-Regularized-Leader (Dec-BFTRL), and evaluate each agent's played action against the average of all local objectives. Each agent maps an internal iterate to a feasible action through an approximate gauge projection, communicates only a cumulative surrogate-gradient dual state, and invokes the local HybridNewton procedure to approximately minimize its post-communication BFTRL potential. For every agent, we achieve expected network-aggregate regret of $\widetilde O(\sqrt{T})$. Over $T$ rounds, each agent uses $T$ neighbor-mixing steps and $\widetilde O(T)$ separation-oracle calls. We give four wrapper instantiations covering three DR-submodular maximization problems.
Yiyang Lu, Mohammad Pedramfar, Vaneet Aggarwal· 0 citations
We estimate the conditional population-risk curve of a realized smooth nonconvex gradient flow from the training sample. Flow approximate leave-one-out (Flow-ALO) propagates a deletion response and evaluates omitted observations at approximate deleted paths. The risk-curve error decomposes into response approximation, exact-LOO fluctuation, and deletion-to-full risk transfer. On each fixed finite horizon, bounded centered training-loss gradients, a one-sided Hessian lower bound, locally Lipschitz Hessians, and a strict tube-closure condition yield an explicit $(n-1)^{-2}$ bound for the deletion-response error. Bounded evaluation-loss gradients transfer the deletion-response bound to the score without requiring the Hessian to be invertible. Direct first-order jackknife cancellation and exact-LOO concentration control deletion-to-full risk transfer and fluctuation, respectively, completing recovery of the conditional population-risk curve. For bounded smooth two-layer mean-field networks training both layers, the score-error bound is uniform in width.
While it is well-established that prosody carries crucial cues for syntactic structure, the degree and nature of correspondence between these two domains remains contested. We investigate the syntax-prosody interface through an information-theoretic lens, quantifying the interaction between prosodic features and syntactic representations as their mutual information. We provide a general-purpose framework for estimating this quantity over large speech-text corpora using multimodal language models. Our framework is structure-agnostic and modular, insofar as it can be used to measure the contributions of individual prosodic features or components of structure. We evaluate the syntax-prosody relationship for two features (word duration and inter-word pauses) across two domains--read audiobooks and spontaneous conversations--both in English. Our results demonstrate that prosody contains measurable syntactic information, with prosodic features reducing syntactic uncertainty in spontaneous conversations by up to 10.2%. Our findings offer new empirical support for several theoretical accounts of the syntax-prosody interface.
Junghyun Min, Alex Warstadt, Tamar I. Regev et al.· 0 citations
The fundamental theorem of statistical learning states that, under suitable measurability assumptions, finite Vapnik--Chervonenkis (VC) dimension guarantees that every proper consistent learning rule is probably approximately correct (PAC). Blumer, Ehrenfeucht, Haussler, and Warmuth showed, assuming the Continuum Hypothesis, that the "well-behavedness" condition of the concept class cannot be omitted: they constructed a concept class of Borel sets of VC dimension one admitting a consistent learning rule that is not PAC. We show that the Continuum Hypothesis is unnecessary. Working in Zermelo--Fraenkel set theory with the Axiom of Choice (ZFC) alone, we construct a concept class of Borel sets on $[0,1]$ of VC dimension one and a proper consistent learning rule that is not PAC. More precisely, for a suitable Borel probability measure and target concept, the rule has true risk one at every sample size on a set of samples of outer probability one. Consequently, finite VC dimension and Borel measurability of the individual concepts do not suffice to guarantee that every proper consistent learning rule is PAC. The result shows, with no need of extra set-theoretical assumptions, that the additional regularity assumption in the fundamental theorem cannot in general be omitted.
Mateus Jesus de Arruda Campos, Gabriel Fernandes, Vinicius de Oliveira Rodrigues· 0 citations
General embodied agents should perceive, predict, act, evaluate, and improve within a unified system. World models have shown great promise in building such agents, yet existing models typically append an action output head to a world simulator, without coupling them into a closed decision-and-learning loop for policy improvement. We present Motus2, a self-evolving general world model for dexterous manipulation. Motus2 advances world modeling through model scaling and data scaling. For model scaling, a single model with shared weights exposes three control interfaces: a policy (world-action model), a simulator (action-conditioned world model), and an evaluator (value model). The policy proposes candidate action chunks, the simulator predicts their visual consequences, and the evaluator assesses the predicted outcomes. Their coupling forms a closed decision-and-learning loop for policy improvement. This formulation uses curated expert demonstrations for action learning, while failed and suboptimal interactions provide valuable evidence for dynamics modeling and value learning. For data scaling, Motus2 progresses from large-scale monocular egocentric data to synchronized stereo egocentric data, followed by robot-domain adaptation with robot trajectories and supplementary human-robot alignment data. Motus2 further studies global-autoregressive and hybrid-memory extensions of its sliding-window context, adds tactile feedback for contact-aware control, and is instantiated on a fully biomimetic platform with stereo vision, dual arms, dual dexterous hands, and tactile sensing. Together, egocentric data scaling and closed-loop general world model scaling provide a general path toward self-evolving dexterous manipulation.
Hongzhe Bi, Zihao Zhou, Yihang Tang et al.· 0 citations
We propose a new design of fair classifiers for multi-class classification problems in the presence of vector-valued sensitive attributes. In that scenario each sensitive attribute has multiple values and forms several groups relevant to the fairness consideration. Naturally those groups are overlapping and one should also analyze the interaction of factors. Additionally, the decision makers aided by the classification should not violate individual rights at the expense of satisfying fairness metrics at the group level. We propose an approach using the theory and methods of coherent measures of risk aiming at resolving the fairness challenges. Further, we propose a specialized numerical method for solving the resulting optimization problem. The method scales well with the increase of the number of observations. Additionally, we note that the obtained classifier is robust with respect to corrupted data or to situation when data is scarce. We demonstrate the advantages of the proposed framework in comparison to the support-vector machine framework and other methods handling fairness.
Digital twin technologies have the potential to improve operational flexibility and responsiveness capabilities of nuclear systems. To provide decision support, cyber event characterization, state estimation, predictive control, and real-time dynamic processing of operational data, however, an efficient digital twin needs to integrate multiple models (data-driven as well as physics-based) with explainability while at the same time maintain two-way synchronization with the physical facility at a time constant less than its operational cycle. In this work, we present the Purdue University Reactor One Digital Twin (PUR-1 DT), a cyber-physical digital twin with a complete high-fidelity physics-based and AI-driven virtual model stack (neutronics, thermal-hydraulics, point kinetics) which provides closed-loop explainable diagnostics, forecasting, predictive control, and action recommendation back to the reactor via two-way communications and a cyber-physical testbed. We demonstrate real-time synchronized state estimation and short-term forecasting over a full reactor operational cycle and conduct a series of benchmarking experiments to validate accuracy and latency. Our results show good agreement with experimental results and lay the groundwork for further development and experimental demonstration of DT-enabled functionalities in real-world facilities.
Vasileios Theos, Jonah Lau, Konstantinos Gkouliaras et al.· 0 citations
A new machine-learning framework aims to improve the success rate of computational protein design while moving away from results that reproduce sequences found in nature.
MIT News · Artificial Intelligence· news.mit.eduAug 24, 2026
A new method for surgically removing training examples from a model reveals that as datasets grow, the link between what a model learns and what it produces dissolves.
