We study when and how momentum improves large-batch training in the one-pass regime, using power-law kernel regression as a tractable setting. We first characterize risk stability through the critical learning rate, defined as the largest learning rate for stable training, and obtain $\eta_{\mathrm{SGD}}^{\mathrm{crit}}\eqsim 1$, $\eta_{\mathrm{Polyak}}^{\mathrm{crit}}\eqsim \min\{1,B(1-\rho)\}$, and $\eta_{\mathrm{Nesterov}}^{\mathrm{crit}}\eqsim \min\{1,B^\beta(1-\rho)\}$, where $B$ is the batch size, $\rho$ is the momentum factor, and $\beta>1$ is the capacity exponent. Within this admissible region, we derive scaling laws for the full risk dynamics, capturing the progression from an early transient, through power-law decay, to a noise floor. We then minimize the final-step risk over the admissible learning rates and momentum factors under a fixed data budget, yielding a three-regime batch-size phase diagram that reveals how the role of momentum changes with batch size. Notably, Polyak enlarges the critical batch size, the largest batch size preserving the best small-batch data-scaling exponent, thereby enabling greater parallelism without sacrificing data efficiency. In contrast, Nesterov achieves better data efficiency in the large-batch regime because its look-ahead mechanism suppresses noise accumulation. Numerical experiments validate the predicted stability boundaries, risk dynamics, and batch-size phase diagram.
Jia-Nan Wang, Zixun Huang, Kairui Li et al.· 0 citations
We approximate strongly continuous convex monotone semigroups by learning their Chernoff-type one-step operators with neural operators. First, we introduce the general class of so-called Chernoff-neural operators and show in a universal approximation theorem that they can approximate the Chernoff one-step operators arbitrarily well. By using stability estimates between weighted H\"older spaces, the one-step approximation error can be propagated through the iterations which yields universal approximation of the corresponding semigroup. Second, we introduce the more specialized class of envelope-neural operators for envelope semigroups which allows us to derive quantitative approximation rates. Finally, we illustrate the effectiveness of these neural operators in several numerical examples arising from non-linear partial differential equations, stochastic optimal control and stochastic processes under model uncertainty.
Jonas Blessing, Philipp Schmocker, Alessandro Sgarabottolo· 0 citations
Modern portfolio management increasingly demands a balance between traditional risk-adjusted returns and strict Environmental, Social, and Governance (ESG) mandates. Current Reinforcement Learning (RL) approaches typically optimize for a single ESG provider, neglecting the significant divergence in rating methodologies across the industry and the unintuitive nature of manually weighting conflicting objectives. This paper addresses these limitations by formulating ESG-aware portfolio optimization as a Multi-Objective Reinforcement Learning (MORL) problem that simultaneously incorporates ratings from three distinct ESG agencies. To bridge the gap between high-dimensional algorithmic trade-offs and human decision-making, we integrate a Preference Elicitation framework using Gaussian Processes. This system enables practitioners to infer their latent utility functions through intuitive pairwise comparisons of candidate portfolios based on their Sharpe ratios and aggregate ESG scores. We systematically evaluate our framework by employing Large Language Model (LLM) personas to simulate Portfolio Managers operating under varied regional contexts. Empirical results using historical market data reveal that regional backgrounds fundamentally shift the derived preference weights. For instance, European-based personas tend to prioritize ESG alignment over financial returns, while Texas-based personas favor risk-adjusted performance. This work offers a highly adaptable framework that successfully aligns multi-objective algorithmic trading with diverse, real-world human sustainability preferences.
Giovanni Dispoto, Marcello Restelli, Carmine Ventre· 0 citations
Hyper-Connections (HC) replace the single residual stream of a Transformer with $n$ parallel ones, mixing them at every layer with a learned $n \times n$ residual matrix. Leaving that matrix unconstrained places no limit on the factor by which the mixing step rescales the residual streams, and that factor compounds across layers, which destabilizes training. Manifold-constrained Hyper-Connections (mHC) address this by restricting the matrix to the doubly stochastic matrices. That caps the factor at one, so the mixing can no longer amplify any direction, but nothing bounds it from below. We prove that inside this set the mixing step can reduce the norm of the residual streams only by shrinking the differences between the streams, while their mean is left unchanged; and since the reduction accumulates over layers, the streams grow more alike and their diversity is spent with depth. We therefore propose Orthogonal Hyper-Connections (oHC), restricting the residual matrix to the rotation group $SO(n)$, so that the mixing step can neither amplify nor attenuate the residual streams in any direction, which keeps training stable and no longer forces the differences between the streams to contract. Specifically, at the four streams used by recent HC models we parameterize the group in closed form by a pair of unit quaternions, which adds no parameters, replaces the iterative projection with a fixed pattern of signed additions, and can be constructed faster than mHC. We evaluate oHC across a comprehensive set of downstream tasks, where it outperforms the single-stream residual baseline, mHC and iHC, which fixes the residual matrix to the identity.
Haoqiang Guo, Xuyi Chen, Bo Ke et al.· 0 citations
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The pairwise independent correlation gap is the ratio of the maximum expected value of a set function under arbitrary dependence to that under pairwise independence, measuring the loss from this independence restriction. Under mutual independence, this gap is universally bounded by $e/(e-1)$ for monotone submodular functions. With pairwise independence, a tighter $4/3$ upper bound was established for several special cases, including $n=3$, and conjectured to hold universally. A recent AI-assisted counterexample disproved this conjecture for $n=5$, leaving the validity of the $n=4$ bound and the tight worst case bound open.
We resolve both questions. First, for $n=4$, we establish that the $4/3$ bound holds universally and is tight using an AI-assisted proof combining theoretical analysis and computational verification. The proof combines a structural characterization of optimal numerator vertices, permutation symmetry, cone certificate systems, Bernstein polynomial representations, recursive simplex subdivision, and verification of $2,745$ Bernstein coefficient systems. Second, we show that the worst case pairwise independent correlation gap attains $e/(e-1)$ asymptotically by constructing an instance with identical marginal probabilities and a monotone submodular union coverage function on a ground set partitioned into $m$ blocks. The number of blocks grows sublinearly with the ground set size. The result follows by constructing a feasible solution to a scaled asymptotic reduced dual of the pairwise independent linear program and immediately extends to $t$-wise independent random elements ($t\ge2$), since $t$-wise independence implies pairwise independence. Thus, pairwise independence, despite being the least restrictive form of independence in the $t$-wise independence hierarchy, can be as restrictive as mutual independence in the worst case.
Voice actors often re-read the same script while modifying their delivery in response to performance directions. We study this setting as direction-following TTS, where a system generates a new utterance that reflects a given direction relative to a reference utterance while preserving speaker identity and linguistic content. A key challenge is the lack of training data capturing such relative modifications. To address this, we propose a scalable pseudo-triplet construction pipeline that generates~(reference utterance, direction text, modified utterance) triplets. It generates controlled style variations using an impression-controllable TTS model and uses an LLM to produce natural language directions from estimated impression differences. Experimental results demonstrate that pseudo-triplets alone enable stable speaker-preserving modification, and that combining pseudo and recorded data further improves direction alignment while maintaining speaker similarity. Audio examples are available on our demo page https://ntt-hilab-gensp.github.io/IS2026pseudo/
Volumetric video based on point cloud representations enables immersive virtual and augmented reality applications but introduces significant challenges for efficient and secure content delivery. Prior work proposed a selective coordinate encryption framework for point clouds that encrypts only a subset of coordinates, reducing computational costs while visually degrading unauthorized content. However, it remains unclear whether the remaining unencrypted information is sufficient to enable content reconstruction.
In this paper, we evaluate the robustness of selective coordinate encryption against machine learning-based reconstruction attacks. We consider an attacker with access to selectively encrypted point clouds attempting to recover encrypted coordinates without decryption by exploiting spatial and geometric correlations in the unencrypted data. We evaluate PointNet and Random Forest models under two encryption granularities: \texttt{X}, where all $X$ coordinates are encrypted, and \texttt{2X}, where every second $X$ coordinate is encrypted.
Our results show that reconstructing fully encrypted $X$ coordinates remains challenging, whereas the \texttt{2X} scheme leaks sufficient information through neighboring coordinates to enable accurate reconstruction. These findings demonstrate that the security of selective coordinate encryption depends strongly on encryption granularity.
Mohammad Waquas Usmani, Susmit Shannigrahi, Michael Zink· 0 citations
We study body-only, 12-class acted-emotion classification from skeleton motion under leave-performer-out (LPO) evaluation, a hard, underdetermined setting: chance is 8.3%, and a protocol-matched reproduced STGCN++ baseline reaches only 25.73 +/- 4.03% Macro-F1. We show that reliable gains come not from a new architecture but from combining eleven models with orthogonal error modes: under 10-fold LPO cross-validation on the labeled training performers, an equal-weight logit-mean ensemble reaches 36.80 +/- 4.00% per-fold Macro-F1, a protocol-matched +11.07 pp (+43% relative) over the same-split reproduced baseline. Our central contribution is a tested explanation suite: for a strong ensemble member, part-masking and counterfactual edits show (rather than assert) that its decisions depend on motion-grounded body-region evidence, and this region saliency aligns with rule-based Laban Movement Analysis (LMA) attributes far more than with classical kinematics: region-level saliency-LMA Spearman rho = +0.500 versus +0.033, roughly 15x, and the alignment holds for the submitted 11-way ensemble itself at rho = +0.517; the audit is post hoc and needs no retraining. The same suite faithfully reports a negative: within-window temporal saliency is diffuse rather than localized.
Recommender-system experiments often rely on a single random training seed, assuming that run-to-run stochasticity has limited impact on evaluation conclusions. This assumption is risky, as a training seed may influence several algorithm-dependent mechanisms, including parameter initialization, mini-batch ordering, dropout, masking, latent sampling, and training-time negative sampling. We examine this assumption by fixing the data partition and varying the training seed across hyperparameter configurations. We analyze seed effects at three levels: user-level metric sensitivity, validation-based model selection and recommendation-list agreement. Results show that seed variation is often detectable. Its impact depends on whether configurations are clearly separated, whether validation results transfer to test, and whether similar scores lead to similar top-$k$ lists. Findings suggest that reporting single-seed results can overstate the stability of recommender system evaluation, and that training seeds should be treated as part of the evaluation protocol rather than as incidental implementation noise.
Juan Manuel Rodriguez, Oleg Lesota, Antonela Tommasel· 0 citations
Large language models can look capable of logical reasoning, but correct or incorrect answers alone tell us little about what the model represents internally. We study logical verification in five open-weight transformer models using matched valid--invalid premise--claim pairs that vary across inference families, semantic domains, templates, and difficulty levels. Despite near-chance behavioral performance, logical validity is often almost perfectly decodable from hidden states and remains strongly decodable under held-out templates, domains, and inference families. Validity also remains highly decodable on behaviorally incorrect examples in the conditions where correctness-conditioned evaluation is well defined. At the same time, exhaustive leave-one-out tests reveal clear limits to this generalization, and interventions along probe-derived validity directions have only weak, nonspecific effects compared with random controls. Our results suggest that representing validity, expressing it in behavior, and using it causally are distinct. Validity related information can be strongly decodable from a model's hidden states without being reliably expressed in its output.
Gaussian graphical models (GGMs) are essential tools for interpretable structure learning. However, in high-dimensional, small-sample regimes, the available data is often insufficient for the maximum likelihood estimator to exist. Colored Gaussian graphical models (CGGMs) mitigate this limitation by imposing symmetry constraints through graph coloring, which reduces the required sample size. This minimal number of observations needed to guarantee that the estimator exists almost surely is defined as the maximum likelihood threshold (MLT). Here, we address the computation of the MLT for CGGMs by focusing on its geometric formulation: finding the minimum rank of a sample covariance matrix such that its projection lies almost surely within the interior of the cone of sufficient statistics. We establish a unified theoretical framework, extending results from uncolored to colored models and introducing new symbolic algorithms. Furthermore, we present a computational study integrating sampling with topological data analysis (TDA) to investigate the local geometry of the cone of sufficient statistics. Our results demonstrate the potential of TDA to overcome the computational bottlenecks of traditional symbolic algebraic methods, particularly Groebner basis computations, in analyzing the likelihood geometry of CGGMs.
Roser Homs, Olga Kuznetsova, Bernadette J. Stolz· 0 citations
Humanoid robots responding to emergency stop commands typically execute a fixed maneuver, without reasoning about whether a safe stop is actually feasible from the current state. We cast emergency stopping as a reach-avoid problem and propose Safe-Stop, a task-agnostic framework that pairs a learned stop policy with learned stoppability estimators. The estimators are complementary: a stop-probability estimator supervised by the actual outcomes of the fixed stop policy, and a reach-avoidance estimator supervised by a Hamilton-Jacobi backup over physical state. The first captures emergent stopping behavior of the learned controller; the second provides a complementary recoverability signal. Because the stop policy and estimators do not depend on the behavior policy that preceded the stop command, they transfer across diverse upstream tasks without retraining. At deployment, the two estimates are combined: Safe-Stop commits to the stop only when both estimators indicate that stopping remains feasible, otherwise it hands off to a fall policy, instantiated as a damping fallback. This agreement check yields decisions that are robust without sacrificing reactivity.
Junfeng Long, Pieter Abbeel, K. Sreenath 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.
