Continual knowledge-updating methods are often declared superior from one final checkpoint and one conventional adapter rank. We show that this can be insufficient to identify the better operating point. Holding a periodic hierarchy fixed, we compare it with cumulative replay over a 24-month Wikidata stream while varying evaluation month, replay LoRA rank, and query formulation. The apparent winner changes across this region: on Qwen2.5-1.5B, the hierarchy's 5.0-point advantage over rank-8 replay becomes an 11.6-point deficit against rank-72 replay, and at high ranks a consolidation-aligned endpoint can suggest a tie while time-averaged replay leads by 9-13 points. The same rank-conditioned reversal appears on Llama-3.2-1B and held-out paraphrases.
These results show that method ranking in continual updating can depend jointly on when performance is measured and how much replay-side adaptation capacity the baseline receives. We therefore propose reporting trajectories and capacity sweeps, and declaring a robust winner only when the ordering is stable across the evaluation region; otherwise, comparisons should report winner regions and retention-stability-cost frontiers. Under this protocol, the periodic hierarchy is a lower-update-cost operating point, not a quality winner.
Attention mechanisms are central to modern foundation models, yet their training dynamics remain poorly understood, especially when the attention matrices have extensive rank. In this work, we study attention-indexed models, a broad framework that can represent multi-layer and multi-head attention architectures. First, we show that, in a suitable high-dimensional limit, the population-loss landscape is characterized by a finite set of trace order parameters. In contrast, online stochastic gradient descent (SGD) is governed by an infinite hierarchy of matrix moments, which we show can be exponentially well-approximated by a finite truncated system. Second, this framework reveals that attention parameterization itself can act as an architectural implicit bias. Direct optimization of an attention matrix $S\in\mathbb{R}^{d\times d}$ can remain trapped in an uninformative state. Tied attention ($S=WW^\top$) induces an automatic symmetry-breaking mechanism and yields weak recovery in $\Theta(d^2\log d)$ samples. For untied attention, $S=UV^\top$, we uncover a fast-slow mechanism: the pre-activation mean first evolves on a fast timescale, while the overlaps evolve on a slower one. Weak recovery on the $\Theta(d^2\log d)$ scale occurs when the state selected by the fast dynamics breaks the initial symmetry.
Yizhou Xu, Margarita Sagitova, Lenka Zdeborov\'a et al.· 0 citations
Federated Learning (FL) with Differential Privacy (DP) is increasingly adopted to preserve data confidentiality in distributed machine learning. However, DP noise distorts learned representations and degrades explanation fidelity, limiting differentially private FL where trustworthy explanations are required, such as assistive clinical diagnosis. Prior work adapted DP noise with static feature-importance signals, restricting explainability to post hoc analysis and precluding noise calibration to explanation quality during training. We propose XCal-FL, a closed-loop, explainability-driven local training algorithm for image classification in cross-silo FL that dynamically calibrates DP noise from three complementary signals: (1) prediction logit variations, measuring causal influence on model confidence, (2) counterfactual margins, capturing decision-boundary sensitivity, and (3) saliency concentration, quantifying spatial coherence of model attention, while enforcing formal DP guarantees via adaptive privacy accounting. Experiments on three medical imaging datasets across varying FL configurations show that XCal-FL yields more accurate and interpretable global models, improving predictive performance by over 10\% and explanation fidelity by up to 5$\times$ over static-noise FL, and outperforming state-of-the-art adaptive DP methods in fidelity. XCal-FL also achieves higher privacy-budget efficiency, turning each unit of cumulative privacy loss into larger gains in both accuracy and explanation fidelity. Our analysis further reveals that, unlike predictive performance, which scales roughly linearly with privacy loss, explanation fidelity exhibits non-linear dynamics. These findings suggest explainability is a distinct dimension of the privacy trade-off that cannot be inferred from utility alone, with implications for training and privacy-budget allocation in decision-critical applications.
Michael Khavkin, Kichang Lee, Jaeho Jin et al.· 0 citations
Offline reinforcement learning (RL) must reconcile two competing requirements: policy updates should stay near dataset-supported actions to keep value estimates reliable, yet meaningful gains often require moving beyond the behavior distribution. We develop a geometric view of offline actor updates by modeling policies as a probability manifold endowed with a chosen metric geometry. Under this lens, a broad class of offline actor objectives can be interpreted as a single proximal policy improvement step (SPI), i.e., an implicit discretization of a manifold gradient flow induced by a critic-defined energy. Building on this insight, we propose multi-step proximal policy improvement (MPI), a plug-in refinement mechanism that composes sequential re-centered proximal steps. MPI enables controlled policy improvement beyond dataset support while retaining proximal control at each refinement. The framework accommodates multiple policy geometries and admits practical instantiations for deterministic and diagonal-Gaussian policies. Experiments on D4RL benchmarks show that small numbers of MPI refinements improve strong offline baselines, including TD3+BC, ReBRAC, and IQL, on many tasks. Focused diagnostics further distinguish re-centered refinement from fixed-objective update scheduling and characterize limitations under critic error.
Energy consumption is one of the largest operational expenditure items for mobile network operators, yet site-level energy inefficiencies such as faulty cooling controllers, idle radio equipment, and parasitic auxiliary loads often remain undetected because no ground-truth inefficiency labels exist and historical measurements may already contain embedded inefficiencies. This study proposes an unsupervised peer-relative approach based on the premise that sites with similar structural and operational characteristics should exhibit comparable energy consumption. To capture these relationships, a novel energy-aware Minimum Distortion Embedding (MDE) formulation is introduced that extends the standard MDE objective with an energy-based repulsion mechanism. This encourages sites with anomalously high energy consumption relative to comparable peers to become displaced from their local neighbourhoods in the embedding space. The resulting low-dimensional representation simultaneously preserves structural similarity and encodes energy-related deviations, enabling the identification of potentially inefficient sites through peer-relative comparison. The derived anomaly scores provide a practical mechanism for prioritising field investigations, allowing mobile network operators to focus engineering resources on sites most likely to yield energy savings. Experimental results demonstrate that the proposed approach outperforms conventional anomaly detection baselines and provides a robust foundation for large-scale energy-efficiency optimisation in mobile networks.
Eliud Nyakweba Koto, Jaco du Toit, Adham Stoltz et al.· 0 citations
We study the ordered Bernoulli-word kernel f(p,n,k)=p^k(1-p)^(n-k) and the geometry generated by its inverse-integer level sets. The binary level 2^(-n) selects p=1/2 as the unique real split-independent anchor. Under complement-preserving complex continuation, the pair becomes z=1/2+iu and 1-z=1/2-iu, producing a conjugation-symmetric vertical geometry before any zeta-function input is introduced. The quadratic coordinate Q(z)=z(1-z)=1/4+u^2 has a sharp minimum at the central point and admits an exact integer quantization. For critical-line zero ordinates gamma_k, the induced levels L_k=1/4+gamma_k^2 are decomposed exactly as L_k=N_k+delta_k, where N_k is the nearest integer and delta_k is a periodic first-Bernoulli residual. Circularization gives Z_k=exp(2 pi i delta_k), isolating gamma_k^2 mod 1 as the residual phase variable. Unique factorization resolves the integer shells into prime-generator coordinates, while a distinct complex exponent s lifts the same construction to the Dirichlet atoms m^(-s), linking the Dirichlet-series and Euler-product assemblies. Exact identities, classical zeta connections, numerical controls, and open conditional Weyl tests are kept explicitly separate. No proof of the Riemann Hypothesis is claimed.
Athlete monitoring data may be recorded minute by minute throughout a match or training session, while injury information may only indicate whether the entire session was injury-associated.
This creates a modelling problem: assigning the same session-level label to every minute would imply that injury status is known at each exact time, even though within-session injury onset is unknown.
Our novelty is a fixed-landmark, one-representation-per-athlete-session formulation that directly addresses this mismatch. Instead of labelling every minute, we construct one representation per athlete-session at each landmark using information observed up to that point. This keeps the target at the session level and avoids unsupported minute-level injury supervision.
A landmark is a fixed time point within the same session, such as 10, 20, or 30 minutes. At each landmark, we assess whether the whole session is injury-associated or non-injury-associated and examine how discrimination changes as more within-session information becomes available.
Using 2020 SoccerMon data, we analyse 3,743 athlete-sessions from 48 elite women's football athletes, including 22 injury-associated sessions from five athletes. We evaluate pre-session, cumulative, dynamic, and combined representations with athlete-disjoint validation, athlete-cluster bootstrap uncertainty, common-cohort sensitivity analysis, alternative negative-athlete fold allocations, equal-athlete weighting, and Logistic Regression, Random Forest, and XGBoost benchmarks.
Primary CUM+DYN Logistic Regression yields ROC-AUC 0.367-0.607 and PR-AUC 0.0080-0.0150 across landmarks, with wide uncertainty. PRE-containing representations show higher point estimates at several landmarks but remain uncertain.
Institutions practising outcome-based education compute learning outcome attainment routinely, while reviews of curriculum analytics report an absence of evidence on how that computation informs decisions. This paper presents OBER+, an extension of a deployed institutional attainment platform that computes the step from a measured shortfall to an evaluated corrective action. Five connected stages accumulate attainment across deliveries of a course, signal a shortfall and a persistent shortfall, grade it on cutoffs the regulator already uses, record the decision against a catalogue of practices annotated with their evidence, log the change, and quantify the subsequent movement in the shortfall. A further rule compares successive statements of an outcome, so attainment is never read as a series across a point at which the outcome changed. Applying the rules to the live record of two real courses produced three results. Every outcome of a core course was substantively redefined between consecutive deliveries, with subject matter moving between outcome numbers, so a naive reading would have reported a twenty-five point collapse between quantities that do not refer to the same learning. Recomputing the platform's figures from its documented rule showed six of ten differing by more than rounding explains, in a pattern that identified a defect since reported to the institution. Across fifteen statement pairs from three transitions, five were identical character for character, and among the ten that were not, the outcome carrying a given number was nearest to a differently numbered earlier outcome in six, a result resting on an ordering of similarities and requiring no threshold and no labelling. The contribution is a computational design for outcome-based reporting, stated as rules any attainment platform can implement, with evidence of what they make visible in a live institutional record.
Accurate cloud-cover forecasts are important for temperature prediction, radiation forecasting, and solar-power operations. Short-range forecasting methods can preserve observed cloud placement during the first forecast hours, but their skill decreases when cloud fields evolve through formation, dissipation and deformation. Longer lead times require accounting for atmospheric evolution, but operational numerical weather prediction (NWP) forecasts may not accurately represent the satellite-observed cloud state at initialization. We develop CloudCast v2, a machine-learning model for 12-hour cloud-cover forecasting from observation-based initial conditions. The model is first trained on the Copernicus European Regional Reanalysis (Ridal2024) to learn cloud-evolution dynamics, and is then adapted to satellite-derived cloud fields using conditional flow matching (Lipman2023), a generative method that transforms noise into cloud-cover forecasts conditioned on the observed initial cloud fields and NWP inputs. CloudCast v2 reduces mean absolute error by 10% relative to its predecessor, CloudCast v1 (Partio2025), over the 1-12 h range. It also overtakes CloudCast v1 in fractions skill score, a neighborhood-based measure of spatial agreement, after approximately 3-6 h, depending on the cloudiness category. These results show that observation-initialized machine-learning forecasts can extend beyond the usual 1-3-hour nowcasting range while retaining spatial detail from satellite cloud fields.
Mikko Partio, Leila Hieta, Ossi Laine· 0 citations
The computation of the Bures-Wasserstein (BW) barycenter of an ensemble of positive definite matrices arises throughout machine learning, optimal transport, and quantum information. Riemannian gradient descent (RGD) at unit step size -- the fixed-point iteration used in practice -- converges rapidly, yet existing analyses present a dichotomy: unit-step guarantees carry worst-case exponential dependence on the dimension, while dimension-independent guarantees require small step sizes that forfeit the empirical speed. We resolve this dichotomy, not by improving the guarantees for unit-step RGD, but by proposing a Projected RGD algorithm that achieves dimension-independent linear convergence at unit step size. The achieved rate, $(1 - \kappa^{-3/2})$, where $\kappa$ is the condition number of the ensemble, also polynomially improves on the best small-step guarantee ($\kappa^{3/2}$ versus $\kappa^{5/2}$ iteration complexity). The crux is a novel Projection Lemma: clipping the eigenvalues of a positive matrix to an interval $[\alpha, \beta]$ is the closed-form, non-expansive (1-Lipschitz) BW-metric projection onto the set $\{S : \alpha I \leq S \leq \beta I\}$ -- a statement which, unlike its known one-sided counterpart, does not follow from convexity. The projection is moreover free: it reuses an eigendecomposition the next iteration must perform in any case, so the projected and unprojected iterations cost the same per step. The same analysis covers the invariant matrix projection problem of Brahmachari et al. (2025), whose fixed-point algorithm we identify as unit-step RGD on a totally geodesic submanifold, thereby extending the dimension-independent guarantee to that setting verbatim.
In this paper we study linear non-Gaussian acyclic models (LiNGAM) when used in federated environments. These causal models allow one to go beyond Markov equivalence. However, in many domains data are scarce, and increasing the sample size by centralising data from different clients is not advisable due to regulations such as the GDPR. The federated environment offers an attractive option to balance privacy and causal discovery accuracy. Unfortunately, the standard centralised estimator in the LiNGAM setting, i.e., DirectLiNGAM, cannot be straightforwardly federated. Higher-order cumulant tensors offer a way around this obstacle: they depend only on the joint distribution of the variables involved and add exactly across independent sample groups, so a single communication round suffices in horizontal, vertical, and hybrid partitions.
However, FedISHC, i.e., the current federated method along these lines, breaks down under near-symmetric noise. To overcome the above limitation, we introduce the FedRCD family of causal discovery algorithms, and investigate three variants that trade off communication rounds against algebraic noise; two of them are exact federated counterparts of the centralised high-order cumulant (HC) and HC-LiNGAM algorithms, and the single-round variants further effectively support exact unlearning at any granularity, from a single observation to a whole client. Numerical experiments show that at sample sizes typical of real deployments, the entire cumulant-based federated family does not actually rank variables by the population asymmetry that the scores encode at zero. It ranks them by a variance ladder induced by the DAG along its directed paths, the cumulant counterpart of varsortability. Marginal standardisation collapses every cumulant method to near-random ordering, while scale-invariant DirectLiNGAM, not federable under this protocol, is unaffected.
Pablo Torrijos, Fabio Stella, Jos\'e A. G\'amez et al.· 0 citations
Experimental design is commonly framed as choosing the experiment expected to provide the most information. Under partial identifiability however, persistent nuisance uncertainty can make the same observation carry different structural meanings. We introduce Resolution-Aware Experimental Design (RAED), which selects an experiment by the smallest expected nonempty structural candidate set achievable subject to false-exclusion control. We prove an exact cross-nuisance aliasing separation: an experiment can be preferred by structural and full-latent information gain, average classification, and nuisance-marginalized informativeness while having arbitrarily poorer valid structural resolution. RAED nevertheless preserves the expected ordering under a genuine composite Blackwell comparison. To make this criterion operational, we develop a learned score-based implementation with finite-sample nuisance-average and positive-tail calibration, and characterize a rare-tail sample-complexity obstruction. Under constrained sensing, two subsurface-flow benchmarks exhibit genuine RAED--expected-information-gain (EIG) experiment-selection disagreements, with the clearest and largest held-out resolution differences in WCA. In a fluvial benchmark, tail protection changes the selected physical experiment and replaces hard-region false exclusions primarily with explicit ambiguity. In a mechanistic methane-oxidation benchmark, a prospectively specified 5\% false-exclusion tolerance also yields a nontrivial finite-sample population guarantee for tail-sensitive nuisance risk, with 95\% joint confidence across all three structural families.
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.
