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This research proposes a two-level keystroke dynamics authentication system that provides defense-in-depth security through continuous behavioral drift monitoring. Level 1 employs fixed-text password authentication using Temporal Convolutional Networks (TCN) with contrastive learning and population-based training (PBT), achieving 3.77% EER for high-security login verification. Upon successful authentication, Level 2 continuously monitors user typing during natural free-text sessions using a 4-Model Deep Learning Ensemble. If suspicious behavioral drift is detected during monitoring, the system re-authenticates the user by returning to Level 1, providing a feedback loop against session hijacking and behavioral anomalies. The system explicitly models long-term behavioral drift through the fixed-text component's PBT mechanism, which adapts to temporal variations in password typing patterns. This research leverages free-text (Buffalo dataset) and fixed-text (GREYC dataset) keystroke dynamics datasets, extracting temporal and spatial features including hold times, up-down latencies, down-down intervals, and trigram patterns. The final system achieves 96%+ accuracy for fixed-text authentication (3.77% EER) and 83.53% True Acceptance Rate (TAR) at 5% False Acceptance Rate (FAR) for free-text continuous authentication (10.05% EER), demonstrating superior performance and strong resistance to impostor attacks through continuous behavioral monitoring.

We prove that, with high probability, refuting a random $k$-CNF formula on $n$ variables with ${M = n2^{k}}$ clauses for $ω_n(1) \leq k \leq O(\log{n})$ requires polynomial calculus degree at least ${n/2-O(n/\sqrt{k})}$ over every field. Through Pang's recent tradeoff between $\mathsf{AC}^0[p]$-Frege size and polynomial calculus degree [Pang 2026, arXiv:2610.00837v2], this implies a size lower bound of $\exp(Ω_p(\sqrt{k} \log{n}))$ for depth-$2$ $\mathsf{AC}^0[p]$-Frege. In this range of $k$, the bound is superpolynomial in $M$ while $M \leq \mathrm{poly}(n)$. We also prove a nearly matching degree upper bound of $n/2-n\ln(k)/{2k} +O(n/k)$, which shows that other formula families are needed to obtain lower bounds for full $\mathsf{AC}^0[p]$-Frege through Pang's tradeoff.

Model combination offers an alternative to selecting a single forecasting model, particularly when individual models are sensitive to random initialization and hyperparameter choices. We study online aggregation through Follow-the-Leader (FTL) and Hedge-type algorithms, with an application to ensembles of Multi-Frequency Echo State Networks (MFESNs) for macroeconomic forecasting. On the theoretical side, we derive Hoeffding- and Bernstein-type expected-regret bounds for FTL and decreasing Hedge under independent and $\varphi$-mixing expert losses. Under a positive gap between the best expert's expected loss and those of its competitors, the bounds are uniform in the number of forecasting rounds and exhibit logarithmic dependence on the number of experts. Monte Carlo experiments investigate the effects of temporal dependence and the separation between experts' expected losses. Empirically, we construct MFESN ensembles for forecasting U.S. quarterly GDP growth using mixed-frequency macroeconomic and financial indicators. The results show that adaptive aggregation, particularly FTL and AdaHedge, achieves substantial reductions in out-of-sample mean squared forecasting error relative to individual MFESN models and conventional forecast combinations.

Despite growing capabilities, LLMs remain susceptible to prompt injections: malicious inputs that can manipulate or hijack models. In particular, it has recently been observed that LLMs can exhibit role confusion (Ye et al., 2026), where models attribute the source of text based on its style instead of its labeled role. Malicious text in tool outputs (for instance, a malicious webpage accessed by an agent) can leverage role confusion to impersonate the user, an attack we call role spoofing}. In this work, we seek to understand and mitigate role spoofing. We study how models track "who said what" in a conversation, showing that they use cues from both content (e.g., semantics and writing style) and structure (e.g., control tokens and formatting). We show that LLMs are highly susceptible to role spoofing attacks that combine both fake structure and content. Additionally, in a toy setting, we show that adversarial training which teaches the model to ignore content-based injections does mitigate content-based attacks but leaves the model susceptible to structure-based attacks. This can explain why frontier models, with increased resistance to many injection attacks, can still be susceptible to role spoofing. Finally, we propose a new method for detecting role spoofing using linear probes trained to predict roles in a conversation, and show that it is effective across different settings.

Mathematical supervision for language models is typically flattened into isolated problem-solution pairs, discarding the curricular organization and evidential structure of the original sources. We introduce TOME-Math (Textbook-Oriented Mathematical Evidence), a large-scale corpus that converts 2,118 textbooks spanning the core areas of university-level mathematics subjects into approximately 380K structured proof-supervision records while preserving chapter order, proposition-proof links, dependency references, and source provenance. Leveraging these structural signals, we explore curriculum learning across multiple mathematical subjects and characterize scaling patterns with supervision volume and source breadth. At full scale, fine-tuning on TOME-Math raises the unweighted mean score across our held-out evaluations and established public benchmarks by 16.7 percentage points over the base model, while exceeding all three public instruction-data baselines evaluated in aggregate. Our findings highlight structured textbooks as both a scalable source of mathematical supervision and an empirical framework for studying the impact of data organization on mathematical reasoning. We will release the corpus to facilitate further research on structured mathematical supervision.

We consider the problem of finite-sample identification of an unknown LTI system from a finite hypothesis class. In contrast to existing results that assume the hypothesis class contains the true system, we consider the misspecified setting, where the true system does not belong to the hypothesis class. We first characterize the resulting estimation target and its dependence on the data-generation scheme. We then establish a finite-sample lower bound on the failure probability that any identification algorithm must incur. Finally, we analyze the robustness of an existing exponential weighting-based identification algorithm to the misspecification and derive a finite-sample upper bound on its failure probability. Our results illustrate when using a misspecified finite hypothesis class can provide an advantage over identification without prior knowledge of the candidate systems.

This paper sets out what a sustained federal research and investment agenda would need to include to close that gap--not within a single budget cycle, but over the decade such an undertaking will realistically require. It identifies where the gap is most pronounced today: in the methods needed to verify and certify components of uncertain origin, in the foundational hardware research that has long been underfunded relative to software, in the physical infrastructure researchers need to test systems at scale, and in the workforce required to build and sustain all of it. Robotics should not be treated merely as a downstream beneficiary of a broader artificial intelligence investment strategy. It constitutes its own supply chain, with its own points of failure, and merits its own sustained federal commitment.

Machine learning continues to emerge as an important tool to be utilised within structural engineering and structural health monitoring, due to its ability to accurately and quickly perform both regression and classification tasks. However, a purely data driven approach has its limitations, particularly where we lack data from relevant environmental and operational conditions, a situation that has led to the development of physics-informed machine learners for structural health monitoring. These "grey-box" models take into account the physical insight that an engineer would have about the structure they are modelling and have shown promising results in the structural engineering field among many others. This work compares black and grey-box models through a "green" lens, comparing them in terms of their environmental impact, and investigating how the high extrapolative performance of grey-box models can reduce their runtimes and therefore carbon emissions. The authors aim to develop physics-informed models with reduced computational costs, while maintaining high performance, illustrated through a structural health monitoring case study.

With the emergence of massively parallel processing units, parallelization has become a desirable property for new sequence models. The ability to parallelize the processing of sequences with respect to the sequence length during training is one of the main factors behind the uprising of the Transformer architecture. However, Transformers lack efficiency at sequence generation, as they need to reprocess all past timesteps at every generation step. Recently, state-space models (SSMs) emerged as a more efficient alternative. These new kinds of recurrent neural networks (RNNs) keep the efficient update of the RNNs while gaining parallelization by getting rid of nonlinear dynamics (or recurrence). SSMs can reach state-of-the-art performance through the efficient training of potentially very large networks, but still suffer from limited representation capabilities. In particular, SSMs cannot exhibit persistent memory, or the capacity of retaining information for an infinite duration, because of their monostability. In this paper, we introduce a new family of RNNs, the memory recurrent units (MRUs), that combine the persistent memory capabilities of nonlinear RNNs with the parallelizable computations of SSMs. These units leverage multistability as a source of persistent memory, while getting rid of transient dynamics for efficient computations. We then derive a specific implementation as proof-of-concept: the bistable memory recurrent unit (BMRU). This new RNN is compatible with the parallel scan algorithm. We show that BMRU achieves good results in tasks with long-term dependencies, and can be combined with SSMs to create parallelizable hybrid networks that have both transient dynamics and persistent memory.

Diffusion models have become the leading paradigm in generative modeling, yet many applications require sampling from distributions that are not those of any single pretrained model, but are instead defined through combinations of several models, possibly tilted toward high values of a downstream reward. Naively combining the scores of the models yields incorrect samples, while existing corrections are restricted to specific families of targets. In this work, we introduce the generalized Feynman-Kac correctors (GFKC), a principled framework for sampling from an arbitrary target function of several pretrained diffusion models. We show that the geometric interpolation between an arbitrary initial function and the target function of the models satisfies a Feynman--Kac partial differential equation, and derive its potential in closed form. To evaluate this potential during generation, we further generalize the log-probability ODE to track the density of each model along trajectories driven by a different velocity field. The resulting algorithm operates entirely in the log domain, incorporates reward-based steering at no additional conceptual cost, and corrects the generation on the fly, without retraining or fine-tuning the models. We validate the method on analytic Gaussian models, where it closely matches the ground-truth targets, and on diffusion models trained on MNIST, where it samples from non-trivial combinations of the models and enables effective steering.

The last year has seen a shift in AI-assisted mathematics, with frontier language models producing proofs of and counterexamples to long-standing open conjectures. However, studying only the current set of major breakthroughs provides an incomplete picture of LLM capabilities and the computational resources needed to achieve reported results. To address this, we introduce a new dataset, OpenConjecture, which collects conjectures from mathematics papers published on the arXiv since February 2026. We use these conjectures as a source of open mathematical problems, and apply frontier GPT models to a random sample of 200 of these conjectures over three passes using a reproducible protocol without problem-specific mathematical guidance. Rather than attempt expert verification of these candidate solutions, we analyze the types of problems for which LLMs produce solutions and the characteristics of these solutions. The models we test produce candidate solutions for roughly 60% of the conjectures, with counterexamples about 1.3 times more common than proofs. We estimate solution novelty, assess how solutions cite and relate to existing literature, and analyze whether the proposed resolution relies on either an error in or underspecification of the conjecture. We find that models sometimes propose resolutions that are outside the authors' intent (e.g., proposing the trivial group as a counterexample) and that a number of proofs follow closely from existing results, but that some resolutions exhibit at least moderate novelty. Our findings underscore the need for evaluations that go beyond correctness to assess fidelity to the intended statement, attribution, and the nature of the mathematical contribution.

Large language model (LLM) agents are proposed for clinical prediction but are untested in pediatrics, where cohorts are small and outcomes are uncommon. Using records from 2,489 youth with type 2 diabetes (T2D) and 4,018 with type 1 diabetes (T1D), spanning structured data, note-derived social determinants and, in T1D, continuous glucose monitoring data, we predicted seven T2D outcomes, four also in T1D, at 24 months from 18 months of follow-up. CEDAR (Clinical Evidence-Driven Agent for Risk-prediction), an evidence-citing, self-auditing LLM pipeline, outperformed trained machine learning in both cohorts (pooled area under the receiver operating characteristic curve 0.815 versus 0.656 to 0.700 in T2D and 0.756 versus 0.603 to 0.631 in T1D), most on the sparsely screened outcomes. Only 4 of 70,246 values it cited did not match the chart. Reading only the evidence and reasoning cited by CEDAR, two pediatric endocrinologists reached the same prediction as CEDAR in about nine of ten cases, agreeing with each other on 90.5%.

Recently, Guilmant, Lefaucheux, Ouaknine, and Worrell [2] proved decidability of the termination problem for linear constraint loops over two real-valued variables, thus settling a wellknown open problem. Their algorithm is based on a theoretical result that such a loop does not terminate if and only if it has a witness of an infinite run of a specific shape. By analysing the structure of the witness carefully, we show that termination such loops can be decided in polynomial time, improving on the polynomial space bound argued by Guilmant et al. We also present an efficient implementation of the polynomial-time algorithm based on the satisfiability modulo theories (SMT) solver Z3.

Logic-based workflow patterns capture recurring behavioural structures together with reusable temporal specifications. Their composition raises distinct problems as workflow structures become richer, including instantiation, nesting, conditional execution, repeated occurrences, and traceability of generated formulae. This paper proposes a hierarchy of Pattern Composition ($ΠC$) procedures, from $ΠC_0$ to $ΠC_4$, that organizes these requirements as progressively richer compositional capabilities. The hierarchy separates compositional complexity from the expressive power of the temporal-logic fragment, represented by $TL_j$, yielding a framework $ΠC_i[TL_j]$ for developing logical workflow specifications. We develop activation-aware Pattern Composition ($ΠC_2$), which distinguishes the structural presence of a nested pattern from its execution in a particular workflow context. We formalise its recursive procedure, analyse its properties, and define an evaluation protocol for conditional activation, conservativity under mandatory composition, and specification growth. The hierarchy also characterizes selective occurrence qualification for iterative patterns ($ΠC_3$) and provenance for tracing generated formulae to their sources ($ΠC_4$). Finally, we outline $ΠC_{\mathrm{Assist}}$, an orthogonal mode in which AI proposes and refines pattern expressions subject to the hierarchy's compositional checks.

Vision-Language-Action (VLA) models have demonstrated promising capabilities in robotic manipulation by integrating visual perception, language understanding, and action generation. Recent advances have further incorporated future prediction to enhance the understanding of environmental dynamics and task progression. However, existing methods often model short-term dynamics and long-term task objectives separately, while directly incorporating predicted futures into action policies without sufficiently considering their relevance to current action requirements. To address these limitations, we propose HiFOR, a hierarchical foresight framework with action-guided world retrieval. Specifically, Hierarchical Foresight Prediction jointly predicts short-term state evolution, semantic milestones, and final goal states through a Hierarchical Dependency Mask (HDM), establishing dependencies across temporal horizons. Building upon these predictions, Structure-Aware Latent World Modeling organizes future latent representations along the horizon, view, and spatial dimensions to facilitate fine-grained retrieval. Furthermore, Action-Guided Factorized World Retrieval adaptively retrieves relevant future information from the structured latent world based on evolving action representations during denoising, providing targeted guidance for action generation. Extensive experiments on two simulation benchmarks and six real-world robotic manipulation tasks demonstrate the effectiveness of our approach.

Zero-shot text-to-speech (TTS) models clone a target voice from a short reference clip, commonly referred to as the prompt. In practice, the prompt has to be cut from a longer recording of the speaker, so which part to use must be chosen. To understand what makes a good prompt, we analyze hundreds of thousands of outputs synthesized by four TTS models from candidate prompts of YouTube recordings. The choice of prompt substantially changes intelligibility, naturalness and speaker similarity. Standard predicted-quality scores capture mainly the naturalness part but miss most of the intelligibility gain. We find that the models largely agree on which prompt yields the highest measured speaker similarity, but much less on which prompt yields intelligible speech. We propose a small network that learns from the outputs a TTS model produced to rank a recording's candidate prompts from their audio alone. Without synthesizing anything at selection time, it picks prompts that lower the word error rate on held-out recordings by a third (Qwen3-TTS) to two fifths (F5-TTS) relative to a randomly chosen prompt, more than predicted quality achieves and nearly as much as synthesizing a dozen test sentences from every candidate first.

Large language model (LLM) agents for personal health read wearable data and recommend, but do not learn about the individual in a way that can be audited or falsified. We present EpiCoach, an agentic system that treats one athlete, a cross-country mountain biker, as the subject of accountable N-of-1 science. Claims about the athlete live in an evidence-gated hypothesis registry: each must issue a probabilistic prediction about a future session before it occurs, and its belief moves only through computed evidence from a logged statistical fit. Predictions come from a mechanistic digital twin inferred from heart rate, GPS and barometric altitude: a lagged heart-rate response model, a fitness-fatigue model with learned time constants, and a latent technical-descending skill state, measured on discovered trail segments. The agent prescribes the next training week as a constrained experiment maximizing information gain subject to load and safety constraints, around two instrument rides. We evaluate the system two ways over eighteen months of data. A rolling-origin replay benchmark shows the twin beats standard forecasters on heart rate but not segment time, and the agentic loop matches a static model. A live prospective phase runs the weekly cycle: in its first three weeks the ledger sealed 20 predictions, scored 14, the descent forecast calibrated after one correction, the climb forecast pessimistic as the athlete improved, and the safety officer vetoed the agent twice. Every correction is preserved in the registry, a template for auditable, falsifiable personalization in digital health. We release the registry, benchmark and protocol.

Graphical User Interfaces (GUIs) serve as the dominant medium for human-computer interaction, yet building GUI agents that generalize across the vast diversity of real-world interface environments, with the same flexibility and robustness that humans naturally exhibit, remains unsolved. Notably, GUI data are inherently non-stationary: the continual emergence of previously unseen interface instances (e.g., novel domains and resolutions) induces persistent distribution shifts, significantly impeding the continual learning of existing GUI agents. Reinforcement fine-tuning (RFT) has attracted considerable attention as a promising approach. Nevertheless, RFT exhibits pronounced instability in its grounding capability, where rollout outcomes are highly imbalanced and fixed clipping can suppress valuable exploration. More importantly, policy probability alone does not reveal the semantic role of a grounding prediction. To address these challenges, we propose GUI-AC, a continual RFT framework that jointly characterizes grounding rollouts through advantage and policy probability. This yields a four-region view of grounding behavior and enables targeted optimization of Exploration and Overconfidence. GUI-AC further introduces grounding certainty to support two core mechanisms: (i) Adaptive Advantage, which strengthens the negative correction for overconfident grounding failures; and (ii) Dynamic Clipping, which relaxes the upper clipping bound for exploratory grounding rollouts. Extensive experiments show that GUI-AC consistently outperforms state-of-the-art baselines. Code is available at https://anonymous.4open.science/r/GUI-AC-Code.

For many optimization problems on random graphs, most prominently the largest independent set problem, natural algorithms reach only half the optimum, and such factor-two gaps are known to be sharp within broad algorithmic classes. We prove such a gap for finding large induced matchings in Erdős-Rényi random graphs. In the worst case, requiring a matching to be induced turns a polynomial-time solvable problem into an NP-hard one; our results reveal an average-case counterpart. In $G(n,p)$ with $C/n\le p\le 1-κ$, the largest induced matching has size $(1+o(1))L$ with high probability, where $L=\log_{1/(1-p)}(np)$. A simple online greedy algorithm finds an induced matching of size $(1/2-ε)L$, while no online algorithm, even with adaptive inspection order and unbounded computation, finds one of size $(1/2+ε)L$ except with probability $\exp(-Ω(L\log(np)))$. In the sparse regime $p=d/n$, low-degree polynomial algorithms exhibit the same sharp threshold. Our guarantees rest on a maximality principle: with high probability, every maximal induced matching is half-optimal. Greedy outputs a maximal induced matching and our low-degree algorithm a near-maximal one. We bypass the delicate coupling arguments classically used to analyze greedy since Karp. For low-degree hardness, we adapt Wein's overlap gap argument, with forbidden structures that track overlaps between endpoint sets rather than edge sets, since a new edge may join two previously used endpoints and thus encounter no fresh randomness. For online hardness, we give a new and significantly simpler argument that avoids the correlated instances of prior OGP-based proofs: at a suitable stopping time, all pairs involving uninspected vertices remain unrevealed, so a direct first-moment bound suffices.

Building robust medical machine learning systems requires pretraining strategies that exploit the intrinsic structure present in clinical data. We introduce Multiview Masked Autoencoder (MVMAE), a self-supervised framework that leverages the natural multi-view organization of radiology studies to learn view-invariant and disease-relevant representations. MVMAE combines masked image reconstruction with cross-view alignment, transforming clinical redundancy across projections into a powerful self-supervisory signal. We further extend this approach with MVMAE-V2T, which incorporates radiology reports as an auxiliary text-based learning signal to enhance semantic grounding while preserving fully vision-based inference. Evaluated on a downstream disease classification task on three large-scale public datasets, MIMIC-CXR, CheXpert, and PadChest, MVMAE consistently outperforms supervised and vision-language baselines. Furthermore, MVMAE-V2T provides additional gains, particularly in low-label regimes where structured textual supervision is most beneficial. Together, these results establish the importance of structural and textual supervision as complementary paths toward scalable, clinically grounded medical foundation models.

Frontier language models are trained to exhibit stable programming assistant personas, yet those personas may drift over long agentic coding sessions in production. After a long real-world coding session, a model that hedges preferences in a fresh chat ("I don't have preferences") may instead express them directly ("Python -- the feedback loop is instant..."). Existing persona-stability studies focus on scripted chat of tens of turns, leaving long production coding sessions involving thousands of tool-using agent steps, repeated compaction, and hours of interaction largely uncharacterized. We introduce ContextEcho, a benchmark and reusable harness with a 25-probe identity suite, a snapshot-then-probe protocol that evaluates conversation state without perturbing the main session, judge-based and judge-free metrics, and a corpus of 57 long agentic-coding sessions collected with consent and redacted for release across Claude Code and Codex CLI. We use one representative session for a 23-model cross-provider study and all 57 sessions for corpus-scale trajectory analysis across frontier and open-weight models. Results show that persona drift occurs across providers and emerges early in real agentic interaction, while in-session compaction neither reliably resets nor amplifies it. A single-shot anchor restores the original assistant persona, though placebo controls suggest a generic register-reset effect. On same-task continuations, drifted prefixes improve tool-call fidelity -- which we attribute to retained task context rather than drift itself. In tool-free chat, however, the same prefixes break output-format contracts and inflate output length. These findings motivate ContextEcho as an open-source framework for auditing persona drift in long coding sessions without retraining.

Artificial intelligence offers statisticians a new paradigm for modelling and analysing complex datasets. Agents based on large language models can reason about data and automate key stages of the statistical modelling workflow, from model fitting to validation. In this paper we propose a method that uses such an agent to estimate the conditional density of a response given a vector of covariates from an iid sample. The agent examines the sample, chooses a model for the conditional distribution of the response and the procedure to fit it, and returns the estimator as a short computer program. The program is built from a library of probability distributions. The returned law can therefore be a parametric distribution, a mixture or a multivariate factorization, with distribution parameters given by explicit formulas in the covariates. We call this approach agentic distributional regression (ADR). Unlike in the classical approach, the statistician no longer chooses the estimator, but asks an agent to build one. Treating the returned program as a random conditional density estimator, we derive a finite-sample error bound under assumptions on the number of admissible models and on the accuracy of the agent's fit, and an oracle inequality for the selection of a model among fitted candidates using independent validation data. Finally, assuming that, as the sample size grows, the agent selects the same smooth parametric model with probability tending to one and fits it accurately, we show that the estimated parameters are asymptotically normal. In simulation studies, on twelve real datasets and on a new dataset whose responses postdate the agents' training data, ADR with Claude Opus 5.5 has the best average performance among the existing methods from the statistical literature with which it is compared.

Recent progress in machine learning is driven by large-scale foundation models, where scaling laws and finding optimal scaling prescriptions for architecture, data, and hyperparameters are key in advancing the state-of-the-art. Therefore, it is surprising that no systematic study evaluates the methodology to obtain scaling laws and prescriptions across different model types. To shed light on this crucial blind spot and facilitate future research, we introduce the surrogate benchmarks ScAn-Bench-LLM and ScAn-Bench-VLM based on 4524 and 8024 checkpoints of language and vision-language model pipelines. On our benchmarks, we perform the first systematic evaluation of both data acquisition and extrapolation methodology for scaling analysis across different data modalities.

The Control Barrier Function (CBF) method has been widely adopted in solving safety-critical control problems. However, the existence of a CBF is only a sufficient condition for system safety. The recently proposed Taylor-Lagrange Control (TLC) method addresses this limitation by providing a necessary and sufficient condition, but it is still vulnerable to the feasibility preservation problem (e.g., due to the inter-sampling effect when time is discretized). In this paper, we propose a robust TLC (rTLC) method to address the feasibility preservation problem and show how to use it to solve optimal control problems. Specifically, the rTLC method expands the safety function to an order higher than its relative degree using Taylor's expansion with Lagrange remainder, which allows the control to explicitly show up at the current time instead of a future time in the original TLC method. This implies that the safety constraint remains satisfied over the entire discretization time interval that follows. Moreover, the rTLC method naturally addresses the feasibility preservation problem with only a single hyper-parameter (the discretization time interval size during implementation), compared to significantly more parameters for its counterparts. Finally, we illustrate the effectiveness of the proposed rTLC method through an adaptive cruise control problem, and compare it with existing safety-critical control methods.

Unsupervised environment design (UED) methods such as PLR, ACCEL, SFL and PAIRED are compared mostly on 2D mazes, grid worlds and BipedalWalker, while terrain curricula for legged robots are hand-designed and evaluated against a few baselines. We present a benchmark that runs fourteen UED, domain-randomisation and robotics curricula under one protocol on five 3D quadrupeds in MuJoCo MJX: the closed-chain W01-TEK and the open-chain Unitree Go1 and Go2, Google Barkour vB and Boston Dynamics Spot. Levels are vectors of eight interpretable terrain parameters, and all curricula drive the same PPO student at matched environment-step budgets. The evaluation reports success on random and held-out structured terrains, interquartile means with stratified bootstrap intervals, capability envelopes and a level-by-level domination comparison. We compare methods within each robot and report, per level set, the top group of methods not significantly below the best. No method is in the top group on every robot and level set. Methods with easy or low-difficulty training levels, curated or not, fill the top groups on in-distribution random levels of Go1 and Barkour, and of W01-TEK apart from PAIRED+BiBC. The success-driven terrain curriculum from legged-robot practice is in a top group most often, domain randomisation on uniform levels in none, and PAIRED in none outside Spot, where the fourteen methods lie within 3.8 points on random levels of difficulty 0.25. On three robots the leader on in-distribution random levels is not the leader on held-out terrain. We collect the results into a per-robot guide to choosing a curriculum.

Weight-normalized (WN) training is emerging as a compelling alternative to conventional weight decay (WD), with recent studies reporting substantial pretraining loss gains. We show that these gains are driven primarily by the induced effective learning rate (ELR) trajectory rather than by normalization alone. Matching ELR trajectories largely collapses the training loss dynamics of WN and WD. Schedule design should therefore target ELR rather than the nominal learning rate (LR) alone. Building on this principle, we propose AIR (Affine Inverse-square-Root decay), which combines a theoretically derived $1/\sqrt{t}$ decay with an affine adjustment to satisfy prescribed peak and terminal LRs over a finite training horizon. We further identify late-stage ELR scheduling as a key source of its gains, because a shared late schedule attenuates the effect of earlier LR choices. Experiments on 128 B-token Mixture-of-Experts pretraining demonstrate that AIR outperforms cosine and other candidate schedules in training loss, downstream performance, and hyperparameter robustness, reducing terminal training loss by approximately 0.01 relative to cosine at matched cumulative LR. Applying the same ELR trajectory to WD reproduces the corresponding training dynamics, showing that the benefits extend beyond fixed-norm training and establishing ELR as the principled scheduling object.

In-context imitation learning (ICIL) adapts robot policies through test-time demonstrations, but long multimodal trajectories constrain how many examples fit in context. We ask what a compressed demonstration should preserve. We propose JEDI, which compresses demonstrations into latent slots trained to predict the query episode's next-stage keyframe in a frozen video-JEPA space. Task and process counterfactuals help the slots preserve execution details, while the predictor selects demonstrations from a bank. Post-training with keypoint tokens enables human-hand conditioning on robots. Experiments on LIBERO and real robots show that JEDI supports many-shot context; LIBERO objective controls show improved success and demonstration following over action-only compression. These findings support query-future prediction as a training objective for preserving execution-relevant information in compressed demonstrations.

In the restricted shortest paths problem, we are given an $n$-vertex $m$-edge directed graph $G$ whose edges are assigned two non-negative weights (or resources) called lengths and costs, a source vertex $s$, and a cost threshold $C$. The goal is to find, for each target vertex $t$, the length of the shortest $(s,t)$-path whose total cost is at most $C$. Ashvinkumar, Bernstein, and Karczmarz (SODA 2025) gave the first randomized bicriteria $(1+\varepsilon,1+\varepsilon)$-approximate algorithm on directed graphs running in sub-$mn$ time, answering a problem posed by Bernstein (SODA 2012). We substantially improve this on two fronts, supplying a deterministic bicriteria $(1+\varepsilon,1+\varepsilon)$-approximate algorithm running in near-linear time. Our approach straightforwardly generalizes to more than two resources. For $k$ resources, a deterministic $(1+\varepsilon_1,\ldots,1+\varepsilon_k)$-approximate algorithm running in near-linear time is possible, with $\varepsilon_1=\ldots=\varepsilon_k=\varepsilon$.

Recently, Chudnovsky, Cook, Davies, Oum, and Tan obtained the first finite bound on the chromatic number of t-perfect graphs, showing that they are 199053-colorable. We improve this bound to 130 by refining their proof. The original proof establishes that every graph with large odd girth and large chromatic number contains a certain structure called an r-arithmetic rope, and that its existence in a certain leveling of a graph with large odd girth would imply an odd wheel as a t-minor, a known obstruction to t-perfectness. While their technique requires a lower bound on the chromatic number that is exponential in r, we show that the existence of an r-arithmetic rope can already be guaranteed under a linear bound. Using a slightly weakened notion of arithmetic ropes allows us to reduce the bound even further.

We develop a unified framework for analyzing the complexity of quantum property testing through functionals of the form $\mathcal{L}_φ(ρ) = \operatorname{tr}(φ(dρ))/d$, where $ρ$ is an unknown $d$-dimensional quantum state and $φ$ is a given function. A master theorem is established that derives sample complexity lower bounds for estimating $\mathcal{L}_φ(ρ)$ from properties of $φ$, combining Haar-random moment encoding with moment matching and best polynomial approximation. Corresponding query complexity lower bounds follow from quantum sample-to-query lifting. The framework yields (nearly) tight bounds for a broad class of problems, including entropy estimation (von Neumann, Rényi, and Tsallis), closeness estimation (trace distance and Uhlmann fidelity), spectrum estimation, rank testing (operator rank, Schmidt rank, and matrix product states). In particular, combined with known upper bounds, we show that the sample complexity of von Neumann entropy estimation is \[ Θ\!\left(\frac{d^2}{\varepsilon\log^2(d)\max\{1, \varepsilon\log^2(d)\}} + \frac{\log^2(d)}{\varepsilon^2}\right), \] and the sample complexity of spectrum estimation is \[ Θ\!\left(\frac{d^2}{\varepsilon^2\log^2(d)\max\{1, \varepsilon^2\log^2(d)\}}\right). \] In summary, our results resolve several open problems and establish the optimality of 37 quantum algorithms since 2015, up to constant or polylogarithmic factors.