Papers

Demonstration-conditioned policies provide a natural interface for specifying robot behavior, yet long-horizon manipulation remains difficult when visually similar states recur across different stages or when demonstrations and executions proceed at different speeds. We identify the resulting failure mode as stage confusion and introduce Progress-Aligned Context for Execution (PACE), a stateful method that continually reinterprets a complete demonstration according to realized execution progress. PACE compresses the demonstration into ordered multimodal prompt tokens and uses training-only dual-edge attention supervision to expose its latent stage structure. During execution, an episode-local fast-weight memory causally encodes realized action-observation transitions and modulates prompt cross-attention, producing a progress-aligned context for a unified diffusion action expert without test-time stage labels or stage-specific policies. PACE improves success from 88.9% to 94.0% on LIBERO-Gen Goal Chain, from 79.1% to 83.3% on Spatial Combination, and from 33.3% to 73.3% on the two-step Block Routing tasks. Failure analysis further indicates that structured demonstration alignment and causal execution memory jointly mitigate stage confusion.

Image Manipulation Localization (IML) is commonly formulated as a fully supervised learning task that estimates the optimal manipulation mask $y$ for a given image $x$. In this work, we first reveal the latent nature of artifacts and thus reinterpret IML as a latent-variable problem, $P(y|x)=\int P(y|z)\,P(z|x)\,dz$, where $z$ denotes the artifacts. Following this interpretation, we pinpoint the cause for the current IML models' insufficiency as their implicit artifacts modeling strategy, highlighting the necessity of modeling $z$ in an explicit manner. Without direct labels, feature disentanglement is the most appropriate solution for this explicit modeling. Accordingly, we propose a two-stage learning paradigm with the Pairwise Artifacts Learning (PAL) and Standard Localization (SL) phases to estimate $P(z|x)$ and $P(y|z)$ via edit relations. To support our edit-relation-based learning, we further curate EditGroup-45K, a source-anchored dataset organized into edit groups for pair construction. Extensive experiments show that our PAL paradigm yields consistent improvements across diverse IML architectures, and empirical analyses further verify that PAL does capture artifacts explicitly through feature disentanglement. Code and dataset are available at https://github.com/venus-guangjian/PAL

Understanding the formation and dynamics of two-exciton bound states (BSs) is crucial for harnessing multi-exciton phenomena and designing next-generation organic semiconductor materials. While various mechanisms such as intermolecular exciton-exciton interactions or multi-level intramolecular configurations can generate these BSs, a fundamental understanding of their underlying lattice dynamics remains a key challenge. Within this context, the Merrifield exciton model stands out as a premier framework for capturing the intricate quantum mixing between single-site doubly-excited states and two-particle scattering continuum. In this work, by constructing a set of exact two-exciton Bloch states and applying a plane-wave ansatz to treat the resulting inhomogeneous tridiagonal matrices, we provide a complete, rigorous solution to the two-exciton problem in a finite-size Merrifield chain. We analytically map the parameter regions that support two-exciton BSs, proving that at most two distinct types of BSs can emerge, located either above or below the scattering continuum. Furthermore, we provide a quantitative interpretation of how these two types of BSs evolve as a function of the total wave number within the whole Brillouin zone. The obtained closed-form expressions for the eigenenergies and wave functions offer valuable benchmarks for exploring exciton dynamics and optical responses in related molecular aggregates.

This work focuses on the dynamic behaviors, particularly the asymptotic periodicity, of solutions to nonlinear fractional-order dynamical systems modeled by Caputo fractional evolution equations in Banach spaces. We propose a new class of weighted pseudo $S$-asymptotically $(\xi,\tau,a)$-periodic functions, which unifies well-established function types such as standard periodic functions and $S$-asymptotically periodic functions as its special instances. We then systematically derive the fundamental properties of this new function family, and rigorously prove its completeness, corresponding convolution theorems, and nonlinear composition rules. Building on these newly established results, we demonstrate that under reasonable hypotheses, the mild solutions to a broad class of nonlinear fractional-order dynamical systems — both delay-free and with finite delay — in Banach spaces admit the (weighted pseudo) $S$-asymptotically $(\xi,\tau,a)$-periodic property, which further implies that no bifurcation or chaotic behavior emerges in these fractional-order systems. The theoretical conclusions are finally validated by illustrative examples describing memory-dependent complex dynamic processes, supplemented with supporting numerical simulations. Additionally, the presented weighted pseudo $S$-asymptotically $(\xi,\tau,a)$-periodic framework can be extended to functions with first-kind discrete discontinuities, so that systems with discontinuous nonlinear terms can be handled via the same analytical paradigm.

Gastric adenocarcinoma (GA) is a leading cause of cancer-related mortality worldwide, and accurate histopathological subtype classification from whole-slide images (WSIs) is essential for effective treatment planning. While multimodal approaches that integrate pathology report text with WSIs can improve classification, existing methods often depend on computationally expensive transformer architectures and large language models. We propose a multimodal knowledge distillation (MKD) framework that combines a pretrained WSI image encoder and a clinical text encoder using Low-Rank Multimodal Fusion (LMF) to efficiently model cross-modal interactions during training. Each WSI is represented as a bag of patches paired with a slide-level diagnostic caption. The teacher model learns fused image-text representations for subtype classification, while the student model distills this knowledge to enable accurate image-only inference. We evaluate our method on the PatchGastric benchmark dataset and achieve at least 3.35% higher mean accuracy than state-of-the-art approaches, without relying on transformer-based fusion, multi-task learning, or large language models. The source code is available at https://github.com/helomelo1/MKD-LMF.

We prove that finite-dimensional geodesic locally compact Alexandrov spaces with curvature bounded below (CBB), and in particular complete Riemannian manifolds with lower bounded sectional curvature, satisfy a Besicovitch covering theorem by showing that they are directionally limited in the sense of Federer.

Despite recent advances in video generation, motion customization remains challenging due to content leakage, where appearance attributes from the reference video unintentionally propagate into the generated output. We identify this issue as a consequence of the generative process collapsing toward the reference video, which arises from formulating the learning objective as a direct regression on the reference. To address this, we propose Control-based Motion Customization (CMC), a principled training framework that is structurally robust to content leakage. Our key idea is to steer generative dynamics toward desired motion while avoiding collapse toward the reference video, which we formalize using Stochastic Optimal Control (SOC). Under this formulation, customized videos acquire the target motion yet remain within the pre-trained model's prompt-conditional distribution, where appearance is determined by the text prompt rather than the reference video. Furthermore, to improve efficiency, we tailor the SOC formulation to motion customization by eliminating the need for an explicit reward and introducing a timestep-adaptive motion cost that focuses only on early generative stages, accelerating training by 2.5 times. Extensive experiments demonstrate that CMC effectively mitigates content leakage and achieves competitive motion fidelity while preserving the diversity of the base model across diverse scenarios.

Deep Reinforcement Learning policies can produce nonsmooth action oscillations that hinder deployment on physical robots. Existing architectural and penalty-based approaches seek spatial smoothness by directly reducing sensitivity to changes in state inputs, but their broad constraints can degrade task performance as stronger smoothing is pursued. Temporal regularization instead constrains action differences along observed transitions, but has been considered unable to provide the spatial smoothness needed under observation noise. We revisit this assumption by proving that the temporal penalty bounds the expected action differences between current states sharing a next state, revealing a spatial effect that empirically extends to spatial smoothness. Building on this finding, we propose Conditioning for Action using only Temporal Smoothness (CATS), which combines a temporal penalty with linear ramp-up. We highlight temporal regularization's ability to provide spatial smoothness while better preserving task performance than explicit spatial regularization. Through linear ramp-up, CATS allows the policy to learn rewarding behavior before progressively smoothing its actions, improving return preservation and both temporal and spatial smoothness. Experiments in both simulation and the real world show that CATS substantially reduces action oscillation without degrading task performance, with little computational overhead.

We prove Mizohata–Takeuchi-type estimates for the Fourier extension operator associated with the truncated hyperbolic paraboloid in $\R^3$. Our main result controls the weighted $L^2$ norm of the extension operator by the $L^2$ mass of the weight over a multiscale family of parallelepipeds arising from $\ell^2$ decoupling for the hyperbolic paraboloid. We deduce this result from a weighted $L^2$ estimate for functions whose Fourier transforms are supported in a small neighborhood of the hyperbolic paraboloid, which we establish using a bilinear refined decoupling estimate.

Assuming projective log resolutions, we construct semiample perturbations over arbitrary fields that preserve all log canonical places. As an application, for divisor classes with finitely generated section rings, we characterize the existence of effective divisors yielding lc or klt pairs in terms of asymptotic orders of vanishing. We also derive minimal model and semiampleness results for generalized threefolds over $F$-finite fields of characteristic $p>5$.

Recurrent neural networks typically compress information into a single vector-valued recurrent state, forcing short-term computation and long-term retention to share the same representation. Past extensions alleviate this bottleneck by increasing the memory capacity or separating timescales, but lack the combination of rapid neuron-level processing and longer-term retention found in biology. To that end, we introduce the Continuous Memory Machine (CMM), a recurrent architecture with matrix-valued short- and long-term memory states serving distinct functional roles. Building on the Continuous Thought Machine (CTM), the CMM's short-term memory tracks recent neural activity, with uniquely parameterized neuron-level models learning to use these activity patterns for computation. A persistent long-term memory stores information for later use, with a Transformer jointly updating both memory stores, providing an expressive bidirectional read–write mechanism such that each store can reorganize its own contents and both read from and write to the other. Across algorithmic, in-context learning, and recurrent reasoning tasks, the CMM outperforms a broad suite of baselines, exhibiting stronger generalization than prior memory-augmented networks while preserving the CTM's interpretable attention patterns. Code is available at https://github.com/SakanaAI/continuous-memory-machines.

We study sequential content sufficiency by investigating whether a representation retains the ordered target information available in its input. An information-theoretic decomposition separates input ambiguity, representation loss, and readout mismatch. We construct recoverable views where perfect agreement and joint isotropic Gaussianity coexist with zero target information, and establish limits imposed by deterministic canonical anchors. Token log-loss provides a one-sided information-loss bound; a fixed-penalty ridge analysis shows why rank alone cannot determine prediction risk. These results motivate CANOPE, a nonautoregressive framework with ordered latent canvases, canonical-token supervision, and geometric regularization. On 40,000 validation sequences, latent-agreement (PL0) and token-grounded (PL2) have nearly identical pooled ranks but reach 13.5% and 98.8% positional Recall@1, respectively, under strong natural corruption when the correct target length is provided. On 3,930 LJSpeech validation utterances, frozen PL2 with a trained MatchaTTS readout yields 21.54% word error rate (WER) on corrupted text, versus 99.22% for frozen PL0, while end-to-end MatchaTTS reaches 10.93%. These results show that geometric regularity alone does not guarantee recoverable sequential content or effective downstream access in the text settings studied here.

Let $K$ be a finite field of characteristic two with $|K| = 2^{n}$, let $\gcd(k,n) = 1$, let $d_{k} = 4^{k} - 2^{k} + 1$ be the Kasami exponent, and let $\Delta_{k} = \{(b+1)^{d_{k}} + b^{d_{k}} + 1 : b \in K\}$ be the image of the normalised derivative of the Kasami monomial in the direction $1$. We show that, for all distinct nonzero $v_{1},v_{2} \in K$, \[ \bigl|\{(x,y,z) \in \Delta_{k}^{3} : v_{1}x + v_{2}y + (v_{1}+v_{2})z = 0\}\bigr| = 2^{2n-3}. \] This establishes the cyclic-additive difference-set condition introduced by Carlet and later posed for the Kasami functions at NSUCRYPTO~2019. Starting from the known half-size property of the derivative image, we express the Fourier correction as twisted root counts and prove their required nonnegativity by an incidence argument on the Fermat cubic. An exact average over the slopes then forces equality pointwise. The argument covers every admissible pair $(n,k)$ and has been formalised and machine-checked in Lean~4 with Mathlib.

We introduce ApexQuant, a calibration-free quantization method that recursively re-quantizes the residual error, serving as a refinement layer on top of existing quantizers. We establish that a fresh random rotation returns each residual to the uniform distribution on the hypersphere, which characterizes the rate of progressive error decay across successive passes. This result lets us determine, before any weight is read, how many passes a layer needs for a target weight-space error. Every prefix is itself a valid lower-rate model, so one artifact serves several precisions. We instantiate ApexQuant with three interchangeable stages, scalar, $E_8$ and trellis, and validate it on four open-weight LLMs and on Earth-observation and medical domains where in-distribution data is often unattainable as imagery arrives under restrictive licences or due to patient material under privacy constraints. Progressive re-isotropization comes within a few percent of full precision at four bits and gives the best two-bit arm we measure, in a completely data-free setting.

Adapting vision-language models to downstream tasks has achieved remarkable success by leveraging pseudo-labels generated from unlabeled data. Existing methods typically assume a uniform unlabeled data distribution, and thus the resulting pseudo-label distribution is likewise uniform. However, real-world data distributions are often long-tailed. To tackle this, we formalize a new scenario termed Unsupervised Long-Tailed Adaptation (ULTA). Under this scenario, existing methods exhibit a contrasting phenomenon: head-class performance drops sharply, which is distinct from supervised long-tailed learning where tail classes suffer the most. In particular, we uncover that the distributional mismatch not only erodes head-class boundaries, but also pushes head samples into confusable classes, reinforcing the model's inherent bias. To address these issues, we propose a novel model called Margin-Aware Refinement with Structural alignment (MARS). Specifically, we mitigate head-class boundary erosion via Boundary-Preserving Alignment, which takes the zero-shot VLM as a fixed visual reference to suppress probability increases that lack visual support in the training targets. Building upon this, we introduce Margin-aware Self-Refinement, which employs a dynamic adjustment strategy to refine tail and confusable classes while preventing prediction bias. Extensive experiments on nine benchmark datasets demonstrate that MARS outperforms state-of-the-art methods, achieving an average accuracy improvement of 4.71 percentage points.

Cantonese lyric writing requires close alignment between lexical tones and melodic pitch. Existing melody-guided lyric generation methods typically rely on symbolic melody to generate lyrics. However, in real songwriting scenarios, melodies are often expressed as raw singing audio or hummed recordings, where pitch is implicit, noisy, and unstructured, making these methods difficult to apply directly. To address this limitation, we propose ARIA, a two-stage audio-driven melody-tone relation modeling framework for Cantonese lyric authoring that generates Cantonese lyrics from singing recordings with provided character-level timestamps. Specifically, we first design a Tri-Stream Relation-Aware Tone Estimator (TRATE) to predict 0243 sequences from timestamped singing audio by modeling multi-stream acoustic cues and relational tonal structure. We then propose a Decoupled Retrieval-Augmented Tone-Conditioned Lyric Generator (DRA-TCLG) to generate fluent lyrics conditioned on predicted tonal plans with retrieval-enhanced lexical guidance. Moreover, we construct a large-scale aligned audio-Jyutping-0243 dataset from real Cantonese singing recordings to support this new task. Experimental results demonstrate that ARIA achieves strong performance in both 0243 prediction and tone-consistent lyric generation, validating the effectiveness of the proposed framework.

We discover a connection between the classical golden section and the online leasing problem: when the number of skis increases from one to two, the optimal competitive algorithm is to rent two pairs until the golden section point$(\sqrt{5}-1)s/2$ within [0,s], then buy one pair, and finally buy the second at time $s$, achieving the optimal competitive ratio of $(5+\sqrt{5})/4$. Building on this, we explore higher-dimensional golden sections and multiple online leasing. For the golden section, we define geometric-type and harmonic-type higher-dimensional golden sections, $\tau^{(m)}$ and $T^{(m)}$, based on two equivalent propositions dividing the unit segment into $m$ segments. We establish equations for the geometric-type ratio ${\lambda}$ and harmonic-type basis ${\omega}$, and investigate their algebraic characteristics. Extending the $k$-generalized Fibonacci sequence to a bi-infinite $m$-generalized Fibonacci sequence, we establish their relationship. We introduce novel concepts including generating sequences and the Fibonacci matrix, investigating its submatrices. Results such as a determinant formula involving the Fibonacci matrix demonstrate its effectiveness in studying generalized Fibonacci sequences. For online leasing, we consider multiple online leasing of $m$ pairs of skis. We design a control and balancing strategy and prove it is optimal via competitive analysis. We show the optimal strategy is precisely the $m$-dimensional harmonic-type golden section method. Since explicit solutions may not exist for dimensions higher than four, we propose a continuous relaxation problem. We explore using its relaxed solution to approximate the optimal solution or the largest real root. We propose the mantissa weighting method to solve the equation, achieving high accuracy through error analysis.

Wi-Fi 9 is expected to go beyond mere communication and provide new services such as sensing or computation. At this juncture, Artificial Intelligence (AI) is taking a leading role in the definition of the 802.11bx amendment, named WLAN Intelligent Networking (WIN). In this tutorial, we survey the recent progress made toward Wi-Fi 9 within IEEE 802.11 standardization, tracing the drivers and technological advances that motivate an AI-ready Wi-Fi 9. We then examine AI's role along three complementary dimensions, i.e., AI as a protocol (AI is applied to Wi-Fi's PHY/MAC operation), AI as a platform (Wi-Fi infrastructure is repurposed to provide AI computation), and AI as traffic (AI flows call for new traffic-handling policies), and discuss candidate features and open challenges along each. As a concrete illustration of the AI as traffic paradigm, we present a case study on AI traffic differentiation, where we explore a potential extension of the current Enhanced Distributed Channel Access (EDCA) to support new AI traffic flows.

Generative actors are transforming offline reinforcement learning (RL) by enabling expressive policy classes that model complex action distributions. However, this expressiveness also exposes a key challenge in heterogeneous datasets: generative policies can reproduce unreliable action modes whose return distributions exhibit high variance, occasionally yielding high returns by chance but lacking consistency. Consequently, maximizing the expected $Q$-value alone is insufficient for identifying reliable actions. We propose VAN-Flow (Variance-Averse $n$-step Flow), a framework that promotes reliable actions in generative offline RL. VAN-Flow combines (i) a categorical distributional critic, (ii) a variance-averse expectation operator that smoothly reweights atom probabilities to favor actions with both high returns and low dispersion, and (iii) a flow-matching generative actor guided via rejection sampling. Unlike CVaR or mean-variance objectives, the operator redistributes probability mass over the categorical return distribution without hard truncation or auxiliary penalty terms. Across more than 40 tasks from D4RL and OGBench, VAN-Flow consistently outperforms strong baselines, with the largest gains in long-horizon and high-variance regimes where reliable action selection becomes critical.

Repository-level software engineering (SWE) is a challenging long-horizon setting: agents must reason over extended interactions, use tools, and adapt to stateful environments. Recent work trains SWE agents with reinforcement learning methods such as Group Relative Policy Optimization (GRPO), which independently sample multiple trajectories per issue, test the resulting patches, and compare terminal rewards within a fixed group. However, this training setup does not reuse verifier feedback from failed patches as context for subsequent attempts, even though this feedback contains valuable diagnostic information about what went wrong. Training on recovery trajectories is challenging because the preceding outcome determines whether the next trajectory is generated, while the failed execution determines its conditioning context. We introduce FC-SWE, a failure-conditioned RL framework that incorporates recovery attempts into policy training. After a patch fails verification, FC-SWE restores the repository to its original task state and uses the failed patch and verifier feedback as context for a recovery trajectory. FC-SWE adapts GRPO to these chains of complete, multi-turn tool-use trajectories through two mechanisms. Trajectory-local rewards preserve each attempt's verifier outcome, preventing recovery success from rewarding an earlier failed patch. Active-set advantage estimation forms a comparison group from all initial and recovery trajectories actually executed for the same issue, so failed attempts remain in the group while unexecuted attempts are excluded. On all 500 SWE-bench Verified tasks under a verifier-assisted protocol, FC-SWE with Qwen3.5-4B and SWE-agent achieves 41.7% Resolved@1 and 52.8% Resolved@2, compared with 38.9% and 48.5% for GRPO. Although trained with at most two attempts per chain, FC-SWE reaches 70.7% Resolved@11 under an eleven-attempt test-time budget.

We study the HKT geometry of compact locally conformally hyperkähler manifolds. We prove that on these manifolds the quaternionic Monge-Ampère equation is always solvable, extending results of Alesker and of Dinew-Sroka, and we confirm the conjecture on the maximal existence time of the HKT-Ricci flow. On quaternionic Hopf surfaces we construct non-trivial HKT solitons and prove convergence of the normalized flow for symmetric initial data.

This paper presents the design and control strategy for MetaMorpher, a metamorphic Unmanned Aerial Vehicle (UAV), capable of both spinning-wing hover and fixed flying-wing cruise flight. Since control of the cruise configuration is comparatively well established in the literature, this paper focuses on control of the MetaMorpher in hover mode, building on the flight dynamics model and conceptual design validated in previous work. The control algorithm is implemented using one of two phase-synchronized strategies: motor propulsion, which pulses motor thrust in synchrony with the vehicle's rotation, or flap propulsion, a novel strategy that pulses the deflection of the wing-mounted elevons. We evaluate both strategies in simulation through different flight experiments. Simulation results confirm the mathematical model and show stable reference tracking, demonstrating flap propulsion as a lightweight, decoupled alternative for hover control. Experimental testing validated the vertical-dynamics propulsion model against the physical prototype, demonstrating very good steady-state agreement across different configurations.

Sea surface temperature (SST) forecasting depends on local temporal persistence, regional spatial dependence, and environmental conditions that evolve with the forecast date. We study how these heterogeneous conditions can be presented to a large language model (LLM) for regional multi-step forecasting without serializing the full SST grid as text. We formulate forecasting as conditional numerical generation: historical SST and anomaly sequences, date-aligned environmental records, and static ocean knowledge form a textual context, while regional spatial state is supplied through continuous graph-derived prefixes. A static graph encodes persistent geographic–climatological relations, and a dynamic graph encodes recent SST correlations and localized tropical-cyclone influence. Two graph neural networks produce a target-node representation that is mapped by a spatial-prefix fusion and injected into the LLM input. On SST forecasting in the South China Sea, the complete configuration achieves the best MAE and $\Rtwo$ among the compared methods over ten forecast steps. Alongside the numerical forecast, a rule-based module matches predicted trends and environmental-factor directions with knowledge entries to return source-linked, post-hoc contextual explanations.

Large language models (LLMs) are expected to answer questions faithfully based on the provided context, abstaining when the context information is insufficient to answer the questions. Existing faithfulness evaluations typically assess each question-context instance in isolation; however, such instance-level evaluation fails to capture a fundamental requirement of faithful behavior: the ability to adapt model responses to changes in available contexts. In particular, a model should provide correct answers when sufficient evidence is present and abstain when it is not. In this work, we propose a Pairwise Faithfulness Benchmark (PFaithBench) that evaluates whether a model can switch between answering and abstaining for the same question under supporting versus non-supporting contexts. Our evaluations across thirty-nine models with seven model families demonstrate that faithfulness fundamentally involves a trade-off between answering and abstaining, and that most current models exhibit a strong bias toward answering, with most faithfulness errors arising from over-answering, i.e., models tend to fabricate a response even when the provided context is insufficient. We further conduct a series of studies on faithfulness training under different data constructions. Our results show that training outcomes are highly sensitive to the specific composition of answering and abstaining data. Constructing answering and abstaining data from mismatched sources can cause models to rely on dataset-specific shortcuts rather than actual context sufficiency. Moreover, increasing answer-supervised data improves answering performance but exacerbates over-answering, while increasing abstaining data reduces hallucination but leads to over-abstention. The code and data are released at https://github.com/tmlr-group/PFaithBench.

We consider the localization and removal of a stationary omnidirectional radio source using a mobile sensor with bounded bearing errors and an unknown reception radius within known bounds. The objective is to minimize expected remaining action time under a fixed continuation policy while guaranteeing reception and source removal under the sensing model. A three-disk filter ensures reception, and a minimum enclosing circle certifies coverage of all bearing-consistent source positions. Monte Carlo sample-average search ranks a finite candidate set by complete mission time, including travel, readings, terminal service, and a finite fallback scan that ensures completion under the stated assumptions. In the reference case, 5000 independent validation missions average 60.40 s (approximate 95% confidence interval: [59.96, 60.84] s), saving 19.39% relative to a prescribed lateral point and 0.79% relative to a short-travel point. All 25,000 selected-point validation missions across five initial geometries succeed, with lower mean completion times than both prescribed designs. A same-grid objective ablation shows that minimizing travel or reading count alone can increase mean completion time.

For a finite ring $R$, we investigate the probability that the product of two randomly chosen elements in $R$ is nilpotent, which we call the nilpotent product probability (NPP) of $R$ and denote by $P_{nil}(R)$. We derive bounds for $P_{nil}(R)$ that depend on the structure of $R$, and prove that among all commutative rings with identity, the class of local rings with residue field $\mathbb{Z}_{2}$ attains the maximum value of NPP, which is equal to $3/4$. Further, we determine the set of all values of NPP for commutative rings with identity and classify all rings attaining those values. Finally, we investigate the relationship between NPP of $R$ and NPP of some subrings of the matrix ring over $R$.

Humanoid whole-body teleoperation translates human motion into stable robot behavior in real time. Existing systems typically rely on online motion retargeting to bridge human–robot morphological differences, but this process adds latency and can produce physically infeasible targets. Meanwhile, diverse, noisy, and partial human-motion observations often fall outside the training distribution, potentially causing unstable robot behavior. We propose a retargeting-free policy that maps raw human motion directly to robot joint commands in a single forward pass, eliminating online kinematic adaptation. To improve robustness, we learn a codebook of full-body motion primitives that projects out-of-distribution observations onto plausible motion prototypes and recovers full-body motion from partial inputs. Experiments on a Unitree~G1 in simulation and on hardware, using virtual reality, optical mocap, text-to-motion generation, and monocular video inputs, show that our method outperforms baselines in latency and robustness.

We prove the Mumford-Tate conjecture in every degree for hyper-Kähler varieties over fields finitely generated over $\mathbb{Q}$. The proof establishes semisimplicity of $\ell$-adic cohomology by eliminating the unipotent radical of the algebraic monodromy group of total cohomology. We also prove the weight-monodromy conjecture for hyper-Kähler varieties over $p$-adic fields. For hyper-Kähler varieties over number fields with $b_2\geq 4$, we establish, after suitable finite extensions, strong compatibility of the associated Weil-Deligne representations valued in Mumford-Tate groups and its integral refinement away from finitely many primes.

Open Radio Access Network (O-RAN) architectures extend programmability in next-generation cellular networks through Near-Real-Time and Non-Real-Time RAN Intelligent Controllers (RICs), enabling AI/ML-driven xApps and rApps to optimize network behavior dynamically. However, validating automated closed-loop control algorithms in live environments presents significant operational risks and deployment costs. To address this challenge, this paper introduces the O-RAN Digital Twin (ONDT), a modular, virtualized, and cloud-native experimentation framework developed as a 6G enabler within the SNS SUNRISE-6G project. We present the ONDT architecture and its end-to-end experimentation workflows, showing how the framework automates O-RAN-compliant rApp/xApp onboarding, RAN scenario configuration and initialization, Key Performance Metric (KPM) collection, and closed-loop control validation. Experimental validation using Juniper RIC platforms and the Keysight RICtest emulation framework demonstrates ONDT ability to provide an isolated and reproducible environment for KPM monitoring, cell ON/OFF control, automated dataset generation, and rApp/xApp validation.

This paper proposes a framework for modeling probability of default via functional data analysis. By representing a series of credit variables as functions, we investigate whether intra-monthly information improves default predictability in linear models. We further show how a range of widely used variables, among them available funds, utilization rate, and overdraft, can all be derived from three quantities observed over time. Namely, 1) the type of each account, 2) the balance of the account, and 3) the size of the credit limit on the account. Retaining these quantities as continuous-time processes, rather than reducing them to monthly aggregated values, yields a continuous faithful representation of the borrower. When analyzing these three processes, we discovered that recurring events associated with the ordinal position among banking days created strong cyclical patterns. We therefore develop a relative time framework that aligns the recurring events across borrowers, ensuring that borrowers possess the same cyclical pattern, regardless of real time. We assess the framework using functional logistic regression. This approach accommodates the continuous representation while remaining closely related to a logistic regression model commonly used in credit risk practice, due to strict regulatory constraints. We show that, when equipped with an effective functional representation of transactional trajectories, the proposed model attains predictive performance on par with XGBoost while consistently outperforming logistic regression. Importantly, the model balances predictive performance of a machine learning model with the interpretability of linear default models, potentially enabling financial institutions to use the model, even under strict regulation.