Papers

Practical O-band quantum-dot (QD) mode-locked comb sources must combine wide flat-top bandwidth, low radio-frequency (RF) timing noise, error-correctable bare-line modulation, and feedback tolerance, yet these functions are usually optimized separately and their relation to comb-formation dynamics remains unclear. Here we map the gain-current/saturable-absorber-bias plane of a simple two-section InAs/GaAs QD mode-locked laser to resolve distinct application-specific regimes. A low-injection, high-reverse-bias regime produces 0.80 ps pulses, consistent with amplitude-modulated operation, whereas a high-injection, intermediate-bias regime yields a 16.16 nm (2.75 THz) flat-top comb with 110 lines and a 14.98 ps extended waveform, consistent with a stronger frequency-modulated contribution. To our knowledge, this is the broadest reported 3 dB bandwidth among QD mode-locked comb sources. At a separate low-noise bias, the beatnote exhibits a 0.58 kHz Lorentzian linewidth and a 41.6 fs integrated timing jitter over the 4 to 80 MHz range, to our knowledge the lowest reported for a high-channel-count O-band QD passive comb. In isolator-free 25 Gb/s NRZ transmission, all 94 carriers across a 13.73 nm 3 dB band remain below the 7 percent HD-FEC threshold. Using all 110 carriers at the maximum-bandwidth bias gives a projected aggregate rate of 2.75 Tb/s. At a separate feedback-test bias, broadband mode locking is preserved and, beyond approximately -28 dB feedback, the RF beatnote enters a feedback-stabilized regime whose linewidth is reduced 42-fold. Thus, short-pulse, broadband, low-noise, transmission-ready, and feedback-stabilized operation occupy distinct selectable regions rather than a single universal optimum. This regime-resolved map links QD comb-formation physics to isolator-free, terabit-scale O-band interconnects.

Autonomous agents powered by large language models (LLMs) are rapidly evolving into an open agentic ecosystem. To support trustworthy collaboration, industry initiatives increasingly assess agent reputation from past behavior and provide performance leaderboards. However, reputation derived from past performance may not reliably predict an agent's behavior on new tasks, particularly when malicious agents can adapt their behavior and influence other agents during collaboration. We study reputation in multi-agent debate (MAD), where multiple agents answer the same query, debate to improve their answers, and aggregate them into a final output. We present MiniRep, a reputation-based aggregation system for MAD under malicious agents. To ground our threat model in established research, we construct an attack taxonomy drawing on reputation-system attacks and software-testing mutation operators, covering strategic exploitation of reputation and subtle corruption of agent proposals. Guided by this taxonomy, MiniRep evaluates agents based on both their behavior on the current task and their reputation over time, while preventing groups of agents with highly similar responses from dominating the final decision. We assess MiniRep across diverse tasks, LLM-agent compositions, corruption placements, and attack types drawn from our taxonomy. Our experimental results show that, MiniRep outperforms both conventional MAD aggregation and conventional reputation-based approaches on MATH no matter being attacked or not. Also, under a heterogeneous 10-agent setting on MATH, MiniRep outperforms all baselines in all 28 attack conditions.

Video semantic communication has attracted increasing attention as a promising approach to improving video transmission efficiency. However, most existing approaches rely on computationally intensive deep learning-based video encoders and decoders, which hinders their deployment in resource-constrained scenarios. To address this issue, we propose a lightweight semantic-aware joint source-channel optimization (SAJSCO) scheme that can be integrated into existing digital video communication systems as a plug-in module. Specifically, we develop a video communication system model in which the transmitter jointly optimizes source and channel coding parameters based on the inter-frame semantic importance of the input video and estimated channel state information. On this basis, we formulate an optimization problem that maximizes semantic importance weighted video reconstruction quality under a maximum bitrate constraint. To solve it, we first quantify inter-frame semantic importance using a cosine similarity-based metric with a shifted window mechanism. We then develop a multi-actor proximal policy optimization (MPPO) algorithm to solve the formulated problem by jointly adapting the source compression rate and channel coding rate. The learned policy can be directly applied to different video encoders without encoder-specific retraining or fine-tuning. SAJSCO achieves Bjøntegaard Delta rate reductions of 34.86% and 18.01% when integrated with H.265, a conventional video encoder, and DCVC-RT, a deep learning-based video encoder. Over-the-air experiments on a hardware testbed further demonstrate a PSNR gain of up to 1.448 dB with H.265 and an LPIPS reduction of up to 0.033 with DCVC-RT compared with the respective best-performing fixed-parameter baselines.

Nonlinear transformations are important in quantum machine learning and other quantum numerical applications, which can be reduced to the implementation of element-wise polynomials through polynomial approximation. Existing works establish the feasibility of transformations and improve query or auxiliary-space efficiency, but circuit depth remains linear in scale with degree. In this work, we develop a resource-tunable quantum framework that decomposes a $(2^d-1)$-degree polynomial into $m$ lower-degree factors, with $m$ controlling the degree of parallelism. By varying $m$ from $1$ to $2^d-1$, the framework provides a trade-off among query complexity, additional gate complexity, ancilla count, and normalization, ranging from a binary-tree implementation to a $\mathcal{O}(n+d)$-depth construction with highly parallel oracle queries that match the query lower bound. The effects of polynomial approximation and implementation errors are further analyzed. We demonstrate the framework for nonlinear activation functions such as sigmoid and tanh, as well as pixel-wise image transformations.

Precise numerical reasoning with Large Language Models (LLMs) is essential for expanding their applicability to complex real-world tasks. However, text-based tokenization often fragments numbers, significantly hindering precise arithmetic reasoning. Meanwhile, numerical embeddings, despite arithmetic precision, rely on context-agnostic substitution that disregards the semantic role of numbers as identifiers. To combine the complementary strengths, we propose ANI (Adaptive Numerical Injection), a hybrid framework that governs the selective injection of numerical features based on the semantic context. By employing a context-aware gating mechanism, we selectively inject numerical embeddings (specifically FoNE) into the latent space, explicitly preserving nominal identifiers while enhancing quantitative operands. Through extensive evaluations across various LLMs, we demonstrate that ANI enhances MATH performance by 9.5 points over the official reference model, while maintaining robust performance on general linguistic benchmarks.

Ekedahl's theory relates diagonal complexes to \(F\)-gauges, but turning this equivalence into explicit calculations requires careful control of its constructions. These notes explain the equivalence and clarify the generators-and-relations definition of \(\rmt\). At each finite level, we construct bounded projective resolutions of bounded coherent gauge complexes by finite sums of the standard generators. Morita equivalence expresses \(\rmt\) as a tensor product functor. Comparing the constructions across levels yields an exact fully faithful embedding of the diagonal heart into \(\Ch(R)\). Finally, we compute three distinct domino types arising from abelian threefolds that are all supergeneral.

In this paper, we explore the $(1,2)$-center problem for polygonal curves under continuous Fréchet distance. The $(k,\ell)$-center problem, in general, is known to be NP-hard. Aronov, Filtser, Horton, Katz, and Sheikhan (WADS'19) gave a polynomial-time algorithm for the $(1,2)$-center of curves in the plane under the discrete Fréchet distance. To the best of our knowledge, the $(1,2)$-center under continuous Fréchet distance has not been studied yet. We present a polynomial time algorithm to solve the problem exactly under both $\mathbb{L}_2$ and $\mathbb{L}_\infty$ norm, running in $O\bigr((n^2r+nr^2)^{2+\epsilon}\bigl)$ time for curves in the plane where $r$ is the number of input curves and $n$ is the maximum complexity of any curve. Further, for curves in any dimension $d$, the expected time to compute the center using the algorithm is $O\bigr((n^2r+nr^2)^{2(d-1)+\epsilon}\bigl)$. We have also shown that an $(1+\widetilde{\epsilon})-$factor approximation of $(1,2)$-center can be computed in $O(n^2r+nr^2+1/\epsilon^s)$ time for any $\epsilon>\widetilde{\epsilon}>0$ and some constant $s$ for curves in the plane. For curves in the plane, we have shown that, with the center restricted to be horizontal, we can compute the exact center in $O(n^2r+nr^2)$ time. An algorithm has been introduced to find a $3$-factor approximation of the $(1,2)$-center in time linear in the number of curves. A formulation was introduced by de Berg, Mehrabi, and Ophelders (CCCG'17) to measure Fréchet distance between a curve and a query segment under $\mathbb{L}_2$ norm for curves in the plane. We have shown the formulation is valid under both $\mathbb{L}_2$ and $\mathbb{L}_\infty$ norm for curves in $\mathbb{R}^d$.

Physics-informed computational methods usually optimize parameters within a functional representation whose structure is fixed in advance. This work proposes a Physics-Informed Method of Group Data Handling (PI-GMDH), in which representations of coupled physical fields are progressively constructed during solution. Candidate functional directions are evaluated through the first variation of the complete physical and observational objective, introduced in packages, and followed by block-coordinate damped Gauss-Newton coefficient optimization. The framework is demonstrated with tensor-product Chebyshev functions on the incompressible Navier-Stokes equations using a two-dimensional time-dependent Taylor-Green benchmark. Under the tested configuration, adaptive PI-GMDH reached validation and held-out test losses of 5.299e-19 and 5.296e-19 with 204, 201, and 175 active functions for u, v, and p. Complete degree-by-degree and all-terms PI-GMDH variants, together with selected PINN and KAN reference configurations, are used to examine the effect of structural construction policy. The results show that, for this controlled synthetic benchmark, selective progressive construction can provide a favorable combination of accuracy, representation size, and wall-clock time. The comparison is illustrative rather than a claim of universal superiority over alternative physics-informed approaches.

Let \( G \) be a finite group, and consider its common non-zero graph, which we denote by \( \Gamma_{nv}(G) \). In this graph, the vertices represent the non-linear irreducible characters of \( G \). There is an edge connecting two distinct vertices \( \chi_1 \) and \( \chi_2 \) if there is a vanishing element \( g \in G \) such that \( \chi_1(g) \chi_2(g) \neq 0 \). A finite group \( G \) is described as a strongly \( \mathcal{H}_1' \)-group if the set of vanishing elements of each of its non-linear irreducible character is equal to the set of vanishing elements of \( G \). In this paper, we prove Conjecture 1 from \cite{ourself}, which states that if \( \Gamma_{nv}(G) \) is null (has no edge), then \( G \) must either be a strongly \( \mathcal{H}_1' \)-group or a Frobenius group, whose Frobenius complement is isomorphic to \( Q_8 \). Additionally, we show that if there are no triangles in \( \Gamma_{nv}(G) \), this implies that the group is solvable. We also look at the situation where the common non-zero graph of a finite group \( G \) contains only one edge. This leads us to conclude that \( G \) is either isomorphic to \( S_4 \); or that the single edge in \( \Gamma_{nv}(G) \) is of the form \( \{\theta, \zeta\theta\} \) for some \( \zeta \in \Irr(G/G') \) and \( \theta \in \Irr(G|G') \), $G$ is a $p$-nilpotent group for some prime $p$ and for all characters \( \chi \in \Irr(G|G') - \{\theta, \zeta\theta\} \), we find \( \Van(\chi) = \Van(G) \). Lastly, our study also explores groups whose common non-zero graph forms a star shape, concluding that such configurations can only occur if \( G \) has exactly one non-linear irreducible character.

Presence research has often proceeded by addition, treating immersion, embodiment, agency, ownership, co-presence, reciprocity, and temporal simultaneity as conditions that stabilise the sense of being there. Yet immersive video suggests that several of these conditions can be weakened without eliminating Presence. Building on Bodyless Presence and Bodyless Presentness, this paper asks what is disclosed when such conditions are progressively subtracted. I distinguish three levels that should not be conflated: stabilising conditions that strengthen or support Presence; empirically resilient articulation-forms through which Presence is lived as here and now; and a transcendental limit-condition concerning the first-personal givenness of experience. Subtraction provides evidence for the resilience of here and now, but empirical resilience does not by itself establish constitutivity or transcendental necessity. I argue, on phenomenological rather than experimental grounds, that for-me-ness names the limit-condition within which any such spatial or temporal articulation can be experienced at all. The paper bridges operational Presence research with Husserlian givenness, Leibhaftigkeit, and image consciousness; rereads Bodyless Presence as exposing the resilience of here; rereads Bodyless Presentness as exposing the resilience of now; and develops a stratified account of Presence through Zahavi's pre-reflective self-awareness while taking Derrida's critique of self-presence seriously. It concludes by proposing immersive media as dissociation apparatuses for loosening conditions ordinarily coupled within experiential there-ness.

We develop a unified formulation of leading soft photon theorems for nondegenerate static spherical horizons. By fixing the photon mode normalization from the horizon symplectic form, we obtain a common angular soft factor whose sign follows from the boundary orientation. We determine the geometric coefficients in the local angular and momentum representations for a chosen radial normalization. The charge balance includes horizon endpoint data and contributions from other boundaries. This formulation brings black hole and cosmological horizons into a common description. Applying the same construction to Yang-Mills fields yields the corresponding tree-level soft gluon theorem. These results identify the common soft structure underlying different horizon geometries.

We present the conceptual framework of the Astronomical Hub (AstroHub), a unified platform combining various optical instruments at a single observatory. Its major approach lies in arranging conditions for research groups to install telescopes and equipment and participate in joint projects. AstroHub is planned to integrate Virtual Observatory (VO) tools, FAIR data principles, and a telescope network to create a powerful and attractive ecosystem for both robust near-Earth object (NEO) monitoring and diverse deep space research. We provide an overview of the AstroHub development directions in the case study of the Assy-Turgen Observatory.

In an adiabatic evolution, the wave function follows the path of ground states $|\Phi_0(s)\rangle$ of a Hamiltonian $H(s)$ as $s$ is tuned from $0$ to $1$. The geometry of this adiabatic path is described by quantities such as its length $L=\int_0^1 \|\partial_s |\Phi_0(s)\rangle\|\,ds$ and its total curvature $K$. This geometry affects the evolution time $T$. For instance, $T$ is at least of order $L/\Delta_*$, where $\Delta_*$ is the minimum energy gap over $s\in[0,1]$. The traditional approach gives $L=O(\Delta_*^{-1/2})$ and $K=O(\Delta_*^{-1})$, which are loose in many cases. We improve these bounds by using $\mu_<(\gamma)$, the width of the region in $s$ on which the gap is below $\gamma$. The gap profile is in width class $p$ when $\mu_<(\gamma)$ falls at least as fast as $\gamma^{1/p}$. A typical avoided crossing is in width class $p=1$, which gives $L=O(\sqrt{\log \Delta_*^{-1}})$ and $K=O(\log \Delta_*^{-1})$. A profile in width class $p>1$ gives power laws with exponents $(p-1)/(2p)$ for $L$ and $(p-1)/p$ for $K$. The width class also bounds the evolution time. At $p=1$ we have $T=O(\Delta_*^{-2})$ with a schedule that advances $s$ at a constant rate, and $T=O(\Delta_*^{-1})$ up to a polylogarithmic correction with a schedule that traverses the path at a constant geometric speed. The bounds on $L$ hold for any twice continuously differentiable $H(s)$, and the bounds on $K$ for affine $H(s)$. We also prove the tightness of scaling of $L$ in $\Delta_*$ for every integer $p\ge1$, and the scaling of $K$ at $p=1$. We demonstrate the bounds on the adiabatic Grover search, the XXZ spin chain, and molecular electronic Hamiltonians.

The development of advanced artificial intelligence is increasingly concentrated in a small group of vertically integrated technology companies. These firms control combinations of computing infrastructure, cloud services, data, foundation models, software ecosystems, and channels of distribution. This article argues that such concentration transforms market power into a form of private governance over the conditions in which fundamental rights are exercised. Drawing on an interdisciplinary narrative review, it examines how concentration affects equality of access, privacy, freedom of science, working conditions, access to essential resources, environmental protection, and the availability of effective remedies. Evidence from data-centre expansion in Ireland, the United Kingdom, the United States, and Chile, together with studies of automation and collective bargaining, shows that benefits may be widely distributed while decision-making power and economic returns remain concentrated. Concentration does not itself establish a rights violation, but it increases dependency, opacity, switching costs, and the risk that social and environmental costs are externalised. The article concludes that competition policy must be combined with rights-based impact assessment, interoperability, public research capacity, worker participation, and enforceable access to review and remedy.

While large language models have achieved remarkable success in isolated code generation, authentic software engineering requires sustained reasoning, complex state management, and continuous cross-domain abstraction. However, current evaluations of skill evolution in autonomous agents suffer from a critical identifiability problem: they structurally confound genuine capability abstraction with rote solution leakage (i.e., copying highly similar code from historical training data). To resolve this, we introduce EngramBench, a rigorous, capability-grounded benchmark governed by the strict axiom of capability overlap without solution overlap. Comprising 30 diverse learning tasks and 13 unseen transfer tasks, EngramBench challenges agents to navigate interactive, multi-hour development cycles driven by LLM-simulated users. Our extensive evaluation across 48 multi-hour execution trajectories – corroborated by human-expert validation – reveals a profound insight into procedural memory. We demonstrate that static skill banks do not magically bypass the "last mile" of exact code implementation, which remains bottlenecked by the base model's inherent reasoning limits. However, they serve as an indispensable execution compass. By navigating agents away from catastrophic, token-heavy trial-and-error, genuine capability abstraction slashes redundant context bloat and reduces overall coding time by over 55%. Ultimately, EngramBench shifts the evaluation paradigm from trivial pattern matching to the verifiable measurement of deep, cross-domain capability transfer.

In this paper, we investigate a viscous regularization for the BGK model of the Boltzmann equation and its hydrodynamic limit. First, we establish rigorous convergence toward the viscous Euler equations, by exploiting bounds derived from spatial Fisher information. We then analyze the formal derivation of the Euler equations with an entropy inequality for both single-and multi-species case, comparing our results against symmetric hyperbolic thermodynamically compatible theory.

An old conjecture in non-Kähler geometry states that if the Chern holomorphic sectional curvature of a compact Hermitian manifold is equal to a constant $c$, then the metric must be Kähler when $c\neq 0$ and be Chern flat when $c=0$. The conjecture is known to be true in dimension two by the work of Balas–Gauduchon and Apostolov–Davidov–Muškarov in the 1980s and 1990s. Recently, Qin and Tian proved the conjecture in complex dimension three when $c\neq 0$, and the $c=0$ case was proved by Chen–Li under the additional assumption that the metric is balanced. In this article we remove this additional hypothesis and complete the confirmation of the conjecture in complex dimension three. The proof relies heavily on the fact that in dimension three the torsion $3$-tensor can be equivalently expressed as a $2$-tensor twisted by the canonical line bundle, plus Bochner type integration formulas. In particular, the method cannot be directly generalized to higher dimensions.

We investigate inflationary dynamics and isotropization in a phantom-field model with five families of potentials on Bianchi I, Bianchi III, and Kantowski-Sachs backgrounds. First, the general properties of the model are established, and Heusler's proposition is extended. To address the limitations of this proposition, a powerful dynamical-systems approach is then adopted to provide a comprehensive analysis of the cosmological evolution. In total, 87 critical points are identified and their properties are analyzed. Throughout the analysis, we emphasize the physical interpretation of the mathematical results and aim to provide a thorough explanation of the rationale behind the choice of each mathematical tool and variable. Within this framework, the conclusions of Collins and Hawking and of Burd and Barrow are revisited, and several challenging questions with deep conceptual implications are posed and discussed.

We give collective tomography protocols for quantum states and channels with known symmetries, using random purification and dilation to reduce learning to pure-state estimation. For states commuting with a compact-group representation with multiplicities $m_\lambda$, the optimal copy complexity is $\Theta((\sum_\lambda m_\lambda^2+\log\eta^{-1})/\varepsilon^2)$ for sufficiently small trace-distance error $\varepsilon$ and failure probability $\eta$ for the nontrivial case $\sum_\lambda m_\lambda^2>1$. For $G$-covariant channels with finite-dimensional unitary representations of a compact group $G$, parallel $\widetilde{O}(D_G/\varepsilon^2)$ queries achieve a diamond-distance error $\varepsilon $ at fixed success probability $2/3$, where $D_G$ counts the real parameters of covariant Choi operators before imposing trace preservation. For permutation-covariant channels on $k$ qudits of fixed local dimension $d$, at sufficiently small fixed error and fixed success probability $2/3$, we obtain the optimal query scalings $\Theta_d(k^{d^4-1})$ for diamond distance and $\Theta_d(k^{d^4-d^2})$ for Choi trace distance. Furthermore, we resolve an open problem in quantum tomography of constructing efficient quantum circuits that approximate the Hayashi measurement for optimal pure-state estimation. We encode states in the symmetric subspace into bosonic occupation modes, realize the measurement by heterodyne detection and normalization, and approximate this procedure on qubits using the quantum Hermite transform. Combined with our symmetry-compatible purification and dilation circuits, this yields query-optimal and gate-efficient learners of permutation-covariant states and channels with gate complexity $O_d(\mathrm{poly}(k,\varepsilon^{-1},\log\eta^{-1}))$.

Machine unlearning has emerged as a crucial mechanism for removing hazardous knowledge and enforcing safety alignment in Large Language Models (LLMs). However, recent studies reveal a persistent security risk: unlearned models remain highly vulnerable to retraining attacks, where suppressed malicious behaviors rapidly resurface after benign fine-tuning. In this work, we investigate the optimization dynamics of unlearning and identify that this vulnerability stems from shallow alignment. Rather than effectively erasing target knowledge, models often exploit a shortcut by activating previously dormant parameters to act as spurious suppressors, forming a fragile inhibitory shell over intact malicious representations. To address this issue and enforce authentic memory deletion, we propose FDCU, a novel dual-constrained subspace projection framework. FDCU restricts parameter updates through a highly scalable, element-wise dual-masking rule: it preserves general knowledge manifolds via Fisher Information and strictly prohibits the abnormal activation of spurious suppressors via the Principle of Minimal Functional Intervention (PMFI). By reliably blocking the model's ability to superficially hide knowledge, FDCU promotes the authentic dismantling of target representations. Extensive experiments across specific knowledge erasure and safe output control tasks demonstrate that FDCU achieves state-of-the-art robustness against retraining attacks while maintaining near-lossless general utility, ensuring durable safety for LLMs.

Atomically precise graphene nanoribbons (GNRs) have electronic properties tunable through their width and edge structure, making them promising building blocks for nanoscale electronics and optoelectronics. Their integration into devices also requires understanding how the supporting surface and neighbouring ribbons affect their vibrations. Here, we use temperature-dependent Raman spectroscopy to compare five configurations of 9-armchair GNR arrays differing in substrate, alignment and coverage. Transferring the same unaligned film from Au to a Raman-optimised Al$_2$O$_3$-coated support reduces the measured $D$- and $G$-mode redshift rates by about 80%. This reduction is consistent with a substantial thermoelastic contribution. The fitted strain and anharmonic contributions depend on the assumed thermal expansion and strain transfer. Compared with the low-coverage array, the dense aligned Au array has higher extrapolated reference frequencies ($\omega_0$). On first heating, its $G$-mode linewidth decreases and then increases, forming an unusual intermediate-temperature minimum. The $D$-mode linewidth shows a similar, less pronounced variation. These findings establish substrate choice and array arrangement as routes to engineer nanoribbon vibrations, extending control beyond the atomic structure defined during synthesis.

Looped models reason by applying the same block of weights many times, so compressing that block saves memory traffic on every loop. Compressed looped models, however, often collapse, and the collapse is usually blamed on rounding error that accumulates from loop to loop. In this work we test that account on more than 30 models from five families and find, to our surprise, that it holds only for loops that never settle. When a loop settles, a fixed rounding error does not accumulate. It moves the point where the loop settles, much as tilting a bowl moves where a ball comes to rest, and the answer is lost only when the shift is larger than the readout tolerates. This picture lets us predict which models fail from a single label-free measurement, and it tells us why failed models recover: their loops still settle, so a few final loops with 8-bit weights bring the answer back. Motivated by these findings, we build a controller that stops when the model's halting head fires and then finishes with 8-bit loops. On Sudoku-Extreme and Maze-Hard it beats fixed-depth inference by up to 15 points under a third of the weight traffic.

We prove interior curvature estimates for admissible graphical solutions of curvature quotient equations in the range $3\leq k<n$ on the full Gårding cone $\Gamma_k$. No convexity, semiconvexity, or $\Gamma_{k+1}$-admissibility assumption is required. The proof combines a new quantitative compression inequality, a two-surface comparison and doubling argument, and a Pogorelov estimate.

On-policy distillation (OPD) trains a student on its own generated prefixes with token-level teacher feedback, but transmitting or storing the teacher's full-vocabulary distribution at every token is costly. Entropy-aware OPD (EOPD) adds forward supervision to reverse KL to help the student recover plausible tokens it underestimates, using only the teacher's top-$k$ probabilities to limit cost. Because EOPD renormalizes these probabilities, its target assigns no mass to the omitted vocabulary. We prove that the resulting loss keeps pushing the student's top-$k$ mass toward one even after the student matches the teacher's relative probabilities within the top-$k$ set, so the teacher itself is not a stationary point whenever the omitted tokens have positive teacher probability. We propose ReTaCo (Residual-Target Control), which keeps the top-$k$ tokens individually and groups the remaining tokens into one residual symbol, and pairs this forward target with a single-sample estimator whose expectation equals the full-vocabulary reverse KL. With teacher top-$k$ mass $m$, the residual target is $(1-\beta)(1-m)$ for $\beta\in[0,1]$: $\beta=0$ preserves the teacher's mass, and larger $\beta$ moves more mass onto the top-$k$ tokens without changing their relative probabilities. At a fixed prefix, we prove that the population objective has a unique optimum whose top-$k$ mass lies between $m$ and $m+\beta(1-m)$ and increases monotonically with $\beta$; at $\beta=0$, underestimated top-$k$ tokens still receive non-vanishing recovery gradients. Numerical optimization confirms these predictions, and across three teacher-student pairs, ReTaCo outperforms EOPD on most mathematics and code benchmarks.

Reinforcement learning and contextual bandit algorithms have become increasingly common in sequential decision-making applications. When these methods are deployed in high-stakes domains, there is growing interest not only in learning effective policies, but also in conducting statistical inference for quantities learned under adaptive data collection. However, classical procedures applied naively in these settings can fail: even when estimators are unbiased, their variance becomes path-dependent and as a result may not be asymptotically normal. A growing literature has emerged to ameliorate this problem, but solutions tend to be problem specific and often rely on correct specification of a working model. In this work, we develop a unified framework for constructing asymptotically valid confidence intervals to cover smooth functionals of nonparametric M-estimands under adaptive sampling. Under Neyman orthogonality, we provide two novel methods for performing inference: (1) a self-normalized statistic based on the realized quadratic variation of the influence function and (2) a statistic using a plug-in estimate of the conditional variance based on reweighted influence function increments. Our results allow for flexible nonparametric estimation of nuisance parameters and remain valid under model misspecification. Our theory is supported by a simulation study for a dynamic pricing application which demonstrates that this method can produce asymptotically valid confidence intervals where standard methods fail.

This report presents MegaAvatar, a controllable talking avatar generation framework built on top of the Wan2.2-TI2V-5B model. Compared with previous talking-avatar methods that mainly rely on audio or reference-image conditioning, we introduce additional SMPL-X-derived 3D guidance, enabling global control over body pose and head motion. Specifically, we render the driving SMPL-X sequence into dense mesh frames and encode them with a lightweight 3D convolutional encoder, whose outputs are injected into the latent tokens to provide overall motion control. Furthermore, we extend Wan2.2-TI2V-5B with additional audio and face cross-attention modules to enable fine-grained expression control and preserve the input identity, respectively. In addition, we implement an audio-to-SMPL-X model to predict an SMPL-X sequence conditioned on the reference image and input audio, allowing MegaAvatar to support audio-driven inference without user-provided SMPL-X frames. Experiments show that MegaAvatar achieves high-quality talking avatar generation with controllable body and head motion, speech-synchronized facial expressions, and consistent identity preservation. MegaAvatar also supports inference with flexible resolutions and video lengths. Codes, dataset, models will be avaliable in https://github.com/Jeoyal/MegaAvatar

The Three-Dimensional Trailer Loading Problem (3D-TLP) involves determining the optimal placement and orientation of heterogeneous items within the confined space of a trailer while maximizing volume utilization and satisfying a wide range of complex logistical and safety constraints. The 3D-TLP is NP-hard, rendering exact optimization approaches computationally impractical for large-scale industrial applications. To address this challenge, we propose an enhanced Biased Random-Key Genetic Algorithm (BRKGA) accelerated through a novel island-based parallelization framework, PANGEA. The proposed method combines the search efficiency and robustness of BRKGA with a multi-population evolutionary scheme for genetic algorithms. This island-model strategy promotes population diversity, mitigates premature convergence, and significantly reduces computational times. The proposed solution was validated in a real trailer loading process, providing an effective solution approach for real-world large-scale logistics.

Manifold-valued data, and consequently the distributions they induce, are prevalent across many domains, ranging from the locations of geospatial events, such as earthquakes, to biomolecular torsion angles that encode information about three-dimensional structure. While diffusion and flow-based generative models have been successfully extended to compact manifolds, sampling typically requires tens or hundreds of sequential network evaluations. We introduce RW-Flow, a theoretically grounded framework for learning one-step generative models on compact manifolds via Wasserstein gradient flows. The main challenge is identifiability: driving the velocity field to zero should guarantee that the model distribution matches the target distribution. We establish a necessary and sufficient condition for identifiability on compact, connected Riemannian manifolds. We specifically show that, for a symmetric, Lipschitz-continuous cost function, the velocity field induced by the Sinkhorn divergence is identifiable if and only if the associated Gibbs kernel is nondegenerate. This characterization provides a general principle for designing identifiable costs on compact manifolds. It also reveals that the squared geodesic distance, the natural manifold analogue of the squared Euclidean distance, does not always guarantee identifiability. Across benchmarks involving geospatial events, protein side chain torsion angles, RNA backbone torsion angles, and general manifolds discretized as triangular meshes, RW-Flow outperforms existing one-step methods in nearly all settings under fair comparison conditions.

We investigate a stochastic individual-based population model with trait-dependent reproduction, death, competition, variation, and deleterious transfer. Nonlinearities appear in the competition term and the transfer form, which moreover is asymmetric. In the large-population limit, the process converges to a deterministic measure-valued equation. The latter helps us to uncover the past history of living individuals. We replace in the interactions the original stochastic process with the deterministic large population approximation obtaining a nonhomogeneous measure-valued branching process, for which we use a spinal decomposition, generalizing a method that existed only for the stationary case. Reversing time, we identify the law of typical ancestral lineages. This approach encompasses a variety of settings and requires delicate functional analysis. In contrast to earlier approaches in the literature, which relied either on stochastic calculus or on favourable jump structures under stationarity assumptions, our method provides a more direct and more general point of view.

Dynamic Discretisation Discovery (DDD) is a framework for solving a problem by iteratively solving and refining a relaxed version of the problem. DDD is the basis for state-of-the-art algorithms for various problems, including the continuous-time service network design problem (CTSNDP), which we study here. In the refinement step, such algorithms must identify conflicts in the relaxation solution that make it infeasible for the original problem and then apply fixes to the relaxation to prevent them from recurring. We study the optimal refinement problem of selecting from a set of fixes a subset that fixes all conflicts and yields a relaxation of minimum size, with the aim of making it easier to solve. We demonstrate that while the number of conflicts may be exponential in the instance parameters, we can represent them more compactly, using only pseudo-polynomial space and time. Based on our more compact representation, we develop exact methods for solving the refinement problem. The best method allows us to find small relaxations in negligible amounts of time, more than 100 times faster than a natural integer programming formulation for some instance classes. Using this refinement approach in a DDD algorithm for the CTSNDP, we observe reductions in model sizes and running times of about 10 to 20 % compared to existing approaches.