Papers

We study Galois coinvariants of the geometric étale fundamental group and étale cohomology of varieties over a finitely generated field $k$. We establish finiteness properties of these coinvariants for (possibly infinite) Galois extensions $L/k$ such that $\operatorname{Gal}(L/k)^{\mathrm{ab}}$ has finite exponent. As an application, we obtain a finiteness result for étale fundamental groups of arithmetic schemes over number fields.

Latent diffusion models generate images as codes of an image tokenizer, whose decoder turns them into the pixel image. Recent tokenizers improve how well these codes reconstruct an image and how easily a generator learns them. Yet a generator does not reproduce the codes of training images, and when a generated code lands outside what the decoder expects, the decoded image contains imperfections. Current methods make the decoder more robust to generated codes by adding noise during training. However, generated codes lie between the training codes and resemble their mixture more than one of them plus noise. To improve generated images, decoders should therefore be trained on codes in the space between training samples. We propose InterpTok, which fine-tunes MAETok to decode mixtures of image codes into natural images. Since no target image exists between two training samples, a discriminator judges whether each decoded mixture looks as natural as its two sources. A mixing ratio loss requires the decoded mixture to keep the mixing ratio of the two codes. Together, they prevent collapse to a trivial solution and yield a sharp and natural composition of both images. InterpTok keeps MAETok's reconstruction quality and improves interpolation quality more than threefold, the best of all tokenizers in a recent benchmark. Beyond interpolation, InterpTok improves the generation FID of a matched diffusion transformer from 11.61 to 8.48 without guidance, and even reaches 8.11 at an eighth of the sampling steps, where the generator on MAETok's codes worsens. The generator trained on our tokenizer also reaches the final result of the one trained on MAETok at half the training steps. Our findings show that the space between image codes can and should be explicitly supervised rather than ignored.

We study finite involutive multivalued groups associated with Schur rings. Their reduced valency is shown to equal the least common multiple of the sizes of the basic sets of the corresponding ring. We prove that the double-coset group associated with a complemented subgroup of a finite group is isomorphic to a Schur multivalued group over the complement. In particular, every coset multivalued group is a Schur multivalued group. Using affine Schur rings, we construct families of pairwise nonisomorphic commutative multivalued groups over elementary abelian groups. We obtain asymptotic bounds for the sizes of these families and prove that the proportion of double-coset groups in them tends to zero.

Comparing machine-labelled sentiment across social media platforms is now routine: differences in classifier scores between platforms are read as differences in public opinion. These comparisons rest on an assumption that the classifier measures the same construct, on the same scale, on every platform. Some studies check a classifier's validity platform by platform, but to our knowledge none has modelled the platform as a facet of the classifier's measurement. We adapt the psychometric equivalence toolkit (generalizability theory, measurement invariance and differential item functioning, and score linking) to machine-labelled policy sentiment, treating the platform as a survey mode, and specify a six-step protocol with anchor events fixed in advance, an anchor-density audit, and a two-classifier convergence control. A simulation with known ground truth illustrates what the assumption can cost in one generating configuration fixed in advance: across 500 replications, because the platforms measure through different functions, a pooled index that takes platform scores at face value reports the wrong sign of aggregate sentiment on nearly a quarter of days, whereas an index adjusted with each platform's known measurement function does so on under one day in sixty on average. A case study of the instrument from the first author's MSc dissertation, a fine-tuned BERT classifier over 255,446 UK economic-policy comments from Twitter/X, Reddit, YouTube, and Quora, motivates the design and illustrates the instrument-dependence the protocol addresses. The full four-platform application, under fresh collection with the pre-specified design, is the designated follow-up study. The protocol lets a researcher test whether pooling platforms is defensible in a given corpus, or whether platform scores must be linked before any average is taken.

Bergeron, Garsia, Haiman, and Tesler conjectured that $(-1)^{n-\ell(\mu)}\nabla\widetilde H_\mu[X;0,t]$ and $\nabla\omega \widetilde H_\mu[X;0,t^{-1}]$ are Schur positive, and that $\nabla\omega \widetilde H_\mu[X;0,t^{-1}]-\nabla\omega \widetilde H_\nu[X;0,t^{-1}]$ is Schur positive when $\mu$ dominates $\nu$. The first statement follows from the compositional shuffle conjecture of Haglund, Morse, and Zabrocki, proved by Carlsson and Mellit. We prove the other two statements. All three statements also hold for $\nabla^r$ with $r\geq1$. The main new step is an identity: when $\mu$ covers $\nu$, the difference $\omega \widetilde H_\mu[X;0,t^{-1}]-\omega \widetilde H_\nu[X;0,t^{-1}]$ is minus a power of $t$ times one LLT polynomial. Using the Catalanimals and the Cauchy identity of Blasiak, Haiman, Morse, Pun, and Seelinger, we show that $\nabla^r$ of this LLT polynomial is, up to sign, a positive sum of LLT polynomials. We also extend the main results to the Schiffmann algebra setting.

Text generated by Large Language Models (LLMs) often remains limited in diversity compared to that produced by humans. Recent advances demonstrate the presence of inter- and intra-model collapse in open-ended generation of English text, raising concerns about the long-term homogenization of LLM, and more importantly, human thought. However, our understanding of whether this homogenization extends to languages beyond English is limited. In this work, we investigate the role of language on output diversity. Specifically, we aim to understand whether multilingual LLM-generated text is also homogeneous, and whether this homogeneity matches what we observe in humans. Across 23 open-weight models and 13 languages, we find that the artificial hivemind effect is pervasive but uneven in its extent. The intra-model effect holds in three different embedding spaces and under a lexical metric that uses no embedding model, so it is not an artifact of how diversity is measured. The size of the homogenization gap is associated with a model's competence in a language, measured on a held-out translation benchmark, robustly across embedding spaces. Thus, we demonstrate a performance-diversity tradeoff in multilingual LLMs.

Event studies with panel data are widely used to estimate treatment effects. With repeated cross-sections, future treatment dates are unobserved for untreated individuals. Pseudo-panel event studies impute pre-treatment outcomes of the treated using matched untreated individuals. This paper establishes identification in such designs and characterizes bias when identification conditions fail. I show that the pseudo-panel regression is equivalent to weighted least squares with group means. This representation simplifies computation and yields analytical inference. In simulations, analytical confidence intervals attain near-nominal coverage, whereas conventional intervals substantially undercover. I also develop a doubly robust estimator using richer covariates, a symmetric matching design with synthetic type fixed effects, and a fully nonparametric estimator that accommodates heterogeneous treatment effects. In a Korean panel survey, the pseudo-panel regression yields an employment child penalty of 42.1%, close to 46.9% in the actual panel. Applications to repeated cross-sections yield employment penalties of about one-third.

We improve the Plesken–Souvignier algorithm for computing automorphism groups and isometries of positive definite integer quadratic lattices by exploiting characteristic sublattices and refining vector enumeration. For lattices with roots, we also use the Weyl group to accelerate the computation of canonical forms. Experiments with concrete implementations demonstrate substantial speedups and show that canonical forms can be computed at a cost comparable to that of computing automorphism groups.

We derive a distance between thermodynamic states from a positive Hermitian transport tensor within a mesoscopic canonical model. An exact first-order factorization of the evolution generator gives a commutator norm and the metric $G=2g$, where $g$ denotes the symmetric transport tensor. Gradients of the antisymmetric tensor can change the evolution, but they leave this distance unchanged. The construction allows coordinate-dependent coefficients. For constant Onsager coefficients, a Clifford representation gives the same metric. In a two-channel thermoelectric system, the ratio of normalized principal distances is $\sqrt{1+ZT}+\sqrt{ZT}$. Transport coupling thus fixes the anisotropy of this metric. The construction requires neither an independent metric nor a physical spin variable.

The classical Hurwitz bound gives a linear upper bound in terms of the genus for automorphism groups of algebraic function fields in characteristic zero, whereas algebraic function fields in positive characteristic can have much larger automorphism groups. Usually, one considers the case where the constant field is an algebraically closed field. Here we focus on function fields over a finite constant field. It turns out that the situation is very different. We firstly investigate solvable subgroups and $p$-subgroups of $\rm{Aut}(F/\Bbb{F}_q)$, where $p=\rm{char}(\Bbb{F}_q)$ and $F/\Bbb{F}_q$ is a function field of genus $g_F\ge2$ with full constant field $\Bbb{F}_q$. We prove that there are explicit constants $C_q^{(sol)}$ and $C_q^{(p)}$, depending only on $q$, such that, for every solvable subgroup $G\le\rm{Aut}(F/\Bbb{F}_q)$ and every $p$-subgroup $P\le\rm{Aut}(F/\Bbb{F}_q)$, $$ |G|\le C_q^{(sol)}(g_F-1),\qquad |P|\le C_q^{(p)}(g_F-1).$$ In particular, one may take $C_q^{(sol)}=12q^2(q-1)$ for $q\ge4$ and $C_q^{(p)}=5q$ for every $q$. In the second part of this article, we give asymptotic lower bounds for solvable automorphism groups. For every $q$ there is an explicit constant $L_q>0$ and a sequence of function fields $F_i/\Bbb{F}_q$ with $g_{F_i}\to\infty$, together with solvable subgroups $G_i\le\rm{Aut}(F_i/\Bbb{F}_q)$, such that $$ |G_i|\ge L_q(g_{F_i}-1) $$ for all $i$. For $q\ge5$ one may take $L_q=2q(q-1)/(q-2)$. If $q=r^2$ with $r\ge3$, an unramified tower construction over the Hermitian function field gives the stronger choice $L_q=2r^3(r-1)/(r-2)$. Moreover, as an application of our tower construction above, we improve the asymptotic lower bound of Ma and Xing for subgroups of $\rm{Aut}(F/\Bbb{F}_q)$ whose order is relatively prime to $p$. As another application, we extend our method to obtain explicit linear bounds for $p$-solvable groups in terms of the genus.

We present NFMap, a dimensionality reduction method for 2D visualisation that extends Generative Topographic Mapping (GTM) with a bijective normalizing flow. Like GTM, NFMap places a fixed mixture grid prior over a 2D latent map, giving a parametric embedding, an explicit likelihood, and the ability to project new points onto an existing map; the likelihood is an effective out-of-distribution signal on chemical datasets. Unlike GTM, whose latent-to-data mapping is an RBF network of bounded flexibility, NFMap's mapping is a normalizing flow, and is therefore fully invertible: any location on the map can be carried back to data space. To alleviate map crowding on large datasets, NFMap additionally supports heavy-tailed Student-t mixture components. NFMap maps data to a latent space of the same dimension, split into a 2-dimensional navigable map and an off-manifold residual. Because the flow is bijective and its objective penalises volume contraction, variance squeezed out of the residual must reappear in the navigable map. The residual scale is the main control between local neighbourhood fidelity and global distance fidelity; its effect depends on the dimensionality of the data and is coupled to the extent of the latent grid.

Recent foundation models have drastically improved the generalization of monocular relative depth estimation, yet recovering accurate metric depth from their estimates for depth perception tasks remains challenging due to scale ambiguity and local metric-scale inconsistency. Existing approaches recover metric depth from sparse observations using either explicit global affine transformation algorithms or implicit data-driven depth completion networks. The former cannot accommodate spatially varying relative-to-metric relationships, while the latter are sensitive to the distribution of sparse observations and may not fully exploit generalizable relative depth priors. To simultaneously address these issues, this study extends our previous work MTD and proposes MTDv2, a hybrid metric depth perception framework that combines explicit depth metricization with data-driven metric depth refinement. The explicit depth metricization process performs segment-wise affine transformations to recover spatially varying metric scales while preserving the geometric structure of relative depth, followed by pixel-wise depth refinement that propagates metric observations along paths with minimal accumulated geometric variation. The data-driven depth refinement process subsequently extends the explicit single-path depth propagation to a learnable multi-path formulation while preserving its interpretability. Extensive experiments conducted on 16 public datasets demonstrate the robust and generalizable depth scale recovery capability of MTDv2 across diverse sources of sparse observations and different depth estimation paradigms, as well as its broad applicability to downstream 3D perception tasks. Code will be publicly available at https://mias.group/MTD upon publication.

We study two sharp competition thresholds in the Lotka-Volterra competition-diffusion system: the zero-speed threshold for bistable traveling fronts and the linear-determinacy threshold for monostable traveling fronts. Building on our previous results on propagation direction and the classification of traveling waves, we derive explicit Gaussian integral representations of both critical parameters, without involving unknown traveling-wave profiles or speeds. These formulas provide exact characterizations of the optimal competition parameters separating the corresponding propagation regimes. The derivation of these representations was assisted by ChatGPT (OpenAI) Pro, while the underlying theoretical foundations were established in our earlier works.

We study endpoint Schatten class properties of commutators $[I_\theta^\epsilon,M_x]$ on quantum tori of dimension $d\geq2$, where $I_\theta^\epsilon$ is the Riesz potential of order $\epsilon$ and $M_x$ denotes the left multiplication operator by an operator $x$ on quantum tori $\mathbb T_\theta^d$. For $-\frac{d}{2}<\epsilon<1$, $\epsilon\neq0$, and $x\in L_1(\mathbb T_\theta^d)$, we prove that $[I_\theta^\epsilon,M_x]\in \mathcal L_{\frac{d}{1-\epsilon},\infty}$ if and only if $x\in\dot W_{\frac{d}{1-\epsilon}}^1(\mathbb T_\theta^d)$. We also determine the singular value asymptotics of this commutator for $x\in\dot W_{\frac{d}{1-\epsilon}}^1(\mathbb T_\theta^d)$. The necessary Sobolev condition holds throughout $1-d<\epsilon<1$, $\epsilon\neq0$. For $\epsilon\leq-\frac{d}{2}$, we characterise Hilbert–Schmidt membership, with a logarithmically weighted Fourier condition at $\epsilon=-\frac{d}{2}$. In order to get the singular value asymptotics of commutators, we prove singular value asymptotics for pseudodifferential operators of arbitrary negative order on quantum tori using $C^*$-algebraic principal symbols. This asymptotic result confirms Conjecture~7.1 of McDonald and Ponge (Adv. Math. 412 (2023), 108815).

Generalizing the setting of the second author's work on indecomposable modules without nonzero hollow factors, we characterize quivers $Q$ for which the dual algebra $R$ of the path coalgebra of $Q$, equivalently the complete path algebra, has no nonzero uniform right ideals: this happens exactly when every vertex of $Q$ can reach a vertex emitting at least two distinct arrows. Equivalently, the injective hull $E(R)$ of the right regular module is superdecomposable. These conditions are also equivalent to the path coalgebra having no nonzero hollow factor modules as a left module over its dual algebra.

Attention sinks are usually studied after they have formed. We ask whether a measurable hidden-state change appears beforehand and whether changing that geometry alters what happens later. To remove network depth as a shortcut, we compare prompts in the same model and at the same layer. When sink timing varies across prompts, simple spectral summaries of the hidden states add information beyond current attention, with the clearest prompt-specific signal in a short window about two to three layers before sink formation. The predictive strength varies across cohorts, so we treat the spectrum as a readout of a pre-sink state change rather than a universal warning statistic. The signal is broader than one measured extreme activation. We then modify only the singular values of the post-layer hidden states after current attention has already been computed. These interventions change later sink behavior in Qwen2.5, GLM-Z1, and GPT-OSS relative to norm-matched random spectral perturbations. In Qwen2.5, the immediate suppressive effect is accompanied by a reduction in next-layer query–key preference for position~0, and the learned spectral directions remain stable when estimated from substantially less training data. Together, the results show that attention sinks are preceded by a short spectral reorganization of hidden states, and directly perturbing this geometry can causally alter subsequent sink formation.

Video large language models (Video LLMs) encode each frame into hundreds of visual tokens, making video inference expensive. Existing methods reduce this cost through similarity-based merging or attention-based selection but face two challenges: Hierarchy-blind Pruning, which overlooks regional compressibility and can discard critical evidence, and Attention Drift, where positional effects and attention sinks shift text-to-vision attention away from task relevance. We propose FoveaTree, a two-stage, training-free visual-token pruning framework. First, Merge-Gain Density Estimation measures the feature distortion caused by regional merging and constructs a quadtree-derived density map to guide token dropping, merging, and retention. Second, Attention Tree Pruning uses the surviving units and inherited tree topology to refine text-to-vision attention in intermediate LLM layers, preserving relevant regional evidence while removing low-relevance content. We evaluate FoveaTree on InternVL3.5-8B and Qwen3-VL-8B across five video question-answering benchmarks and one captioning benchmark at 50%, 30%, and 10% visual-token retention. FoveaTree consistently achieves overall state-of-the-art performance across the evaluated settings, offering a strong accuracy-efficiency trade-off.

Let $f$ be a homeomorphism of a closed orientable surface of genus at least one that is isotopic to a pseudo-Anosov homeomorphism, possibly relative to a finite invariant set. We construct an intrinsic monotone factor by collapsing the maximal continua whose iterates have uniformly bounded diameter in the universal cover. The quotient is homeomorphic to the original surface and the factor is isotopic to $f$ and has several strongly chaotic dynamical features. It is infinitely continuum-wise expansive, tight, and topologically mixing, and it has a dense family of rotational horseshoes, dense periodic points, and a single topological homoclinic class. The factor can be taken as an area-preserving homeomorphism. The quotient preserves stable translation length on the fine curve graph and the applicable homological rotation sets. When $f$ is $C^\infty$, a companion paper gives a unique measure of maximal entropy for the factor; it has full support and is Bernoulli.

We present the cross-match of galaxy clusters detected by redMaPPer using the first three years of Dark Energy Survey (DESY3RM) operations, and the first release of the eROSITA-All Sky Survey (eRASS1) taken by eROSITA on board the Spectrum Roentgen Gamma telescope. We define a sky region ($60^{\circ}<{\rm R.A.}<90^{\circ}$ and $-58^{\circ}<{\rm Dec}<-48^{\circ}$) whereby the mean eRASS1 exposure time of clusters falling within this footprint is $\sim$2.5 times longer than the mean exposure time of the full eRASS1–DESY3RM overlap. Limiting to a redshift range $0.2 < z < 0.65$ and redMaPPer estimated richnesses to $>$50, we obtain a sample of 57 clusters. We match these clusters to the cluster catalogue constructed for the eRASS1, finding 45 clusters with a match and 12 with no match in the catalogue. X-ray properties of the 12 unmatched clusters are estimated via a forced photometry analysis. We investigate the form of the luminosity-richness relation, finding the relation using the full 57 cluster sample is statistically consistent with using only the 45 matched clusters, and will require the deeper data of future eRASS releases (or dedicated X-ray follow-up) to explore further potential differences. Using external data from XMM, ACT and SPT, we find detections of 5 of the 12 unmatched clusters, indicating the presence of virialised gas. Finally, we found the 12 unmatched clusters occupy a higher redshift range and lower richness range (compared to the matched clusters), and find no evidence for an underlying physical reason for the lack of X-ray emission.

We present the cross-calibration of the eROSITA and XMM telescopes, using galaxy clusters detected by redMaPPer from the first three years of Dark Energy Survey observations (DESY3RM). We use the X-ray: Generate and Analyse (XGA) Python module to measure eROSITA properties, and validate our methodology using a deep pointed eROSITA CAL-PV observation of A3158, and a sample of 119 clusters from the expanded HIgh FLux Galaxy Cluster Sample (eeHiFLUGCS). Next, we construct a sample of DESY3RM clusters matched to XMM observations analysed by the XMM Cluster Survey (XCS), and to clusters in the first release of the eROSITA All-Sky Survey (eRASS1). This produced a sample of 114 DESY3RM clusters with both XMM and eROSITA detections. Our resulting X-ray temperatures determined from eROSITA were compared to eRASS1 catalogue values, showing consistency between the two analyses. Comparisons between XMM and eROSITA temperatures reveal a systematic offset, with XMM temperatures 28$\pm$7% higher on average. Finally, we fit $L_{\rm X,soft}$-$\lambda_{\rm RM}$ and $T_{\rm X}$-$\lambda_{\rm RM}$ scaling relations for both eROSITA and XMM using the same cluster sample, finding minimal differences in the $L_{\rm X,soft}$-$\lambda_{\rm RM}$ relation but a clear normalisation offset in the $T_{\rm X}$-$\lambda_{\rm RM}$ relation, particularly for the highest richness systems. This study will enable future work combining eROSITA and XMM observatories for DESY3RM clusters.

We study one-dimensional marginals of an isotropic, log-concave probability measure in $\mathbb{R}^n$. We show that the Kolmogorov distance between a typical marginal and the standard Gaussian distribution is at most $C/n$, for a universal constant $C > 0$. This bound is optimal in general, up to the value of the universal constant. It improves the Gaussian approximation bound of Bobkov, Chistyakov and Götze by a logarithmic factor in the log-concave setting.

In artificial (micro)capsules or cells such as red blood cells for example, the two-dimensional (2D) rheology of the membrane (or the shell) is viscoelastic and not only elastic. The deformation and inclination of such a capsule are theoretically studied under shear and extensional flows. The membrane mechanics is described by the Kelvin-Voigt model: the 2D dissipation with the Boussinesq-Scriven law associated to specific dilational and shear Boussinesq numbers $Bq_d$ and $Bq_d$ respectively while the elastic constitutive law is either Hookean, strain-softening (neoHookean) or strain-hardening (Skalak). The dynamics depends on the elastic capillary number $Ca$, the Poisson ratio (or $C$ in Skalak law), the viscosity ratio $\lambda$, the nonlinearities included in the constitutive law and both boussinesq numbers. Three dynamics are identified in the limit of weak deformations: a tank-treading motion in the limit of small elastic capillary number with a characteristic time depending on $\lambda$, $Bq_s$ and $Bq_d$, an oscillation without any elasticity and a damped oscillation leading to a tank-treading motion in the limit of large Boussinesq numbers. In all cases, both shear and dilational 2D dissipations contribute differently leading to non-trivial results. In the case of a Skalak law with $C=1$, $Bq=Bq_s=Bq_d$ and $Bq>>\lambda$, the deformations in the limits $Ca<<1$, $Bq=O(1)$ and $Ca=O(1)$, $Bq>>1$ determined in the seminal work of \cite{barthes1985role} are recovered.

We reconstruct a geometry of thermodynamic coordinates from transport coefficients within a mesoscopic canonical model. Self-adjoint flux observables determine a compatible evolution generator containing symmetric and antisymmetric transport coefficients. When the Hermitian transport tensor is positive, an exact graded first-order factorization reproduces this generator on its scalar sector. Its commutators define a spectral distance whose metric depends only on the symmetric tensor. Gradients of the antisymmetric tensor can change the evolution while leaving the metric unchanged. The construction allows coordinate-dependent coefficients. In the constant Onsager regime, a Clifford representation gives the same distance and an algebra fixed by the transport matrix. Published transport data for a $\mathrm{Bi_2Te_3}$ film give a principal-distance ratio of approximately $2.12$ in normalized coordinates at $ZT\simeq0.68$. We also examine a separate quadratic entropy-production observable and distinguish its discrete spectrum from the spectrum of the evolution generator. The spinorial representation adds no physical spin degrees of freedom.

Video-to-robot pipelines for quadrupedal imitation insert a learned lifting stage, either a monocular depth model or a per-clip 3D reconstruction, to recover the one axis a side-view camera cannot see. We present CopyQuad, which omits that stage and pins the missing axis to the robot's own stance width instead. The setting is side-view footage of sagittally dominated motion, where limb motion is almost entirely in the image plane. A frozen 2D keypoint detector and a fixed analytic retargeting then turn a single uncalibrated clip into a robot reference whose foot targets are reachable by construction, so no per-clip trajectory optimization is needed. One phase-indexed reward structure, whose only per-behavior freedom is three scalars from a shared sweep, learns a dog walk, a horse walk, a horse trot and two non-periodic gestures, all deployed zero-shot on hardware. We then measure what omitting the axis costs. In a training-free rigidity test, a video depth model varies the distance between the animal's hips by $40$ to $107\%$ of its own mean and a single-image metric model by $22$ to $58\%$, though that distance cannot move. Motion capture puts the true lateral paw travel of a dog walk at $4.5$ cm peak to peak, a mean deviation near $1.4$ cm against the $3.5$ cm of lateral foot error our policies already leave, so the discarded axis sits below the pipeline's resolution. Depth repaired to feasibility never beats the constant, and the unrepaired estimates put the robot on the ground.

Monte Carlo sampling algorithms aim to produce samples from a target distribution with a given unnormalised probability density function. The high cost of running Monte Carlo algorithms, with many simulation steps or particles needed to obtain a good empirical approximation to the target, can be reduced by introducing learnable components into the sampler – a form of amortisation. Once these components are trained, amortised samplers can produce high-quality samples with less computation at sampling time than training-free algorithms would require. We propose an amortised sampler built upon the framework of adaptive importance sampling – a hierarchical importance sampling procedure where the proposal is iteratively adapted. Our amortised adaptive importance sampling algorithm fits a lightweight neural network that adapts the proposal using information obtained over the course of sampling. By training our sampler over many different targets taken from the same family of distributions, we obtain a sampler that can adapt to a specific target at sampling time without a priori access to the target's parameters. We show that our procedure can efficiently sample from targets within the family the sampler was trained on, giving improvements over target-specific amortised samplers and training-free adaptive importance sampling algorithms. We also explore the potential for generalisation, where the trained sampler is used to sample from targets outwith its training family.

Multimodal reinforcement learning with verifiable rewards commonly assigns one sequence advantage to an entire response. This outcome-level signal distinguishes overall response quality but leaves changes in visual-evidence use across generated tokens implicit. We introduce VAttnPO (Visual Attention-Guided Policy Optimization), which uses answer-conditioned visual attention to refine token-level credit while preserving the verifier-derived trajectory-mean advantage. A frozen old policy constructs a visual reference by teacher forcing the known correct answer and produces a visual distribution for each rollout token. VAttnPO measures their agreement in visual-attention space using Jensen–Shannon divergence, rather than reading guidance from teacher output-token distributions or introducing an attention-matching objective. Trajectory centering, relative-position weighting, and credit balancing turn this agreement into a zero-mean, position-aware correction to the GRPO sequence advantage. Token intervention, visual-index permutation, and trajectory analysis provide diagnostic evidence linking this signal to model behavior, visual correspondence, and generation position. On Qwen3-VL-8B-Instruct, VAttnPO raises six-task image AVE from 70.97 with GRPO to 73.50 and scores higher on every reported structured, video, and MME metric. Gains over GRPO also hold on Qwen2.5-VL-7B-Instruct and InternVL3-8B-Instruct.

The diagnostic capability of WSI agents relies on effective slide navigation to identify diagnostically relevant regions and efficiently integrate evidence across the slide. While in clinical practice, pathologists dynamically examine slides across multiple scales, integrating global and cellular evidence in a sequential manner, existing AI navigation approaches mostly operate at a single fixed magnification or rely on predefined magnification traversal. This mismatch prevents existing methods from modeling cross-magnification interactions and adaptive magnification selection inherent to real diagnostic workflows. We propose PathPilot, a clinically consistent multi-magnification WSI navigation agent that explicitly models cross-magnification localization and evidence-adaptive exploration. Specifically, we introduce a CrossMagLoc that learns magnification-specific diagnostic localization from pathologist viewing behavior and integrates information from adjacent magnifications to identify the diagnostically most relevant region within the current ROI, thereby providing a diagnostically informed starting point for subsequent question-conditioned exploration. We further introduce an EviRegionSearch that starts question-conditioned exploration from this region, progressively accumulating question-relevant evidence and adaptively determining the next navigation action according to the remaining evidence requirement. Their iterative interaction enables PathPilot to sequentially explore across ROIs and magnifications until sufficient evidence is acquired. Extensive QA evaluations across five cohorts demonstrate consistent superiority over competing SOTA methods on inter/external cohorts, respectively, validating question-conditioned evidence acquisition across regions and magnifications that mirrors the sequential, knowledge-driven navigation of pathologists.

We present a statically and dynamically arbitrage-free European option market model with smooth interpolation between option prices, based on the SANOS framework, and prove that its dynamics admit a unique strong solution. In spirit, it is a stochastic model for local volatility when the latter is used as a representation of a European option price surface, not as a pricing model. We illustrate the strength of our approach on S&P Index Option data from January 2022 to August 2025. We show that the model's initial state fits within bid/ask for more than 95% of relevant market option prices. We then train the model dynamics under $\mathbb{P}$ and $\mathbb{Q}$ and show that the model is indeed free of arbitrage while fitting the dynamics of the market well. We also propose a range of BHW-tests to test for absence of arbitrage.

The canonical component of the character variety of a hyperbolic 2-bridge link complement M is an algebraic surface, from the work of Thurston. If we fix a boundary component T of M and perform a Dehn-filling on T, we get a 1-cusped manifold whose character variety is commonly a generalized curve that is naturally embedded in the character variety of M. If we perform distinct Dehn-fillings on M, we get various generalized curves on the canonical surface. In this paper, we analyze how these curves intersect with each other in the surface and study the topological implications for these intersection points. We also classify the intersection points that correspond to reducible characters, using the twisted Alexander polynomials associated to the Dehn-fillings. Throughout the paper, we use the Whitehead link as a motivating example to illustrate our core methodology, while some generalizations to other 2-bridge links will also be discussed.

The rapid advancement of foundation models and edge intelligence is transforming wireless networks from data-oriented communication systems into artificial intelligence (AI)-native service platforms. Token communications (TokenCom) has emerged as a promising paradigm that directly transmits task-oriented AI representations. However, existing studies typically assume that generated tokens can be transmitted immediately, overlooking the queueing dynamics arising from the mismatch between token workload generation and time-varying wireless service capability. To address this limitation, we introduce Queue-Aware TokenCom, which explicitly incorporates token queues into the AI service pipeline. We present an end-to-end architecture integrating AI representation generation, token workload management, wireless transmission, and downstream task inference. We then discuss two key design directions: budget-aware token representation optimization and queue-aware token service optimization, with the token budget serving as a critical interface between AI performance and communication efficiency. Moreover, we investigate fixed and adaptive token budget strategies to characterize the fundamental tradeoff between AI performance and communication efficiency in dynamic wireless environments. Finally, we outline research directions toward closed-loop, task-aware, and scalable TokenCom systems.