Papers

Lack of effective authentication has resulted in numerous security and privacy breaches, including unauthorized access to protected information, identity theft, and fraud. One approach to mitigating such attacks is Multi-Factor Authentication (MFA), in which users must provide multiple pieces of information for authentication. Some secondary authentication factors include SMS text verification codes, biometrics, and tokens. Each contains at least one notable flaw: SMS is notoriously insecure; biometrics rely upon access to sensitive personal data; and tokens require dependence on third-party providers (e.g. OAuth providers). This work explores CPU-Auth, a novel authentication mechanism based on unique variations in the physical characteristics of the CPU of a computing device. By measuring the behavior of the Dynamic Voltage and Frequency Scaling (DVFS) governor remotely from within a browser, unique properties of the CPU can be leveraged to establish a hardware-based device fingerprint for use in CPU-Auth. The performance of CPU-Auth is evaluated on over 50,000 data traces using distance-based and deep learning methods. CPU-Auth is part of a larger research project, and the results provided in this report reflect only the contributions made to the project by members of this group.

We establish a geometric rigidity theorem for a class of monomial varieties in finite-dimensional unit balls. Every ball automorphism mapping one such variety onto another is unitary, and whenever such an equivalence exists, it can also be realized by a permutation of the ambient coordinates. As a consequence, we obtain a complete isometric classification of the multiplier algebras of integrally generated complete Nevanlinna–Pick Dirichlet series kernels in terms of their defining weight and frequency data. We also obtain an explicit isometric classification for a class of complete Nevanlinna–Pick kernels on bounded Reinhardt domains.

We develop a constructive framework for characterizing modulated symmetries and their gauging in $d$-dimensional lattice systems. The modulation profiles are organized as a finite-dimensional representation of the space group acting on a finite Abelian internal symmetry group. Since the corresponding automorphism group is finite, the nontrivial spatial action factors through a finite quotient of the space group, leading to periodic modulation patterns and providing a classification framework for discrete Abelian modulated symmetries. The symmetry-allowed local interactions are systematically obtained from a kernel construction, which also yields an algebra of open operators. Upon gauging, its elements are transmuted into extended Wilson and boundary operators while retaining their algebraic relations. In the deconfined regime, the resulting algebra realizes a mixed 't Hooft anomaly, providing a microscopic route to Abelian crystalline symmetry-enriched topological phases (SETs). These SETs do not mix electric and magnetic sectors, which transform in mutually contragredient representations, thereby preserving their braiding pairing. We illustrate the framework through explicit examples and show that several models present in the literature fit naturally within our construction.

Effective models make complex quantum dynamics tractable by retaining only the states, processes, and timescales relevant to a given physical question. Their predictive power, however, depends on treating the retained manifold, initial state, observables, micromotion, dissipative channels, and eliminated degrees of freedom consistently. We develop a unified framework for constructing and validating effective descriptions using projection methods, Schrieffer–Wolff transformations, Magnus expansions, adiabatic elimination, small rotations, time coarse graining, and Floquet theory. The quantum Rabi model and its dispersive limits serve as recurring benchmarks for identifying control parameters, virtual processes, spectral corrections, observable dressing, and breakdown. Higher-order resonances and applications to collective light–matter coupling, Raman processes, spin-chain buses, lossy mediators, and driven lattices illustrate how effective interactions can be interpreted and designed. A physical prediction is organized into three order-consistent steps: encoding into the retained description, evolution under the effective dynamics, and reconstruction of the physical observable. This viewpoint exposes failures caused by leakage, small denominators, neglected micromotion, inconsistent observables, memory effects, or incorrectly transformed dissipation, while linking derivation, physical interpretation, and mechanism-guided discovery. Companion notebooks provide QuTiP implementations, convergence tests, and microscopic-to-effective comparisons.

Let $f\in\mathbb Q[t]$ be an irreducible integer-valued polynomial of positive degree with positive leading coefficient. We show that there is a constant $c_f>0$ such that, for every sufficiently large real $X$, the interval $(X/2,X]$ contains a block of at least $c_f\log X\log\log X$ consecutive integers $n$ for which $f(n)$ is composite. The exponent of $\log\log X$ does not depend on the degree of $f$. This improves a result of Ford and Gabdullin, replacing a small fixed power of $\log\log X$ by $\log\log X$. The result includes the case $f(t)=t^2+1$.

Linear attention is a tractable model for understanding the mechanisms governing in-context learning in transformers. For linear regression tasks, recent asymptotic analyses have characterised its learning and generalisation behaviour. We extend this theory to nonlinear single-index targets, $y=f(x^\top w)+\varepsilon $. Our main result establishes a nonlinearity-noise equivalence: linear attention extracts only the linear Hermite component of $f$, while the remaining nonlinear structure contributes to the generalisation error as effective noise. This reduction allows results from the corresponding linear theory to be transferred to nonlinear tasks. We illustrate its implications for finite pretraining data and for the transition from task memorisation to task generalisation as task diversity increases. These results identify a limitation of the reduced linear-attention model and provide a tractable starting point for studying nonlinear in-context learning.

Prompt optimization for text-to-image (T2I) generation has been pursued almost entirely as text rewriting, in which a short user brief is expanded into a longer, model-preferred token sequence. We argue that such a language-space formulation is ill-suited to structured visual design tasks such as logo creation, where a one-line brief leaves most design decisions unspecified. These decisions depend on relational priors that a linear sequence cannot encode, and they leave an uncontrolled channel through which protected marks may be reproduced. We therefore recast logo prompting as sampling within a structured design space, and instantiate this idea as DOGS (Design-space prompting with an Originality-aware GFlowNet Sampler). From a large corpus of real-world logos, we mine a typed, graph-structured design grammar whose edges record empirical co-occurrence. A GFlowNet sampler then generates design graphs with probability proportional to a terminal reward that combines recognizability, aesthetics, and corpus-relative originality. Every slot draws only from a closed design-level vocabulary, and any infringement-inducing or harmful token is removed during parsing. The originality reward further penalizes proximity to existing logos, thereby incorporating infringement avoidance into the method by construction. On two open-source renderers and against nine baselines, DOGS produces logos that are more recognizable and aesthetic, substantially more diverse, and far less prone to trademark infringement.

Scene flow can capture low-level 3D motion displacements in dynamic scenarios. Early pairwise estimators relying on instantaneous two-frame motion lack long-term temporal correlation and also struggle with poor extrapolation ability in future prediction. Although some recent methods attempt to explore multi-frame scene flow estimation in a sequence-to-sequence manner, they typically suffer from heavy computational overhead with increasing input frames and long-horizon prediction degradation due to ineffective motion propagation. To address these problems, we propose a novel memory-enhanced sequential scene flow pipeline, called MESSENGER. To sufficiently mine long-term temporal dependencies naturally within consecutive sequences, a memory buffer is designed by explicitly storing multiple history flow estimates and latent states. For each input frame, the temporally stored flows and states are correlated and retrieved to predict the current initialized flow in a next-frame forecasting manner. Furthermore, we develop an uncertainty-aware reweighting module to filter unreliable retrievals and mitigate accumulated errors. Extensive experiments on nuScenes and Argoverse 2 demonstrate state-of-the-art performance of our MESSENGER, reducing EPE3D by 71.6% on nuScenes and 67.7% on Argoverse 2 in long-horizon future extrapolation. This superiority can be attributed to our designed autoregressive forecasting paradigm, which naturally forces the network to progressively learn the next-frame distribution based on history observations. Code will be released at https://github.com/liujiuming123/Messenger.

Enterprise conversation analytics asks many questions of millions of interactions. Each question can require reconstructing what people mean and identifying which information matters, repeating costly interpretive work across the same transcripts. We propose a simple principle: clarify the text, then focus the reader. Statement normalization transforms dialogue into short, speaker-attributed statements with source references and semantic tags. The statements make meaning more explicit; the tags support selecting evidence for a particular question. Downstream models can use the full representation or a relevant subset, depending on what helps them make the decision. In an offer-suppression task on customer-service calls, normalization improves a supervised classifier without selection, while weaker prompted readers benefit from both normalization and selection. A small model can learn the normalization contract, while lightweight encoders handle tagging and downstream decisions. Sharing this preparation across questions supports an inference pipeline built entirely from small models, making analytics over millions of conversations substantially less expensive.

We show that, given a closed connected non-orientable surface $F$ and a simple branched cover $p \colon F \rightarrow \mathbb{RP}^2$ of degree $d \geq 5$, every self-diffeomorphism of $F$ is isotopic to the lift of a self-diffeomorphism of $\mathbb{RP}^2$ with respect to $p$. As an application, we show that every Lefschetz fibration over a connected surface $B$ with $\partial B\neq \emptyset$ and closed non-orientable regular fiber can be expressed as the composition of a simple cover of $B\times \mathbb{RP}^2$ branched over a surface braided over $B$ and projection onto the $B$-factor.

Many potential future events have devastating consequences, from the onset of earthquakes to financial black swan events. Accurate predictions of their probability of occurrence are vital. Yet as the stochastic systems underlying such events become increasingly complex, these probabilities can depend on ever-growing amounts of past data, which require ever more memory to track. The accuracy of our estimates is ultimately limited by both computational and memory constraints; the former to reduce sampling error, the latter to avoid sampling bias. Traditional quantum algorithms – such as amplitude estimation – address only the former, and become untenable especially in near-future quantum devices where quantum memory is a premium. Here, we offer quantum-algorithmic means to reduce systematic bias while maintaining a quadratic speed-up. Our results thus advance the timeline for the practical deployment of quantum technologies, and illustrate their additional benefits when simulating processes of growing complexity.

Galaxies with stellar masses $M_\star<10^8~M_\odot$, hereafter referred to as extreme dwarf galaxies (EDGs), represent one of the least explored regimes in the search for accreting intermediate-mass black holes. Using the recent Vera C. Rubin Observatory Data Preview 2 (DP2; covering 2025-04-25 to 2026-01-06), we present the first systematic search for variability among EDGs in the ELAIS-S1 field, the most extensively observed LSST Deep-Drilling Field in DP2. Applying single-band and cross-band variability statistics to difference-imaging light curves for $6.2\times10^4$ EDGs with archival multiwavelength characterizations, we identify seven variable EDG candidates, all brighter than $i$-band magnitude of 24 and located within $z<0.3$. The two brightest candidates are previously known AGNs, three have light curves more consistent with supernovae, and two do not have a clear nature. The sample corresponds to an apparent EDG variable fraction of $6.8_{-2.1}^{+3.1}\times10^{-4}$ at $i$-band magnitudes brighter than 24 and is expected to consist primarily of AGNs and supernovae. Compared to a magnitude-matched massive-galaxy sample with the same variability selection applied, the EDG variable fraction is comparable or at most lower by up to a factor of three. This proof-of-concept study demonstrates that Rubin will identify a statistically meaningful sample of variable EDG candidates, opening a new regime for black-hole demographics. Spectroscopic follow-up will nevertheless be required to secure redshifts and confirm individual candidates.

In a neighborhood of the origin in $\mathbb{R}^9$, we construct a minimal hypersurface with respect to a smooth conformally Euclidean metric, whose singular set consists of the origin and a sequence of isolated singular points converging to it. At each of the isolated singular points the hypersurface has the unique tangent cone $C_{4,3}$, the cone over $S^4(\sqrt{4/7})\times S^3(\sqrt{3/7})$, whereas at the origin its unique tangent cone is the cone $C_{3,3}\times\mathbb{R}$. The metric is Euclidean near each isolated singular point and agrees with the Euclidean metric to infinite order at the origin. A key step, of independent interest, is the construction of an entire stationary hypersurface in Euclidean $\mathbb{R}^9$ with exactly one singular point at the origin, at which its unique tangent cone is $C_{4,3}$, and whose unique tangent cone at infinity is $C_{3,3}\times\mathbb{R}$.

Network slicing over multi-domain optical networks enables resource isolation for high-bandwidth, virtually-dedicated networks. However, guaranteeing end-to-end (E2E) performance remains challenging when domains withhold internal topology and performance metrics from external entities. Under this limited visibility, a control function (slice coordinator) needs to select E2E monitoring paths to detect and localize link failures. This paper formulates two complementary optimization problems, the initial and progressive monitoring path selection problems, which together realize closed-loop autonomous monitoring at the slice coordinator level. The initial problem maximizes failure coverage without prior information, while the progressive problem concentrates additional paths around suspected failure locations identified from prior monitoring. We propose a deep reinforcement learning (DRL) algorithm that adaptively selects an optimal set of monitoring paths for each phase. Experiments using the GNPy optical network simulator demonstrate that our approach outperforms baseline algorithms for both problems and achieves near-optimal localization in the initial selection, suggesting the feasibility of AI-driven closed-loop failure localization in future multi-domain optical network architectures.

Audio deepfake detectors remain vulnerable to adversarial perturbations that suppress the acoustic cues used for detection, allowing manipulated utterances to evade the detector. Although existing defenses can improve robustness, they require retraining the detector or introduce additional distortion. Diffusion-based purification instead leaves the pretrained detector unchanged, but existing methods use the same purification strength for all inputs, creating a trade-off between removing adversarial perturbations and preserving the subtle spoofing cues needed for detection. In this paper, we propose Detection-Guided Adaptive Purification (DGAP), a diffusion-based defense that adjusts purification strength per input. Building on the observation that a light purification perturbs the detector score of an adversarial input far more than that of a benign one, the framework uses the resulting score shift as a reference-free indicator of adversarial manipulation. Inputs with small shifts are passed unchanged, whereas flagged inputs undergo stronger purification before final detection. We evaluate the framework against three adversarial attack settings across three deepfake detectors, and compare it with nine existing defenses. Our results show that DGAP achieves the best defense performance across all detectors while leaving benign inputs nearly unaffected, and remains effective under the defense-aware adaptive attack.

We study the singular set of the free boundary for solutions of the thin Stefan problem in $\mathbb{R}^{n+1}\times \mathbb{R}$, which models the melting of a thin sheet of ice over water. After a suitable transformation, we reduce to studying the parabolic Signorini (thin obstacle) problem with a time-monotonicity condition. First, we prove that the free boundary is locally the graph of a differentiable melting function $t=\tau(x)$ defined on the $n$-dimensional thin space, and that the singular set coincides with the critical set of $\tau$. Next, we show that the singular set has parabolic Hausdorff dimension at most $n$. We then establish generic regularity up to dimension $n+1=4$, proving that the free boundary is regular for almost every time. Finally, under smoothness assumptions on the obstacle, we show that the singular set is contained in a $C^\infty$-hypersurface outside a set of parabolic dimension at most $n-1$. Our analysis combines ideas developed for the classical Stefan problem with several new ingredients specific to the thin setting, including frequency formulas for second blow-ups, epiperimetric inequalities, higher order expansions, and a fine stratification of the singular set.

Primordial black holes, whose formation in the early Universe was first hypothesized by Ya.B.~Zel'dovich and I.D.~Novikov in 1966 (the text of this pioneering article is provided in Appendix II to this review), have attracted increasing attention in recent years. Modern astronomical data across the electromagnetic spectrum, together with observations of gravitational waves and cosmic neutrinos, have revealed a number of unique astrophysical phenomena that may be related to primordial black holes formed in the pre-stellar cosmological epoch. This review describes various models of primordial black hole formation, as well as methods for testing these models with astronomical and astrophysical observations. In particular, we discuss in detail the formation of primordial black holes and their clusters through the collapse of closed domain walls and through effects associated with extra spatial dimensions of the Universe.

Large audio-language models (LALMs) fuse an audio encoder into a large language model (LLM) through multi-stage training. This coupling means that a new domain or a stronger LLM requires retraining, and their answers cannot be traced to what the model heard: a chain-of-thought is a post-hoc account. We propose Listen-to-Reason (L2R), an interpretable-by-design pipeline that passes audio to the LLM through an explicit, human-readable tree: small heads on frozen expert encoders map each chunk of a clip to semantically meaningful nodes on the tree (for speech, music and environmental sound), and a frozen text-only LLM answers from these nodes and an ASR transcript without hearing the clip. Every answer can therefore be traced to the nodes and transcript it read, and the nodes are causal: replacing the deciding node with a distractor overturns 78% of correct answers on SAKURA. With a 7B reader, L2R outperforms all LALMs we compare against on SAKURA and trails them by 6-12 points on MMAU and MMAR, despite training about 1,400x fewer parameters on orders of magnitude less audio data. However, because any LLM can serve as the reader, we show that a stronger reader narrows this gap without retraining any audio component. A new domain is added with one small head: with five labelled clips per species, it outperforms QLoRA fine-tuning of an LALM on the same clips by 13-26 points.

Navigation in vision-denied environments is challenging for humanoid robots because proprioceptive odometry drifts and localization uncertainty accumulates rapidly. We present TAPNAV, a tactile active-perception framework that enables humanoid navigation toward a goal by actively probing surrounding structures without relying on vision. TAPNAV maintains a pose belief from odometry, IMU, and tactile contact observations, and couples uncertainty-aware global route planning with information-gain-driven local probing. The global planner searches for routes that keep predicted localization uncertainty bounded by exploiting opportunities for tactile correction, while the local planner selects probe actions that maximize expected information gain. A whole-body controller coordinates the humanoid's locomotion and end-effector contact to execute the planned navigation and probe motions. We evaluate TAPNAV in simulation and on a Unitree G1 across different floor plans and obstacle geometries. TAPNAV achieves lower state estimation error and a higher task completion rate than baselines. These results demonstrate that actively planning physical interactions with the environment can provide localization cues for reliable humanoid navigation without vision.

We study Legendrian realizations of double twist knots in the standard tight contact 3-sphere. For the family K(4,m), we give upper bounds on the number of oriented and unoriented Legendrian isotopy classes of maximal Thurston–Bennequin representatives. The proof uses bypass techniques in convex surface theory and the classification of tight contact structures.

We present a new derivation of the exact compact oscillon in the signum-Gordon model using Fourier methods. This approach decomposes the oscillon into an infinite, uniformly convergent series of discrete modes consisting of a fundamental frequency and its odd higher harmonics, in contrast to standard analytic potentials, where the corresponding infinite perturbative series fails to converge. Crucially, our oscillon evades the non-existence theorem for spatially localized, small-amplitude periodic states. We investigate the accuracy of truncating the Fourier series and find that the primary mode alone provides a remarkably accurate approximation of the exact solution, with agreement improving significantly when the first two non-vanishing harmonic modes are included. Furthermore, we generalize this framework to a swaying compact oscillon with a periodically moving boundary. We show that describing such an oscillon requires even-order modes, whose coupling with the odd source terms induces a dynamic modulation that generates the swaying motion, even though the spatial Fourier profiles themselves are time-independent.

We study gauge-invariant two-matrix polynomials of degree $L$, corresponding to the states in the $su(2)$ sector of $\mathcal{N}=4$ super Yang-Mills theory with gauge group $U(N)$ or $SU(N)$ at finite $N$. For the $U(N)$ theory, the state space has the structure of an algebra $\mathcal{A}_N(L)$, which is a direct sum of permutation centraliser algebras, i.e. sub-algebras of the group algebra $\mathbb{C}[S_L]$ of $S_L$. For $N \ge L$, $\mathcal{A}_N (L) = \mathcal{A} (L)$ is independent of $N$, and the one-loop dilatation operator acts on $\mathcal{A}(L)$ with $N$ as a parameter. For $N < L$, $\mathcal{A}_N (L)$ is a subspace of $\mathcal{A}(L)$ defined using a finite-$N$ cutoff on Young diagrams with $L$ boxes. We establish two results on the eigenspaces of the one-loop dilatation operator. Our first main result is that the characteristic polynomial of the one-loop dilatation operator on $\mathcal{A}_N(L)$ divides the characteristic polynomial from $\mathcal{A}(L)$, continued to $N < L$. Our second result is that each eigenstate of the one-loop dilatation operator in the $SU(N)$ theory generates an infinite tower of eigenstates in the $U(N)$ theory, through the multiplication of single-letter traces. These towers define an eigenspace factorisation of the $U(N)$ theory labelled by the number of such traces. Further, we conjecture that the space of $SU(N)$-invariant polynomials in two traceless matrices at finite $N$ is isomorphic to the intersection of $\mathcal{A}_N(L)$ with the subspace of $\mathbb{C}[S_L]$ spanned by derangements. This intersection conjecture is supported by dimension counting. Finally, we propose a one-loop dilatation operator on the intersection, thus providing a direct permutation framework for the $SU(N)$ spectral problem at finite $N$. The computed spectra based on the proposal agree with the prediction from the eigenspace factorisation in the $U(N)$ theory.

We propose a continuous policy-value iteration framework for infinite horizon stochastic control problems, in which the policy evolves through Langevin type dynamics driven by the gradient of the inhomogeneous Hamiltonian, while the value function is updated simultaneously with optimal policy iterations, avoiding directly solving its corresponding PDE at each iteration. The iteration scheme enjoys policy improvement under suitable regularity and admissibility assumptions. We show the exponential contraction of the joint policy value dynamics in Wasserstein-2 distance under the Lipschitz condition in expectation via the inhomogeneous synchronous coupling and verify these conditions for linear quadratic problems. Numerical experiments on linear quadratic models and the optimal consumption-investment problems in an incomplete market factor model illustrate policy improvement, convergence toward optimal policies, and the effect of decaying exploration noise.

Although critical AI literacy has emerged as an important educational goal, the construct remains conceptually broad and insufficiently specified for guiding students' day-to-day interactions with AI. This study examines how students critically evaluated AI-generated content. Drawing on an analysis of students' chatbot interactions and written reflections, we first identified seven stages of AI-supported academic task completion and five functional roles assumed by AI. More importantly, we identified eight evaluative lenses that students used to assess AI-generated responses (accuracy, completeness, task alignment/relevance, personalization, practicality, creativity, ethics, and bias). The findings suggest that critical AI literacy extends beyond verifying the factual accuracy of AI-generated information. Rather, critically engaging with AI involves situated and multidimensional judgment about the epistemic quality, contextual fit, practical feasibility, creative value, and ethical implications of AI-generated content. The framework offers both a conceptual contribution to the emerging literature on critical AI literacy and a practical tool for educators seeking to help learners move from passive acceptance of AI toward deliberate, context-sensitive, and responsible human judgment.

AI systems increasingly rely on Large Language Models (LLMs) as core reasoning engines, making them targets for prompt injection and jailbreaks. Guardrails monitor and validate model inputs and outputs, yet their isolated, task-focused detection leaves gaps in their classification making them susceptible to bypasses. In response, guardrail systems formed by multiple scanners have emerged that collaboratively detect different types of malicious instructions, whereby shared latent representations across classification boundaries render established bypassing techniques ineffective. We propose BRANCH, a bypassing methodology designed for multi-scanner guardrail systems. Our method leverages a branching tree search approach that dynamically applies adversarial perturbation against individual scanners, with subsequent perturbation optimization and technique selection based on overall improvement across all guardrail system scanners, effectively decoupling bypass evaluation from attack signal optimization. Our findings demonstrate that BRANCH achieves 100% attack success rate across 6 guardrail systems in 120 scenarios with 72% fewer queries and 4.5x reduced wallclock time compared to established techniques, while preserving semantic meaning within the bypass. We also show how bypasses generated by BRANCH transfer to 29 unseen guardrails, including 8 commercial black-box guardrails, improving attack success in some cases up to 100% with no additional optimization.

The complex relationship between galaxies and diffuse gas at large scales depends strongly on astrophysical feedback and cosmology. The dispersion measure (DM) of Fast Radio Bursts (FRBs) is a column of cosmic baryon density and is dominated by the intergalactic medium, which is not necessarily captured by traditional halo model prescriptions. We introduce a generative model to reconstruct 3D gas density fields from galaxy surveys, including redshift space distortions. The probabilistic model is trained on the CAMELS50 simulation suite (IllustrisTNG) and learns to predict the posterior distribution of gas fields conditioned on stellar mass-weighted galaxy density, cosmological parameters, the minimum stellar mass threshold for the galaxy sample, and the baryon suppression power spectrum as a measure of baryonic feedback. Our method uses the 3D gas reconstruction to estimate per-sightline FRB DMs and their posteriors. We validate the model on test boxes by showing agreement between predicted and true DM across individual lines of sight and the overall DM distribution. The model generalizes to a box size $\sim$\,4$^3$ times larger in volume than the training boxes and can cover the volumes spanned by cosmological FRB sightlines. The model's 3D gas density predictions vary with input power spectrum and feedback scenarios, offering an inference path to constrain feedback models from FRBs and other probes such as X-rays, the SZ effect, and weak lensing.

Conversational task disambiguation over tabular data uses dialogue to resolve missing information about a user's intended task before producing a solution over tables or databases. Existing evaluation and training lack a leakage-aware foundation. Task success mixes the agent's disambiguation and solution-generation capabilities and can also reflect oracle leakage, that is, information that a user simulator reveals beyond what a real user would. Existing datasets also lack a shared representation of ambiguities and access boundaries. We introduce the notion of an ambiguous verifiable task, which formalizes ambiguities and resolutions, decomposing the agent into an asking policy and a solution policy, and the environment into an oracle and verifier. This framework provides baselines and metrics for evaluating task disambiguation separately from solution generation, formal definitions of oracle leakage, judge-free leakage diagnostics, and a training objective for the asking policy. We instantiate the framework in text-to-SQL with AmbiTab, a benchmark suite that unifies six ambiguous datasets under a common representation specifying what the agent, oracle, and verifier may access. We evaluate clarification strategies and oracle leakage, and train an asking policy with reinforcement learning. The trained asker improves our disambiguation metrics on all six datasets and task success on five, and our leakage diagnostics measure how training affects oracle leakage.

Post-asymptotic giant branch (PAGB) stars share many advantages with the tip of the red giant branch (TRGB) for Population II distance measurements, including minimal internal reddening, easy identification, a solid theoretical foundation, and an expected weak metallicity dependence. At visual wavelengths PAGB stars are the brightest members in old populations, appearing up to $\sim2$ mag brighter than the TRGB and $\sim4$ mag brighter than RR Lyrae stars. Stellar evolution theory predicts that these objects occupy a narrow luminosity strip across the top of the Hertzsprung-Russell diagram, making them excellent standard candles. Observations in Galactic globular clusters (GCs) support this prediction, but a comprehensive survey is required to define their luminosity function and test for systematic errors. In this work, we construct a multi-wavelength catalog, spanning the ultraviolet (UV) to infrared (IR), for PAGB stars in 39 Galactic GCs. We validate cluster membership with Gaia astrometry, identify 21 objects across 16 GCs using ground-based uBVI and space-based UV photometry, and perform Bayesian spectral energy distribution (SED) fitting with stellar atmosphere models to estimate their effective temperatures, luminosities, and radii. We find that PAGB stars occupy a narrow luminosity range centered at $\log(L_{\mathrm{bol}}/L_{\odot})=3.25\pm0.03$, with dispersion $\sigma=0.12$ dex, supporting their use as reliable Population II distance indicators. Comparisons with theoretical tracks show excellent agreement with evolutionary models. We confirm that PAGB stars occur preferentially in metal-poor clusters with blue horizontal branches. Our results demonstrate that PAGB stars provide a powerful probe of late stellar evolution and a promising Population II standard candle.

Our work explores learning a compressed latent representation of text, at the intersection of data compression and representation learning. We propose an autoencoder architecture that performs residual downscaling and upscaling of hidden representations along the time axis, with a residual low-dimension discrete bottleneck. We analyze our approach for different quantization methods, training objectives, and datasets. For different levels of compression, we evaluate the similarity between the original and reconstructed text both at the surface-level (BLEU) and at the semantic-level (LLM-based judge). Additionally, we evaluate our models on downstream question-answering and semantic text similarity benchmarks. Our approach results in compressed representations which are on par with lossless text compression algorithms at 2.24 bits per byte on web text data, while having good reconstruction and downstream task performance.

A graph is $H$-free if it has no induced subgraph isomorphic to $H$. In 2020, Chudnovsky, Goedgebeur, Schaudt, and Zhong characterized all graphs $H$ such that there are only finitely many minimal obstructions to $3$-colouring $H$-free graphs. In general, the minimal obstructions to $k$-colouring $H$-free graphs are the $(k+1)$-vertex-critical $H$-free graphs, those are, the $H$-free graphs $G$ with $\chi(G)=k+1$ but $\chi(G-v)=k$ for every vertex in $G$. In this paper we complete the characterization for all $k > 4$ by showing that there are onky finitely $k$-vertex-critical $H$-free graphs if and only if $H$ is an induced subgraph of $P_4+\ell P_1$ for some $\ell \geq 0$.