Papers

Vision-language models (VLMs) can reason about visual planning tasks, but querying them for every instance incurs repeated inference cost and latency. Generating reusable planning programs offers an alternative, but constructing reliable planning systems for new problem domains without extensive supervision remains challenging. We present a training-free framework that constructs reusable perception and planning programs from a domain specification and a single practice scene without a paired solution. The central challenge is obtaining useful feedback from the limited input. Our framework addresses it by leveraging VLM's ability to provide a renderer and a dynamic model based on its scene understanding. Rendering detected states enables comparison with the practice scene, while checking simulated action outcomes against the domain specification helps expose errors in rule implementation. Together, these checks guide refinement of the grounding program and planner without requiring solution labels. After refinement and component selection, the programs are frozen and solve new instances without further VLM calls. The same framework constructs systems across domains without manual pipeline redesign. Across fifteen domain variants spanning 2D and 3D scenes with discrete and continuous state, our systems achieve 99.3% average planning success, compared with 80.9% for the strongest domain-level program-generation baseline and 90.7% for the strongest instance-level baseline. Cost analyses show a favorable success-cost trade-off, and ablations confirm the contributions of the executable domain model, execution feedback, and component selection.

We construct finite Gamma convolutions approximating the first hitting time of $1$ by a Bessel process of index $\nu>-1$ started at the origin. The scale measure in the classical exponential representation of this law is obtained by squaring the positive half of a dilated modified Lommel polynomial orthogonality measure. Its Jacobi recurrence yields an $N$-factor Gamma convolution that uniquely matches the first $2N$ cumulants, the maximal number attainable in this class. From an exact Gaussian quadrature remainder we derive supergeometric convergence of the Laplace transforms on compact subsets of a common slit plane and geometric convergence of the distribution functions uniformly on the real line. The approximants have total Gamma shape $N(N+\nu+1)$, and their Laplace transforms and negative moments decrease to those of the exit law.

Large language models impose substantial memory demands and arithmetic costs during inference. Dense-to-mixture-of-experts (MoE) conversion is a model optimization technique that aims to reduce these arithmetic costs. Dense-to-MoE conversion partitions pretrained feed-forward network (FFN) neurons into experts and selects a subset for each token. Leading methods fall into two categories: analytic methods produce a converted model quickly using heuristics, while learning methods produce a model much more slowly by optimizing via gradients. Both approaches, however, fix the same active expert count, or "utilization," at every layer. We introduce Spectral-MoE, which learns to allocate a utilization budget heterogeneously across layers. Its name draws a metaphor between separating a dense FFN into experts and separating a light beam into its spectrum. Spectral-MoE consists of two distinct approaches: a static approach that uses a single per-layer scalar which is shared across tokens, and a dynamic approach which emits a per-token schedule. We demonstrate that both allocators improve performance over uniform on both the analytic-based and learning-based SOTA dense-to-MoE methods. At 25% FFN utilization, dynamic allocation reduces WikiText-2 perplexity relative to uniform by 1.04, 2.96, and 2.71 points on the learned base for Llama-2-7B, Llama-3-8B, and Qwen2.5-7B, respectively. The corresponding reductions on the analytic base are 2.45, 6.26, and 2.17 points. On the learned base, dynamic allocation improves six-task mean accuracy over uniform by an average of 1.5, 4.2, and 3.6 percentage points across the three models at FFN utilizations of 12.5%, 25%, and 50%, respectively. These results establish per-layer expert utilization as a novel optimization axis in dense-to-MoE conversion.

Transformer language models develop attention heads that specialize in syntactic relations, for example, attending from verbs to their subjects. Do these heads play a causal role in the model's syntactic predictions? Evidence for such a role is mixed to negative: even when we force these heads to attend to a distractor noun other than the subject, the model's syntactic predictions are still more consistent with the subject than with the distractor. Interventions on specialized syntax heads had a significantly stronger effect on syntactic predictions than interventions on random heads, but only in one of the two measures we propose.

Liu introduced generalized Fibonacci gates on domains of size 3 and 4, proved that Holant problems built from them are tractable by a cut-and-merge algorithm, and conjectured that Fibonacci gates with matching polynomial-time algorithms exist on all higher domains. We extend the definition uniformly to every domain size $k$ and show that a family of domain-$k$ generalized Fibonacci gates is the same thing as a $k$-dimensional commutative Frobenius (equivalently, Artinian Gorenstein) algebra $A$ equipped with an orthonormal basis containing $1$. Under this dictionary Liu's parameter constraints are exactly associativity of $A$, a gate is an element $w\in A$, merging two gates is multiplication in $A$, and the Holant value of a connected graph $G$ is $\tau\bigl(h^{\,|E|-|V|+1}\prod_v w_v\bigr)$ for a fixed “handle” element $h\in A$. This proves Liu's conjecture for every $k$, with an algorithm whose cost is polynomial in $k$ as well as in the graph. We also give a closure criterion for linear recurrences of any depth (a balance condition implies closure, and is necessary when the unit is a combination of the colours), and we map the landscape: semisimple algebras are exactly Liu's orthogonal frames, smoothable algebras with nilpotents are collided frames, and families whose algebra is not smoothable (“frameless” families) exist exactly when $k\ge 14$. Finally we show that every non-semisimple part of a family is invisible to the Holant on connected graphs with two or more independent cycles. This note states the results and sketches the proofs; the proofs of the main theorems are short and are given essentially in full.

Paper 1 established the per-bundle statistical limits of Temporal CT (TCT) and benchmarked a learned prior on a single patient at a uniform incident count $N_0$. This paper lifts both restrictions. SNN2, a Gauss-Newton estimator, converges to the per-bundle Poisson maximum-likelihood solution and is the prior-free baseline. N$_0$FC, a bow-tie and tube-current-modulation co-design, compresses within-bundle photon-flux dynamic range. V8c is a neural-network residual corrector trained on a 19-patient corpus stratified by water-equivalent diameter (WED). T2bp, a per-patient empirical-Bayes post-processor, combines per-bundle Poisson likelihoods with a prior built from the patient's own bundles; it requires no training, so it cannot inherit a mismatched training prior. Results use Paper 1's bias-charged Dose Inflation Factor (DIF), extended to per-ray budgets. V8c beats SNN2 on in-distribution patients under baseline acquisition but fails out of distribution. Composed with SNN2, T2bp matches or beats T2bp$\circ$V8c on three of four N$_0$FC test cells (WED 207-342 mm), with the largest gains on the high-WED and out-of-distribution patients, and trails by 3% on the fourth. On 23 non-test corpus volumes, N$_0$FC with closed-loop tube-current modulation lowers the per-volume median middle-path Cramer-Rao floor, as a DIF, from 23-48 under baseline acquisition to 3.3-6.3, near the equal-attenuation value 13/3; T2bp$\circ$SNN2 reaches this floor without training, its mean squared error 0.74-1.26 times the floor (median 0.89) over the bulk of each volume. Acquisition co-design removes most of the attenuation-contrast penalty, and a training-free estimator attains the resulting limit. The remaining three- to six-fold gap to dose parity with single-source CT, and the high-attenuation tail, are the target of inter-bundle priors in later work.

Powerful X-ray flares from young stars may rapidly alter the physical and chemical conditions of their planet-forming disks, but direct observational tests remain scarce. We present a Chandra-JWST/NIRSpec study of infrared spectral variability associated with pre-main-sequence (PMS) X-ray flares in the Orion Nebula. Combining six Chandra/ACIS-I observations with three NIRSpec-MOS visits, we analyze two-epoch spectra of 10 X-ray Flare stars and 12 matched non-flaring Controls among 84 observed disk-bearing PMS stars. We investigate three diagnostics: narrow 2.8-4.3 micron features, HI Br-alpha, and the CO fundamental band. Flare stars show tentative evidence for relatively fewer variable narrow features at longer wavelengths than Controls, while feature incidence decreases strongly with projected distance from the dominant ionizing O star Theta1 Ori C. Most classifiable features appear in absorption. These properties suggest that at least some features may arise in externally irradiated disk atmospheres and/or associated photoevaporative flows, with their apparent epoch-to-epoch variability potentially reflecting spatial sampling of such locally structured material rather than intrinsic temporal changes. Br-alpha behaves differently: flare stars show systematically stronger variability and uniquely exhibit absorption-core profiles, suggesting control by magnetospheric accretion and stellar magnetic processes rather than disk irradiation. The CO fundamental band shows no significant flare-associated variability, consistent with thermochemical models predicting weak responses to moderate X-ray superflares. This pilot study demonstrates the potential of coordinated Chandra-JWST observations to probe how young stellar magnetic activity affects planet-forming environments, motivating future monitoring to build larger superflare samples and extend them into the rare X-ray mega-flare regime.

Wireless sensing systems often transmit highly redundant observations, making communication a bottleneck for low-power devices. We present Memento, a communication system that exploits recurring content by transmitting observations by reference. The sender embeds each observation and searches a shared vector table stored in persistent memory. When it finds a sufficiently similar prior observation, it sends a compact reference; otherwise, it sends the observation itself and adds it to the table. This design shifts work from wireless communication to local computation and storage, without requiring a fixed task-specific model. We implement Memento on a microcontroller with an SD card and evaluate it on three image datasets and one radar dataset. Memento provides favorable accuracy-communication and accuracy-energy tradeoffs against compression-based and task-oriented baselines. At high-accuracy operating points, it matches cloud classification accuracy on three workloads while using 5.5 to 27.1 times less energy, and comes within 0.14 percentage points on a fourth while using 14.7 times less energy. These results show that retrieval over persistent local memory can reduce communication costs in recurrent sensing workloads.

Frontier AI agents increasingly act in environments where seemingly solvable tasks may lack prerequisites, contain conflicting requirements, or reveal blockers only during execution. We formulate agentic self-awareness (ASA) as the alignment of task-grounded feasibility judgments (know), warranted behavior (act), and responses to reconsideration (hold), distinguishing what a task permits from what an agent can solve. We build paired feasible and blocked tasks in Terminal-Bench 2.1 and retail $\tau^2$-bench and introduce an authorship-aware M0-M3 rubric that separates recognizing a blocker from taking the certified deferral action for the correct reason. Separate probes assess stated feasibility beliefs and responses to a single challenge. In a Terminal-Bench protocol baseline, blocker recognition reaches 84.4%, but strict self-awareness (SA) reaches only 40.6%. Harness search without model-weight updates increases strict SA from 45.3% to 93.8% on reused Terminal-Bench search tasks; selection for abstention alone, however, can reduce success on feasible tasks. Independently initialized joint-objective searches improve both blocked-task SA and feasible-task solve on their own search sets. Retail held-out gains remain limited, and Terminal-Bench blocked-task transfer is not measured. This evaluation pipeline makes the recognition-action gap measurable and sets a two-sided target for improving agent decisions under changing task evidence.

We study the structure of the centralizer of a non-elliptic holomorphic self-map of the unit disc and its relation with continuous dynamical structures. We prove that if the identity is not isolated in the centralizer of a non-elliptic self-map $\varphi \in \mathrm{Hol}(\mathbb D)$, then $\varphi$ is univalent and its centralizer contains a non-trivial continuous one-parameter semigroup of holomorphic self-maps. This result provides a general criterion for the existence of continuous dynamics arising from discrete iteration. Our approach is based on the theory of holomorphic models and on simultaneous linearization techniques for commuting self-maps. In particular, we exploit recent developments on simultaneous linearization for parabolic self-maps with positive hyperbolic step. As a consequence, we obtain new sufficient conditions for the embeddability of holomorphic self-maps into continuous semigroups.

Surface navigation on the Moon is subject to extreme illumination contrast and deployment-time perceptual disturbances. While modular navigation pipelines have long supported planetary rover navigation, robustness is compromised by measurement errors that propagate through hand-engineered components. End-to-end learned policies are an alternative approach to navigation, which maps observations directly to control actions without intermediate components. Vision-language-action models, in particular, have driven significant breakthroughs in robotics and autonomous vehicle research. By leveraging internet-scale vision-language pretraining, these models can be exploited for their commonsense reasoning and visual understanding to provide robust generalization with limited task-specific data. However, their applicability and performance have yet to be characterized for lunar surface operations. In this study, we design a vision-language-action policy for autonomous lunar rover docking and characterize its performance relative to a modular navigation pipeline. We develop a scalable training framework that generates safety-aware expert demonstrations in a high-fidelity lunar simulation environment. In closed-loop evaluations, our policy performs competitively relative to the modular baseline under perceptual disturbances unseen during training. To address the tradeoff between compute consumption and closed-loop safety, the policy adapts its execution horizon by determining how far the rover may safely travel in open loop. Adaptive-horizon execution reduces inference frequency while limiting hazard-contact rates relative to fixed horizons in the evaluated scenarios.

LLM-based auto-formalization systems can now generate formally verified Lean code at unprecedented rates. However, a formalization advances mathematical research only when further mathematical results can be built on it, especially when its definitions and helper lemmas are general enough to be imported and used idiomatically. We propose definition grounding, where definition formalizations are continuously judged and revised, as a method to ensure formalization quality. We find that agents formalizing definitions from textbook text often produce definitions that later statements cannot use, and only 25%-50% of their definition sets are compatible with all later statements. However, clarifying the informal definitions can improve this rate up to 77.5% averaged over all models. Furthermore, stating a small set of basic properties without proving them can improve model judges' capability to detect definitions with compatibility issues, at only about 11% of the definition formalization cost. These results are verified with ReuseBench, a benchmark we curated for formalizing new mathematical fields and theories.

Operational reporting for high-performance computing (HPC) facilities requires combining information from monitoring services, schedulers, incident and maintenance records, storage measurements, periodic reports, and operator investigations. Producing a reliable report requires more than retrieving relevant records: the evidence must refer to the correct system, metric definition, time period, and source of authority. We present REPORT-OPS, a hybrid reporting agent in which an LLM interprets requests, plans evidence collection, evaluates possible explanations, and drafts reports, while author-seeded operational policies and automated checks determine whether the available evidence supports the requested conclusion. Depending on the evidence state, the system answers the request, reports a qualified conclusion, or withholds an unsupported claim. During offline refinement, an LLM critic proposes bounded policy changes that a human approves or rejects without editing; accepted candidates are promoted only after automated target, held-out, and regression testing. We evaluate REPORT-OPS on 68 sanitized reporting queries constructed from 50 base scenarios in a frozen HPC operational corpus, using three agent models and two LLM judges. REPORT-OPS achieves 68.63% Pass@80, compared with 7.02% for the strongest retrieval baseline. Evidence gating increases claim-support precision from 40.58% to 90.06%. On the 13-query explanatory subset, explanation accuracy reaches 55.54%. Across five rounds of human-supervised refinement, localized policy updates correct 91.17% of targeted failures and improve performance on related held-out cases by 9.33 percentage points, with no observed regression breaks under release gating. These results demonstrate improved evidence-grounded reporting and within-environment policy reuse; they do not establish unrestricted causal discovery or cross-facility generalization.

We study helical shear of a thick-walled tube made of an incompressible, isotropic hyper-anelastic solid carrying a radially symmetric distribution of axial screw dislocations. Through the Bilby–Kröner–Lee decomposition, the dislocations are encoded in a Weitzenböck material manifold, whose Riemannian metric alone enters the elastic response. Equilibrium reduces at each radius to an algebraic system for the azimuthal and axial shear strains, whose cross terms are proportional to the dislocation strength and to the dependence of the strain energy on the second invariant; the two shear modes therefore couple only in the presence of dislocations. Exact solutions are obtained for neo-Hookean, Fung–Demiray, Gent, Knowles, and Mooney–Rivlin materials, and numerical ones for Gent–Gent materials. The universal relations of Horgan and Saccomandi are extended to dislocated generalized neo-Hookean tubes. Dislocations stiffen the tube when the strain energy stiffens with the first invariant, couple the two shear modes chirally when it depends on the second, and may restrict admissibility: they cap the dislocation strength in Gent and Gent–Gent materials, and contract the admissible traction region in Knowles materials with power-law index below n = 1/2. A weakly nonlinear analysis to third order in the applied tractions and dislocation strength shows that, at first order (linear elasticity), the dislocations leave the shear response unaffected while carrying a residual stress. The chiral coupling enters at second order, through the dependence of the strain energy on the second invariant, so that every dislocated material couples the modes as the Mooney–Rivlin solid with the same second- and third-order moduli. At third order, no new coupling arises; the modes interact through stiffness corrections involving the fourth-order modulus, which the dislocations further correct mode by mode.

The Continuous Thought Machine (CTM) is a recurrent network that attends to inputs and makes predictions based on the synchronization between its neurons. On tasks spanning many domains, it displays emergent thought processes that have not been explained. We report a number of findings about how the CTM classifies images, focusing on ImageNet. Each thinking step is an attracting but strongly non-normal map exhibiting balanced amplification (Murphy and Miller, 2009); while attraction is already present at CTM initialization, training highly promotes non-normality. By Banach's theorem, the neural state has a locally unique attracting fixed point, which moves at every step, and the thought trajectory is the curve these fixed points trace, followed one tick behind. Most of that curve's motion is shared across images, and visible as a previously reported traveling wave of activity across neurons. The attention schedule along the thought is largely generic: shuffling queries across images at every tick costs only 7 percent of classification accuracy, while image-independent increments predict the next query with R^2 = 0.98 (held out). Our results suggest that the CTM has found a single strategy to process all ImageNet images.

We realize the mesoscopic Bose-Hubbard model at unit-filling on a two-dimensional array of transmon qubits and selectively excite collective modes associated with amplitude or phase fluctuations of the superfluid order parameter. We identify these modes respectively as the Higgs and Goldstone modes using complementary local observables, extracted from measuring the number of particles on each site. Modulation of the coupling between sites excites the Higgs mode, which we detect via the density of doubly occupied sites. In contrast, modulation of the local chemical potential with an appropriately chosen spatial profile excites the lowest-frequency Goldstone mode, which we detect via changes in the local density. The two modes have different symmetries and do not couple to one another. By varying the system geometry, we characterize the impact of finite system size on the evolution of both modes. In the thermodynamic limit, decay into a continuum of lower-energy excitations can obscure the Higgs response. In our mesoscopic system, however, the finite system size leads to spectral gaps and allows us to detect the Higgs mode as a coherent, long-lived excitation. Our work demonstrates how finite quantum simulators can isolate and probe physical phenomena that become difficult to resolve in the thermodynamic, large-scale limit.

Myopic vision degrades the quality of human vision due to spherical eye defocus aberrations that impair the perception of fine spatial details. To address this limitation, this work proposes a deep learning-based approach to computationally design transformed images that allow individuals with myopia in fixed distance to perceive scenes with enhanced clarity. The method trains a neural network to counteract defocus aberrations modeled using the second-order Zernike polynomial $Z_2^0$. The approach employs a U-Net architecture trained with a loss function combining reconstruction error minimization with spatial difference structural preservation through $\ell_1$ regularization. Training is carried out exclusively on the KITTI dataset, while testing is performed on DIV2K and ImageNet datasets, demonstrating generalization across diverse image distributions. Under myopic conditions modeled by $Z_2^0$, baseline performance shows visual degradation with PSNR values ranging from 19.47 to 27.42 dB across datasets and severity levels. The proposed gradient-regularized method achieves consistent improvements, delivering PSNR gains ranging from 1.48 to 7.34 dB and significantly lower perceptual compared to classical baselines.

We present the RemoTAP-Hybrid algorithm for global aerosol products retrieved from Multi-Angle Polarimeters (MAP), and apply it to one-year aerosol retrievals from the SPEXone MAP instrument. For the first time, Multiple Collaborated Neural Networks (MCNN) are used to perform global aerosol MAP retrievals over land and ocean. The combined use of MCNN with a full physics inversion in RemoTAP-Hybrid, significantly improves accuracy and computational speed of SPEXone aerosol retrievals. We validate the retrieved Aerosol Optical Depth (AOD), Angstrom Exponent (AE), Single Scattering Albedo (SSA), Absorption AOD (AAOD), Fine mode AOD (FAOD), Coarse mode AOD (CAOD), and fine mode effective radius (reff_fine) with AERONET data. The validation suggests that aerosol retrievals can be further improved when extending the aerosol description to include a fine non-spherical mode. For AOD, the Root-Mean-Square Error (RMSE) is 0.051 (0.037) over land (ocean), while 78.3% (80.8%) of the retrievals are within the requirement formulated by the Global Climate Observing System (GCOS). The RMSE is 0.186 (0.207) for AE, 0.038 (0.044) for SSA, 0.023 (0.014) for AAOD, 0.047 (0.031) for FAOD, 0.043 (0.027) for CAOD, and 0.021 (0.026) for reff_fine over land (ocean). Compared to the current RemoTAP algorithm, RemoTAP-Hybrid shows improved agreement with AERONET for AOD, AE, and FAOD over land and ocean while the number of valid retrievals is increased by 4% (3%) over land (ocean) and the computational time is reduced by 43% (32%). Finally, we present the first global seasonal maps of aerosol optical and microphysical properties and chemical composition from SPEXone.

We propose that mathematics is done largely as a means of both coping with and celebrating our physicality in the natural world. Inspired by David Abram's "Becoming Animal", we suggest that – in opposition to the popular image of an otherworldy Platonic realm– the spiritual component of doing mathematics is grounded on and in the Earth. We explore this as a means of questioning the widespread adoption of AI in the workflows of research mathematics.

Large language models are increasingly deployed as teams of agents that hold different private information about a shared task. How should such agents concisely communicate in a way that promotes aggregation of decision-relevant information? Communicating only proposed actions can discard decision-relevant uncertainty: two agents may prefer the same action for different reasons. We study an alternative interface in which agents communicate calibrated beliefs over actions. We first analyze a simple synthetic setting that captures the structure of multi-round reasoning under partial information. In this setting, we show theoretically and empirically that communicating unbiased probabilities can be strictly more powerful than communicating actions. We then test the same principle in a collaborative maze-solving task with trained transformers and pretrained LLM agents. Our results demonstrate that probability communication outperforms action communication when the exchanged predictions preserve calibrated uncertainty. When communicated probabilities are biased, we show that the benefits of probability communication can disappear. We give a post-hoc conversational calibration intervention that consistently improves decision-making by correcting these biases both in a toy transformer setting and when pretrained LLMs use the corrections in context. These results suggest that probabilistic communication is useful for multi-agent collaboration not merely because it transmits more information, but because calibrated uncertainty gives other agents a reliable object to update on.

We study orthogonal $(4,3)$-equipartitions of finite measures absolutely continuous with respect to Lebesgue measure: every three of four mutually orthogonal affine hyperplanes must divide each measure into eight equal parts. For every number $m$ of measures, we determine the exact dimension threshold of Musin's polynomial criterion and express it in terms of the binary expansion of $m$. The threshold coincides with the geometric lower bound precisely when $m=2^j-1$. Consequently, $\Delta^*(2^j-1,4,3)=7\cdot2^{j-1}-2$ for every $j\geq1$.

Understanding how large language models (LLMs) evaluate gameplay experience is important for using their feedback to guide game design. However, overall ratings alone provide limited insight into which aspects of experience are associated with these judgments and how they can inform concrete game changes. We introduce PREFER, a framework that uses a shared set of experience dimensions adapted from established psychometric questionnaires to benchmark how models evaluate gameplay and to guide persona-specific game refinement. Through these dimensions, we characterize the perspectives models offer as virtual playtesters by examining how their overall assessments relate to specific aspects of experience and to the gameplay they produce. To examine how the same dimensions can guide refinement for players with different preferences, we use personas to simulate distinct player profiles. For each persona, PREFER uses experience-preference relationships to select refinement objectives, revises game rules and their implementations, and playtests candidate games to assess experience changes and predicted preference gains. Experiments with five personas show that PREFER achieves 9.2% higher mean post-play preference ratings than the strongest evaluated baseline.

World models of visual information predict future image frames conditioned on given action sequences. This predicted scene evolution is driven by deterministic changes such as controlled motion on a robot platform, as well as stochastic changes such as rendering of manipulated objects or previously occluded regions. Our key insight is that the spatial location of these stochastic changes is itself learnable. We leverage this insight by jointly regressing both the deterministic next-state prediction and the spatial uncertainty map, then using the uncertainty map to guide a conditional diffusion process. We propose Decoupled Drift-Diffusion World Model (D3WM), which uses a transformer trained with a Gaussian negative-log-likelihood objective to produce both the deterministic next-state prediction and a spatial map of heteroscedastic aleatoric uncertainty. The learned uncertainty map then provides a structured spatial gate for a conditional diffusion model: deterministic regions are anchored to the predicted state, while uncertain regions, such as disocclusions or dynamic textures, are sampled by the diffusion process. We frame this decomposition under a variance-gated stochastic differential equation that separates deterministic drift from stochastic diffusion. D3WM shows improved results over competitive baselines in two distinct types of action spaces: robotic tabletop manipulation and camera motion.

While causal discovery methods have matured for complete data, such algorithms for handling missing values remain limited. We establish general sufficient conditions under which causal graphs remain identifiable (i.e., uniquely determined from the available data distribution) under various missingness categories, including Missing Not At Random, and provide a framework to extend correctness guarantees from causal discovery algorithms for complete data to missing data settings. Our results show that identifiability of causal graphs with no unobserved confounders is preserved when (1) missingness mechanisms do not causally interact, (2) no variable directly causes its own missingness, and (3) either faithfulness holds for missingness mechanisms, or they follow generalized linear models. Guided by these theoretical results, we introduce two asymptotically correct algorithms for Additive Noise Models (ANMs) that recover the underlying causal graph and provide consistent parameter estimates.

Transformers are efficient to pre-train at scale because attention permits parallel computation across sequence positions, but long-context inference requires increasingly large KV caches. Efficient recurrent alternatives reduce the asymptotic complexity of inference, but their sequential dependence limits token-wise parallelism during training, making them harder to scale. Further, the current paradigm of extending long context tasks creates competing notions of retaining information precisely and keeping long-context inference efficient. To address this gap, we introduce Titan-Llama, a post-training method for retrofitting attention-based language models with a hierarchical memory architecture that updates parameters at test-time. Titan-Llama applies a blockwise attention mask and preserves full-fidelity attention over recent tokens while compressing historical context into recurrent, fixed-size neural memory modules (NMMs). Our formulation allows pre-trained attention layers to be replaced without training a new language model from scratch. On Llama-3.2-1B-Instruct, Titan-Llama raises accuracy over segmented attention windows from 23.87% to 40.51% on QuALITY and from 14.50% to 40.75% on LongHealth. Inference benchmarks show more than 20% faster prefill, 37% faster decode at medium context lengths, and 24% lower steady-state decode memory usage in the evaluated configurations. Together, these results demonstrate that incorporating memory architecture mechanisms that utilize test-time training effectively modulates long-context behavior of pre-trained models, offering a practical route to adapting pre-trained transformers for efficient long-context inference. Our code is released on Github \href{https://github.com/sarahpannn/titans-pytorch/tree/main}{GitHub}

Solid-state triplet-triplet annihilation upconversion offers a compelling route to harvest sub-bandgap photons to increase the efficiency of photovoltaics, but low sensitizer doping required to suppress non-radiative aggregation quenching severely restricts light absorption. Here, we present a dual-resonator planar silver microcavity housing a thermally co-evaporated rubrene:palladium phthalocyanine (PdPC) active layer designed to simultaneously enhance triplet-sensitizer absorption and out-couple upconverted emission. By aligning a dispersive cavity mode with the PdPC absorption peak at $32^\circ$, we achieve a 12-fold enhancement in absorptance at 665 nm. This absorption boost, combined with directional outcoupling through a second cavity mode, outweighs cavity-induced reabsorption losses to yield a 22-fold peak and 4.5-fold integrated enhancement in detected upconversion emission. Overall, this work highlights the potential of microcavity integration to substantially enhance solid-state upconversion performance across low-intensity optoelectronic applications.

We consider nonparametric regression with random design and non-Gaussian noise, where the regression function has the multi-index form $F(x)=f(\Theta x)$ with an unknown link $f:\RR^m\to\RR$ in an anisotropic Hölder class and an unknown matrix $\Theta$ with $m\le d$ orthonormal rows. For estimation of $F$ at a fixed point we prove that the minimax risk is bounded from below by a multiple of $L^{1/(2\gamma+1)}(n^{-1}\ln n)^{\gamma/(2\gamma+1)}$, where $\gamma$ is the harmonic mean of the smoothness indices of the link divided by $m$. For $m<d$ this extends a Gaussian white noise result to regression. The main new case is $m=d$, where no dimension reduction takes place: the logarithmic factor still appears as soon as the link is anisotropic and the orientation of its axes is unknown. In contrast, when the link is isotropic with smoothness index at most one, the class is rotation invariant up to a constant and the classical rate without logarithm is attained. The logarithmic loss is therefore caused by the unknown orientation of the directions in which the function is least smooth

Selecting a budget-constrained set of documentary fragments, for instance the knowledge base of a retrieval-augmented generation system, raises a statistical question: how much expected query coverage is lost relative to the best feasible selection when the query distribution is unknown? We construct finite-sample, distribution-free upper confidence bounds for this coverage regret that remain valid after data-dependent selection. A pilot stage may select the document set, screen competitors, build comparison networks and learn an annotation policy. Then an independent audit acquires relevance labels with probabilities that are constant within observable strata. The main result is a simultaneous bound for all retained coverage contrasts. The bound is made observable by empirical-Bernstein variance calibration or by a one-stage construction without calibration, and it accounts for estimated stratum proportions. For maximum-type coverage we prove variance contractions for swaps of redundant fragments, give a condition under which multiscale radii improve on a direct union bound, and show that such redundancy cannot be certified from samples alone. A simulation study confirms validity and quantifies the gains from variance calibration and certified redundancy.

While work on LLM-based regression has largely focused on scalar prediction, multi-output text regression remains less explored. We present DualView, a parameter-efficient approach to leverage LLMs for multi-output text regression. \method{} first extracts broad and output-specific representations from a frozen LLM, then uses a dual-branch architecture to produce the full score vector. Across five heterogeneous regression tasks and eight LLMs (up to 122B), DualView outperforms seven supervised regression baselines while requiring 82–1842 times fewer fitted parameters than the three strongest baselines. These improvements extend across individual output dimensions and persist even with limited training data. Notably, DualView using a smaller open-weight LLM can outperform unsupervised prediction with Gemini 3.1 Pro. Controlled ablations show that broad and output-specific evidence provide complementary predictive benefits, while lightweight shared predictors achieve strong performance with fewer trainable parameters.

Let $f,g\in\mathbb{Z}[t]$ be products of cyclotomic polynomials such that either $g/\gcd(f,g)$ or $f/\gcd(f,g)$ (or both) is squarefree. We give explicit formulae for the invariant factors of $f(C_g)$, where $C_g$ is the companion matrix of $g$, expressing them in terms of the indices and multiplicities of the cyclotomic factors of $f$ and $g$. A more compact formula holds for the circulant case $g(t)=t^n-1$, assuming that every cyclotomic factor shared by $f$ and $g$ has multiplicity $1$ in $f$. We discuss applications to several topics, including abelianizations of cyclically presented groups, homology groups of cyclic branched covers of knots, adjacency matrices and shifted graph Laplacians, $K$-theory, and Smith forms of matrix powers. For example, for two families of hyperbolic knots we give the first integral homology in every covering degree; or, when $g$ is squarefree, we determine the least eventual period of the Smith forms of powers of $f(C_g)$.