Papers

Molecular mixing models for the conditional scalar diffusion (CSD) term in the filtered mass density function (FMDF) transport equation used in Large Eddy Simulation (LES-FMDF) approach are evaluated against direct numerical simulation (DNS) of spatially evolving jets. A database of DNS of turbulent mixing slot jets of $C_{7}H_{16} / O_2$ and $C_{7}H_{16} / Air$ is developed. The formulation includes the compressible form of the governing equations, a generalized multicomponent diffusion model, a cubic real gas equation of state and realistic property models. Simulations are conducted over a wide range of initial pressures ($1 atm < P_0 < 100 atm$) and jet width based Reynolds numbers of 850 and 1300. FMDF of mixture fraction at various filter widths are obtained from the simulation at several spatial locations within the flow. The CSD term in the exact transport equation of FMDF is calculated from the DNS. An a priori analysis of Interaction by Exchange of Mean (IEM), Modified Curl (MC) and Mapping Closure (MAPPING) mixing models for CSD is conducted. At high pressures, significant deviations are observed between the CSD measured from the DNS and those predicted by the models. The source of the deviations is determined to be the mixing frequency used in the models. The significance of the mixing frequency and its variation with change in pressure and diffusion models is studied. The primary objective of this work is to assess the applicability of aforementioned mixing models to flows at large pressures and determine the causes for deviation in prediction.

This work introduces innovation-based sampling of continuous stochastic processes, in which a sample is generated only when the process reveals “sufficiently new” information relative to all previous samples. The resulting innovation process admits a lattice structure and a three-dimensional state representation. For a Wiener process, we characterize the direction, timing, and frequency of innovations. We show that direction reversals become increasingly rare and establish limit theorems for their number. Innovations also become progressively sparser: the expected number of innovations grows only as the square root of time, and hence the sampling rate vanishes asymptotically. We then study remote estimation from sparsely received innovations. Notably, the absence of an innovation carries information: the minimum mean-square error (MMSE) estimate evolves with the age of information (AoI) and achieves a substantial MSE reduction over the conventional silence-ignorant zero-order hold (ZOH) estimator. Finally, we develop tractable affine-age and exponential-age approximations for practical use. Overall, information is conveyed not only by the content of innovations, but also by their direction and timing.

Supersaturated screening experiments study many candidate factors with few runs. The experimenter must first identify the active factors, then optimize the response. One-shot regularized regression tends to select many factors, and the second-order response surface model in the selected factors is then large and needs many further runs to fit. We propose Sequential Supersaturated Screening ($S^3$), a two-stage framework for supersaturated designs. $S^3$ builds each screening round by coordinate exchange under a new positive-cone design criterion that uses no practitioner-chosen Welch calibration constant. It then removes low-importance factors one round at a time, using a graduated quantile rule. The criterion scores a design by how far its column correlations sit above the Welch lower bound, and it adapts to the current number of runs and candidate factors. We give a round-by-round bound on the probability that a noise factor is ever fixed, under conditions on noise survival and commitment at each round, together with an explicit upper bound on the total number of Stage 1 runs. Across simulated screening problems and the Borehole benchmark, $S^3$ achieves lower Type I error and higher $F_1$ scores than one-shot cross-validated Lasso (LassoCV). It also improves optimization quality in most settings and runs faster.

Purpose: Most Greek papyri remain unpublished and undigitised; a handwritten text recognition (HTR) pipeline that transcribes them automatically would let scholars discover documents and literary works that have so far gone unread. Recognition systems for Ancient Greek papyri are in statu nascendi, and how accurate they must be for a given papyrological task has not been examined. To answer this and set a benchmark for Greek papyrus HTR, we test a range of character error rates (CER) against four papyrological tasks, using published editions as ground truth. Methods: From 63,846 current editions of Greek texts in papyri.info, we imitate a letters-only "perfect HTR" output by removing the editorial layer, then degrade it with a seeded algorithm to exact CERs of 1 - 50%, with lost lines and four error-shape variants. On these data we train small models (TF-IDF, fastText, a character CNN, ByT5-small) for document type, dating and documentary-versus-literary classification, and apply eight keyword search methods. We compare models trained on clean text with models retrained at a specific CER level, and evaluate across CERs. Results: Tolerance differs by task. With clean-trained models, documentary-versus-literary classification retains 90% of its metric up to 20% CER; document type up to 7.5%; subtypes and search up to 5%; dating only up to 3%. Retraining on text containing character errors largely eliminates the sharp degradation that otherwise sets in above 15% CER. Models generally tolerate concentrated damage in a long document better than small errors spread across a short text. Conclusion: The study provides a CER target for each of the four tasks and shows that models trained on noisy text make current, imperfect text recognition useful for them.

For integers $m\geq 2$ and $m\mid N$, let $G(N;m)=\gcd\{\binom{N}{k}:0<k<N,\ m\mid k\}$. We prove a complete $p$-adic valuation formula for $G(N;m)$ at primes $p\equiv -1\pmod m$, under the hypotheses $m\geq 3$, $m\mid N$, and $m<N$. Writing $N=\sum_i d_i p^i$, put $A=\sum_{i\text{ even}}d_i$ and $B=\sum_{i\text{ odd}}d_i$. Then $v_p(G(N;m))$ is $2$ in the exceptional mixed case $(A,B)=(1,1)$ with $p=m-1$, is $1$ in the mixed case $(A,B)=(1,1)$ with $m<p$, is $1$ in the one-parity cases $(A,B)=(m,0)$ and $(A,B)=(0,m)$, and is $0$ otherwise. The proof uses Kummer's theorem to translate the problem into digitwise borrow counts and a minimal signed zero-sum classification. A source-level literature audit through 25 September 2026 located no equivalent prior theorem for the full minus-one classification: McTague's corrected same-residue extension covers the one-parity $p>m$ subcases, but not the mixed-parity branch or the $p=m-1$ regime. The theorem, its plus-one companion, a scaling reduction, and the $m=3,4,6$ specializations have been formalized in Lean 4 / Mathlib.

We study common flux offsets in a three-dimensional InAs Aharonov-Bohm waveguide formed by two quarter-circle bends of opposite curvature. Each bend contains a through-opening that separates two conducting arms and encloses an independently specified flux. For a spin-independent, two-terminal model with ideal confined fluxes, microreversibility and a rotation exchanging the complete modules imply $\mathcal{T}(\phi_1,\phi_2)=\mathcal{T}(-\phi_2,-\phi_1)$. The counter-wound configuration is therefore stationary against common offsets, while the same-winding configuration is stationary against differential offsets. This constraint does not require cancellation of every interference phase, and it extends to a spatially uniform ambient field perpendicular to the plane of the guide, even though that field also penetrates the conductor. Three-dimensional scattering calculations at $R=350$ nm and $E_F\simeq 7.283$ meV retain three open orbital lead modes and strong reflection at the openings. The finest sampled counter-wound sweep has a visibility of approximately 3.56%; referring the grids to a common threshold gives an estimated continuum visibility of 2.6-2.9%. The response coefficients vary strongly with energy, while a 100 mK electron temperature retains about 98% of the visibility. For weak, purely common Gaussian phase noise, the leading transmission variance is quartic in noise amplitude, whereas the mean shift remains quadratic. Flux imbalance and asymmetric scalar potentials restore a linear response; symmetric scalar disorder preserves stationarity without guaranteeing high transmission. The proposed experimental test requires few-mode coherent transport, calibrated flux controls, and a magnetic-source design whose leakage fields and spin-dependent terms are assessed explicitly.

We discuss some contexts in which the topological dynamics of certain Anosov subgroups of higher-rank Lie groups on "bad" subsets of flag manifolds can be analyzed using results from homogeneous dynamics in the infinite-covolume rank-one setting. For example, we show that a group of projective transformations dividing a strictly convex domain in projective space and intersecting Zariski-densely the stabilizer of an ellipsoid has a dense orbit in the complement of the domain, and acts minimally on the space of full projective flags tangent to the domain. This accounts for all known examples of divisible strictly convex domains in sufficiently high dimensions. We also provide examples of Zariski-dense groups that are Anosov in a partial flag manifold but such that the equivariant projection from the Benoist-Guivarc'h limit set in the Furstenberg boundary to the Anosov limit set is not a fibration.

Sparse mixture-of-experts (MoE) large language models scale model capacity by routing each token to a small subset of experts. Their routers are regularized with load balancing terms and learn affinity scores through the language-model objective. However, these objectives do not provide direct alignment between routing affinities and token-level error. We introduce token-error supervision for sparse routing in two forms. The first form predicts an error score per expert. The affinity-weighted aggregate of these scores is aligned to the next-token cross-entropy loss, while the individual scores attenuate affinity before top-$K$ selection. The second directly aligns the router's affinities to the model's objective without requiring an additional head or inference-time modification. Both formulations use the Itakura–Saito divergence or an exponential negative log-likelihood for aligning affinities and token errors. Across two sparse MoE backbones and four multiple-choice question-answering benchmarks, we evaluate both supervision mechanisms. On Granite, our method improves accuracy by approximately 2.3 percentage points on average over a parameter-matched routing baseline. With stronger supervision, the gain on ARC-Challenge reaches 2.94 points. Both mechanisms preserve the native sparse execution budget and aggregation policy. Our code is available in the supplementary materials.

Pulmonary embolism (PE) is a leading cause of cardiovascular mortality, yet the real-world performance of FDA-cleared AI detection models remains incompletely characterized. We retrospectively evaluated two FDA-cleared AI algorithms from a single commercial platform (Aidoc Medical BriefCase), one for PE triage on dedicated CT pulmonary angiography (CTPA; n = 30,678) and one for incidental PE (iPE) detection on routine contrast-enhanced CTs (n = 37,191), across a 17-facility academic health system. Reference-standard labels were extracted from radiology reports using a validated LLM pipeline (97% accuracy, kappa = 0.94). The PE model achieved 86.8% sensitivity and 99.1% specificity, with sensitivity declining from 99.3% for saddle emboli to 72.9% for subsegmental PE, and from 89.7% for acute to 65.3% for non-acute PE. The iPE model achieved 73.5% sensitivity and 99.8% specificity. Both models demonstrated lower sensitivity than FDA-clearance benchmarks while exceeding cleared specificity, with diminishing performance for peripheral and non-acute emboli mirroring known human reader limitations and underscoring the need for standardized post-market surveillance of AI-enabled medical devices.

The increasing importance of Information Retrieval (IR) in managing large datasets has highlighted significant limitations in traditional keyword-based search systems. Context-aware chat-based search methods, such as Retrieval Augmented Generation (RAG), have recently emerged, but their evaluation compared to keyword-based systems often relies on subjective user feedback. A rigorous, quantitative comparison between these paradigms remains lacking. This work introduces a novel, preliminary framework to quantitatively assess IR accuracy of search systems that produce different output formats, such as lists and messages. It focuses on two key aspects: the ranking accuracy for keyword-based systems and the completeness of retrieved information for semantic chat-based systems. Our approach enables semi-automatic comparisons of semantic and keyword-based methods using interchangeable equivalence classes tailored to domain-specific contexts (e.g., companies or problems). We validate the framework through an industrial case study, demonstrating statistically significant improvements in context-aware search over keyword-based methods, supported by analyses including the Mann-Whitney U-Test. With its adaptable design, the proposed framework provides a strong foundation for objectively assessing keyword-based and semantic chat-based search methods.

We study weak and strong forbidden subposet problems in the linear lattice $L_n(q)$. We show that the $q$-analogues of the Bukh–Griggs–Lu conjecture fail for every prime power $q$. If $q\ge 3$ and $n$ and $d$ have opposite parity, then $La_q(n,L_d(q))=La_q^*(n,L_d(q))=\Sigma_q(n,d)$. We also show that $La_q(n,D_s)=La_q^*(n,D_s)=\Sigma_q(n,2)$ for $2\le s\le q$ and all $n$, and for $s=q+1$ when $n$ is odd. For $n$ even, a maximum strong $D_{q+1}$-free family can be contained from the three middle layers. The case $s=2$ settles the $q$-analog of the diamond conjecture in the affirmative.

We study the finite element approximation of the Dirichlet problem for the Bessel $(p,s)$-Laplacian, $\operatorname{div}^{s} \left(|\nabla^{s} u|^{p-2}\nabla^{s} u\right)$, built from the Riesz fractional gradient $\nabla^s$ and posed on the Bessel potential space $X^{s,p}$, obtained by complex interpolation between $L^p$ and $W^{1,p}$. For $p = 2$ this operator reduces to the fractional Laplacian, while for $p \neq 2$ it differs from the fractional $p$-Laplacian arising from real interpolation. Since a direct Galerkin discretization requires reassembling a dense stiffness matrix at every nonlinear iteration, we propose an augmented Lagrangian formulation based on the projected fractional gradient $B_h = \mathbf{\Pi}_h \nabla^s$, in which the only dense matrix is assembled once and the nonlinearity decouples elementwise. We analyze the resulting consistency error, establish a priori convergence rates in $X^{s,p}$, conditional on a discrete inf-sup condition for the augmented Lagrangian scheme, and present numerical experiments that illustrate the convergence of the method and its ability to deal with degenerate and strongly nonlinear problems.

We introduce an exact algebraic architecture that evaluates an arbitrary finite Fourier series using a two-mode ($2 \times 2$) linear optical circuit, with the only tunable components being single-mode phase shifters encoding the function argument. We prove that such a circuit must exist for every Fourier series and derive an analytical method for its construction based on spectral factorisation. The resulting optical system exhibits an $\mathcal{O}(N)$ depth for an $N$-harmonic expansion, executing function evaluations in the passive optical time-of-flight. Finally, we validate our claims numerically, demonstrating that even for sequences with thousands of Fourier terms, our proposed circuit construction correctly synthesises continuous and discontinuous nonlinear functions. Our architecture thus provides a universal, deterministic foundation for single-variable nonlinear optical computing on integrated photonic platforms.

Neural scaling, in which loss falls as a power law with training, is central to large language models, and one recent proposal is that a $1/3$ exponent emerges from learning peaked distributions. That account describes SGD, but models in practice are trained with adaptive optimizers. Here we separate two exponents the $1/3$ account does not distinguish: how fast the loss falls with training steps along a single run, and how fast the optimally tuned loss falls with dataset size $D$. We show that the first, a dynamic exponent, is optimizer-specific while the second, an optimal data exponent, converges to $1/3$ across optimizers. In an online teacher-student model we decompose the loss into norm growth (radial) and alignment toward the teacher direction (tangential), each decaying as a power law with dynamic exponents $\alpha_{r}$ and $\alpha_{t}$. Under SGD, both are close to $1/3$, so the data exponent is also $1/3$ across different learning rates. Under Adam the two separate: $\alpha_{r} \simeq 0.48$ but $\alpha_{t} \simeq 0.08$. Since the total loss is minimized when these two parts are balanced, the optimal learning rate is optimizer-dependent: $D$-independent for SGD but falls with $D$ for Adam. Yet tuned to that optimum, the loss returns to $D^{-1/3}$ for both. A stochastic-dynamics analysis explains why: the optimizers can trade decay speed between the two channels, but they all fall on a single dynamic exponent relation, $2\alpha_{r}+ \alpha_{t} = 1$, which fixes the optimal data exponent at $1/3$. Across seven optimizers, including Muon, the measured exponents are consistent with this relation, and the optimal-loss envelopes agree with $D^{-1/3}$ across them. The optimizer sets how fast a model learns per step; tuned optimally, it changes the prefactor but not the rate at which loss falls per sample.

In 1977, Erdős posed the problem of determining the maximum number $f_r(n)$ of edges in an $n$-vertex $r$-uniform hypergraph in which all disjoint pairs of edges have distinct unions. Füredi later conjectured that, for every fixed $r\ge 4$ and all sufficiently large $n$, $f_r(n)=\binom{n-1}{r-1}+\lfloor \frac{n-1}{r}\rfloor$. In this paper, we prove this conjecture and determine all extremal configurations. Our proof combines a stability theorem for such dense hypergraphs with a delicate deletion argument applied to an associated bipartite $3$-graph. The stability theorem also resolves a conjecture of Mubayi.

LLM agents performing long-horizon tasks accumulate tool results that later steps may need. Passing the full history to every invocation is costly even when it fits within the context window, while reducing it risks omitting needed information. Existing context management methods can overlook how earlier tool results are used in subsequent execution, leaving needed information out of context. We introduce ContextRender, which manages context through a persistent graph of execution dependencies. We develop Tool-Flow Analysis to track how later operations reuse information from earlier tool results, providing a signal called observed reuse. A renderer combines this signal with recency and semantic relevance to select results within a fixed history budget, retaining omitted results for later use. Across AppWorld and 8-objective QA with three execution models, ContextRender outperforms the evaluated context management baselines using a 6K history budget, well below the models' maximum context windows. Within this budget, it achieves task performance close to or above that of passing the full history while reducing mean inference cost by 10.2%-32.2% relative to Full history. Ablations show that observed reuse improves task performance and retention of results reused later.

Modern cameras widely use temporal High Dynamic Range (HDR) to improve visibility by capturing a sequence of exposures with different integration times and fusing them into a single image. This process implicitly assumes that scene illumination remains sufficiently stable during capture. We introduce FLASH (Fusion-Level Attack by Saturating HDR), an external pulsed-light attack that deliberately attacks this assumption by creating cross-exposure inconsistency before downstream perception. FLASH exploits an algorithmic assumption rather than relying on sensor damage or hardware failure, and requires neither physical camera access, access to raw exposure brackets, knowledge of the fusion algorithm, nor exact phase lock to the camera. Across eight physical camera platforms spanning embedded, surveillance, photography, smartphone, and automotive use cases, and matched optical controls, FLASH causes pipeline-dependent darkening, overexposure, and visibility loss. This includes extreme-darkening rates of 50.0% on an iPhone 16 Pro and 33.7% on a Wyze Battery Cam Pro. On the Wyze camera, FLASH triggers the system-level low-visibility response in 10/10 trials, compared with 0/10 continuous-light and randomized-frequency flashing controls. In a controlled stationary OpenPilot case study, 23.0% of frames exhibit severe darkening in the traffic-cone target region, with target-background CNR decreasing by up to 90.8%. Under FLASH, the OpenPilot interface also fails to display the system-level path state observed in the corresponding control trials. In a controlled night-only HDR reconstruction stress test, a proof-of-concept exposure-rejection defense reduces median output-brightness deviation by 79.16%. These results show that temporal HDR fusion itself requires security-aware validation of exposure evidence.

We develop a non-perturbative framework for stochastic-volatility option pricing built on the two-particle-irreducible (2PI) effective action and the Dyson-Schwinger gap equations of quantum field theory. In log-price, log-volatility or Lamperti coordinates, the joint law of the state variables is approximated by a self-consistent Gaussian whose mean and effective diffusion follow from the 2PI stationarity conditions, with the exponential and CEV vertices evaluated through the exact Gaussian moment-generating function rather than a Taylor cut. For exponential vertices the skeletons beyond this level sum in closed form: in exp-OU the evaluated melon level cuts the Hartree error by 20-130x, to 0.01-0.11 bp. Whether the dressed inverse propagator is local in time separates Markovian models, where the gap equation collapses to a few ODEs, from rough (Volterra) models, where the full two-time propagator is retained. At nonzero correlation the field is integrated deterministically by conditioning on its two leading Gaussian modes, with exact conditional moments and a moment-matched law for the integrated variance and leverage integral; in the CEV models the correlated drift enters a Dyson equation around the exact absorbed-CEV propagator, resummed by jumps along the variance clock. These closures match Monte Carlo references for rough Bergomi approximately at their resolution (0.01-0.1 bp) down to H=0.07, rho=-0.9, and price SABR to 0.97 bp over a 72-cell grid with maturities to ten years (75 bp for Hagan's expansion) and rough SABR to 0.92 bp. Conditional on the volatility field, forward-start smiles and continuously-monitored barriers reduce to field-only quadratures on the native Volterra field, and the causal response block yields the impulse-vega curve in one adjoint contraction. Derivations, extended benchmarks and secondary applications are in an ancillary technical supplement.

While attaining remarkable results for many applications, Deep Learning models are notoriously difficult to explain. This work introduces HyDI, a hybrid ensemble architecture for hierarchical multi-label classification. It combines a Deep Learning (DL) model with rule-based classifiers generated by Inductive Logic Programming (ILP). For leaf classes of the label hierarchy, the rule-based classifiers replace the DL model, leading to more transparent classification results. HyDI is applied to the Chemical Entities of Biological Interest (ChEBI) ontology, providing ILP-generated rules for 314 classes. For these classes, HyDI can generate global explanations as well as local explanations that combine visual and text-based descriptions.

In this paper, we obtain a classification of isoparametric submanifolds with arbitrary codimensions in products of simply-connected space forms, except for isoparametric hypersurfaces in $\mathbb{S}^n \times \mathbb{S}^m$ and $\mathbb{H}^n \times\mathbb{H}^m$.

Recently derived exact expressions for the distributions of scattering matrix elements show that all combinations of ingoing and outgoing spin orientations are equally distributed. We propose a model suitable for experimental realization that breaks this degeneracy by introducing a spin preference in the channels. With the help of supersymmetry we derive a corresponding nonlinear sigma model. We exactly calculate the distributions of real and imaginary part in first order of the parameter measuring the preference. Quite remarkably, while breaking the spin degeneracy leads to different distributions for the favored and unfavored spin orientation, the real and imaginary parts of these altered distributions are the same as in the case of unbroken spin degeneracy.

When a prompt injection attack succeeds, a Large Language Model (LLM) abandons its assigned system role to comply with an adversarial instruction. While prior work has extensively quantified how often this occurs, we ask a more fundamental question: where inside the network does the model actually decide to break the rules? Using layer-by-layer causal activation patching across five models (4B to 32B parameters), we find a clear dissociation: attack information is linearly decodable from the first layer, yet causal leverage over the model's behavior is negligible until a late-layer bottleneck in the final third of the network. Patching this bottleneck reverses compliance in 77–92% of cases. We show that the compliance mechanism occupies a compact linear subspace (rank-8 in 4B and 14B models, scaling to rank-64 at 32B) and is architecturally stable across varying model families. Finally, we validate our mechanistic account by showing that this causal peak layer is also the representationally optimal site for detecting attacks, outperforming early-layer classifiers that degrade under surface-level obfuscation such as leetspeak substitution. This alignment between causal leverage and detection performance provides converging evidence that the late-layer bottleneck captures decision-relevant computation rather than merely reflecting an artifact of the intervention.

The 290-Theorem of Bhargava-Hanke completely classifies all universal quadratic forms over the rational integers in terms of a finite criterion set: a positive definite quadratic form is universal if and only if it represents every integer in this finite set. In this article, we study diagonal forms of higher degree over a totally real number field and prove the existence of a unique finite criterion set, minimal with respect to inclusion, for universal diagonal forms of higher degree. As part of the proof, we establish an analog of the asymptotic local-global principle for such forms and develop a local theory for the representation of integers by diagonal forms of higher degree.

Single-cell cancer datasets are predominantly cross-sectional and rarely provide paired or longitudinal observations linking individual healthy-like cells to tumor-associated states. We introduce CancerZigZag, a seed-initialized diffusion-based framework for exploratory generation of tumor-associated single-cell candidate clouds from unpaired epithelial cell populations. For each cancer context, a diffusion model is trained exclusively on tumor-derived epithelial cells and applied through repeated partial latent-space perturbation and reverse diffusion to held-out healthy-like seeds, generating stochastic candidate clouds without paired measurements or classifier guidance. We applied CancerZigZag to colorectal, breast, lung, and renal cell carcinoma contexts and explored parameter landscapes defined by perturbation depth and the number of ZigZag cycles. Across the reported operating configurations, candidate clouds contained outputs classified toward held-out tumor-derived reference populations for each evaluated seed. Residual seed-dependent organization varied across contexts, with the clearest structure in colorectal cancer, more modest organization in lung cancer, and limited cloud-level structure in breast and renal cell carcinoma. Representative candidates also showed directional concordance with transcriptional shifts observed between held-out healthy-like and tumor-derived reference populations. CancerZigZag is not interpreted as a model of deterministic healthy-to-tumor transformation or cellular progression. Instead, it provides a reference-informed framework for exploring tumor-associated candidate distributions from unpaired healthy-like seeds and quantifying the context-dependent relationship between tumor-associated displacement and residual seed dependence.

Research in modular robotics has produced capable approaches allowing a robot's morphology to change online, with recent efforts also developing approaches to decide which morphology to assume and automatically propagate that decision into the robot's motion planning and control. These approaches are powerful and increase adaptability in the field. However, an alternative objective is not to build robots whose structures can change, but robots whose fundamental capabilities can change, where capability is a joint function across several domains, including kino-dynamics, perception, compute, and high-level coordinating behaviors. A robot designed to be reconfigured across these domains has a greater capacity to alter its capability than one that can be reconfigured in a single domain. We refer to this cross-domain reconfigurability as integration span, and recognize a complementary measure of the resistance to reconfiguration, which we refer to as integration inertia. Current modular robots have reduced integration inertia in the structural domain while it remains high in the other domains that contribute to integration span. We assert that the systems that can provide the most utility through reconfiguration in practice are those maximizing span and minimizing inertia and call this general problem recompositional robotics: adaptation over a heterogeneous set of modules including hardware, software, compute, and behavior that abstracts each component by the interfaces it requires and provides such that they can be reasoned over holistically. We define the problem, ground it in two deployed systems and active research efforts, and pose open questions about the future of recompositional robotics.

Second-quantized neural-network quantum states have achieved accurate molecular energies, but extending them across molecular geometries requires a shared representation of the geometry-dependent wavefunction coefficients. We introduce geometry-conditioned foundation neural-network quantum states for molecular electronic structure in second quantization. A single autoregressive model learns a family of ground states from sparse anchor geometries and provides wavefunctions at untrained geometries without further optimization. Orbital alignment matches orbital identities and transports their phases, establishing an aligned orbital basis across geometries. Frozen energies reach chemical accuracy at every untrained query geometry for N$_2$, CO, and H$_4$. On additional molecular paths, the energy-trained wavefunctions yield dipoles, quadrupoles, and natural occupations without property labels. Across three paired N$_2$ training seeds, orbital alignment lowers the mean absolute energy error over all untrained query geometries from 34-37 mHa to 0.049-0.085 mHa. At approximately 1 mHa mean absolute error, frozen evaluation reduces the per-geometry cost by $986\times$ relative to independent optimization, yielding an estimated $25.8\times$ end-to-end GPU-cost reduction on a 161-point N$_2$ grid.

Instruction-based image editors insert objects, restyle scenes and render new viewpoints, but it is unknown which camera they assume when they paint into a photograph. Asked to cover the floor with a checkerboard, an editor paints projective structure from which classical vanishing-point geometry reads pitch, roll, focal length, yaw and, on renders, the principal point, without any training. Unlike a calibrator such as GeoCalib, which estimates the camera of an image, this isolates the camera under which the editor paints. On 120 rendered cameras with exact ground truth, Qwen-Image-Edit-2511 paints tile edges that meet their vanishing points within 0.26 degrees, and its implicit camera matches the true one to 0.8 degrees in pitch and 6% in focal length, more accurately than GeoCalib except in roll. Asked to draw the horizon or mark a vanishing point instead, the editor fails, so this knowledge is revealed by painting and not by the explicit tasks we tried. The implicit camera has two priors: roll is pulled towards level (slope 0.71), and telephoto perspective towards a default of about 30 mm, which roughly matches the camera the models paint without any scene. For Qwen, the priors do not grow when blur removes four fifths of the line evidence. They are stronger on real photographs, and on NYUv2 a shorter wording of the task removes the difference for roll. On photographs from a 24–240 mm zoom lens the painted perspective grows with only 0.62 of the lens's slope, while GeoCalib and MoGe-2 saturate at about 52 and 42 mm. FLUX.1 Kontext and LongCat-Image-Edit are pulled much harder. Finally, from a level camera a camera-control LoRA executes pose commands at only 50–70% of their strength, and a board painted into its output agrees with the camera it produced.

Activation space and parameter space provide complementary views of model computation. Activations represent information, while weights read, transform, and write that information. Yet existing interpretability methods largely study the two spaces separately, leaving the connection between represented information and parameter-level computation underexplored. We introduce Activation-Supported Parameter Decomposition (ASPD), which jointly decomposes activation and parameter spaces and grounds each learned weight component in the activation features it reads or writes. This grounding constrains otherwise non-unique parameter decompositions using the model's internal activations, while an internal reconstruction objective provides a local learning signal at the weight matrix being analyzed. Together, these properties enable scalable, interpretable, and causally editable parameter decomposition in pretrained large language models, demonstrated on Qwen-3-8B. The learned read–write components can also be composed into parameter-level mechanism circuits. We use ASPD to recover mechanisms underlying the classic IOI circuit and trace semantic transformations through model weights.

Seizure detection and prediction from EEG are clinically important but challenging because seizures are rare, temporally localized, and propagate as coordinated events across multiple channels. Recent dynamic graph neural networks model this by running a temporal model over a sequence of per-time-step pairwise channel edges. However, this pairwise construction misses the spatiotemporal coupling that constitutes a seizure, at substantial training cost. We propose HyBrain, which summarizes spatiotemporal EEG evidence through a small set of soft hyperedges rather than pairwise edges. A per-channel Mamba backbone produces one token per (channel, second), and a spatiotemporal hyperedge block pools these tokens into E_h shared group embeddings through soft memberships and broadcasts them back. The same encoder serves three downstream tasks: window-based detection, one-second point-wise detection, and preictal seizure prediction. On TUSZ and CHB-MIT, HyBrain achieves the best AUROC on every reported setting against ten baselines, with the largest gap on long-clip preictal prediction. It also matches the most efficient baselines in training time and peak GPU memory. A qualitative analysis shows that even a single learned hyperedge cleanly captures the preictal -> ictal -> postictal trajectory on a real seizure clip.

We compute jet quenching observables–the nuclear modification factor $R_{AA}$ and elliptic anisotropy coefficient $v_2$–for open-heavy flavor mesons with high transverse momentum in an improved CUJET model, in which the strong coupling parameter as well as the temperature-dependent fraction of chromo-magneto monopoles are extracted through Bayesian inference using high-$p_T$ light-hadron $R_{\mathrm{AA}}$ and $v_2$ measurements from RHIC and the LHC. We show in this work that such a Bayesian-inference-improved CUJET model provides a good description of available high-$p_T$ charm- and bottom-hadron observables based on the same posterior parameters. The corresponding heavy-quark spatial diffusion parameter, $2\pi T D_s$, is also computed, which is broadly consistent with current phenomenological and lattice-QCD constraints. These results support a universal description for the medium modification of high-$p_T$ light- and heavy-flavor energy loss and indicate an important role played by the chromo-magnetic degrees of freedom near the confinement transition region of quantum chromodynamics (QCD).