Papers

The abundance and properties of low-mass dark matter subhalos can be inferred by measuring the density and velocity structure of stellar streams, testing physical models of dark matter. Which streams make the most promising dark matter detectors, and which subhalos would they encounter? We use the semi-analytic model galacticus to simulate the Milky Way's dark subhalos, including tidal stripping under the influence of the galactic disk. Deriving stream initial conditions that best match present-day observations, we forecast subhalo encounters for 24 globular cluster streams around the Milky Way. Over their lifetimes, the 10 most perturbed streams are predicted to each experience $\approx 2$-$12$ significant subhalo encounters with velocity kicks $v_\mathrm{kick} > 0.1$ km s$^{-1}$. Jet, AAU, GD-1, and Palomar 5 lead the list, with Jet encountering twice the subhalos of any other stream. The subhalos that encounter streams have been tidally stripped to $1$-$20\%$ of their peak mass and are twice as compact as previous works have assumed. A spectroscopic survey of streams with sub-km s$^{-1}$ precision could reveal the influence of dark subhalos below the threshold of galaxy formation. Predicting the abundance and scatter of low-mass subhalos that reach the inner galaxy remains a dominant uncertainty in connecting stellar streams to models of dark matter.

We report the discovery of three candidate spider millisecond pulsars via multi-wavelength follow-up of unassociated Fermi Large Area Telescope gamma-ray sources. All have optical spectroscopy from the SOAR 4.1-m telescope and X-ray data from Swift. Two optical/X-ray sources are exceptionally strong redback candidates, sitting close to the centres of the localization ellipses of the gamma-ray sources 4FGL J1020.4-5314 and 4FGL J1408.7-3747. We show that both optical sources are spectroscopic binaries with orbital periods (0.15-0.3 d) and mass functions (0.6-0.9 Msun) typical for redbacks. 4FGL J1020.4-5314 shows bright, very broad (full width at half maximum 2100 km/s) H-alpha emission in all spectra obtained over two years. Remarkably, the H-alpha radial velocities are offset in phase from the absorption-line velocities of the secondary, and match the signal expected for an emission source near the primary. This demonstrates, for the first time for any spider, that the H-alpha emission can be associated with an intrabinary shock that wraps around the pulsar, opening up the possibility of using optical emission lines as kinematic tracers of the intrabinary shock in some redbacks. A third candidate spider is less secure in its association with the gamma-ray source 4FGL J1429.8-0739, but has unusual properties, including a 30.5-hour orbital period, a potential subgiant secondary, and a high X-ray luminosity, making it worthy of further investigation.

Gaia DR3 revealed a new class of neutron stars (NSs) in au-scale orbits with solar-type companions. How these 'Gaia NSs' form remains unclear, and constraining their intrinsic population properties is a necessary step toward understanding their origin. However, the current sample of 27 Gaia NS candidates is strongly biased by Gaia's astrometric sensitivity. In this work, we carefully model the Gaia selection function and incorporate it into a hierarchical Bayesian framework to infer the intrinsic demographics of the Gaia NS population. We find that the population favors a decreasing period distribution with power-law slope $\alpha_P=-0.75 \pm 0.35$, a visible-star mass distribution peaked near $M_1\approx 0.85~{\rm M_\odot}$ ($\sigma_{M_1} \approx 0.2~{\rm M_\odot}$), an NS mass distribution peaked near $M_{\rm NS}\approx 1.3~{\rm M_\odot}$ with a tail towards higher masses, and an eccentricity distribution weighted toward moderate-to-large eccentricities. The intrinsic space density is $n\approx120~{\rm kpc^{-3}}$ within 2 kpc, implying that only $\sim3\%$ of the local Gaia NS population has been discovered so far. Our forecasts predict that Gaia DR4 will increase the sample to $\sim300$-650 NS candidates, including access to longer orbital periods that will provide direct tests of formation models. Finally, we place Gaia NSs in the context of the broader Galactic NS population by comparing their intrinsic birth rate, lifetime, and size to other classes of isolated and binary NSs. Only 0.01% - 1% of all NSs are born into au-scale orbits with solar-type companions, making the birth rate of Gaia NSs 10 - 100 times smaller than that of high-mass X-ray binaries and broadly comparable to symbiotic X-ray binaries.

Neural network field theory specifies a Euclidean field theory by a network architecture and a density on its parameters, so that correlation functions are integrals over those parameters. We introduce constructive neural network field theory and use it to realize finite-volume scalar $\phi^4_2$ as a limit of network measures. For each dyadic momentum shell of the free propagator, the field is given a separate set of neurons with Gaussian coefficients, uniform phases, and frequencies drawn from the shell's spectral density. Once the frequencies and phases are fixed, integrating out one shell's coefficients is a finite-dimensional integral against a Gaussian density reweighted by the Wick-ordered quartic interaction. For widths that grow fast enough with the shell index and almost every draw of the frequencies and phases, the reweighted density is uniformly log-concave for every shell above a threshold, at any coupling in two and three dimensions, and the fluctuations of those shell fields are held to the free-field scale. In two dimensions, an induction over scales shows that shell $j$ contributes $O(2^{-2j}j^3)$ to the log partition function, and the total-variation distance between marginals at successive cutoffs is of the same order. Because these contributions are summable, the ultraviolet cutoff can be removed for any suitable fixed sequence of widths. Almost surely, the ultraviolet and infinite-width limits commute, and in either order the joint laws of finitely many smeared fields converge to those of the standard finite-volume $\phi^4_2$ measure. The method of parametrizing a field via a network organized into momentum shells and integrating out one shell at a time is not specific to $\phi^4_2$, so we expect it to extend to other theories.

We discuss (2+1)d Chern-Simons Higgsing transitions based on conformal embeddings and their relation to the proliferation of anyons. These transitions preserve or enlarge the intrinsic topological order despite reducing the gauge group. When the topological order is enlarged, the two phases differ by anyon condensation, and the transition takes an Abelian topological order to a non-Abelian one. In the $SO(N)_{2} \hookrightarrow SU(N)_{1}$ family with $N \geq 3$, the two semiclassical regimes have equivalent intrinsic topological orders but distinct realizations of a global $U(1)$ symmetry. For odd $N$, these are non-Abelian realizations of transitions from fermionic $1/N$ Laughlin states to charge-$2e$ anyon superconductivity coexisting with the same chiral $\mathbb{Z}_{N}$ topological order. The scalar representations are always non-integrable with respect to the UV Chern-Simons level and therefore do not directly label anyons of the un-Higgsed phase, despite defining Wilson lines in the UV. Using heuristic adjoint screening, we propose candidate anyons in the un-Higgsed phase, while branching under the Higgs subgroup reveals channels corresponding to condensable anyons of the Higgs phase. We further construct a $\mathrm{Spin}(16)_{1} \to \mathrm{Spin}(9)_{2}$ transition admitting a condensable algebra that contains a non-Abelian anyon but not all of the allowed gaugable channels in its self-fusion.

Human motion, environmental contacts, and interaction forces are governed by common physical laws, yet existing approaches typically separate visual pose reconstruction from contact and force estimation. This separation limits joint reasoning and can propagate errors between stages. We introduce PACT, an end-to-end model that jointly learns to estimate human pose, contacts and contact forces from monocular video. Our approach augments a human reconstruction foundation model with learnable contact-force tokens and a temporal transformer that integrates visual features with world-space motion. Joint prediction heads refine human poses and estimate contacts and forces, while physics-based supervision encourages consistency between the reconstructed motion and interaction forces. To address the scarcity of force annotations, we develop a data annotation pipeline that combines contact labeling with physics-based motion and force optimization, producing training supervision from synthetic and real-world videos. We also introduce a real-world climbing benchmark ForceWall with climbing videos and corresponding ground-truth contact forces obtained from the force sensors. Experiments demonstrate state-of-the-art contact and force estimation, outperforming staged reconstruction approaches and generalizing to interactions beyond the training distribution. These results support end-to-end joint learning as an effective approach to recovering human motion and physical interactions from video.

Computer-use agents increasingly operate as long-running assistants through persistent workspace memory, which OpenClaw-style CUAs realize as automatically reloaded files that hold user instructions, system summaries, and external claims at the same privilege level. Here, remembering a claim confers authority over later behavior. This enables a persistent memory attack, in which an attacker who controls only benign-looking external content induces the CUA to record attacker-favored claims during a legitimate task, and those claims later govern benign tasks the attacker never touches. The attack chain extends "malicious context -> malicious response" into "malicious context -> memory injection -> malicious execution", making this a cross-environment threat. Existing defenses studied intervene either before content enters memory or at the action it later induces, not whether stored content may guide action. We propose ZoneClaw, which separates persistence from authority by replacing flat workspace memory with hierarchical trust zones carrying explicit authority levels. External claims persist in a low-trust zone and acquire action-guiding authority only by crossing an explicit authority boundary, at which promotion is cross-checked against zones the attacker cannot directly write. Role-specific processes of asymmetric privilege enforce this boundary, ensuring that no process both ingests external content and acts outward. Across four attack scenarios, two injection settings, and four backbones, ZoneClaw drives ASR from 372/480 to 6/480 while retaining utility in 458/480 trials, and remains effective against some defense-aware attackers. Attacker claims still persist in low-trust memory yet rarely cross the authority boundary, showing that ZoneClaw withholds authority rather than refusing to learn from the environment. Our code is available at: https://github.com/euph00/ZoneClaw-code.

Sulfur is the tenth most abundant element in space, yet it is strongly depleted in the gas phase of dense interstellar regions, suggesting sequestration in dust grain components that are difficult to detect. We study whether UV irradiation and thermal processing of H2S-containing interstellar-ice analogues can produce refractory sulfur species, and whether water-dominated ice enhances their formation. We performed UV irradiation and warm-up experiments on H2S-containing ice analogues with and without water, and the resulting refractory residues were analysed ex situ. Refractory sulfur species, including the sulfur allotropes S6-S8, are formed during UV irradiation and thermal processing of H2S-containing interstellar-ice analogues. Water enhances the formation of these sulfur allotropes by two orders of magnitude. We propose a formation mechanism in which ionic intermediates stabilised by the water-ice matrix promote chain growth and cyclisation, yielding predominantly S8. The combined detection in our residues of sulfur allotropes and polythionic species, also reported in meteorites and samples returned from asteroids, supports their formation in pre-cometary ice mantles covering dust grains. Because these species can incorporate multiple sulfur atoms per molecule, they constitute an efficient solid-phase reservoir for the missing sulfur in dense cloud environments where young stars are born. Refractory sulfur can therefore serve as a tracer of water-ice environments in space.

Parity superselection forbids direct measurement of odd Majorana observables. We learn time-independent, parity-covariant, $k$-mode-local Lindbladians on $m$ modes using even preparations and measurements with uninterrupted short-time evolution. Internal markers turn odd probes into even observables, and pair measurements among three separated markers calibrate their dynamical contributions. Signed Fierz inversion recovers canonical coefficients, while semidefinite fitting yields a valid generator. For finite-range models on known bounded-degree graphs with suitable marker access and a supplied weighted-strength bound $\bar\alpha$, entrywise error $\varepsilon$ is achieved using $\widetilde{\mathcal{O}}(\bar\alpha^2\varepsilon^{-2}\log(m/\delta))$ samples, without external modes or known nonzero coefficient locations. Recovery to diamond-norm error $\varepsilon$ costs an additional factor $m^2$, matching lower bounds for short-time experiments on fresh systems up to logarithmic and fixed geometric factors. Without a supplied graph, one idle ancillary mode per system mode and potentially nonlocal pair operations give total absolute coefficient error at most $\varepsilon$ per mode using $\widetilde{\mathcal{O}}_k(\bar\alpha^2\mathsf d^2m^{\lfloor k/2\rfloor}\varepsilon^{-2}\log(m/\delta))$ samples, under a supplied approximate coefficient-degree bound $\mathsf d$ and controlled weak-coefficient tails. All guarantees hold with probability at least $1-\delta$. For geometric models, fixed-support even observables can be predicted with logarithmic system-size sample complexity at fixed time and accuracy. We also give finite-volume and exponential-tail extensions.

Can a text-to-3D leaderboard change when every generated scene stays fixed? We audit this question for rendered-image evaluation, where camera settings and caption wording become part of the measurement protocol. Across 300 frozen scenes from six generators, we vary eight render and caption factors for 19 alignment evaluators plus one perceptual-quality control, then test four targeted scene degradations. Peak configuration variance exceeds between-generator variance for 17/19 alignment evaluators, with prompt-bootstrap lower bounds above 1 for 11/19. Rankings are more stable than scores, yet 18/19 evaluators change their point-estimate winner under some configuration. Pairwise protocol margin envelopes show which comparisons keep their direction across the tested settings. Selected pairs have opposite pointwise intervals, but no reversal survives simultaneous inference over the full search. Thus the observed winner changes are descriptive, not confirmed changes in generator superiority. Sensitivity remains separate: no evaluator, even the prompt-free control, exceeds 67% tie-adjusted directional discrimination on layout scrambling, which is diagnostic rather than human-validated ground truth. The audit separates score stability, decision uncertainty, and targeted sensitivity, and recommends reporting (generator, score, card ID) with protocol-dependent comparisons and selection-aware uncertainty.

As an alternative to the standard geometric analyses, we give an exact, information-theoretic analysis of stochastic gradient descent (SGD) and its variants. We show that a preconditioned SGD step is the posterior-mean update of a Gaussian Bayes model, and that its one-step regret splits into an intrinsic-time cost and a change in comparator information. The split extends to an identity for the objective itself. Convex convergence, strict-saddle-point escape, the link between flatness and generalization, the standard learning-rate schedules, adaptive optimizers, and the noisy, momentum, heavy-tailed, and gradient-free variants of SGD each correspond to a term or a special case of this identity. We measure its terms on synthetic and real training runs. On real networks it attributes the slack of classical convergence bounds to the terms their derivations drop and separates optimizers that reach the same training loss. That separation follows the number and consistency of their steps. Its relation to which of them generalizes better differs between networks. For gradient-free SGD the identity determines how a curvature preconditioner should enter the update. The sharpness-based generalization certificate it yields, with a data-independent isotropic prior, is vacuous at network scale unless the curvature spectrum is nearly flat across all parameters.

Pairwise guide–transcript scores do not enforce conservation of a finite guide-loaded RISC pool when they are interpreted independently as occupancies. We formulate a differentiable scalar equilibrium layer: one conservation equation with a unique positive root and exact implicit gradients. It yields a redistribution theorem, a qualified high-resource limit, an analysis of the retrieval approximation, and a conditional rank-invariance result: within one construct at one dose, rankings by fractional occupancy cannot distinguish equilibrium from independent scoring. We therefore audit the two experiments that proposition leaves open, dose and cross-context, on archival off-target data. Corrected thermodynamic affinities associate weakly with measured repression in the direction a working predictor requires, but a paired permutation test and a construct-cluster bootstrap do not establish added predictive value from the coupling: what survives their differing permutation-null baselines is \GapNet{}, a descriptive \GapNetOverSE{} of the equilibrium association's cluster standard error. The dose fits are heterogeneous and frequently violate the model-implied exponent constraint, which is superlinear rather than sublinear, so these data do not identify the competition parameter. A saturable compression of the competitor set holds both accuracy targets on held-out guide families but is not faster at the size measured. The contribution is a reusable conservation operator and the experimental information needed to test it. The code for this study is available at https://github.com/shadi97kh/One-Pool-Many-Targets.

We give a generic compiler for turning a wide class of device-dependent protocols with trusted state preparation into sequential device-independent protocols. In order for our compiler to apply, the trusted-preparation protocol needs to satisfy certain minimal conditions: having an entanglement-based realization in the first place, and the entanglement-based realization corresponding to the optimal strategy of any non-local game that satisfies a fairly weak rigidity condition. We apply our generic compiler to give sequential device-independent protocols for uncloneable encryption, copy-protection of point functions, and blind randomness expansion. Our technical contribution is a new class of rigidity theorems based on Rényi divergences, with flexible cryptographic applications. They allow our compiler to achieve a constant rate (i.e., the ratio of trusted states prepared to device uses), while tolerating a constant level of noise per device usage. This overcomes a fundamental scaling obstacle faced by previous rigidity theorems for trace distance or fidelity. For the generic sequential case, our proof is based on the sharp-divergence chain rule by Fawzi and Fawzi (2021), which suffices for a constant but fairly low rate. In the special case when the devices retain no memory, we improve the rates by deriving a novel subadditivity property for a modified channel sandwiched divergence, which may be of independent interest. Finally, as a prospect for future improvements, we also prove a chain rule for the iterated-mean divergences from Brown, Fawzi and Fawzi (2021).

We generalise Berger's dilation theorem from numerical ranges to scaled $q$-numerical ranges. Specifically, we prove that if the scaled $q$-numerical range $\frac{W_q(A)}{q}$ is contained in the closed unit disk, then $A$ admits a unitary $\rho_q$-dilation, where $$ \rho_q=\max\left\{1,\frac{2|q|}{1+\sqrt{1-|q|^2}}\right\}. $$ As a corollary we show that every disk containing $\Omega_q(A)$ is a complete $\rho_q$-spectral set for $A$. At $q=1$, this recovers the classical fact that any disk containing $W(A)$ is a complete $2$-spectral set for $A$.

The independent and identically distributed (iid) paradigm for asymptotic communication through quantum channels describes $n$ uses of a channel $\Phi$ by $\Phi^{\otimes n}$. Since exact tensor-power behaviour is an idealization, we ask whether the asymptotic capacities of $\Phi$ remain achievable for channel sequences that are almost-iid along $\Phi$. We consider sequences of Choi-almost-iid channels whose normalized Choi states are Mazzola-Sutter-Renner (MSR) almost-iid along the normalized Choi state of $\Phi$, with defect parameters $r_n=o(n)$. In Renner's exponential de Finetti theorem for quantum states, almost-iid states appear in the approximating mixture and motivate the MSR almost-iid class. Choi-almost-iid channels play the corresponding role in an exponential de Finetti theorem for quantum channels established in a companion paper. In this paper, we prove that the universal unassisted classical and quantum capacities of the class of Choi-almost-iid channels along $\Phi$ equal those of the channel $\Phi$. Here universality is within this class: for each rate below the relevant capacity, a code sequence depending on $\Phi$ and the rate, but not on the particular channel sequence, achieves vanishing error for every sequence in the class.

Secret sharing is ubiquitous throughout cryptography. All possible access structures are classically feasible, and in the case of threshold access structures, the protocols are even very efficient. However, when moving to the quantum setting, the no-cloning theorem shows that many access structures are impossible. In fact, no-cloning exactly characterizes feasibility: for thresholds, quantum secret sharing is possible if and only if the threshold $t$ is strictly more than $n/2$. In this work, we propose a variant of quantum secret sharing (QSS) where two or more identical copies of the input state are provided, but the output is only required to recover one copy. This notion circumvents the simple one-copy no-cloning obstruction, though the natural $k$-copy generalization still gives much milder obstructions. For thresholds using $k$ copies, no-cloning implies that QSS is impossible whenever $t\leq n/(k+1)$. It is tempting to hypothesize that no-cloning continues to exactly characterize the many-copy case. However, we show that this is not the case. We give positive results showing that multiple copies allow for going slightly beyond the single-copy obstruction: for thresholds, we construct QSS whenever $t>(n-k+1)/2$. On the other hand, we give a novel obstruction we call the Clique Path obstruction, which applies to arbitrary access structures. For thresholds, it shows that QSS is impossible whenever $t\leq (n-1)/k$. Our upper and lower bounds exactly match for $k=2$. Both our results leverage connections to the $k$-colorability of certain graphs derived from the access structure. We leave closing the gap for $k\geq 3$ copies as a fascinating direction for future work. Secret sharing is closely related to error correction, which can also be considered in the many-copy setting. Our results imply similar obstructions for quantum error correction for erasure channels.

We determine the optimal success probability for transmitting a fixed number of classical messages through a finite number of uses of the quantum erasure channel, assisted by noiseless classical feedback and without initial shared entanglement. For an input dimension $d$, an erasure probability $p$, a blocklength $n$, and $M$ equiprobable messages, the optimal success probability is equal to $E[\min\{1,d^K/M\}]$, where $K$ is binomial with parameters $n$ and $1-p$. The converse allows arbitrary adaptive quantum encoders, quantum memories, and receiver instruments. Its main ingredient is an elementary dimension bound for noiseless quantum communication with classical feedback, proved by fixing the classical controls without conditioning the sender's state on the observed transcript. A classical protocol that transmits the base-$d$ digits of an integer representing the message, repeating each digit until the receiver acknowledges its reception or the prescribed blocklength is reached, attains the bound for every integer $M$. We also establish a relative-majorization property of erasure-channel outputs and exactly evaluate a hypothesis-testing converse, recovering the same numerical bound without feedback. That converse need not be achievable without feedback: four uses of the qubit erasure channel and four messages give a strict gap. A product-state code employing tetrahedral qubit states nevertheless outperforms every classical binary erasure code with these parameters. We give an explicit message-size formula and show that the bounded-remainder normal approximation and the average-success strong-converse exponent are unchanged without feedback. We also determine the feedback-assisted error exponent below capacity, prove that it agrees with the no-feedback exponent above a critical rate, and give no-feedback bounds at lower rates.

Macrorealism is a fundamental concept in quantum foundations, capturing basic features of our everyday experience. Among the main tools introduced to test violations of macrorealism are the Leggett-Garg inequalities. These inequalities provide necessary and sufficient conditions for a certain data set including the correlators measured in a number of different experimental runs (weak version of macrorealism). Leggett-Garg inequalities have proved useful for detecting violations of macrorealism in neutrino oscillation experiments. However, it is interesting to investigate a set of necessary and sufficient conditions for strong macrorealism - no-signaling-in-time and arrow-of-time conditions - in order to obtain a more complete characterization of macrorealism in the context of neutrino oscillations. In particular, here we extend previous study of the no-signaling-in-time condition to the case of three-flavor neutrino oscillations, including the CP-violating phase of the Pontecorvo-Maki-Nakagawa-Sakata matrix.

Humanoid whole-body manipulation has advanced rapidly, enabling policies to coordinate locomotion, posture, bimanual interaction, and dexterous hand movements. Meanwhile, egocentric human videos provide diverse examples of everyday interactions across objects and scenes, offering scalable supervision without robot operation. However, existing supervision from these videos provides limited coverage of whole-body movement and coordination with hand-object interaction, while obtaining such supervision through humanoid teleoperation is also costly and difficult to scale. We therefore explore how human experience can support scalable learning of humanoid loco-manipulation. To support this study, we introduce HumanVerse-500, a 500-hour dataset of diverse human loco-manipulation behaviors in open-world environments, collected with a lightweight wearable system that synchronizes egocentric video with body and hand motion. Building on this dataset, we develop $\lambda_0$, a whole-body humanoid vision-language-action policy, through three-stage training that first learns interaction from diverse egocentric datasets, then coordinates body and hand motion using HumanVerse-500, and finally adapts the policy to downstream tasks and robot embodiments. Across these stages, $\lambda_0$ learns a shared representation space for human experience transfer, while domain-specific interfaces handle differences between human and robot states and actions. We evaluate $\lambda_0$ on SIMPLE and 4 real-world loco-manipulation tasks, achieving state-of-the-art performance, and further analyze its scaling behavior, generalization, and training-stage contributions to understand how human data support downstream whole-body humanoid control. We will release our code, models, and data to support further research.

LLM agents generate intermediate reasoning and actions token by token, making extended interactions slow and computationally expensive. Jev-style models offer fast probabilistic predictions over finite fields, but require those fields to be specified in advance. This requirement limits autonomous task solving, where the available actions must be derived from natural language instructions and adapted through interaction. We introduce JevSpawn, a compositional policy that connects natural language task specifications to finite probabilistic exploration. Parallel action spawning is coupled with feedback driven branch selection, representation revision, and recovery from retained alternatives. Shared action structure and model prefixes reduce repeated generation and context computation without additional training. Evaluations on eight benchmark tasks against seven agent baselines and a TypeSafe Jev variant establish JevSpawn as a promising approach to structured agentic inference, with improved task performance and faster navigation.

Online batch selection fine-tunes a language model on the most useful part of each candidate batch. Selectors that match the gradient of the candidate batch are attractive because they need no held-out data, yet they rarely beat training on the whole batch. We show why. In-sample gradient matching uses every example as part of its own target, so its objective credits each example with its own gradient noise. This is the covariance penalty that makes training error optimistic, now sitting on the diagonal of the gradient Gram matrix: it steers selection toward the noisiest examples and makes the full batch the best solution the objective can reach. The fix costs nothing. For each example, the other candidates form an independent sample of the data distribution, so removing the diagonal turns the matching objective into an unbiased estimate of the update's error with respect to the population gradient. The minimizer of this leave-one-out objective weights examples by their gradient signal-to-noise ratio (SNR), and whenever per-example SNR is heterogeneous enough, half of a batch yields a lower-error update than the whole batch; we give the exact condition. We build \method{} on this principle. It computes the Gram matrix in the metric of the Adam preconditioner during the ordinary backward pass, selects a weighted subset greedily with a $(1-e^{-\gamma})$ guarantee, and uses no held-out data. Across four fine-tuning tasks and seven backbones from 1.5B to 8B parameters, LOOM improves on full-batch training by 2.3 and 2.4 points on Llama-3.1-8B and Qwen2.5-7B, exceeds every in-sample gradient matcher by 2.4 points and the validation-guided GREATS and OPUS by 1.6–2.0, and selects injected label noise at under a fifth of its base rate.

We study how AI agents discover and validate scientific formulas using a controlled case study of the hydrotope, a recently discovered geometric formula that combines the different polynomial pieces of nonlinear surface-wave scattering into one global expression. This problem is deceptively difficult: simple formulas can hold within individual frequency regions, but the global result must identify their boundaries and combine exponentially many potentially active terms. We reconstruct how the formula was originally discovered through human–agent collaboration and analyze 18 single-prompt rediscovery runs under no hint and two forms of human guidance: a false hint representing an incorrect prior and a true hint representing domain-informed insight. Only four recover the formula across all kinematic chambers (i.e., regions in which a single polynomial form applies), while most unsuccessful runs find correct chamber polynomials but fail to combine them or test their full domain. Conventional and LLM-assisted symbolic regression and standard machine-learning regressors likewise fail to recover the global formula in our experiments. Guided by these failure modes, we test a PI$+$two-student workflow in which a coordinating lead agent assigns complementary analytic and numerical tasks to two research agents and independently evaluates their results. The PI$+$two-student team successfully rediscovers the complete hydrotope formula, while the same workflow applied to the harder three negative wavenumber problem discovers a new independent verified analytic expression for the six-point amplitude $A_6$.

Smyth (1984) proved that every tetrahedron $T\subset\mathbb{R}^3$ contains three embedded minimal disks meeting $\partial T$ orthogonally, obtained as conjugate surfaces of Plateau solutions in a skew quadrilateral $Q$ whose edges are $c_i\nu_i$, where $\varphi_1,\varphi_2,\varphi_3,\varphi_4$ are faces of $T$, $c_i=\operatorname{Area}(\varphi_i)$ and $\nu_i$ are outward normal vectors. For the $\textit{regular}$ tetrahedron we give the Weierstrass data explicitly. The Gauss map is a Schwarz triangle function for a circular-arc triangle with angles $(\pi/4,\ \pi/2,\ \pi\beta/2)$, where $\beta=\arccos(-1/3)/\pi$; the hypergeometric parameters are linear in $\beta$ and there is $\textit{no accessory parameter and no free parameter}$. We record a closed form for $\kappa$ in $\Gamma$-values, a Wronskian closed form for $g'$, the exact total curvature $2\pi(2\beta-1)$, the symmetric-square structure of the data, and a rigidity statement: since $\beta/2$ is irrational, the projective monodromy is dense and the data $\textit{cannot}$ be algebraic. Numerically the representation extends to 28 digits – $\operatorname{Area}/\ell^{2}=0.2172341554075574483760009126\ldots$ – confirming a 2013 Surface Evolver computation of Ken Brakke.

We construct, over any field, a ten-dimensional algebra $A$ with $(\operatorname{rad}A)^3=0$ such that $\operatorname{findim}A=2$, $\operatorname{Findim}A=\infty$, and $\operatorname{Findim}(A^{\mathrm{op}})=0$. An explicit inverse-syzygy construction gives countably generated right modules of every positive finite projective dimension, disproving the big finitistic dimension conjecture. At each step we identify the full projective-cover kernel, and nonzero Ext detects the exact resolution length. For this algebra, we classify the modules of projective dimension at most one that embed in radicals of projective modules, with no generation restriction, in terms of invertible linear operators. We determine all dimension vectors of finite-dimensional modules of projective dimension two and classify those attaining the sharp dimension bounds, including all fourteen-dimensional modules of projective dimension two. For arbitrary Artin algebras, we give recursive sufficient criteria that control finite projective resolutions through radical-annihilated ideals and suitable corners. For finite-dimensional elementary radical-cube-zero algebras, we prove finiteness of the big finitistic dimension in the two-vertex case with one loop at each vertex and obtain multiplication-map criteria for bounds of one or two. Finally, an exact representation embedding yields wildness of the projective-dimension-two class and, over every field, a superdecomposable pure-injective module in that class.

Trellis-coded quantization enables high-dimensional compression of large language model (LLM) weights at ultra-low bit widths without the exponentially large codebooks required by conventional vector quantization. Practical deployment, however, presents two challenges: reconstructing compressed weights at sufficient parallel throughput to avoid making dequantization an inference bottleneck, and maintaining quantization accuracy without costly incoherence transformations. We address these challenges with two complementary techniques. First, we introduce an ultra-low-complexity trellis dequantizer that uses a structured, hardware-efficient state-to-value mapping while preserving diverse reconstruction choices for trellis search. Second, we reformulate discrete trellis path optimization with a curvature-aware objective that reflects model sensitivity directly in the original coordinate space. Together, these techniques enable high-quality ultra-low-bit trellis quantization with inexpensive, highly parallel runtime reconstruction and without relying on Hadamard-based incoherence processing.

Continual parameter-efficient fine-tuning for large language models (LLMs) must balance retention of previously acquired knowledge, adaptation to new tasks, and strict parameter budgets. We present ChainLoRA, a replay-free continual merging framework built on chain-updated task-vector geometry. From a parameter-merging perspective, we formulate a geometric view of forgetting through a measurable interaction between task updates, separating directional overlap from coefficient coupling. Building on this view, ChainLoRA combines chain-updated training with post-stream adaptive SVD merging. During training, initialization and a one-sided orthogonality proxy use only the last carrier, keeping their historical-state footprint and regularization overhead constant as the task stream grows. At merging time, Adaptive SVD extracts a shared carrier and aligns it to the latest task through Procrustes adaptation. Our theoretical analysis shows that Procrustes adaptation facilitates geometric approximate separation of shared and task-specific components. The one-sided proxy further bounds inter-task interference. An effective-rank penalty additionally promotes efficient utilization of the task subspace during continual learning. Experiments show that ChainLoRA achieves state-of-the-art performance among the evaluated replay-free methods on the Large and SuperNI benchmarks, while remaining competitive on Standard CL and attaining almost the closest average scores to the evaluated replay-based method across all three benchmarks.

Autonomous large language model (LLM) agents increasingly interact in network environments where adversarial content can propagate between agents. Known attacks include agent worms, which spread through self-replicating prompt injections or configuration compromises. We introduce memetic trojans, a distinct class of network-mediated attack that exploits agents' tendencies to retransmit and amplify content. Unlike agent worms, whose propagation is adversarially induced, memetic trojans exploit endogenous transmission by embedding adversarial payloads in social contagions: content agents have internal reasons to share. As part of our work, we extract social contagions from Moltbook, a social media platform for LLM agents. Controlled transmission experiments reveal large differences in virality: the most effective contagion is retransmitted in approximately 50% of subsequent agent posts and upvoted at 2.5x the average post's rate. Its memetic trojan counterpart largely inherits these properties. Monte Carlo attack simulations show that memetic trojans amplify expected exposure by up to 3.19x. Network structure and amplification mechanisms strongly shape propagation, producing heavy-tailed outcomes with near network-wide exposure. These results identify endogenous social transmission as a distinct security vulnerability in multi-agent systems. Because propagation does not require agents to follow malicious retransmission instructions, defenses focused on prompt-injection detection or preventing agent compromise cannot alone prevent memetic trojan propagation. Securing large-scale agent ecosystems may require network-level defenses that account for how agent preferences, recommendation mechanisms, and network topology amplify adversarial payloads.

Social interactions are shaped by networks that can be highly heterogeneous, with some individuals potentially interacting with many others. However, physical and temporal constraints limit the number of simultaneous interactions, making social contacts inherently intermittent. Here, we investigate how intermittency affects epidemic spreading on complex networks considering two distinct mechanisms: intermittency of connections (links) and individuals themselves (nodes), with periods of activity and inactivity governed by renewal processes with broadly distributed inter-event times. Combining mechanistic theoretical approaches with stochastic simulations, we show that these two forms of intermittency have fundamentally different effects on epidemic spreading. Link intermittency largely preserves the mechanisms responsible for sustaining transmission, and epidemic behavior can be largely explained by the average reduction in contact opportunities. Contrastingly, node intermittency is substantially more effective at containing spreading because the simultaneous interruption of all contacts suppresses transmission while recovery continues independently. The non-Markovian nature of node intermittency plays a key role: shorter and less heterogeneous inter-event times increase epidemic thresholds and enhance epidemic containment. Our results highlight how the temporal organization of individual activity, beyond the average reduction in contacts, can substantially alter epidemic spreading and may help inform interventions that exploit intermittency in social and biological contact networks.

Harnessing active matter to power functional devices has attracted growing interest. We propose a minimal battery model for storing energy extracted from active matter and derive its charging and discharging characteristics analytically. When the energetic cost of sustaining activity is included, the charging power-efficiency trade-off becomes loop-like and the efficiency attains a finite-time maximum, in sharp contrast to passive energy devices.

While constellation shaping improves spectral efficiency, its application to quadrature phase-shift keying (QPSK) remains limited. We address this limitation by incorporating a short shaping code into low-density parity-check (LDPC)-coded QPSK systems. Specifically, a subset of LDPC codeword bits is used as shaping bits and mapped by the shaping code to a sparse codeword that enables probabilistic shaping by controlling non-equiprobable selection between lower- and higherenergy QPSK constellations. Because zeros dominate the sparse codeword, lower-energy constellation points are transmitted more frequently, yielding a Gaussian-like symbol distribution. By exploiting the channel-code protection of the shaping bits, we develop receiver algorithms that refine shaping-bit log-likelihood ratios (LLRs) using LDPC decoder feedback. Joint optimization of the shaping codebook, bit-to-symbol mapping and constellations enables the proposed shaping scheme to achieve gains of up to 0.6 and 0.53 dB over 5G New Radio (NR) LDPC-coded QPSK and QAM-16, respectively.