Papers

Speech-to-speech systems must solve tasks whose requirements emerge across conversational turns. We introduce SpeechConversationBench (SCB), a focused evaluation of spoken mathematical reasoning using 103 sharded GSM8K problems. The framework compares the original problem delivered in one turn (full), its concatenated information shards delivered together (concat), and incremental spoken disclosure across turns (sharded). We report final-answer accuracy for four commercial speech systems and LEGO, a proprietary speech pipeline developed internally by the SCBX Innovation Lab team with explicit conversational context management. Relative to concat, sharded accuracy decreases by 5.0-25.3 percentage points across the four commercial systems. LEGO achieves 77.5 percent accuracy in all three conditions, compared with 76.6 percent sharded accuracy for GPT-4o Realtime. The two single-turn baselines distinguish sensitivity to problem reformulation from the additional challenges introduced by incremental spoken interaction.

Extreme events are often studied through regression models describing how covariates modify tail parameters. In many applications, however, interest lies directly in identifying the parts of the covariate space associated with tail events and with elevated exceedance probabilities. We formalize these ideas through tail halos, covariate-defined regions associated with extremes. Risk halos, when they exist, are minimum-mass covariate regions accounting for a prescribed fraction of exceedance probability, while favorable halos collect covariate values where conditional exceedance probability exceeds its marginal level. To make these set-valued objects interpretable beyond low dimensions, we introduce halo-induced covariate laws and, when densities exist, corresponding halo densities. We develop a Bayesian structured additive distributional regression framework based on extended generalized Pareto marginals, covariate-dependent copulas, and spike-and-slab effect selection to learn marginal and joint halo-induced covariate laws while propagating posterior uncertainty. The approach extends Bayesian shrinkage methods for conditional tail modeling to multivariate bulk-and-tail modeling, nonlinear effect selection, and covariate-region inference. Simulations show recovery of relevant nonlinear effects and increasingly accurate finite-sample halo representations as sample size grows. An application to PM2.5 and NO2 extremes in Edinburgh reveals distinct environmental and temporal configurations associated with high pollution.

We give a conformal mating description for the class $\Sigma_d$ of hyperbolic Schwarz reflections with connected and full filled Julia set; this parallels the recent development in several non-hyperbolic settings. We show that the escaping dynamics of $\Sigma_d$ can be characterized independently by the class of annular Schwarz reflections we introduce. Our main result is that each $\sigma\in\Sigma_d$ decomposes into a unique hyperbolic polynomial factor and a unique annular Schwarz reflection factor and, conversely, any two such factors may be mated to determine a unique such Schwarz reflection. We also show that annular Schwarz reflections converge to Nielsen maps in suitable settings, connecting the hyperbolic and non-hyperbolic mating descriptions.

Long-term egocentric video enables personalized AI assistants to reason about daily life. However, as video histories grow to hundreds of hours spanning months or years, reprocessing raw clips for every query becomes computationally prohibitive. Memory systems offer a scalable alternative by compacting videos into text representations, but often fail on practical benchmarks: either the memory does not preserve key evidence, or the retriever fails to locate relevant entries due to retrieval competition in growing search spaces. To address these challenges, we introduce MemLife, a multimodal memory system that constructs entity-grounded, first-person text episodes and retrieves them via a time-indexed agentic reader. Without training or query-time video access, MemLife improves over the strongest training-free baseline by 4.6–12.0% across four long-horizon benchmarks. To further improve memory quality, we propose MemOpt, a reinforcement learning framework that optimizes the memory writer to produce faithful, informative, and retrievable memories. MemOpt consistently improves MemLife by 2.7–5.0% across different video and question distributions, with gains that generalize across writer and reader backbones and memory systems.

Quantum one-time programs (Broadbent, Gutoski and Stebila, CRYPTO 2013) or OTPs for short, enable a functionality to be encoded into a quantum token that can be evaluated on a single chosen input and then becomes unusable. While powerful, this primitive is inherently stateless and tied to a setting in which a quantum token needs to be issued and distributed for every single evaluation of a circuit. This raises a natural question: can the one-time computation paradigm be extended to richer, stateful forms of controlled access, and would such an extension offer inherent advantages beyond standard OTPs? We introduce $\textit{query-limited RAM programs}$ (QLPs), a RAM-generalization of QOTPs that supports structured, stateful computation under bounded or policy-driven access. QLPs allow controlled sequences of evaluations while preventing adversarial forking or rollback of computational state. This enables new applications beyond stateless one-time programs, including quantum tokens for Turing Machines whose size depends only on $\textit{code length}$ (and not runtime), transferable $k$-time or budget-limited programs, and low-communication mechanisms for delegating computation in settings such as Software-as-a-Service. To construct QLPs, we introduce $\textit{one-shot programs}$, unifying one-shot signatures (Amos, Georgiou, Kiayias and Zhandry, STOC 2020) with the single effective query paradigm (Gupte, Liu, Raizes, Roberts and Vaikuntanathan, STOC 2025). We prove that one-shot programs generically imply query-limited programs, demonstrating that the strengthened unclonability guarantees of one-shot signatures translate into enhanced functionality. Along the way, we clarify the relationship between signature-token primitives and quantum one-time programs via generic constructions, essentially showing that one-time signing programs imply one-time general computation.

We establish near-linear accuracy bounds for the classical Moreau–Yosida unadjusted Langevin algorithm (MYULA). The target is $\pi\propto e^{-f-g}$, where $f\in C^2(\mathbb{R}^d)$ is $m$-strongly convex with Lipschitz gradient and $g$ is convex and globally Lipschitz. Under an explicit parameter-dependent step-size condition, we bound the invariant-measure bias relative to the Moreau-smoothed target by $\widetilde O(h)$, with only logarithmic dependence on the inverse smoothing parameter in the error coefficient. Combining this estimate with the Moreau approximation bias and Wasserstein contraction gives $\widetilde O(\varepsilon^{-1})$ iterations to make the $N$th-iterate law $\mu_N$ satisfy $\sqrt m\,W_2(\mu_N,\pi)\le\varepsilon$, for fixed model parameters and initialization. We bound the stationary error directly, without assuming third derivatives or a Lipschitz Hessian. Each iteration uses one gradient evaluation and one exact proximal evaluation. The key idea in our analysis is to convert a second-order stationary residual into a Wasserstein bound using a Poisson-based estimate.

A well-known problem of Erdős and Hajnal from the 1960s asks whether every graph with huge chromatic number contains a subgraph with large girth and large chromatic number. Very recently, Kohlmeyer and Kruer provided a strong negative solution to this problem: a construction of triangle-free graphs with arbitrarily large chromatic number whose subgraphs with no four-cycle have chromatic number at most $6$. The purpose of this exposition is to explain the construction method, relate it to relevant literature, and optimise the bound '$6$' to '$3$'.

A dcpo \(D\) is called \(C_{\sigma}\)-unique if for every dcpo \(Q\), \( \Gamma(D)\cong \Gamma(Q) \) implies \( D\cong Q, \) where \(\Gamma(D)\) denotes the lattice of Scott-closed subsets of \(D\). We give an intrinsic characterization of \(C_{\sigma}\)-uniqueness in terms of Skula-density and Scott closure, identifying precisely when a proper sub-dcpo can preserve the lattice of Scott-closed sets. Based on this characterization, we answer three open problems: (1) every power $\J^I$ of Johnstone's dcpo is $C_{\sigma}$-unique; (2) $C_{\sigma}$-uniqueness is not preserved by binary products, even when both factors and their product are sober; and (3) a sober countable complete lattice need not be $C_{\sigma}$-unique, even when it is a frame.

Sampling several answers and keeping the one a verifier scores highest is one of the simplest ways to buy accuracy at test time. Its effect is reported as a scaling curve: accuracy against the number $k$ of sampled answers. The curve is cheap to draw and expensive to trust. A budget read off it is chosen after looking at every point, so only a band that covers all budgets at once protects the choice, and on a 100-question benchmark a fixed exact-binomial design needs 192,000 generated answers to certify 64 budgets to within $\pm1/32$ at 95%. Most of that cost pays for the wrong uncertainty. A benchmark is a fixed list of questions; at budget 64, about three quarters of the variance of a selected answer's correctness lies between questions, and an audit that revisits every question need not pay for it. We derive the minimax cost of certifying the whole curve, up to logarithmic factors. It has three parts: calibrating the tail of the score distribution, telling the questions apart, and within-question noise summed along the curve. At a single benchmark the last part sharpens to the variance of one answer's influence under the best allocation of answers to questions, which every valid audit pays and an audit that learns the allocation attains, up to a logarithm, as the precision grows. A paired audit built on an exponential inequality for two independent draws at the same question needs no pilot. On 185 held-out score pools it uses 0.74 times the answers of the cheapest competing certified audit at 64 budgets and 0.53 times at 1,024, and on a newly generated MMLU-Pro study it certified the curve with 79,133 answers, within 0.6% of what a cost law fitted beforehand predicted from the study's within-question variance. The same paths certify pass@$k$ and majority voting, and the bands extend to populations of questions and to answers that depend on earlier ones.

In this note, we study complete and quantum Gromov-Hausdorff convergence of operator systems obtained using smoothings of C*-algebras, where our smoothings arise from the action of a compact quantum group on the C*-algebra. Specifically, we show how if $\mathbb{G}$ is a co-amenable compact quantum group acting on unital C*-algebra $\mathcal{A}$, and both are equipped with suitable quantum metrics, bounded approximate identities in $L^{1}(\mathbb{G})$ may be used for approximations of the original space $\mathcal{A}$ under the complete and quantum Gromov-Hausdorff distance. We finish by presenting some applications to the convergence of spectral truncations of compact groups and connections to previous results.

Neutrino telescopes observe neutrinos through the muons produced by charged-current interactions. Most of those muons are born kilometers outside the detector, and how much energy they lose on the way is stochastic. We show that we can compute analytically the distance a muon travels before it falls below the detection threshold, while describing the statistical properties of its losses. Our result reproduces Monte Carlo propagation to within $3\%$, and with two parameters per detector it matches the effective areas published by IceCube, KM3NeT/ARCA, and P-ONE to about $1\%$. We then show how this model can be used in point-source sensitivities, energy reconstruction, and consistency checks between detectors. The calculation disentangles muon-transport physics from a detector's response, so a new detector or loss model can be quickly benchmarked.

The classical cost of simulating free-fermion (matchgate) circuits depends on both the input state and the computational task. We develop classical algorithms for circuits with non-Gaussian inputs, addressing exact sampling and both additive-error and exact estimation of expectation values. For inputs consisting of $n$ copies of the four-mode magic state, we give exact sampling algorithms, generalizing the Clifford and Clifford algorithm for Boson sampling, for passive and active free-fermion dynamics with worst-case arithmetic cost $O(2^n)$ per sample, without any multiplicative polynomial prefactor. The passive algorithm enables an exact simulation of the non-interacting regime of a recent trapped-ion experiment. We also extend recently developed additive-error estimation of number correlators and related observables from passive to active dynamics with runtime polynomial in $n$ and the inverse additive-error, for input states formed by products of $n$ four-mode even parity states. Our estimator uses a Gaussian-state decomposition adapted to each sampled state to control its second moment. This includes estimation of individual output probabilities. Finally, we show that for even-parity product inputs composed of constant-size blocks, expectation values of Majorana monomials of logarithmic weight can be computed exactly in polynomial time, improving on prior Majorana propagation-style algorithms with quasi-polynomial runtime. The exact algorithm processes the input blocks by dynamic programming, sharing calculations across subsets of Majorana factors. Our suite of algorithms provide classical benchmarks for fermionic quantum simulations across a broad spectrum of computational tasks.

We develop a general framework for higher-order quantum resources that treats the resourcefulness of quantum states, channels, and supermaps (also called processes) in a unified manner. By generalizing well-established concepts from resource theories of states and channels, we introduce and study supermap resource monotones and supermap distillation and dilution. As free supermaps, we consider free networks (supermaps that can be implemented with free channels), compatible supermaps (sets of supermaps closed under arbitrary composition), and maximally free superchannels. Specializing to approximate channel-to-channel conversions, we show that under mild assumptions, the conversion error with respect to the diamond distance and the worst-case infidelity coincide. We then apply the general framework to resource theories of dynamical coherence, where we establish the existence of largest sets of compatible supermaps. By characterizing these sets with semidefinite constraints, we show that they are strictly larger than the corresponding free networks but do not contain all maximally free superchannels. We finish by investigating the operational differences of these sets in one-shot channel distillation and dilution, providing solutions for both tasks in the parallel setting and for dilution in the adaptive setting.

Constrained generation aims to sample from language models (LMs) conditioned on hard constraints. Existing constrained-generation techniques for nondeterministic finite automaton (NFA) constraints either distort the distribution or sacrifice efficiency. Theoretically, this task reduces to counting the length-$n$ sequences accepted by an NFA (#NFA), and the exact #NFA problem is #P-complete. Recent work has shown that #NFA admits a fully polynomial randomized approximation scheme (FPRAS). Inspired by this result, we propose NFA-LM, a polynomial-time engine for NFA-constrained generation with theoretical guarantees under mild assumptions. Experiments show that NFA-LM efficiently generates high-quality outputs with theoretically bounded approximation error.

Quantum cryptography leverages unclonability to enable a wide range of cryptographic applications that are impossible classically, such as digital currency protected against counterfeiting by quantum mechanics. Security requires that no efficient user can produce even one additional valid banknote beyond those already in their possession. However, existing security bounds weaken as the number of banknotes available to a user increases. In this paper, we study a construction of quantum money whose asymptotic query security does not deteriorate as long as the number of banknotes available to a user remains below the scale required for state tomography. In particular, we show that the construction based on an $n$-qubit Haar-random state and a reflection oracle achieves optimal query security: unless a user holds $\Omega(2^n)$ banknotes, their existing banknotes cannot asymptotically speed up counterfeiting — their best possible attack is the same as if they do not have any banknotes. To establish this result, we develop a framework based on the compressed-oracle technique for defining and analyzing progress measures for quantum tasks such as Haar state cloning. Furthermore, we prove a tight lower bound for generating $r$ additional copies, give a matching attack, and apply our results to quantum copy-protection.

In the IKKT matrix model, the dimension, geometry, and metric signature of spacetime must emerge from the matrix dynamics. We classify the Lie-algebraic saddles of the model: classical solutions in which the ten Hermitian matrices realize a finite-dimensional real Lie algebra in a unitary representation. For this class the equations of motion collapse to a single algebraic equation for a symmetric bilinear form $h$ on the algebra, and the signature of the emergent spacetime can be read off from $h$. Two facts control the outcome. First, when the complexified algebra is simple, a Casimir obstruction allows only $h=0$; this explains why fuzzy spheres and the expanding-universe solutions need mass terms or infrared regulators. Second, semisimple algebras admit saddles only through couplings between distinct simple ideals; such saddles first appear in six dimensions and reach every signature only from twelve. These facts yield criteria for the emergence of time. Every nondegenerate Lorentzian saddle in at most eleven dimensions—hence every Lorentzian background of the ten-dimensional model—has a nonzero solvable radical. The only nontrivial possibility of the semisimple part is the Lorentz algebra $\mathfrak{so}(1,3)$, which is purely spacelike, and every timelike direction has a component in the radical. When the semisimple part is nontrivial, it acts on the radical only from ten dimensions on; at ten dimensions, the radical must be abelian and must carry the Weyl-spinor representation, which solves the Lorentzian equations of motion; a nonabelian radical first appears in eleven dimensions. As a result, space can be semisimple; time must be solvable.

We develop a mixing time method for estimating the sample complexity of quantum state discrimination. We start with considering the minimum-error discrimination of geometrically uniform pure state ensembles, and prove that its sample complexity has a tight estimate given by a quantum homogeneous mixing time [George et al., 2026] and a quantum version of the generalized Dobrushin coefficient [Wolfer, 2020]. This quantum mixing time further reduces to a classical one when the generating group $G$ forms a Gelfand pair with the stabilizer subgroup $H$ of the generator state. In this case the generalized Dobrushin coefficient can be fully expressed by representation-theoretic quantities of the commutative Hecke algebra $\operatorname{End}_G(\mathbb C[G/H])$. In particular, this method reduces the sample complexity estimation of learning quantum coupon collector states [Arunachalam et al., 2020] and learning phase states to classical mixing time problems. We apply this framework to answer the open problems of learning degree-$d$ phase states over $\mathbb F_q$ in [Alrabiah et al., 2026] and generalized Boolean phase states over $\mathbb Z_q$ [Arunachalam et al., 2023]. The framework also applies to hypergraph state ensembles, giving estimates expressed fully in terms of hypergraph data and recovering estimates for graph state ensembles in [Montanaro and Shao, 2022]. Finally, we extend the discussion to arbitrary mixed state ensembles with uniform priors, prove a sandwiched bound for minimum-error discrimination sample complexity by a quantum weakly mixing time, and provide a tight estimate for the minimax discrimination sample complexity from [D'Ariano et al., 2005] by a Dobrushin-type coefficient. We also discuss the method of strengthened data processing inequality [Gao and Rouzé, 2022] and give an upper bound in terms of a strengthened data processing inequality constant.

We introduce Index-Translate, a multilingual translation model family that combines a shared multilingual foundation with specialized training for general translation, instruction following, speech translation, controlled dubbing, and long-document translation. It includes three model sizes, 2B, 9B, and 35B-A3B, and supports translation in 150 languages, with multilingual instruction following. Evaluations on general translation and complex translation instructions show that Index-Translate outperforms translation models of comparable size and achieves performance comparable to 100B-scale translation models and frontier models. Image-text evaluation shows that translation remains possible without image examples in Index-Translate-specific training, although results vary by model size. Index-Echo provides end-to-end speech-to-text and speech-to-speech translation, outperforming existing end-to-end models and achieving performance comparable to frontier omni models. Index-Homura extends the family to syllable-controlled dubbing. Index-NativeLong introduces native long-document translation with a dedicated task formulation and benchmark. These capabilities support diverse translation tasks, including multilingual content production.

We prove the first non-trivial upper bound for the quantum query complexity of Boolean Matrix Product Verification ($\mathsf{BMPV}$), answering a longstanding open question in quantum query complexity. For $n\times n$ matrices, our upper bound is $\widetilde O(n^{17/12})$, improving on the standard $O(n^{3/2})$ bound obtained using Grover search by Buhrman and Špalek [SODA 2006]. We complement this result by showing an $\Omega(n^{5/4})$ lower bound, which improves over the previous best known lower bound of $\widetilde\Omega(n^{19/18})$ by Childs, Kimmel, and Kothari [ESA 2012]. Our approach centers on a connection with Orthogonal Vectors ($\mathsf{OV}$), which asks whether an indexed list of $n$ Boolean vectors of dimension $n$ contains two vectors with disjoint supports. In particular, we prove equivalences between $\mathsf{OV}$ and $\mathsf{BMPV}$ and establish the above bounds for $\mathsf{OV}$. We also prove a tight $\widetilde \Theta(n^{3/2})$ bound for a variant of $\mathsf{BMPV}$ that asks whether the product contains a given row vector. Together, these results imply a polynomial separation between the quantum query complexities of deciding whether a graph has radius at most two and whether it has diameter at most two.

The von Neumann, Tsallis, and Rényi entropies are fundamental measures of quantum information. A common estimation strategy multiplies the worst-case costs of spectral transformation and statistical readout, leaving gaps to query lower bounds. We reduce this overhead with multi-level algorithms that use local normalization and precision allocation, while variable-time estimation accounts for the probability of reaching expensive spectral tests. With controlled purified access and its inverse, we obtain bounds for additive error $\varepsilon$, rank upper bound $R$, and fixed order $\alpha$. Tsallis entropy estimation has near-optimal rank-independent query complexity $\widetilde O(\varepsilon^{-1/(\alpha-1)})$ for $1<\alpha<2$, when the allowed dimension and rank accommodate the lower-bound instances, and $\widetilde O(1/\varepsilon)$ for $\alpha\ge2$, where $\widetilde O$ suppresses logarithmic factors. The first saves a factor $1/\varepsilon$; the second extends known integer-order scaling to noninteger orders. We also improve the von Neumann entropy bound from $\widetilde O(R/\varepsilon^2)$ to $\widetilde O(R/\varepsilon)$ and obtain $\widetilde O(R/\varepsilon)$ for noninteger Rényi orders $1<\alpha<3$, with further bounds at other orders. Our functional-estimation theorem replaces the global product by a sum of local costs weighted by function magnitudes and spectral masses. We further estimate fixed logarithmic moments and entropy variance using $\widetilde O(R/\varepsilon)$ queries, providing efficient access to fluctuation parameters that enter finite-blocklength quantum compression and pure-state entanglement conversion. More broadly, our framework extends beyond entropy to a broad class of density-matrix functionals, offering a systematic approach toward optimal query complexity in quantum spectral estimation.

Open concrete canals play a vital role in water transportation, serving as primary water infrastructure for millions of people across the Phoenix, Arizona, metro area. Over time, the concrete canals can experience a range of issues, including canal lining deformation, cracked concrete, and sediment buildup on the canal floor. Identifying such critical issues is a resource-intensive process, which currently happens only during four-year dry-up cycles. This prevents the maintenance crew from prioritizing operations on the most affected canal segments. To address this issue, the research team has developed and verified an easily deployable and non-invasive method to inspect canal beds without draining the water. This inspection system integrates affordable, off-the-shelf drone and sonar technology (termed dronar). This dronar system includes a consumer-grade sonar system integrated into an unmanned surface vehicle (USV) that carries the sonar transducer just under the surface of the canal water. This paper presents a proof-of-concept demonstration of the dronar system across three field tests on the Arizona Canal in Phoenix. DownScan depth profiles from the sedimented canal segment were consistently shallower than profiles from the same segment after cleaning, with offsets of up to 15 cm observed along the track. Repeated runs over the clean segment produced closely overlapping DownScan depth profiles, confirming that the dronar yields repeatable measurements across the natural variation of the canal bed. These results establish the dronar as a viable proof-of-concept tool for non-invasive canal bed inspection.

Safe social navigation requires a robot to anticipate not only the future consequences of its actions, but also whether a nominal action can actually be executed under surrounding physical and social constraints. We present Social-WM, an efficient latent world-model planning framework trained from egocentric RGB video sequences. Our key observation is that social-navigation experience contains a systematic discrepancy between the nominal action and the realizable action: a nominal forward action may be fully executed in free space, but needs to be constrained when heading towards a pedestrian or obstacle. Social-WM learns these safety-relevant consequences directly through action-conditioned future prediction, where the target is the actual observed future following each command. We further introduce a realizable inverse-dynamics objective that associates observed latent transitions with the action actually realized rather than the nominal one. At deployment, candidate actions are imagined through the latent world model, and the inverse dynamics model estimates their realizability; nominal–realizable discrepancy then provides a safety signal before execution. The learned dynamics and realizability model remain goal-independent and support both position- and image-goal navigation. On Social-HM3D, Social-WM achieves 63.77% success while reducing human collisions to 21.67%, and maintains strong performance under zero-shot transfer to Social-MP3D, without explicit pedestrian tracking, privileged human state, or online reinforcement learning.

Combined baryon acoustic oscillation and cosmic microwave background data have begun to mildly favor departures from $\Lambda\mathrm{CDM}$. This is usually framed as 2-parameter dynamical dark energy. However, a 1-parameter "cosmic glitch in gravity" model, whose cosmological gravitational coupling differs from Newton's constant as in Hořava gravity, fits at least as well. $\textit{Planck}$+ACT+SPT and DESI~DR2 give $G_\mathrm{cosmo}/G_\mathrm{N}=0.9920\pm0.0025$, a $3.3\,\sigma$ preference for weaker cosmological gravity, robust to adding CMB lensing and supernovae. Fitted to the CMB alone, the glitch predicts DESI distances; $w_0w_a$CDM does not.

A symplectic spectral function of a $2n \times 2n$ real positive definite matrix $A$ is a function of its symplectic eigenvalues $0< d_1(A) \leq \cdots \leq d_n(A)$, which is given by a composition $f \circ d$ of some symmetric function $f$ on the set of $n$-vectors with positive entries and the symplectic eigenvalue vector map $d(A)=(d_1(A),\ldots, d_n(A))$. In this work, we rigorously study various types of differentiability and Clarke generalized gradient of symplectic spectral functions, and also provide several applications of our findings. We show that the symplectic spectral function $f \circ d$ is Fréchet differentiable at $A$ if and only if $f$ is Fréchet differentiable at $d(A)$, and we compute the derivative expression explicitly. We also show that $f \circ d$ is strictly Fréchet differentiable (respectively, continuously Gâteaux differentiable) at $A$ if and only if $f$ is strictly Fréchet differentiable (respectively, continuously Gâteaux differentiable) at $d(A)$. We determine the Clarke generalized gradient of a symplectic spectral function $f \circ d$ at $A$, which is given in terms of the Clarke generalized gradient of $f$ at $d(A)$. As an application of our work, we show that the purity, von Neumann entropy, and Rényi entropy of a bosonic faithful Gaussian state are Fréchet differentiable functions of the covariance matrix of the Gaussian state. We also provide explicit expressions of their Fréchet derivatives.

Simulating open quantum systems reveals how environmental coupling shapes relaxation, excitation transport, and the dynamics of quantum correlations. On quantum hardware, dissipative channels add operations and might seem to increase cost. However, we show that a broad class of Pauli noise, including depolarization, can ease quantum and classical simulation by exponentially suppressing high-weight components of Heisenberg-evolved observables. For bounded-degree Lindblad dynamics, this permits system-size-independent Trotter steps when estimating local observables. Combining this compression with Richardson extrapolation, we provide classical and quantum error bounds with respect to the 2-norm of the propagated observable. These give high-probability expectation-value guarantees for random input states or random Hamiltonians acting on a fixed state and control (out-of-time-order) correlators. Concretely, we show that expectation values of local observables at time $t$ can be estimated to accuracy $\varepsilon$ using circuits of maximum depth $O\!\left(\left[1+\left(t/\gamma\right)^{3/2}\right]\log^2(1/\varepsilon)\right)$, independent of the system size $n$. Classically, we show that sparse Pauli propagation runs in time polynomial in $n$, $t$ and $1/\varepsilon$ for every fixed $\gamma>0$, with polynomial degree $O(1/\gamma)$ in the weak dissipation limit. The gap between our quantum and classical upper bounds leaves room for a substantial polynomial quantum advantage as dissipation weakens, an observation further supported by our numerical results.

Classical shadow tomography is widely touted as supplying a family of methods for extracting information from quantum systems with polynomially scaling sample-complexities. In the current era of quantum computers possessing on the order of hundreds of qubits, however, polynomial scaling can nonetheless be prohibitive. Thus, there is a strong practical need for obtaining sample-complexity bounds which are as tight as possible. Here we address this in the case of fermionic (matchgate) shadows. For an arbitrary observable $O$ of Majorana degree $2k$, we improve the previously known sample-complexity bound of $\mathcal{O}(n^{2k}\|O\|_\infty^2)$ to $\mathcal{O}(n^{k}\|O\|_\infty^2)$, which is asymptotically tight. For example, for the estimation of the energy per mode of an open fermionic 50-site Hubbard chain with hopping and on site strenghts respectively given by $t=1$, $V=4$, and for a target additive precision of 0.1, this reduces the number of required shots from $\sim 10^9$ to $\sim 10^5$. That is, the new bound reduces the required number of shots by approximately $99.98\%$.

The control of open-system dynamics provides a powerful mechanism for using quantum information to process sequential tasks. While quantum reservoir computing typically relies on Markovian dissipation to process sequential data, the computational role of non-Markovian memory effects remains largely unexplored. We introduce a framework for quantum reservoir computing where non-Markovianity is explicitly modeled and regulated using fractional derivatives. By employing fractional time subordination, we generate tunable, heavy-tailed relaxation dynamics that govern the information backflow between the system and its environment. Non-Markovian information backflow regulates the overall temporal retention of the system, maximizing short-term linear memory capacity. Within an optimal operating regime, fractional non-Markovianity redistributes the reservoir memory towards recent inputs, improving both linear memory capacity and nonlinear prediction accuracy at short delays, at the expense of long-range temporal retention. System-environment interaction proves being not merely a requirement for quantum reservoir computing, but an active resource that embeds memory retention directly into the quantum evolution.

Gauss constraints make it nontrivial to open, close or join a gauge system while retaining its interior physics. Boundary reconstructions are constructed on a pure SU(3) ladder at six site-singlet cutoffs, with all allowed intertwiner multiplicities. Replacements of prescribed length are obtained using legal column paths and physical self-loops. On their stated physical domains, the channels preserve unnormalized conditional interior matrices, including their weights and within-branch coherence. Lowest-cutoff dephasing controls show that path probabilities alone do not preserve the matched magnetic observables. In that example, coherent resources lower the output energy without purification or global ground-state preparation. Matched interior Hamiltonian terms cancel exactly, so the energy cost is bounded independently of longitudinal length. The vacuum and flux energy densities are then established separately by same-sector gluing and stability. The open and periodic vacuum-subtracted line-energy densities are shown to be equal by two same-length boundary comparisons using the qualified periodic minimizing domain. These limits hold at fixed lattice spacing, transverse width, coupling and chosen cutoff.

MANETs enable flexible infrastructure-less wireless connectivity in dynamic and resource-constrained environments. As modern MANETs exploit multiple frequency channels and support heterogeneous traffic patterns, decentralized transmit-power allocation becomes increasingly challenging. We develop a unified learned optimization framework for decentralized power allocation in dynamic multi-hop, multi-channel MANETs. We formulate a constrained end-to-end throughput maximization problem covering unicast, multicast, multicommodity, convergecast, and many-to-many communication. Although centralized and non-convex, this problem serves as an unsupervised training objective for MANET-GNN, a message-passing GNN that operates as a distributed learned optimizer. MANET-GNN uses only local, possibly noisy, CSI and a prescribed number of neighbor message exchanges, enabling low-latency decentralized inference while generalizing across topologies and network sizes. Numerical results show that MANET-GNN achieves centralized-competitive performance across communication frameworks, remains robust to channel uncertainty, and scales effectively across MANET configurations.

Language agents are expected to solve increasingly complex tasks, creating a growing need for continual improvement. One promising approach is to evolve the agent harness, the software that governs tool use, memory management, and task execution, while keeping the underlying language model fixed. Recent methods automate this process by using a meta coding agent to modify the harness based on execution feedback. However, relying on that agent's existing knowledge and observed failures can restrict exploration and make adaptation reactive. Inspired by how human experts learn from the research literature for new solutions, we introduce ScholarEvolve, a framework that automatically draws on state-of-the-art research to guide harness evolution. ScholarEvolve organizes the harness evolution directions into functional modules and uses topic modeling to identify distinct improvement strategies for each module. It implements these strategies and evaluates their combinations to improve task performance. Moreover, the framework is designed to incorporate new publications over time, allowing research advances to drive proactive lifelong evolution. Experiments demonstrate improvements on AppWorld and Tau2-Bench. ScholarEvolve raises Qwen3.5-27B task goal completion from 49.6% to 63.6% on AppWorld Challenge, and raises GPT-5.4-mini pass@1 from 72.7% to 81.9% on Tau2-Bench Telecom.