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We introduce CyBeR-0, a Byzantine-resilient federated zero-order optimization method that is robust under Byzantine attacks and provides significant savings in uplink and downlink communication costs. We introduce transformed robust aggregation to give convergence guarantees for general non-convex objectives under client data heterogeneity. Empirical evaluations for standard learning tasks and fine-tuning large language models show that CyBeR-0 exhibits stable performance with only a few scalars per-round communication cost and reduced memory requirements.

Regression trees are a popular machine learning algorithm that fit piecewise constant models by recursively partitioning the predictor space. In this paper, we focus on performing statistical inference in a data-dependent model obtained from the fitted tree. We introduce Randomized Regression Trees (RRT), a novel selective inference method that adds independent Gaussian noise to the gain function underlying the splitting rules of classic regression trees. The RRT method offers several advantages. First, it utilizes the added randomization to obtain an exact pivot using the full dataset, while accounting for the data-dependent structure of the fitted tree. Second, with a small amount of randomization, the RRT method achieves predictive accuracy similar to a model trained on the entire dataset. At the same time, it provides significantly more powerful inference than data splitting methods, which rely only on a held-out portion of the data for inference. Third, unlike data splitting approaches, it yields intervals that adapt to the signal strength in the data. Our empirical analyses highlight these advantages of the RRT method and its ability to convert a purely predictive algorithm into a method capable of performing reliable and powerful inference in the tree model., Comment: 49 pages, 6 figures

Dynamic changes in processes necessitate the notion of state equivalence between the old and new workflows. In several cases, the history of the workflow to be migrated provides sufficient context for a meaningful migration. In this paper, we present an algorithm to find the equivalence mapping for states from the old workflow to the new one using a trail-based consistency model called history equivalence. The algorithm finds history equivalent mappings for all migratable states in the reachability graph of the process under migration. It also reports all non-migratable states that fall in the change region for a given pair of old and new Petri Nets. The paper presents the algorithm, its working, and an intuitive proof. The working is demonstrated through a couple of illustrations.

Independence complexes of circle graphs are purely combinatorial objects. However, when constructed from some diagram of a link $L$, they reveal topological properties of $L$, more specifically, of its Khovanov homology. We analyze the homotopy type of independence complexes of circle graphs, with a focus on those arising when the graph is bipartite. Moreover, we compute (real) extreme Khovanov homology of a $4$-strand pretzel knot using chord diagrams and independence complexes., Comment: 11 pages, 7 figures

Causal effect moderation investigates how the effect of interventions (or treatments) on outcome variables changes based on observed characteristics of individuals, known as potential effect moderators. With advances in data collection, datasets containing many observed features as potential moderators have become increasingly common. High-dimensional analyses often lack interpretability, with important moderators masked by noise, while low-dimensional, marginal analyses yield many false positives due to strong correlations with true moderators. In this paper, we propose a two-step method for selective inference on time-varying causal effect moderation that addresses the limitations of both high-dimensional and marginal analyses. Our method first selects a relatively smaller, more interpretable model to estimate a linear causal effect moderation using a Gaussian randomization approach. We then condition on the selection event to construct a pivot, enabling uniformly asymptotic semi-parametric inference in the selected model. Through simulations and real data analyses, we show that our method consistently achieves valid coverage rates, even when existing conditional methods and common sample splitting techniques fail. Moreover, our method yields shorter, bounded intervals, unlike existing methods that may produce infinitely long intervals.

Real-time conversational AI agents face challenges in performing Natural Language Understanding (NLU) in dynamic, outdoor environments like automated drive-thru systems. These settings require NLU models to handle background noise, diverse accents, and multi-intent queries while operating under strict latency and memory constraints on edge devices. Additionally, robustness to errors from upstream Automatic Speech Recognition (ASR) is crucial, as ASR outputs in these environments are often noisy. We introduce Babylon, a transformer-based architecture that tackles NLU as an intent translation task, converting natural language inputs into sequences of regular language units ('transcodes') that encode both intents and slot information. This formulation allows Babylon to manage multi-intent scenarios in a single dialogue turn. Furthermore, Babylon incorporates an LSTM-based token pooling mechanism to preprocess phoneme sequences, reducing input length and optimizing for low-latency, low-memory edge deployment. This also helps mitigate inaccuracies in ASR outputs, enhancing system robustness. While this work focuses on drive-thru ordering, Babylon's design extends to similar noise-prone scenarios, for e.g. ticketing kiosks. Our experiments show that Babylon achieves significantly better accuracy-latency-memory footprint trade-offs over typically employed NMT models like Flan-T5 and BART, demonstrating its effectiveness for real-time NLU in edge deployment settings., Comment: 12 pages, 3 figures, 2 tables

We study the problem of finding a product state with optimal fidelity to an unknown $n$-qubit quantum state $\rho$, given copies of $\rho$. This is a basic instance of a fundamental question in quantum learning: is it possible to efficiently learn a simple approximation to an arbitrary state? We give an algorithm which finds a product state with fidelity $\varepsilon$-close to optimal, using $N = n^{\text{poly}(1/\varepsilon)}$ copies of $\rho$ and $\text{poly}(N)$ classical overhead. We further show that estimating the optimal fidelity is NP-hard for error $\varepsilon = 1/\text{poly}(n)$, showing that the error dependence cannot be significantly improved. For our algorithm, we build a carefully-defined cover over candidate product states, qubit by qubit, and then demonstrate that extending the cover can be reduced to approximate constrained polynomial optimization. For our proof of hardness, we give a formal reduction from polynomial optimization to finding the closest product state. Together, these results demonstrate a fundamental connection between these two seemingly unrelated questions. Building on our general approach, we also develop more efficient algorithms in three simpler settings: when the optimal fidelity exceeds $5/6$; when we restrict ourselves to a discrete class of product states; and when we are allowed to output a matrix product state., Comment: 74 pages

Rapid search and rescue is critical to maximizing survival rates following natural disasters. However, these efforts are challenged by the need to search large disaster zones, lack of reliability in the communications infrastructure, and a priori unknown numbers of objects of interest (OOIs), such as injured survivors. Aerial robots are increasingly being deployed for search and rescue due to their high mobility, but there remains a gap in deploying multi-robot autonomous aerial systems for methodical search of large environments. Prior works have relied on preprogrammed paths from human operators or are evaluated only in simulation. We bridge these gaps in the state of the art by developing and demonstrating a decentralized active search system, which biases its trajectories to take additional views of uncertain OOIs. The methodology leverages stochasticity for rapid coverage in communication denied scenarios. When communications are available, robots share poses, goals, and OOI information to accelerate the rate of search. Extensive simulations and hardware experiments in Bloomingdale, OH, are conducted to validate the approach. The results demonstrate the active search approach outperforms greedy coverage-based planning in communication-denied scenarios while maintaining comparable performance in communication-enabled scenarios.

Action detection and understanding provide the foundation for the generation and interaction of multimedia content. However, existing methods mainly focus on constructing complex relational inference networks, overlooking the judgment of detection effectiveness. Moreover, these methods frequently generate detection results with cognitive abnormalities. To solve the above problems, this study proposes a cognitive effectiveness network based on fuzzy inference (Cefdet), which introduces the concept of "cognition-based detection" to simulate human cognition. First, a fuzzy-driven cognitive effectiveness evaluation module (FCM) is established to introduce fuzzy inference into action detection. FCM is combined with human action features to simulate the cognition-based detection process, which clearly locates the position of frames with cognitive abnormalities. Then, a fuzzy cognitive update strategy (FCS) is proposed based on the FCM, which utilizes fuzzy logic to re-detect the cognition-based detection results and effectively update the results with cognitive abnormalities. Experimental results demonstrate that Cefdet exhibits superior performance against several mainstream algorithms on the public datasets, validating its effectiveness and superiority. Code is available at https://github.com/12sakura/Cefdet., Comment: The paper has been accepted by ACM MM. If you find this work helpful, please consider citing our paper. Zhe Luo, Weina Fu, Shuai Liu, Saeed Anwar, Muhammad Saqib, Sambit Bakshi, Khan Muhammad (2024) Cefdet: Cognitive Effectiveness Network Based on Fuzzy Inference for Action Detection, 32nd ACM International Conference on Multimedia, online first, 10.1145/3664647.3681226

We review $\mathrm{Hom}$-infinite Frobenius categorification of cluster algebras with coefficients and use it to give two applications of Jensen--King--Su's Frobenius categorification of the Grassmannian: 1) we determine the $g$-vectors of the Pl\"ucker coordinates with respect to the triangular initial seed and 2) we express the $F$-polynomials associated with the Donaldson--Thomas transformation in terms of $3$-dimensional Young diagrams thus providing a new proof for a theorem of Daping Weng., Comment: 34 pages

Reducing the atmospheric haze and enhancing image clarity is crucial for computer vision applications. The lack of real-life hazy ground truth images necessitates synthetic datasets, which often lack diverse haze types, impeding effective haze type classification and dehazing algorithm selection. This research introduces the HazeSpace2M dataset, a collection of over 2 million images designed to enhance dehazing through haze type classification. HazeSpace2M includes diverse scenes with 10 haze intensity levels, featuring Fog, Cloud, and Environmental Haze (EH). Using the dataset, we introduce a technique of haze type classification followed by specialized dehazers to clear hazy images. Unlike conventional methods, our approach classifies haze types before applying type-specific dehazing, improving clarity in real-life hazy images. Benchmarking with state-of-the-art (SOTA) models, ResNet50 and AlexNet achieve 92.75\% and 92.50\% accuracy, respectively, against existing synthetic datasets. However, these models achieve only 80% and 70% accuracy, respectively, against our Real Hazy Testset (RHT), highlighting the challenging nature of our HazeSpace2M dataset. Additional experiments show that haze type classification followed by specialized dehazing improves results by 2.41% in PSNR, 17.14% in SSIM, and 10.2\% in MSE over general dehazers. Moreover, when testing with SOTA dehazing models, we found that applying our proposed framework significantly improves their performance. These results underscore the significance of HazeSpace2M and our proposed framework in addressing atmospheric haze in multimedia processing. Complete code and dataset is available on \href{https://github.com/tanvirnwu/HazeSpace2M} {\textcolor{blue}{\textbf{GitHub}}}., Comment: Accepted by ACM Multimedia 2024

This is the third of a series of works (arxiv:2106.05291, arxiv:2205.03301) aimed at renormalizing the Standard Model effective field theory at one loop and to order $1/\Lambda^4$, with $\Lambda$ being the new physics cut-off. On this occasion, we concentrate on the running of two-fermion operators induced by pairs of dimension-six interactions. We work mostly off-shell, for which we obtain and provide a new and explicitly hermitian basis of dimension-eight Green's functions. All our results can be accessed in https://github.com/SMEFT-Dimension8-RGEs ., Comment: 17 pages, 2 figures, complete results: https://github.com/SMEFT-Dimension8-RGEs

In a Mott insulator, a laser pulse with frequency tuned to the gap scale can create a holon-doublon plasma, suppressing the magnetic moment ${\vec m}_i$ and destroying magnetic order. While this disruptive effect is well established experimentally on a square lattice, we investigate the effect of laser pumping on the triangular lattice, where geometric frustration leads to a richer set of ordering possibilities. We work with the Mott-Hubbard problem at a coupling where $120^{\circ}$ order is just stable and employ spatio-temporal mean field dynamics to study the pump response. Moderate pump amplitude just leads to the reduction of $120^{\circ}$ order, but at larger amplitude the suppression of $120^{\circ}$ order is followed by the appearance of `spiral order'. On the electronic side the density of `excited carriers' $n_{exc}$ in the upper Hubbard band increases monotonically with pump amplitude. We show that the long time ordering possibilities in the pumped system, e.g., the emergence of spiral order, can be inferred from a nonequilibrium `energy landscape'. We analyse the growth of spiral order by using an exact diagonalisation based Langevin equation on large lattices and discover that the new order can take $\sim 10^3-10^4$ times the electronic timescale to appear. The threefold combination, of mean field dynamics, landscape construction, and Langevin dynamics, readily generalises to the search for pump induced `hidden order' in other gapped systems., Comment: 13 pages, 9 figures

Recent experiments on nanoclusters of silver (Ag) embedded in a gold (Au) matrix reveal a huge increase in both the zero temperature resistivity and the coefficient of the ``$T$ linear'' thermal resistivity with increasing volume fraction of Ag. A fraction $f \sim 50\%$ of Ag leads to a factor of $20$ increase in the residual resistivity, and a $40$ fold enhancement in the coefficient of linear $T$ resistivity, with respect to Au. Since Au and Ag both have weak electron-phonon coupling we surmise that the huge enhancements arise from a moderately large electron-phonon coupling that may emerge at the Ag-Au interface. We construct nanocluster configurations for varying $f$ in two dimensions, define a Holstein model on it with weak coupling on the `interior' sites and a strong coupling on the interfacial sites, and solve the model through exact diagonalisation based Langevin dynamics. Computing the resistivity, we observe a large $T=0$ increase with $f$ and also a linear $T$ enhancement factor of $\sim 30$. While the enhancement factors are parameter choice dependent, our key qualitative result is that the interface physics is inhomogeneous, with widely varying distortions, and different segments of the interface dictate the residual resistivity and the thermal scattering., Comment: 6 pages, 4 figures, and Supplementary

Skipper CCDs are a mature detector technology that has been suggested for future space telescope instruments requiring sub-electron readout noise in the near-ultraviolet to the near-infrared. While modern skipper CCDs inherit from the radiation-tolerant p-channel detectors developed by LBNL, the effects of high doses of ionizing radiation on skipper CCDs (such as those expected in space) remains largely unmeasured. We report preliminary results on the performance of p-channel skipper CCDs following irradiation with 217-MeV protons at the Northwestern Medicine Proton Center. The total nonionizing energy loss (NIEL) experienced by the detectors exceeds 6 years at the Sun-Earth Lagrange Point 2 (L2). We demonstrate that the skipper amplifier continues to function as expected following this irradiation. Owing to the low readout noise of these detectors, controlled irradiation tests can be used to sensitively characterize the charge transfer inefficiency, dark current, and the density and time constants of charge traps as a function of proton fluence. We conclude with a brief outlook toward future tests of these detectors at other proton and gamma-ray facilities., Comment: SPIE Astronomical Telescopes + Instrumentation 2024

Pump-probe response of the spin-orbit coupled Mott insulator Sr$_2$IrO$_4$ reveals a rapid creation of low energy optical weight and suppression of three dimensional magnetic order on laser pumping. Post pump there is a quick reduction of the optical weight but a very slow recovery of the magnetic order - the difference is attributed to weak inter-layer exchange in Sr$_2$IrO$_4$ delaying the recovery of three dimensional magnetic order. We demonstrate that the effect has a very different and more fundamental origin. Combining spatio-temporal mean field dynamics and Langevin dynamics on the photoexcited Mott-Hubbard insulator we show that the timescale difference is not a dimensional effect but is intrinsic to charge dynamics versus order reconstruction in a correlated system. In two dimensions itself we obtain a short, almost pump fluence independent, timescale for charge dynamics while recovery time of magnetic order involves domain growth and increases rapidly with fluence. Apart from resolving the iridate Mott problem our approach can be used to analyse phase competition and spatial ordering in superconductors and charge ordered systems out of equilibrium., Comment: 6 pages, 4 figures, Supplementary

We introduce CYBER-0, the first zero-order optimization algorithm for memory-and-communication efficient Federated Learning, resilient to Byzantine faults. We show through extensive numerical experiments on the MNIST dataset and finetuning RoBERTa-Large that CYBER-0 outperforms state-of-the-art algorithms in terms of communication and memory efficiency while reaching similar accuracy. We provide theoretical guarantees on its convergence for convex loss functions.

A novel method to reconstruct the energy of hadronic showers in the CMS High Granularity Calorimeter (HGCAL) is presented. The HGCAL is a sampling calorimeter with very fine transverse and longitudinal granularity. The active media are silicon sensors and scintillator tiles readout by SiPMs and the absorbers are a combination of lead and Cu/CuW in the electromagnetic section, and steel in the hadronic section. The shower reconstruction method is based on graph neural networks and it makes use of a dynamic reduction network architecture. It is shown that the algorithm is able to capture and mitigate the main effects that normally hinder the reconstruction of hadronic showers using classical reconstruction methods, by compensating for fluctuations in the multiplicity, energy, and spatial distributions of the shower's constituents. The performance of the algorithm is evaluated using test beam data collected in 2018 prototype of the CMS HGCAL accompanied by a section of the CALICE AHCAL prototype. The capability of the method to mitigate the impact of energy leakage from the calorimeter is also demonstrated.

We present the first on-sky results from an ultra-low-readout-noise Skipper CCD focal plane prototype for the SOAR Integral Field Spectrograph (SIFS). The Skipper CCD focal plane consists of four 6k x 1k, 15 $\mu$m pixel, fully-depleted, p-channel devices that have been thinned to ~250 $\mu$m, backside processed, and treated with an anti-reflective coating. These Skipper CCDs were configured for astronomical spectroscopy, i.e., single-sample readout noise < 4.3 e- rms/pixel, the ability to achieve multi-sample readout noise $\ll$ 1 e- rms/pixel, full-well capacities ~40,000-65,000 e-, low dark current and charge transfer inefficiency (~2 x 10$^{-4}$ e-/pixel/s and 3.44 x 10$^{-7}$, respectively), and an absolute quantum efficiency of $\gtrsim$ 80% between 450 nm and 980 nm ($\gtrsim$ 90% between 600 nm and 900 nm). We optimized the readout sequence timing to achieve sub-electron noise (~0.5 e- rms/pixel) in a region of 2k x 4k pixels and photon-counting noise (~0.22 e- rms/pixel) in a region of 220 x 4k pixels, each with a readout time of $\lesssim$ 17 min. We observed two quasars (HB89 1159+123 and QSO J1621-0042) at redshift z ~ 3.5, two high-redshift galaxy clusters (CL J1001+0220 and SPT-CL J2040-4451), an emission line galaxy at z = 0.3239, a candidate member star of the Bo\"{o}tes II ultra-faint dwarf galaxy, and five CALSPEC spectrophotometric standard stars (HD074000, HD60753, HD106252, HD101452, HD200654). We present charge-quantized, photon-counting observations of the quasar HB89 1159+123 and show the detector sensitivity increase for faint spectral features. We demonstrate signal-to-noise performance improvements for SIFS observations in the low-background, readout-noise-dominated regime. We outline scientific studies that will leverage the SIFS-Skipper CCD data and new detector architectures that utilize the Skipper floating gate amplifier with faster readout times., Comment: 20 pages, 13 figures, 1 table; Proc. SPIE

For the rational group algebra $\mathbb{Q}G$ of a finite group $G$, we provide an effective method to compute a complete set of matrix units and, in particular, primitive orthogonal idempotents in a simple component of $\mathbb{Q}G$, which is realized by a generalized strongly monomial character and has a prime Schur index. We also provide some classes of groups $G$ where this method can be successfully applied. The application of the method developed is also illustrated with detailed computations.

Data structures and algorithms are essential building blocks for programs, and \emph{distributed data structures}, which automatically partition data across multiple memory locales, are essential to writing high-level parallel programs. While many projects have designed and implemented C++ distributed data structures and algorithms, there has not been widespread adoption of an interoperable model allowing algorithms and data structures from different libraries to work together. This paper introduces distributed ranges, which is a model for building generic data structures, views, and algorithms. A distributed range extends a C++ range, which is an iterable sequence of values, with a concept of segmentation, thus exposing how the distributed range is partitioned over multiple memory locales. Distributed data structures provide this distributed range interface, which allows them to be used with a collection of generic algorithms implemented using the distributed range interface. The modular nature of the model allows for the straightforward implementation of \textit{distributed views}, which are lightweight objects that provide a lazily evaluated view of another range. Views can be composed together recursively and combined with algorithms to implement computational kernels using efficient, flexible, and high-level standard C++ primitives. We evaluate the distributed ranges model by implementing a set of standard concepts and views as well as two execution runtimes, a multi-node, MPI-based runtime and a single-process, multi-GPU runtime. We demonstrate that high-level algorithms implemented using generic, high-level distributed ranges can achieve performance competitive with highly-tuned, expert-written code., Comment: To appear in ACM International Conference on Supercomputing (ICS) 2024

A set of high dimensional points $X=\{x_1, x_2,\ldots, x_n\} \subset R^d$ in isotropic position is said to be $\delta$-anti concentrated if for every direction $v$, the fraction of points in $X$ satisfying $|\langle x_i,v \rangle |\leq \delta$ is at most $O(\delta)$. Motivated by applications to list-decodable learning and clustering, recent works have considered the problem of constructing efficient certificates of anti-concentration in the average case, when the set of points $X$ corresponds to samples from a Gaussian distribution. Their certificates played a crucial role in several subsequent works in algorithmic robust statistics on list-decodable learning and settling the robust learnability of arbitrary Gaussian mixtures, yet remain limited to rotationally invariant distributions. This work presents a new (and arguably the most natural) formulation for anti-concentration. Using this formulation, we give quasi-polynomial time verifiable sum-of-squares certificates of anti-concentration that hold for a wide class of non-Gaussian distributions including anti-concentrated bounded product distributions and uniform distributions over $L_p$ balls (and their affine transformations). Consequently, our method upgrades and extends results in algorithmic robust statistics e.g., list-decodable learning and clustering, to such distributions. Our approach constructs a canonical integer program for anti-concentration and analysis a sum-of-squares relaxation of it, independent of the intended application. We rely on duality and analyze a pseudo-expectation on large subsets of the input points that take a small value in some direction. Our analysis uses the method of polynomial reweightings to reduce the problem to analyzing only analytically dense or sparse directions., Comment: updated exposition; added certifiable hypercontractivity of degree-two polynomials for any Poincar\'e distribution

We introduce the paradigm of validated decentralized learning for undirected networks with heterogeneous data and possible adversarial infiltration. We require (a) convergence to a global empirical loss minimizer when adversaries are absent, and (b) either detection of adversarial presence of convergence to an admissible consensus irrespective of the adversarial configuration. To this end, we propose the VALID protocol which, to the best of our knowledge, is the first to achieve a validated learning guarantee. Moreover, VALID offers an O(1/T) convergence rate (under pertinent regularity assumptions), and computational and communication complexities comparable to non-adversarial distributed stochastic gradient descent. Remarkably, VALID retains optimal performance metrics in adversary-free environments, sidestepping the robustness penalties observed in prior byzantine-robust methods. A distinctive aspect of our study is a heterogeneity metric based on the norms of individual agents' gradients computed at the global empirical loss minimizer. This not only provides a natural statistic for detecting significant byzantine disruptions but also allows us to prove the optimality of VALID in wide generality. Lastly, our numerical results reveal that, in the absence of adversaries, VALID converges faster than state-of-the-art byzantine robust algorithms, while when adversaries are present, VALID terminates with each honest either converging to an admissible consensus of declaring adversarial presence in the network., Comment: This is an extended version of the paper at International Symposium on Information Theory 2024

Determining the structure of the Kauffman bracket skein module of all $3$-manifolds over the ring of Laurent polynomials $\mathbb Z[A^{\pm 1}]$ is a big open problem in skein theory. Very little is known about the skein module of non-prime manifolds over this ring. In this paper, we compute the Kauffman bracket skein module of the $3$-manifold $(S^1 \times S^2) \ \# \ (S^1 \times S^2)$ over the ring $\mathbb Z[A^{\pm 1}]$. We do this by analysing the submodule of handle sliding relations, for which we provide a suitable basis. Along the way we also compute the Kauffman bracket skein module of $(S^1 \times S^2) \ \# \ (S^1 \times D^2)$. Furthermore, we show that the skein module of $(S^1 \times S^2) \ \# \ (S^1 \times S^2)$ does not split into the sum of free and torsion submodules., Comment: 32 pages, 20 figures

We study the problem of Hamiltonian structure learning from real-time evolution: given the ability to apply $e^{-\mathrm{i} Ht}$ for an unknown local Hamiltonian $H = \sum_{a = 1}^m \lambda_a E_a$ on $n$ qubits, the goal is to recover $H$. This problem is already well-understood under the assumption that the interaction terms, $E_a$, are given, and only the interaction strengths, $\lambda_a$, are unknown. But how efficiently can we learn a local Hamiltonian without prior knowledge of its interaction structure? We present a new, general approach to Hamiltonian learning that not only solves the challenging structure learning variant, but also resolves other open questions in the area, all while achieving the gold standard of Heisenberg-limited scaling. In particular, our algorithm recovers the Hamiltonian to $\varepsilon$ error with total evolution time $O(\log (n)/\varepsilon)$, and has the following appealing properties: (1) it does not need to know the Hamiltonian terms; (2) it works beyond the short-range setting, extending to any Hamiltonian $H$ where the sum of terms interacting with a qubit has bounded norm; (3) it evolves according to $H$ in constant time $t$ increments, thus achieving constant time resolution. As an application, we can also learn Hamiltonians exhibiting power-law decay up to accuracy $\varepsilon$ with total evolution time beating the standard limit of $1/\varepsilon^2$., Comment: 52 pages; v2 discussed more literature, qualified some claims; v3 minor correction discussing prior work

We prove that an inclusion $\mathcal{B} \subset \mathcal{A}$ of simple unital $C^*$-algebras with a finite-index conditional expectation is regular if and only if there exists a finite group $G$ that admits a cocycle action $(\alpha,\sigma)$ on the intermediate $C^*$-subalgebra $\mathcal{C}$ generated by $\mathcal{B}$ and its centralizer $\mathcal{C}_\mathcal{A}(\mathcal{B})$ such that $\mathcal{B}$ is outerly $\alpha$-invariant and $(\mathcal{B} \subset \mathcal{A}) \cong ( \mathcal{B} \subset \mathcal{C}\rtimes^r_{\alpha, \sigma} G)$. Prior to this characterization, we prove the existence of two-sided and unitary quasi-bases for the minimal conditional expectation of any such inclusion, and also show that such an inclusion has integer Watatani index and depth at most $2$., Comment: 16 pages

We show that thermal states of local Hamiltonians are separable above a constant temperature. Specifically, for a local Hamiltonian $H$ on a graph with degree $\mathfrak{d}$, its Gibbs state at inverse temperature $\beta$, denoted by $\rho =e^{-\beta H}/ \textrm{tr}(e^{-\beta H})$, is a classical distribution over product states for all $\beta < 1/(c\mathfrak{d})$, where $c$ is a constant. This sudden death of thermal entanglement upends conventional wisdom about the presence of short-range quantum correlations in Gibbs states. Moreover, we show that we can efficiently sample from the distribution over product states. In particular, for any $\beta < 1/( c \mathfrak{d}^3)$, we can prepare a state $\epsilon$-close to $\rho$ in trace distance with a depth-one quantum circuit and $\textrm{poly}(n) \log(1/\epsilon)$ classical overhead. A priori the task of preparing a Gibbs state is a natural candidate for achieving super-polynomial quantum speedups, but our results rule out this possibility above a fixed constant temperature.