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The main question raised in the letter is the applicability of a neural network trained on a spin lattice model in one universality class to test a model in another universality class. The quantities of interest are the critical phase transition temperature and the correlation length exponent. In other words, the question of transfer learning is how ``universal'' the trained network is and under what conditions. The traditional approach with training and testing spin distributions turns out to be inapplicable for this purpose. Instead, we propose to use training and testing on binding energy distributions, which leads to successful estimates of the critical temperature and correlation length exponent for cross-tested Baxter-Wu and Ising models belonging to different universality classes., Comment: 5 pages, 1 figure, supplemental materials

The use of machine learning to predict wave dynamics is a topic of growing interest, but commonly-used deep learning approaches suffer from a lack of interpretability of the trained models. Here we present an interpretable machine learning framework for analyzing the nonlinear evolution dynamics of optical wavepackets in complex wave media. We use sparse regression to reduce microscopic discrete lattice models to simpler effective continuum models which can accurately describe the dynamics of the wavepacket envelope. We apply our approach to valley-Hall domain walls in honeycomb photonic lattices of laser-written waveguides with Kerr-type nonlinearity and different boundary shapes. The reconstructed equations accurately reproduce the linear dispersion and nonlinear effects including self-steepening and self-focusing. This scheme is proven free of the a priori limitations imposed by the underlying hierarchy of scales traditionally employed in asymptotic analytical methods. It represents a powerful interpretable machine learning technique of interest for advancing design capabilities in photonics and framing the complex interaction-driven dynamics in various topological materials., Comment: 6 pages, 5 figures

To date, a number of changing-look (CL) active galactic nuclei (AGNs) are known. We studied, in detail what happens to the X-ray spectrum during the CL events using the example of the nearby CL Seyfert NGC1566, which was observed by Swift, NuSTAR, XMM-Newton, and Suzaku. We applied the Comptonization model to describe an evolution of NGC~1566 X-ray spectra during outbursts and compared these results with a typical behavior for other AGNs to identify some differences and common properties that can ultimately help us to better understand the physics of the CL phenomenon. We found that changes in the X-ray properties of NGC1566 are characterized by a different combination of Sy1 (using 1H0707-495 as a representative) and Sy2 properties (using NGC7679 and Mrk3 as their representatives). At high X-ray luminosities NGC1566 exhibits the behavior typical for Sy1, and at low luminosities we see a transition of NGC1566 from the Sy1 behavior to the Sy2 pattern. We revealed the saturation of the spectral indices, \=a for these four AGNs during outbursts (\=a_1566~1.1, \=a _0707~2, \=a _7679~0.9 and \=a_mrk3~0.9) and determined the masses of the black holes (BHs) in the centers of these AGNs namely, M_0707~6.8x10^7 M_sol, M_7679~8.4x10^6 M_sol, M_mrk3~2.2x10^8 M_sol and M_1566~2x10^5 M_sol, applying the scaling method. Our spectral analysis shows that the changing-look of NGC1566 from Sy1.2 to Sy1.9 in 2019 was accompanied by the transition of NGC1566 to an accretion regime which is typical for the intermediate and highly soft spectral states of other BHs. We also find that when going from Sy2 to Sy1, the spectrum of NGC1566 shows an increase in the soft excess accompanied by a decrease in the Comptonized fraction (0.1

This article presents a mathematical model of dynamic pricing for real estate (RE) that incorporates multiple pricing groups, thereby expanding the capabilities of existing models. The developed model solves the problem of maximizing aggregate cumulative revenue at the end of the sales period while meeting the revenue and sales goals. A method is proposed for distributing aggregate cumulative revenue goals across different RE pricing groups. The model is further modified to account for the time value of money and the real estate value increase as construction progresses. The algorithm for constructing a pricing policy for multiple pricing groups is described, and numerical simulations are performed to demonstrate how the algorithm operates.

It is typically assumed that for the successful use of machine learning algorithms, these algorithms should have a higher accuracy than a human expert. Moreover, if the average accuracy of ML algorithms is lower than that of a human expert, such algorithms should not be considered and are counter-productive. However, this is not always true. We provide strong statistical evidence that shows that even if a human expert is more accurate than a machine, an interaction with such a machine is beneficial when communication with the machine is non-public. The existence of a conflict between the user and ML model, and the private nature of user-AI communication will have the effect of making the user think about their decision and hence increase overall accuracy.

For a very long time, computational approaches to the design of new materials have relied on an iterative process of finding a candidate material and modeling its properties. AI has played a crucial role in this regard, helping to accelerate the discovery and optimization of crystal properties and structures through advanced computational methodologies and data-driven approaches. To address the problem of new materials design and fasten the process of new materials search, we have applied latest generative approaches to the problem of crystal structure design, trying to solve the inverse problem: by given properties generate a structure that satisfies them without utilizing supercomputer powers. In our work we propose two approaches: 1) conditional structure modification: optimization of the stability of an arbitrary atomic configuration, using the energy difference between the most energetically favorable structure and all its less stable polymorphs and 2) conditional structure generation. We used a representation for materials that includes the following information: lattice, atom coordinates, atom types, chemical features, space group and formation energy of the structure. The loss function was optimized to take into account the periodic boundary conditions of crystal structures. We have applied Diffusion models approach, Flow matching, usual Autoencoder (AE) and compared the results of the models and approaches. As a metric for the study, physical PyMatGen matcher was employed: we compare target structure with generated one using default tolerances. So far, our modifier and generator produce structures with needed properties with accuracy 41% and 82% respectively. To prove the offered methodology efficiency, inference have been carried out, resulting in several potentially new structures with formation energy below the AFLOW-derived convex hulls.

We set out to explore the possibility of investigating the critical behavior of systems with first-order phase transition using deep machine learning. We propose a machine learning protocol with ternary classification of instantaneous spin configurations using known values of disordered phase energy and ordered phase energy. The trained neural network is used to predict whether a given sample belong to one or the other phase of matter. This allows us to estimate the probability that configurations with a certain energy belong to the ordered phase, mixed phase and, disordered phase. From these probabilities, we obtained estimates of the values of the critical energies and the latent heat for the Potts model with 10 and 20 components, which undergoes a strong discontinuous transition. We also find that the probabilities can reflect geometric transitions in the mixed phase., Comment: 5 pages, 5 figures, 4 tables

Contraction-driven self-propulsion of a large class of living cells can be modeled by a Keller-Segel system with free boundaries. The ensuing "active" system, exhibiting both dissipation and anti-dissipation, features stationary and traveling wave solutions. While the former represent static cells, the latter describe propagating pulses (solitary waves) mimicking the autonomous locomotion of the same cells. In this paper we provide the first proof of the asymptotic nonlinear stability of both of such solutions, static and dynamic. In the case of stationary solutions, the linear stability is established using the spectral theorem for compact, self-adjoint operators, and thus linear stability is determined classically, solely by eigenvalues. For traveling waves the picture is more complex because the linearized problem is non-self-adjoint, opening the possibility of a "dark" area in the phase space which is not "visible" in the purely eigenvalue/eigenvector approach. To establish linear stability in this case we employ spectral methods together with the Gearhart-Pruss-Greiner (GPG) theorem, which controls the entire spectrum via bounds on the resolvent operator. For both stationary and traveling wave solutions, nonlinear stability is then proved by showing how the nonlinear part of the problem may be dominated by the linear part and then employing a Gronwall inequality argument. The developed novel methodology can prove useful also in other problems involving non-self-adjoint (non-Hermitian or non-reciprocal) operators which are ubiquitous in the modeling of "active" matter., Comment: 35 pages, 2 figures

We study the sensitivity of presupernova evolution and supernova nucleosynthesis yields of massive stars to variations of the initial composition. We use the solar abundances from Lodders (2009), and compute two different initial stellar compositions: i) scaled solar abundances, and ii) the isotopic galactic chemical history model (GCH) developed by West and Heger (2013b). We run a grid of models using the KEPLER stellar evolution code, with 7 initial stellar masses, 12 initial metallicities, and two for each scaling method to explore the effects on nucleosynthesis over a metallicity range of $-4.0\leq[Z]\leq+0.3$. We find that the compositions from the GCH model better reproduce the weak \emph{s}-process peak than the scaled solar models. The model yields are then used in the OMEGA Galactic Chemical Evolution (GCE) code to assess this result further. We find that initial abundances used in computing stellar structure have more of an impact on GCE results than initial abundances used in the burn network, with the GCH model again being favored when compared to observations. Lastly, a machine learning algorithm was used to verify the free parameter values of the GCH model, which were previously found by West and Heger (2013b) using a stochastic fitting process. The updated model is provided as an accessible tool for further nucleosynthesis studies.

In this paper, we applied a deep neural network to study the issue of knowledge transferability between statistical mechanics models. The following computer experiment was conducted. A convolutional neural network was trained to solve the problem of binary classification of snapshots of the Ising model's spin configuration on a two-dimensional lattice. During testing, snapshots of the Ising model spins on a lattice with diagonal ferromagnetic and antiferromagnetic connections were fed to the input of the neural network. Estimates of the probability of samples belonging to the paramagnetic phase were obtained from the outputs of the tested network. The analysis of these probabilities allowed us to estimate the critical temperature and the critical correlation length exponent. It turned out that at weak anisotropy the neural network satisfactorily predicts the transition point and the value of the correlation length exponent. Strong anisotropy leads to a noticeable deviation of the predicted values from the precisely known ones. Qualitatively, strong anisotropy is associated with the presence of oscillations of the correlation function above the Stephenson disorder temperature and further approach to the point of the fully frustrated case., Comment: 5 pages, 5 figures

It is possible to have a packing by translates of a cube that is maximal (i.e.\ no other cube can be added without overlapping) but does not form a tiling. In the long running analogy of packing and tiling to orthogonality and completeness of exponentials on a domain, we pursue the question whether one can have maximal orthogonal sets of exponentials for a cube without them being complete. We prove that this is not possible in dimensions 1 and 2, but is possible in dimensions 3 and higher. We provide several examples of such maximal incomplete sets of exponentials, differing in size, and we raise relevant questions. We also show that even in dimension $1$ there are sets which are spectral (i.e. have a complete set of orthogonal exponentials) and yet they also possess maximal incomplete sets of orthogonal exponentials., Comment: 13 pages, no figures

Search-based software testing (SBST) is a widely adopted technique for testing complex systems with large input spaces, such as Deep Learning-enabled (DL-enabled) systems. Many SBST techniques focus on Pareto-based optimization, where multiple objectives are optimized in parallel to reveal failures. However, it is important to ensure that identified failures are spread throughout the entire failure-inducing area of a search domain and not clustered in a sub-region. This ensures that identified failures are semantically diverse and reveal a wide range of underlying causes. In this paper, we present a theoretical argument explaining why testing based on Pareto optimization is inadequate for covering failure-inducing areas within a search domain. We support our argument with empirical results obtained by applying two widely used types of Pareto-based optimization techniques, namely NSGA-II (an evolutionary algorithm) and OMOPSO (a swarm-based Pareto-optimization algorithm), to two DL-enabled systems: an industrial Automated Valet Parking (AVP) system and a system for classifying handwritten digits. We measure the coverage of failure-revealing test inputs in the input space using a metric that we refer to as the Coverage Inverted Distance quality indicator. Our results show that NSGA-II-based search and OMOPSO are not more effective than a na\"ive random search baseline in covering test inputs that reveal failures. The replication package for this study is available in a GitHub repository., Comment: Accepted for publication by Empirical Software Engineering Journal (EMSE) (in October 2024)

We compare ambient and outer Lipschitz geometry of Lipschitz normally embedded H\"older triangles in $\mathbb{R}^4$. In contrast to the case of $\mathbb{R}^3$ there are infinitely many equivalence classes. The equivalence classes are related to the so-called microknots., Comment: arXiv admin note: text overlap with arXiv:2311.18570

One of the main postulates of quantum mechanics is that measurements destroy quantum coherence (wave function collapse). Recently it was discovered that in a many-body system dilute local measurements still preserve some coherence across the entire system. As the measurement density is increased, a phase transition occurs that is characterized by the disentanglement of different parts of the system. Unfortunately, this transition is impossible to observe experimentally for macroscopic systems because it requires an exponentially costly full tomography of the many-body wave function or a comparison with the simulation on an oracle classical computer. In this work we report the discovery of another measurement-induced phase transition that can be observed experimentally if quantum dynamics can be reversed. On one side of this phase transition the quantum information encoded in some part of the Hilbert space is fully recovered after the time inversion. On the other side, all quantum information is corrupted. This transition also manifests itself as the change in the behavior of the probability to observe the same measurement outcome in the process that consists of identical blocks repeated many times. In each block the unitary evolution is followed by the measurement. On one side of the transition the probability decreases exponentially with the number of repetitions, on the other it tends to a constant as the number of repetitions is increased. We confirm the existence of the proposed phase transition through numerical simulations of realistic quantum circuits and analytical calculations using an effective random-matrix theory model., Comment: 18 pages, 10 figures; v2: minor improvements

The spectral form factor (SFF) is a powerful diagnostic of random matrix behavior in quantum many-body systems. We introduce a family of random circuit ensembles whose SFFs can be computed $\textit{exactly}$. These ensembles describe the evolution of non-interacting fermions in the presence of correlated on-site potentials drawn from the eigenvalue distribution of a circular ensemble. For disorder parameters drawn from the circular unitary ensemble (CUE), we derive an exact closed form for the SFF, valid for any choice of system size $L$ or time $t$. When the disorder is drawn from the circular orthogonal or symplectic ensembles (COE and CSE, respectively), we carry out the disorder averages analytically and reduce the computation of the SFF to a combinatorial problem amenable to transfer matrix methods. In each of these cases the SFF grows exponentially in time, which we argue is a signature of random matrix universality at the single-particle level. Finally, we develop matchgate circuit representations of our circuit ensembles, enabling their experimental realization in quantum simulators., Comment: This paper provides proofs of results presented in the author's recent paper, "Single-Particle Universality of the Many-Body Spectral Form Factor", in addition to previously unstated results. The reader may benefit from examining both in parallel. Comments welcome!

One of the most challenging problems in the computational study of localization in quantum manybody systems is to capture the effects of rare events, which requires sampling over exponentially many disorder realizations. We implement an efficient procedure on a quantum processor, leveraging quantum parallelism, to efficiently sample over all disorder realizations. We observe localization without disorder in quantum many-body dynamics in one and two dimensions: perturbations do not diffuse even though both the generator of evolution and the initial states are fully translationally invariant. The disorder strength as well as its density can be readily tuned using the initial state. Furthermore, we demonstrate the versatility of our platform by measuring Renyi entropies. Our method could also be extended to higher moments of the physical observables and disorder learning.

We consider systems of fermions evolved by non-interacting unitary circuits with correlated on-site potentials. When these potentials are drawn from the eigenvalue distribution of a circular random matrix ensemble, the spectral form factor (SFF) of the resulting circuit ensemble can be computed exactly without numerical sampling. In the case of the circular unitary ensemble (CUE) we report an exact closed form for the SFF, valid for arbitrary system sizes, and show that it grows through a sequence of exponential ramps. Using exact numerical methods, we find that the circular orthogonal and symplectic ensembles (COE and CSE, respectively) also lead to exponential growth of the SFF. This exponential growth is characteristic of non-interacting systems with random matrix statistics at the $\textit{single-particle}$ level and, upon introducing interactions, crosses over to a linear ramp consistent with many-body random matrix universality. Our exact results for the SFF provide a baseline for future studies of the crossover between single-particle and many-body random matrix behavior., Comment: A companion paper titled "Exact spectral form factors of non-interacting fermions with Dyson statistics" will be posted shortly with proofs of technical claims made here. Comments welcome!

Transitions from delocalized to localized eigenstates have been extensively studied in both quadratic and interacting models. The delocalized regime typically exhibits diffusion and quantum chaos, and its properties comply with the random matrix theory (RMT) predictions. However, it is also known that in certain quadratic models, the delocalization in position space is not accompanied by the single-particle quantum chaos. Here, we study the one-dimensional Anderson and Wannier-Stark models that exhibit eigenstate transitions from localization in quasimomentum space (supporting ballistic transport) to localization in position space (with no transport) in a nonstandard thermodynamic limit, which assumes rescaling the model parameters with the system size. We show that the transition point may exhibit an unconventional character of Janus type, i.e., some measures hint at the RMT-like universality emerging at the transition point, while others depart from it. For example, the eigenstate entanglement entropies may exhibit, depending on the bipartition, a volume-law behavior that either approaches the value of Haar-random Gaussian states, or converges to a lower, non-universal value. Our results hint at rich diversity of volume-law eigenstate entanglement entropies in quadratic systems that are not maximally entangled.

With intensive Monte Carlo simulations and finite size scaling we undertake a percolation analysis of Wegner's three-dimensional $\mathbb{Z}_2$ lattice gauge model in equilibrium. We confirm that the loops threading excited plaquettes percolate at the thermal critical point $T_{\rm c}$ and we show that their critical exponents coincide with the ones of the loop representation of the dual 3D Ising model. We then construct Fortuin-Kasteleyn (FK) clusters using a random-cluster representation and find that they also percolate at $T_c$ and moreover give access to all thermal critical exponents. The Binder cumulants of the percolation order parameter of both loops and FK clusters demonstrate a pseudo first order transition. This study sheds light on the critical properties of quantum error correction and lattice gauge theories., Comment: 19 pages, 21 figures

Quantum error correction is necessary for achieving exponential speedups on important applications. The planar surface code has remained the most studied error-correcting code for the last two decades because of its relative simplicity. However, encoding a singular logical qubit with the planar surface code requires physical qubits quadratic in the code distance~($d$), making it space-inefficient for the large-distance codes necessary for promising applications. Thus, {\em Quantum Low-Density Parity-Check (QLDPC)} have emerged as an alternative to the planar surface code but require a higher degree of connectivity. Furthermore, the problems of fault-tolerant syndrome extraction and decoding are understudied for these codes and also remain obstacles to their usage. In this paper, we consider two under-studied families of QLDPC codes: hyperbolic surface codes and hyperbolic color codes. We tackle the three challenges mentioned above as follows. {\em First}, we propose {\em Flag-Proxy Networks (FPNs)}, a generalizable architecture for quantum codes that achieves low connectivity through flag and proxy qubits. {\em Second}, we propose a {\em greedy syndrome extraction scheduling} algorithm for general quantum codes and further use this algorithm for fault-tolerant syndrome extraction on FPNs. {\em Third}, we present two decoders that leverage flag measurements to decode the hyperbolic codes accurately. Our work finds that degree-4 FPNs of the hyperbolic surface and color codes are respectively $2.9\times$ and $5.5\times$ more space-efficient than the $d = 5$ planar surface code, and become even more space-efficient when considering higher distances. The hyperbolic codes also have error rates comparable to their planar counterparts., Comment: Accepted to the International Symposium on Computer Microarchitecture (MICRO) 2024. Will be presented in November 2024

We study the integration problem over the $s$-dimensional unit cube on four types of Banach spaces of integrands. First we consider Haar wavelet spaces, consisting of functions whose Haar wavelet coefficients exhibit a certain decay behavior measured by a parameter $\alpha >0$. We study the worst case error of integration over the norm unit ball and provide upper error bounds for quasi-Monte Carlo (QMC) cubature rules based on arbitrary $(t,m,s)$-nets as well as matching lower error bounds for arbitrary cubature rules. These results show that using arbitrary $(t,m,s)$-nets as sample points yields the best possible rate of convergence. Afterwards we study spaces of integrands of fractional smoothness $\alpha \in (0,1)$ and state a sharp Koksma-Hlawka-type inequality. More precisely, we show that on those spaces the worst case error of integration is equal to the corresponding fractional discrepancy. Those spaces can be continuously embedded into tensor product Bessel potential spaces, also known as Sobolev spaces of dominated mixed smoothness, with the same set of parameters. The latter spaces can be embedded into suitable Besov spaces of dominating mixed smoothness $\alpha$, which in turn can be embedded into the Haar wavelet spaces with the same set of parameters. Therefore our upper error bounds on Haar wavelet spaces for QMC cubatures based on $(t,m,s)$-nets transfer (with possibly different constants) to the corresponding spaces of integrands of fractional smoothness and to Sobolev and Besov spaces of dominating mixed smoothness. Moreover, known lower error bounds for periodic Sobolev and Besov spaces of dominating mixed smoothness show that QMC integration based on arbitrary $(t,m,s)$-nets yields the best possible convergence rate on periodic as well as on non-periodic Sobolev and Besov spaces of dominating smoothness., Comment: 56 pages

Anisotropic pair breaking close to surfaces favors chiral superfluid $^3$He-A over time-reversal invariant $^3$He-B. Confining superfluid $^3$He into a cavity of height $D$ of the order of the Cooper pair size characterized by the coherence length $\xi_0$ -- ranging between 16 nm (34 bar) and 77 nm (0 bar) -- extends the surface effects over the whole sample volume, thus allowing stabilization of the A phase at pressures $P$ and temperatures $T$ where otherwise the B phase would be stable. In this work the surfaces of such a confined sample are covered with a superfluid $^4$He film to create specular quasiparticle scattering boundary conditions, preventing the suppression of the superfluid order parameter. We show that the chiral A phase is the stable superfluid phase under strong confinement over the full $P-T$ phase diagram down to a quasi-two-dimensional limit $D/\xi_0 = 1$. The planar phase, which is degenerate with the chiral A phase in the weak-coupling limit, is not observed. The gap inferred from measurements over the wide pressure range from 0.2 to 21.0 bar leads to an empirical ansatz for temperature-dependent strong-coupling effects. We discuss how these results pave the way for the realization of the fully-gapped two-dimensional $p_x + ip_y$ superfluid under more extreme confinement., Comment: 11 pages, 8 figures, including the Supplemental Material

Graph Neural Networks based on the message-passing (MP) mechanism are a dominant approach for handling graph-structured data. However, they are inherently limited to modeling only pairwise interactions, making it difficult to explicitly capture the complexity of systems with $n$-body relations. To address this, topological deep learning has emerged as a promising field for studying and modeling higher-order interactions using various topological domains, such as simplicial and cellular complexes. While these new domains provide powerful representations, they introduce new challenges, such as effectively modeling the interactions among higher-order structures through higher-order MP. Meanwhile, structured state-space sequence models have proven to be effective for sequence modeling and have recently been adapted for graph data by encoding the neighborhood of a node as a sequence, thereby avoiding the MP mechanism. In this work, we propose a novel architecture designed to operate with simplicial complexes, utilizing the Mamba state-space model as its backbone. Our approach generates sequences for the nodes based on the neighboring cells, enabling direct communication between all higher-order structures, regardless of their rank. We extensively validate our model, demonstrating that it achieves competitive performance compared to state-of-the-art models developed for simplicial complexes.

We completely determine the second covering radius for binary primitive double-error-correcting BCH codes. As part of this process, we provide a lower bound on the second covering radius for binary primitive BCH codes correcting more than two errors.

Distributed applications based on micro-services in edge computing are becoming increasingly popular due to the rapid evolution of mobile networks. While Kubernetes is the default framework when it comes to orchestrating and managing micro-service-based applications in mobile networks, the requirement to run applications between multiple sites at cloud and edge poses new challenges. Since Kubernetes does not natively provide tools to abstract inter-cluster communications at the application level, inter-cluster communication in edge computing is becoming increasingly critical to the application performance. In this paper, we evaluate for the first time the impact of inter-cluster communication on edge computing performance by using three prominent, open source inter-cluster communication projects and tools, i.e., Submariner, ClusterLink and Skupper. We develop a fully open-source testbed that integrates these tools in a modular fashion, and experimentally benchmark sample applications, including the ML class of applications, on their performance running in the multi-cluster edge computing system under varying networking conditions. We experimentally analyze two classes of envisioned mobile applications, i.e., a) industrial automation, b) vehicle decision drive assist. Our results show that ClusterLink performs best out of the three tools in scenarios with increased payloads, regardless of the underlying networking conditions or transmission direction between clusters. It is closely followed by Skupper, unless request and reply both transport significant amounts of data. Finally, when requesting smaller amounts of data from a service, Submariner slightly outperforms Skupper and ClusterLink regardless of the inter-node networking conditions., Comment: Submitted to IEEE/IFIP Network Operations and Management Symposium 2025

The process of particle picking, a crucial step in cryo-electron microscopy (cryo-EM) image analysis, often encounters challenges due to outliers, leading to inaccuracies in downstream processing. In response to this challenge, this research introduces an additional automated step to reduce the number of outliers identified by the particle picker. The proposed method enhances both the accuracy and efficiency of particle picking, thereby reducing the overall running time and the necessity for expert intervention in the process. Experimental results demonstrate the effectiveness of the proposed approach in mitigating outlier inclusion and its potential to enhance cryo-EM data analysis pipelines significantly. This work contributes to the ongoing advancement of automated cryo-EM image processing methods, offering novel insights and solutions to challenges in structural biology research.

This paper describes the 2nd edition of the ICML Topological Deep Learning Challenge that was hosted within the ICML 2024 ELLIS Workshop on Geometry-grounded Representation Learning and Generative Modeling (GRaM). The challenge focused on the problem of representing data in different discrete topological domains in order to bridge the gap between Topological Deep Learning (TDL) and other types of structured datasets (e.g. point clouds, graphs). Specifically, participants were asked to design and implement topological liftings, i.e. mappings between different data structures and topological domains --like hypergraphs, or simplicial/cell/combinatorial complexes. The challenge received 52 submissions satisfying all the requirements. This paper introduces the main scope of the challenge, and summarizes the main results and findings., Comment: Proceedings of the Geometry-grounded Representation Learning and Generative Modeling Workshop (GRaM) at ICML 2024

We use molecular dynamics to show that plastic slip is a crucial component of the transformation mechanism of a square-to-triangular structural transition. The latter is a stylized analog of many other reconstructive phase transitions. To justify our conclusions we use a novel atomistically-informed mesoscopic representation of the field of lattice distortions in molecular dynamics simulations. Our approach reveals a hidden alternating slip distribution behind the seemingly homogeneous product phase which points to the fact that lattice invariant shears play a central role in this class of phase transformations. While the underlying pattern of anti-parallel displacements may also be interpreted as microscopic shuffling, its precise crystallographic nature strongly suggests the plasticity-centered interpretation.

Quantum error correction plays a prominent role in the realization of quantum computation, and quantum low-density parity-check (qLDPC) codes are believed to be practically useful stabilizer codes. While qLDPC codes are defined to have constant weight parity-checks, the weight of these parity checks could be large constants that make implementing these codes challenging. Large constants can also result in long syndrome extraction times and bad error propagation that can impact error correction performance. Hastings recently introduced weight reduction techniques for qLDPC codes that reduce the weight of the parity checks as well as the maximum number of checks that acts on any data qubit. However, the fault tolerance of these techniques remains an open question. In this paper, we analyze the effective distance of the weight-reduced code when single-ancilla syndrome extraction circuits are considered for error correction. We prove that there exists single-ancilla syndrome extraction circuits that largely preserve the effective distance of the weight-reduced qLDPC codes. In addition, we also show that the distance balancing technique introduced by Evra et al. preserves effective distance. As a corollary, our result shows that higher-dimensional hypergraph product (HGP) codes, also known as homological product codes corresponding to the product of 1-complexes, have no troublesome hook errors when using any single-ancilla syndrome extraction circuit.

Quantum error correction provides a path to reach practical quantum computing by combining multiple physical qubits into a logical qubit, where the logical error rate is suppressed exponentially as more qubits are added. However, this exponential suppression only occurs if the physical error rate is below a critical threshold. In this work, we present two surface code memories operating below this threshold: a distance-7 code and a distance-5 code integrated with a real-time decoder. The logical error rate of our larger quantum memory is suppressed by a factor of $\Lambda$ = 2.14 $\pm$ 0.02 when increasing the code distance by two, culminating in a 101-qubit distance-7 code with 0.143% $\pm$ 0.003% error per cycle of error correction. This logical memory is also beyond break-even, exceeding its best physical qubit's lifetime by a factor of 2.4 $\pm$ 0.3. We maintain below-threshold performance when decoding in real time, achieving an average decoder latency of 63 $\mu$s at distance-5 up to a million cycles, with a cycle time of 1.1 $\mu$s. To probe the limits of our error-correction performance, we run repetition codes up to distance-29 and find that logical performance is limited by rare correlated error events occurring approximately once every hour, or 3 $\times$ 10$^9$ cycles. Our results present device performance that, if scaled, could realize the operational requirements of large scale fault-tolerant quantum algorithms., Comment: 10 pages, 4 figures, Supplementary Information

We present Jamba-1.5, new instruction-tuned large language models based on our Jamba architecture. Jamba is a hybrid Transformer-Mamba mixture of experts architecture, providing high throughput and low memory usage across context lengths, while retaining the same or better quality as Transformer models. We release two model sizes: Jamba-1.5-Large, with 94B active parameters, and Jamba-1.5-Mini, with 12B active parameters. Both models are fine-tuned for a variety of conversational and instruction-following capabilties, and have an effective context length of 256K tokens, the largest amongst open-weight models. To support cost-effective inference, we introduce ExpertsInt8, a novel quantization technique that allows fitting Jamba-1.5-Large on a machine with 8 80GB GPUs when processing 256K-token contexts without loss of quality. When evaluated on a battery of academic and chatbot benchmarks, Jamba-1.5 models achieve excellent results while providing high throughput and outperforming other open-weight models on long-context benchmarks. The model weights for both sizes are publicly available under the Jamba Open Model License and we release ExpertsInt8 as open source., Comment: Webpage: https://www.ai21.com/jamba

We study a mathematical model for the optimization of the price of real estate (RE). This model can be characterised by a limited amount of goods, fixed sales horizon and presence of intermediate sales and revenue goals. We develop it as an enhancement and upgrade of the model presented by Besbes and Maglaras now also taking into account variable demand, time value of money, and growth of the objective value of Real Estate with the development stage.

We prove that autonomous Hamiltonian flows on the two-sphere exhibit the following dichotomy: the Hofer norm either grows linearly or is bounded in time by a universal constant C. Our approach involves a new technique, Hamiltonian symmetrization. Essentially, we prove that every autonomous Hamiltonian diffeomorphism is conjugate to an element C-close in the Hofer metric to one generated by a function of the height., Comment: 30 pages, 3 figures

We derive exact, universal, closed-form quantum Monte Carlo estimators for finite temperature energy susceptibility and fidelity susceptibility for essentially arbitrary Hamiltonians. We demonstrate how our method can be used to study quantum phase transitions without knowledge of an order parameter and without the need to design system-specific ergodic quantum Monte Carlo update rules by applying it to a class of random models., Comment: 9 pages (5 main, 2 bibliography, 3 supplement), 2 figures

We survey the history of the capset problem in the context of related results on progression-free sets, discuss recent progress, and mention further directions to explore., Comment: This is a survey paper

Traps and structural defects at the hole and electron transport interfaces of the microcrystalline absorber limits the efficiency and long-term stability of perovskite solar cells (PSCs) due to accumulation of the ionic clusters, non-radiative recombination and electrochemical corrosion. Surface engineering using self-assembled monolayers (SAM) was considered as an effective strategy for modification of charge-collection junctions. In this work, we demonstrate the first report about complex integration of a SAM for double-side passivation in p-i-n PSCs. Integrating the novel 5-(4-[bis(4-fluorophenyl)amino]phenyl)thiophene-2-carboxylic acid (FTPATC) as a fluorinated SAM at the hole-transport interface reduced potential barriers and lattice stresses in the absorber. At the electron-transport side, FTPATC interacted with the A-site cations of the perovskite molecule (Cs, formamidinium), inducing a dipole for defect compensation. Using the passivation approach with fluorinated SAM demonstrated benefits in the gain of the output performance up to 22.2%. The key-advantage of double-side passivation was confirmed by the enhanced stability under continuous light-soaking (1-sun equivalent, 65 C, ISOS-L-2), maintaining 88% of the initial performance over 1680 hours and thermal stabilization under harsh heating at 90 C.

Eigenstate thermalization hypothesis (ETH) represents a breakthrough in many-body physics since it allows to link thermalization of physical observables with the applicability of random matrix theory (RMT). Recent years were also extremely fruitful in exploring possible counterexamples to thermalization, ranging, among others, from integrability, single-particle chaos, many-body localization, many-body scars, to Hilbert-space fragmentation. In all these cases the conventional ETH is violated. However, it remains elusive how the conventional ETH breaks down when one approaches the boundaries of ergodicity, and whether the range of validity of the conventional ETH coincides with the validity of RMT-like spectral statistics. Here we bridge this gap and we introduce a scenario of the ETH breakdown in many-body quantum systems, dubbed fading ergodicity regime, which establishes a link between the conventional ETH and non-ergodic behavior. We conjecture this scenario to be relevant for the description of finite many-body systems at the boundaries of ergodicity, and we provide numerical and analytical arguments for its validity in the quantum sun model of ergodicity breaking phase transition. For the latter, we provide evidence that the breakdown of the conventional ETH is not associated with the breakdown of the RMT-like spectral statistics.

Large language models (LLMs) have recently seen widespread adoption, in both academia and industry. As these models grow, they become valuable intellectual property (IP), reflecting enormous investments by their owners. Moreover, the high cost of cloud-based deployment has driven interest towards deployment to edge devices, yet this risks exposing valuable parameters to theft and unauthorized use. Current methods to protect models' IP on the edge have limitations in terms of practicality, loss in accuracy, or suitability to requirements. In this paper, we introduce a novel hybrid inference algorithm, named SLIP, designed to protect edge-deployed models from theft. SLIP is the first hybrid protocol that is both practical for real-world applications and provably secure, while having zero accuracy degradation and minimal impact on latency. It involves partitioning the model between two computing resources, one secure but expensive, and another cost-effective but vulnerable. This is achieved through matrix decomposition, ensuring that the secure resource retains a maximally sensitive portion of the model's IP while performing a minimal amount of computations, and vice versa for the vulnerable resource. Importantly, the protocol includes security guarantees that prevent attackers from exploiting the partition to infer the secured information. Finally, we present experimental results that show the robustness and effectiveness of our method, positioning it as a compelling solution for protecting LLMs.

We explore the idea of using automatic and similar kind of presentations of structures to deal with the conceptual problem of natural proof-theoretic ordinal notations. We conclude that this approach still does not meet the goals., Comment: 19 pages

Polymodal provability logic GLP is incomplete w.r.t. Kripke frames. It is known to be complete w.r.t. topological semantics, where the diamond modalities correspond to topological derivative operations. However, the topologies needed for the completeness proof are highly non-constructive. The question of completeness of GLP w.r.t. natural scattered topologies on ordinals is dependent on large cardinal axioms of set theory and is still open. So far, we are lacking a useable class of models for which GLP is complete. In this paper we define a natural class of countable general topological frames on ordinals for which GLP is sound and complete. The associated topologies are the same as the ordinal topologies introduced by Thomas Icard. However, the key point is to specify a suitable algebra of subsets of an ordinal closed under the boolean and topological derivative operations. The algebras we define are based on the notion of a periodic set of ordinals generalizing that of an ultimately periodic binary omega-word., Comment: 32 pages

These notes are loosely based on an introductory course in algebraic geometry given at Rutgers University in Spring of 2024. We introduce some relatively advanced topics at the expense of the technical details., Comment: 143 pages

The channel output entropy of a transmitted sequence is the entropy of the possible channel outputs and similarly the channel input entropy of a received sequence is the entropy of all possible transmitted sequences. The goal of this work is to study these entropy values for the k-deletion, k-insertion channels, where exactly k symbols are deleted, inserted in the transmitted sequence, respectively. If all possible sequences are transmitted with the same probability then studying the input and output entropies is equivalent. For both the 1-deletion and 1-insertion channels, it is proved that among all sequences with a fixed number of runs, the input entropy is minimized for sequences with a skewed distribution of their run lengths and it is maximized for sequences with a balanced distribution of their run lengths. Among our results, we establish a conjecture by Atashpendar et al. which claims that for the 1-deletion channel, the input entropy is maximized by the alternating sequences over all binary sequences. This conjecture is also verified for the 2-deletion channel, where it is proved that constant sequences with a single run minimize the input entropy., Comment: arXiv admin note: substantial text overlap with arXiv:2202.03024

A modal logic is pretransitive, if the modality corresponding to the transitive closure of an accessibility relation is expressible in it. In the present work we establish the finite model property for pretransitive generalizations of K4, wK4, and GL and their extensions by canonical subframe-hereditary formulas., Comment: 19 pages

We address the challenge of efficiently and reliably deleting data from machine learning models trained using Empirical Risk Minimization (ERM), a process known as machine unlearning. To avoid retraining models from scratch, we propose a novel algorithm leveraging Natural Gradient Descent (NGD). Our theoretical framework ensures strong privacy guarantees for convex models, while a practical Min/Max optimization algorithm is developed for non-convex models. Comprehensive evaluations show significant improvements in privacy, computational efficiency, and generalization compared to state-of-the-art methods, advancing both the theoretical and practical aspects of machine unlearning.

This work introduces a new framework, ProtoSAM, for one-shot medical image segmentation. It combines the use of prototypical networks, known for few-shot segmentation, with SAM - a natural image foundation model. The method proposed creates an initial coarse segmentation mask using the ALPnet prototypical network, augmented with a DINOv2 encoder. Following the extraction of an initial mask, prompts are extracted, such as points and bounding boxes, which are then input into the Segment Anything Model (SAM). State-of-the-art results are shown on several medical image datasets and demonstrate automated segmentation capabilities using a single image example (one shot) with no need for fine-tuning of the foundation model. Our code is available at: https://github.com/levayz/ProtoSAM, Comment: 12 pages, 3 figures, 4 tables, code: https://github.com/levayz/ProtoSAM

Generative AI tools can help users with many tasks. One such task is data analysis, which is notoriously challenging for non-expert end-users due to its expertise requirements, and where AI holds much potential, such as finding relevant data sources, proposing analysis strategies, and writing analysis code. To understand how data analysis workflows can be assisted or impaired by generative AI, we conducted a study (n=15) using Bing Chat via participatory prompting. Participatory prompting is a recently developed methodology in which users and researchers reflect together on tasks through co-engagement with generative AI. In this paper we demonstrate the value of the participatory prompting method. We found that generative AI benefits the information foraging and sensemaking loops of data analysis in specific ways, but also introduces its own barriers and challenges, arising from the difficulties of query formulation, specifying context, and verifying results., Comment: Ian Drosos, Advait Sarkar, Xiaotong Xu, Carina Negreanu, Sean Rintel, and Lev Tankelevitch. 2024. "It's like a rubber duck that talks back": Understanding Generative AI-Assisted Data Analysis Workflows through a Participatory Prompting Study. In Proceedings of the 3rd Annual Meeting of the Symposium on Human-Computer Interaction for Work (CHIWORK 2024)