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Denoising Diffusion Probabilistic Models (DDPMs) achieve state-of-the-art performance in synthesizing new images from random noise, but they lack meaningful latent space that encodes data into features. Recent DDPM-based editing techniques try to mitigate this issue by inverting images back to their approximated staring noise. In this work, we study the relation between the initial Gaussian noise, the samples generated from it, and their corresponding latent encodings obtained through the inversion procedure. First, we interpret their spatial distance relations to show the inaccuracy of the DDIM inversion technique by localizing latent representations manifold between the initial noise and generated samples. Then, we demonstrate the peculiar relation between initial Gaussian noise and its corresponding generations during diffusion training, showing that the high-level features of generated images stabilize rapidly, keeping the spatial distance relationship between noises and generations consistent throughout the training.

Spectrum occupancy detection is a key enabler for dynamic spectrum access, where machine learning algorithms are successfully utilized for detection improvement. However, the main challenge is limited access to labeled data about users transmission presence needed in supervised learning models. We present a distributed federated learning approach that addresses this challenge for sensors without access to learning data. The paper discusses the results of the conducted hardware experiment, where FL has been applied for DVB-T signal detection., Comment: 4 pages, in Polish language, 10 figures

We consider a nonlocal functional equation that is a generalization of the mathematical model used in behavioral sciences. The equation is built upon an operator that introduces a convex combination and a nonlinear mixing of the function arguments. We show that, provided some growth conditions of the coefficients, there exists a unique solution in the natural Lipschitz space. Furthermore, we prove that the regularity of the solution is inherited from the smoothness properties of the coefficients. As a natural numerical method to solve the general case, we consider the collocation scheme of piecewise linear functions. We prove that the method converges with the error bounded by the error of projecting the Lipschitz function onto the piecewise linear polynomial space. Moreover, provided sufficient regularity of the coefficients, the scheme is of the second order measured in the supremum norm. A series of numerical experiments verify the proved claims and show that the implementation is computationally cheap and exceeds the frequently used Picard iteration by orders of magnitude in the calculation time.

We present a benchmark for large language models designed to tackle one of the most knowledge-intensive tasks in data science: writing feature engineering code, which requires domain knowledge in addition to a deep understanding of the underlying problem and data structure. The model is provided with a dataset description in a prompt and asked to generate code transforming it. The evaluation score is derived from the improvement achieved by an XGBoost model fit on the modified dataset compared to the original data. By an extensive evaluation of state-of-the-art models and comparison to well-established benchmarks, we demonstrate that the FeatEng of our proposal can cheaply and efficiently assess the broad capabilities of LLMs, in contrast to the existing methods.

This paper presents a system developed for submission to Poleval 2024, Task 3: Polish Automatic Speech Recognition Challenge. We describe Voicebox-based speech synthesis pipeline and utilize it to augment Conformer and Whisper speech recognition models with synthetic data. We show that addition of synthetic speech to training improves achieved results significantly. We also present final results achieved by our models in the competition.

In this work, we perform a systematic computer simulation study of ice premelting, and explore the thickness and structure of quasi-liquid layers formed at the interface of ice with substrates of different hydrophilicity. Our study shows that interfacial premelting occurs on neutral substrates of whatever hydrophilicity, forming films of limited thickness for substrates with contact angles larger than ca. 50$^\circ$ but exhibiting complete interfacial premelting at smaller contact angles. Contrary to most experimental studies, we focus not only on the premelting behavior with temperature, but also with pressure, which is a matter of relevance in important situations such as ice friction. Our study is guided within a rigorous framework of surface thermodynamics, demonstrating that the premelting film structure is a function of a single thermodynamic variable. By this token we are able to relate properties measured along an isobar, with premelting films at arbitrary temperature and pressure. We also find that adhesion strength in atomically smooth surfaces is one to two orders of magnitude larger than those found in experiments, and conjecture that the reason is substrate roughness and the presence of organic adsorbents. Our theoretical framework also allows us to exploit our results on interfacial premelting in order to gain insight into heterogeneous ice nucleation. We show that apolar smooth substrates of whatever hydrophilicity are unlikely nucleators, and that too large hydrophilicity conspires also against ice nucleation. Furthermore, we exploit statistical-thermodynamic framework to shed light into the nature of the surface intermolecular forces promoting interfacial premelting, and provide a model to predict quasi-liquid layer thickness as a function of the substrate's hydrophilicity with great potential applications in fields ranging from earth sciences to aircraft engineering.

Symbolic music research plays a crucial role in music-related machine learning, but MIDI data can be complex for those without musical expertise. To address this issue, we present MidiTok Visualizer, a web application designed to facilitate the exploration and visualization of various MIDI tokenization methods from the MidiTok Python package. MidiTok Visualizer offers numerous customizable parameters, enabling users to upload MIDI files to visualize tokenized data alongside an interactive piano roll., Comment: in Extended Abstracts for the Late-Breaking Demo Sessionof the 25th Int. Society for Music Information Retrieval Conf., San Francisco, United States, 2024

GPT-4o is an autoregressive omni model that accepts as input any combination of text, audio, image, and video, and generates any combination of text, audio, and image outputs. It's trained end-to-end across text, vision, and audio, meaning all inputs and outputs are processed by the same neural network. GPT-4o can respond to audio inputs in as little as 232 milliseconds, with an average of 320 milliseconds, which is similar to human response time in conversation. It matches GPT-4 Turbo performance on text in English and code, with significant improvement on text in non-English languages, while also being much faster and 50\% cheaper in the API. GPT-4o is especially better at vision and audio understanding compared to existing models. In line with our commitment to building AI safely and consistent with our voluntary commitments to the White House, we are sharing the GPT-4o System Card, which includes our Preparedness Framework evaluations. In this System Card, we provide a detailed look at GPT-4o's capabilities, limitations, and safety evaluations across multiple categories, focusing on speech-to-speech while also evaluating text and image capabilities, and measures we've implemented to ensure the model is safe and aligned. We also include third-party assessments on dangerous capabilities, as well as discussion of potential societal impacts of GPT-4o's text and vision capabilities.

Recent years have witnessed a steady progress towards blending 2D quantum materials into technology, with future applications often rooted in the electronic structure. Since crossings and inversions of electronic bands with different orbital characters determine intrinsic quantum transport properties, knowledge of the orbital character is essential. Here, we benchmark angle-resolved photoelectron emission spectroscopy (ARPES) as a tool to experimentally derive orbital characters. For this purpose we study the valence electronic structure of two technologically relevant quantum materials, graphene and WSe$_2$, and focus on circular dichroism that is believed to provide sensitivity to the orbital angular momentum. We analyze the contributions related to angular atomic photoionization profiles, interatomic interference, and multiple scattering. Regimes in which initial-state properties could be disentangled from the ARPES maps are critically discussed and the potential of using circular-dichroic ARPES as a tool to investigate the spin polarization of initial bands is explored. For the purpose of generalization, results from two additional materials, GdMn$_6$Sn$_6$ and PtTe$_2$ are presented in addition. This research demonstrates rich complexity of the underlying physics of circular-dichroic ARPES, providing new insights that will shape the interpretation of both past and future circular-dichroic ARPES studies., Comment: 12 pages, 7 figures

In this paper, we propose a model-agnostic cost-effective approach to developing bilingual base large language models (LLMs) to support English and any target language. The method includes vocabulary expansion, initialization of new embeddings, model training and evaluation. We performed our experiments with three languages, each using a non-Latin script - Ukrainian, Arabic, and Georgian. Our approach demonstrates improved language performance while reducing computational costs. It mitigates the disproportionate penalization of underrepresented languages, promoting fairness and minimizing adverse phenomena such as code-switching and broken grammar. Additionally, we introduce new metrics to evaluate language quality, revealing that vocabulary size significantly impacts the quality of generated text.

We introduce Bielik 7B v0.1, a 7-billion-parameter generative text model for Polish language processing. Trained on curated Polish corpora, this model addresses key challenges in language model development through innovative techniques. These include Weighted Instruction Cross-Entropy Loss, which balances the learning of different instruction types, and Adaptive Learning Rate, which dynamically adjusts the learning rate based on training progress. To evaluate performance, we created the Open PL LLM Leaderboard and Polish MT-Bench, novel frameworks assessing various NLP tasks and conversational abilities. Bielik 7B v0.1 demonstrates significant improvements, achieving a 9 percentage point increase in average score compared to Mistral-7B-v0.1 on the RAG Reader task. It also excels in the Polish MT-Bench, particularly in Reasoning (6.15/10) and Role-playing (7.83/10) categories. This model represents a substantial advancement in Polish language AI, offering a powerful tool for diverse linguistic applications and setting new benchmarks in the field.

We propose a novel framework for exploring generalization errors of transfer learning through the lens of differential calculus on the space of probability measures. In particular, we consider two main transfer learning scenarios, $\alpha$-ERM and fine-tuning with the KL-regularized empirical risk minimization and establish generic conditions under which the generalization error and the population risk convergence rates for these scenarios are studied. Based on our theoretical results, we show the benefits of transfer learning with a one-hidden-layer neural network in the mean-field regime under some suitable integrability and regularity assumptions on the loss and activation functions., Comment: Under review

We propose an exercise in which one attempts to deduce the formalism of quantum mechanics from phenomenological observations only. Thus, the only assumed inputs are the multi-time probability distributions estimated from the results of sequential measurements of quantum observables; no presuppositions about the underlying mathematical structures are allowed. We show that it is indeed possible to derive in such a way a complete and fully functional formalism based on the structures of Hilbert spaces. However, the obtained formal description -- the bi-trajectory formalism -- turns out to be quite different from the standard state-focused formalism., Comment: We intend to submit this paper in two parts

This work is the first computational study of proppant leak-off through coal cleats that accounts for proppant retention in cleats, occlusion formation at cleat entrances, the resulting control of fluid leak-off, and the influence of realistic cleat roughness on these factors. Suspensions are simulated with a coupled lattice Boltzmann method-discrete element method, which explicitly models all physics, including shear-thinning fluid rheology. Firstly, using a simplified computational geometry, it is demonstrated that leak-off and mounding are both minimised when proppant invades and is retained in the cleat. This occurs most effectively with wide proppant size distributions, such as 100/635 mesh. However, when the proppant is larger than the cleat aperture, occlusions form at the cleat entrance, which can lead to significant mounding; this is observed for 100 mesh and 40/70 mesh. These findings are commensurate with an existing benchmark experiment. The present study additionally demonstrates that mounding is significantly reduced for shear-thinning fluids compared to Newtonian fluids. Simulations are then conducted with rough cleats in a realistic fracture channel. Leak-off is smallest for high cleat roughness and when cleats are narrower than a critical width, while proppant retention is largest at the same critical width but only above a certain roughness. Mounding is primarily dependent on the width, as opposed to the roughness. These results are presented as high-fidelity maps which can be directly incorporated into hydraulic fracturing simulations for improved predictions of fluid leak-off and propped reservoir volumes, and which can be tailored for different treatment and reservoir conditions.

In this research, we quantify an inflow of women into science in the past three decades. Structured Big Data allow us to estimate the contribution of women scientists to the growth of science by disciplines (N = STEMM 14 disciplines) and over time (1990-2023). A monolithic segment of STEMM science emerges from this research as divided between the disciplines in which the growth was powerfully driven by women - and the disciplines in which the role of women was marginal. There are four disciplines in which 50% of currently publishing scientists are women; and five disciplines in which more than 50% of currently young scientists are women. But there is also a cluster of four highly mathematized disciplines (MATH, COMP, PHYS, and ENG) in which the growth of science is only marginally driven by women. Digital traces left by scientists in their publications indexed in global datasets open two new dimensions in large-scale academic profession studies: time and gender. The growth of science in Europe was accompanied by growth in the number of women scientists, but with powerful cross-disciplinary and cross-generational differentiations. We examined the share of women scientists coming from ten different age cohorts for 32 European and four comparator countries (the USA, Canada, Australia, and Japan). Our study sample was N = 1,740,985 scientists (including 39.40% women scientists). Three critical methodological challenges of using structured Big Data of the bibliometric type were discussed: gender determination, academic age determination, and discipline determination., Comment: 27 pages (plus Supplementary Material 15 pages)

In this note, we examine the arrangements of lines and configurations of points that emerge from Fermat (von Dyck) and Komiya-Kuribayashi quartics. These quartics are characterized by having the maximum number of lines of maximal tangency, that is, lines for which the intersection multiplicity at the tangency point is equal to the degree of the curve. Additionally, we delve into the study of sextactic points on these quartics - points at which there exists a conic with the curve having a local intersection multiplicity of at least 6, which is one more than that observed at a general point - alongside the related configurations of conics., Comment: 10 pages

Accelerating molecular docking -- the process of predicting how molecules bind to protein targets -- could boost small-molecule drug discovery and revolutionize medicine. Unfortunately, current molecular docking tools are too slow to screen potential drugs against all relevant proteins, which often results in missed drug candidates or unexpected side effects occurring in clinical trials. To address this gap, we introduce RapidDock, an efficient transformer-based model for blind molecular docking. RapidDock achieves at least a $100 \times$ speed advantage over existing methods without compromising accuracy. On the Posebusters and DockGen benchmarks, our method achieves $52.1\%$ and $44.0\%$ success rates ($\text{RMSD}<2$\r{A}), respectively. The average inference time is $0.04$ seconds on a single GPU, highlighting RapidDock's potential for large-scale docking studies. We examine the key features of RapidDock that enable leveraging the transformer architecture for molecular docking, including the use of relative distance embeddings of $3$D structures in attention matrices, pre-training on protein folding, and a custom loss function invariant to molecular symmetries.

The near-infrared (NIR) emission of the youngest protostars still needs to be characterized to better understand the evolution of their accretion and ejection activity. We analyze James Webb Space Telescope NIRSpec 1.7 -- 5.3 $\mu$m observations of two deeply embedded sources in the S68N protostellar core in Serpens. The North Central (NC) source exhibits a highly obscured spectrum (A_K ~ 4.8 mag) that is modeled with a pre-main-sequence photosphere and a hot disk component. The photospheric parameters are consistent with a young, low-mass photosphere, as suggested by the low surface gravity, log g of 1.94 $\pm$ 0.15 cm s$^{-2}$. The hot disk suggests that accretion onto the central protostellar embryo is ongoing, although prototypical accretion-tracing emission lines HI are not detected. The South Central (SC) source, which is even more embedded (A_K ~ 8 mag; no continuum is detected shortward of 3.6 $\mu$m) appears to be driving the large-scale S68N protostellar outflow, and launches a collimated hot molecular jet detected in \Ht and CO ro-vibrational lines. Shock modeling of the \Ht (ro)vibrational lines establishes that fast $C$-type shocks ($\geq$ 30 km s$^{-1}$), with high pre-shock density ($\geq$ $10^7$ cm$^{-3}$), and strong magnetic field (b ~ 3--10, where $B = b\,\times\,\sqrt{\textrm{n}_{\textrm{H}} (\textrm{cm}^{-3})}\,\mu\textrm{G}$) best match the data. The bright CO fundamental line forest suggests energetic excitation, with the contribution of non-LTE effects, ie irradiation pumping. Detected OH and CH$^{+}$ ro-vibrational lines support this hypothesis. These two Class 0 protostars seem to be in very young evolutionary stages and still have to acquire the bulk of their final stellar masses. These results demonstrate that JWST enables unprecedented diagnostics of these first stages of the protostellar evolutionary phase.

This paper presents a generalization of a method allowing the transformation of the Elliptic Curve Discrete Logarithm Problem (ECDLP) over prime fields to the Quadratic Unconstrained Binary Optimization (QUBO) problem. The original method requires that a given elliptic curve model has complete arithmetic. The new one has no such restriction, which is a breakthrough. Since the mentioned obstacle is no longer a problem, the latest version of the algorithm may be used for any elliptic curve model. As a result, one may use quantum annealing to solve ECDLP on any given model of elliptic curves., Comment: 13 pages, 4 figures, 2 tables

The composition of protoplanetary disks, and hence the initial conditions of planet formation, may be strongly influenced by the infall and thermal processing of material during the protostellar phase. Composition of dust and ice in protostellar envelopes, shaped by energetic processes driven by the protostar, serves as the fundamental building material for planets and complex organic molecules. As part of the JWST GO program, "Investigating Protostellar Accretion" (IPA), we observed an intermediate-mass protostar HOPS 370 (OMC2-FIR3) using NIRSpec/IFU and MIRI/MRS. This study presents the gas and ice phase chemical inventory revealed with the JWST in the spectral range of $\sim$2.9 to 28 $\mu$m and explores the spatial variation of volatile ice species in the protostellar envelope. We find evidence for thermal processing of ice species throughout the inner envelope. We present the first high-spatial resolution ($\sim 80$ au) maps of key volatile ice species H$_{2}$O, CO$_{2}$, $^{13}$CO$_2$, CO, and OCN$^-$, which reveal a highly structured and inhomogeneous density distribution of the protostellar envelope, with a deficiency of ice column density that coincides with the jet/outflow shocked knots. Further, we observe high relative crystallinity of H$_{2}$O ice around the shocked knot seen in the H$_2$ and OH wind/outflow, which can be explained by a lack of outer colder material in the envelope along the line of sight due to the irregular structure of the envelope. These observations show clear evidence of thermal processing of the ices in the inner envelope, close to the outflow cavity walls, heated by the luminous protostar., Comment: Submitted to ApJ. Main text:16 pages with 11 figures

We introduce a model of randomly connected neural populations and study its dynamics by means of the dynamical mean-field theory and simulations. Our analysis uncovers a rich phase diagram, featuring high- and low-dimensional chaotic phases, separated by a crossover region characterized by low values of the maximal Lyapunov exponent and participation ratio dimension, but with high and rapidly changing values of the Lyapunov dimension. Counterintuitively, chaos can be attenuated by either adding noise to strongly modular connectivity or by introducing modularity into random connectivity. Extending the model to include a multilevel, hierarchical connectivity reveals that a loose balance between activities across levels drives the system towards the edge of chaos.

Recent personalization methods for diffusion models, such as Dreambooth, allow fine-tuning pre-trained models to generate new concepts. However, applying these techniques across multiple tasks in order to include, e.g., several new objects or styles, leads to mutual interference between their adapters. While recent studies attempt to mitigate this issue by combining trained adapters across tasks after fine-tuning, we adopt a more rigorous regime and investigate the personalization of large diffusion models under a continual learning scenario, where such interference leads to catastrophic forgetting of previous knowledge. To that end, we evaluate the na\"ive continual fine-tuning of customized models and compare this approach with three methods for consecutive adapters' training: sequentially merging new adapters, merging orthogonally initialized adapters, and updating only relevant parameters according to the task. In our experiments, we show that the proposed approaches mitigate forgetting when compared to the na\"ive approach.

The paper concerns inference in the ill-conditioned functional response model, which is a part of functional data analysis. In this regression model, the functional response is modeled using several independent scalar variables. To verify linear hypotheses, we develop new test statistics by aggregating pointwise statistics using either integral or supremum. The new tests are scale-invariant, in contrast to the existing ones. To construct tests, we use different bootstrap methods. The performance of the new tests is compared with the performance of known tests through a simulation study and an application to a real data example.

Sulfur is depleted with respect to its cosmic standard abundance in dense star-forming regions. It has been suggested that this depletion is caused by the freeze-out of sulfur on interstellar dust grains, but the observed abundances and upper limits of sulfur-bearing ices remain too low to account for all of the missing sulfur. Toward the same environments, a strong absorption feature at 6.85 $\mu$m is observed, but its long-standing assignment to the NH4+ cation remains tentative. We investigate the plausibility of NH4SH salt serving as a sulfur reservoir and a carrier of the 6.85 $\mu$m band in interstellar ices by characterizing its IR signatures and apparent band strengths in water-rich laboratory ice mixtures and using this laboratory data to constrain NH4SH abundances in observations of 4 protostars and 2 cold dense clouds. The observed 6.85 $\mu$m feature is fit well with the laboratory NH4SH:H2O ice spectra. NH4+ column densities obtained from the 6.85 $\mu$m band range from 8-23% with respect to H2O toward the sample of protostars and dense clouds. The redshift of the 6.85 $\mu$m feature correlates with higher abundances of NH4+ with respect to H2O in both the laboratory data presented here and observational data of dense clouds and protostars. The apparent band strength of the SH- feature is likely too low for the feature to be detectable in the spectrally busy 3.9 $\mu$m region, but the 5.3 $\mu$m NH4+ $\nu_{4}$ + SH- R combination mode may be an alternative means of detection. Its tentative assignment adds to mounting evidence supporting the presence of NH4+ salts in ices and is the first tentative observation of the SH- anion toward interstellar ices. If the majority ($\gtrsim$80-85%) of the NH4+ cations quantified toward the investigated sources in this work are bound to SH- anions, then NH4SH salts could account for up to 17-18% of their sulfur budgets., Comment: Accepted for publication in A&A. 20 pages, 14 figures, and 7 tables in the main text; 15 pages, 17 figures, and 10 tables in the appendix

This paper presents preliminary results from the NA61/SHINE experiment on $\phi$ meson production in central Ar+Sc collisions at beam momenta of 150$A$, 75$A$, and 40$A$ GeV/$c$ (corresponding to $\sqrt{s_{NN}}$ = 16.8, 11.9, and 8.8 GeV, respectively). These results include double differential distributions in rapidity ($y$) and transverse momentum ($p_T$), as well as $p_T$-integrated rapidity distributions and total $\phi$ yields. Additionally, the widths of the rapidity distributions of $\phi$ and $\phi/\pi$ yield ratios are compared to those from Pb+Pb and \pp reactions. Notably, this work represents the first-ever measurements of $\phi$ production in a mid-sized system at SPS energies., Comment: Submitted to Proceedings from The 21st International Conference on Strangeness in Quark Matter, SQM 2024, 3-7 Jun 2024, Strasbourg, France

Quantum sensing is one of the most promising applications for quantum technologies. However, reaching the ultimate sensitivities enabled by the laws of quantum mechanics can be a challenging task in realistic scenarios where noise is present. While several strategies have been proposed to deal with the detrimental effects of noise, these come at the cost of an extra shot budget. Given that shots are a precious resource for sensing -- as infinite measurements could lead to infinite precision -- care must be taken to truly guarantee that any shot not being used for sensing is actually leading to some metrological improvement. In this work, we study whether investing shots in error-mitigation, inference techniques, or combinations thereof, can improve the sensitivity of a noisy quantum sensor on a (shot) budget. We present a detailed bias-variance error analysis for various sensing protocols. Our results show that the costs of zero-noise extrapolation techniques outweigh their benefits. We also find that pre-characterizing a quantum sensor via inference techniques leads to the best performance, under the assumption that the sensor is sufficiently stable., Comment: 17+18 pages, 8+2 figures, 1+1 tables

We work in the Baire space $\mathbb{Z}^\omega$ equipped with the coordinate-wise addition $+$. Consider a $\sigma-$ideal $\mathcal{I}$ and a family $\mathbb{T}$ of some kind of perfect trees. We are interested in results of the form: for every $A\in \mathcal{I}$ and a tree $T\in\mathbb{T}$ there exists $T'\in \mathbb{T}, T'\subseteq T$ such that $A+\underbrace{[T']+[T']+\dots +[T']}_{\text{n--times}}\in \mathcal{I}$ for each $n\in\omega$. Explored tree types include perfect trees, uniformly perfect trees, Miller trees, Laver trees and $\omega-$Silver trees. The latter kind of trees is an analogue of Silver trees from the Cantor space. Besides the standard $\sigma$-ideal $\mathcal{M}$ of meager sets, we also analyze $\mathcal{M}_-$ and fake null sets $\mathcal{N}$. The latter two are born out of the characterizations of their respective analogues in the Cantor space. The key ingredient in proofs were combinatorial characterizations of these ideals in the Baire space.

Dynamic quantum simulation is a leading application for achieving quantum advantage. However, high circuit depths remain a limiting factor on near-term quantum hardware. We present a compilation algorithm based on Matrix Product Operators for generating compressed circuits enabling real-time simulation on digital quantum computers, that for a given depth are more accurate than all Trotterizations of the same depth. By the efficient use of environment tensors, the algorithm is scalable in depth beyond prior work, and we present circuit compilations of up to 64 layers of $SU(4)$ gates. Surpassing only 1D circuits, our approach can flexibly target a particular quasi-2D gate topology. We demonstrate this by compiling a 52-qubit 2D Transverse-Field Ising propagator onto the IBM Heavy-Hex topology. For all circuit depths and widths tested, we produce circuits with smaller errors than all equivalent depth Trotter unitaries, corresponding to reductions in error by up to 4 orders of magnitude and circuit depth compressions with a factor of over 6., Comment: 9+1 pages, 6 figures

Quantum dynamics compilation is an important task for improving quantum simulation efficiency: It aims to synthesize multi-qubit target dynamics into a circuit consisting of as few elementary gates as possible. Compared to deterministic methods such as Trotterization, variational quantum compilation (VQC) methods employ variational optimization to reduce gate costs while maintaining high accuracy. In this work, we explore the potential of a VQC scheme by making use of out-of-distribution generalization results in quantum machine learning (QML): By learning the action of a given many-body dynamics on a small data set of product states, we can obtain a unitary circuit that generalizes to highly entangled states such as the Haar random states. The efficiency in training allows us to use tensor network methods to compress such time-evolved product states by exploiting their low entanglement features. Our approach exceeds state-of-the-art compilation results in both system size and accuracy in one dimension ($1$D). For the first time, we extend VQC to systems on two-dimensional (2D) strips with a quasi-1D treatment, demonstrating a significant resource advantage over standard Trotterization methods, highlighting the method's promise for advancing quantum simulation tasks on near-term quantum processors.

Motivated by problems of statistical language modeling, we consider probability measures on infinite sequences over two countable alphabets of a different cardinality, such as letters and words. We introduce an invertible mapping between such measures, called the normalized transport, that preserves both stationarity and ergodicity. The normalized transport applies so called self-avoiding codes that generalize comma-separated codes and specialize bijective stationary codes. The normalized transport is also connected to the usual measure transport via underlying asymptotically mean stationary measures. It preserves the ergodic decomposition. The normalized transport and self-avoiding codes arise, for instance, in the problem of successive recurrence times. In particular, we show that successive recurrence times are ergodic for an ergodic measure, which strengthens a result by Chen Moy from 1959., Comment: 19 pages, no figures

The dynamics of disordered two-dimensional systems is much less understood than the dynamics of disordered chains, mainly due to the lack of appropriate numerical methods. We demonstrate that a single-trajectory version of the fermionic truncated Wigner approximation (fTWA) gives unexpectedly accurate results for the dynamics of one-dimensional (1D) systems with moderate or strong disorder. Additionally, the computational complexity of calculations carried out within this approximation is small enough to enable studies of two-dimensional (2D) systems larger than standard fTWA. Using this method, we analyze the dynamics of interacting spinless fermions propagating on disordered 1D and 2D lattices. We find for both spatial dimensions that the imbalance exhibits a universal dependence on the rescaled time $t/\xi_W$, where in 2D the time-scale $\xi_W$ follows a stretched-exponential dependence on disorder strength., Comment: 11 pages, 8 figures

Understanding the decisions made by image classification networks is a critical area of research in deep learning. This task is traditionally divided into two distinct approaches: post-hoc methods and intrinsic methods. Post-hoc methods, such as GradCam, aim to interpret the decisions of pre-trained models by identifying regions of the image where the network focuses its attention. However, these methods provide only a high-level overview, making it difficult to fully understand the network's decision-making process. Conversely, intrinsic methods, like prototypical parts models, offer a more detailed understanding of network predictions but are constrained by specific architectures, training methods, and datasets. In this paper, we introduce InfoDisent, a hybrid model that combines the advantages of both approaches. By utilizing an information bottleneck, InfoDisent disentangles the information in the final layer of a pre-trained deep network, enabling the breakdown of classification decisions into basic, understandable atomic components. Unlike standard prototypical parts approaches, InfoDisent can interpret the decisions of pre-trained classification networks and be used for making classification decisions, similar to intrinsic models. We validate the effectiveness of InfoDisent on benchmark datasets such as ImageNet, CUB-200-2011, Stanford Cars, and Stanford Dogs for both convolutional and transformer backbones.

Accurate reconstruction of ambient temperature at death scenes is crucial for estimating the postmortem interval (PMI) in forensic science. Typically, this is done by correcting weather station temperatures using measurements from the scene, often through linear regression. While recent attempts to use alternative algorithms like GAM have improved accuracy, they usually require additional variables such as humidity, making them impractical. This study presents two methods for accurate temperature reconstruction using only temperature data. The first, a concurrent regression model, is known in mathematics and is applied here for mid-term reconstructions (several days of measurements). The second, a new method based on Fourier expansion, is designed for short-term reconstructions (only a few hours of measurements). Both models were tested in quasi-indoor conditions, using data from six different environments. The concurrent regression model provided nearly perfect reconstructions for periods longer than six days, while the short-term model achieved similar accuracy after just 4-5 hours of measurements. These findings demonstrate that reliable temperature corrections for PMI estimation can be made with significantly reduced measurement periods, enhancing the practicality of the method in forensic applications., Comment: 12 pages, 7 figures, Original Research Papers, submitted to "Science & Justice"