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Concept-based XAI (C-XAI) approaches to explaining neural vision models are a promising field of research, since explanations that refer to concepts (i.e., semantically meaningful parts in an image) are intuitive to understand and go beyond saliency-based techniques that only reveal relevant regions. Given the remarkable progress in this field in recent years, it is time for the community to take a critical look at the advances and trends. Consequently, this paper reviews C-XAI methods to identify interesting and underexplored areas and proposes future research directions. To this end, we consider three main directions: the choice of concepts to explain, the choice of concept representation, and how we can control concepts. For the latter, we propose techniques and draw inspiration from the field of knowledge representation and learning, showing how this could enrich future C-XAI research.

We initiate the study of tree structures in the context of scenario-based robust optimization. Specifically, we study Binary Search Trees (BSTs) and Huffman coding, two fundamental techniques for efficiently managing and encoding data based on a known set of frequencies of keys. Given $k$ different scenarios, each defined by a distinct frequency distribution over the keys, our objective is to compute a single tree of best-possible performance, relative to any scenario. We consider, as performance metrics, the competitive ratio, which compares multiplicatively the cost of the solution to the tree of least cost among all scenarios, as well as the regret, which induces a similar, but additive comparison. For BSTs, we show that the problem is NP-hard across both metrics. We also show how to obtain a tree of competitive ratio $\lceil \log_2(k+1) \rceil$, and we prove that this ratio is optimal. For Huffman Trees, we show that the problem is, likewise, NP-hard across both metrics; we also give an algorithm of regret $\lceil \log_2 k \rceil$, which we show is near-optimal, by proving a lower bound of $\lfloor \log_2 k \rfloor$. Last, we give a polynomial-time algorithm for computing Pareto-optimal BSTs with respect to their regret, assuming scenarios defined by uniform distributions over the keys. This setting captures, in particular, the first study of fairness in the context of data structures. We provide an experimental evaluation of all algorithms. To this end, we also provide mixed integer linear program formulation for computing optimal trees.

High-strength composite hydrogels cellulose-polyacrylamide were synthesized by free-radical polymerization of acrylamide conducted inside the previously formed physical network of regenerated plant cellulose. Partial hydrolysis of the amide groups of these hydrogels yielded their ionic forms with a degree of hydrolysis of 0.1 and 0.25. The cylindrical hydrogel samples of three compositions were implanted in the preformed osteochondral defects of the rabbit's femoral knee joints. No signs of migration or disintegration of the tested implants were revealed in the course of in vivo tests as long as 90 and 120 days after the implantation. The mechanical behavior of both the virgin hydrogels-implants and the implants extracted from the joints after in vivo experiments was studied in detail. The morphology and chemical composition of the extracted implants were studied by SEM combined with the EDX method. The results obtained were shown that the mechanical characteristics of hydrogel implants remained practically unchanged after in vivo tests. The extracted implants, as well as the initial hydrogels, endured cyclic compression loading at the amplitude up to 50 %. Compression stresses up to 3-10 MPa were recorded in these tests, which is close to the data obtained by several authors for natural articular cartilages in the same conditions of loading. The principal differences in the chemical composition and morphology of the implant area adjacent to the subchondral bone for non-ionic and ionic types of implants have been revealed. If for non-ionic types of implants in this area intensive mineralization with formation of calcium phosphates inside the polymeric hydrogel network is observed, the border area of ionic implants practically does not undergo mineralization., Comment: 39 pages, 19 figures, 8 tables

In the field of Image Quality Assessment (IQA), the adversarial robustness of the metrics poses a critical concern. This paper presents a comprehensive benchmarking study of various defense mechanisms in response to the rise in adversarial attacks on IQA. We systematically evaluate 25 defense strategies, including adversarial purification, adversarial training, and certified robustness methods. We applied 14 adversarial attack algorithms of various types in both non-adaptive and adaptive settings and tested these defenses against them. We analyze the differences between defenses and their applicability to IQA tasks, considering that they should preserve IQA scores and image quality. The proposed benchmark aims to guide future developments and accepts submissions of new methods, with the latest results available online: https://videoprocessing.ai/benchmarks/iqa-defenses.html.

We consider the remote state restoring and perfect transfer of the zero-order coherence matrix (PTZ) in a spin system governed by the XXZ-Hamiltonian conserving the excitation number. The restoring tool is represented by several nonzero Larmor frequencies in the Hamiltonian. To simplify the analysis we use two approximating models including either step-wise or pulse-type time-dependence of the Larmor frequencies. Restoring in spin chains with up to 20 nodes is studied. Studying PTZ, we consider the zigzag and rectangular configurations and optimize the transfer of the 0-order coherence matrix using geometrical parameters of the communication line as well as the special unitary transformation of the extended receiver. Overall observation is that XXZ-chains require longer time for state transfer than XX-chains, which is confirmed by the analytical study of the evolution under the nearest-neighbor approximation. We demonstrate the exponential increase of the state-transfer time with the spin chain length., Comment: 22 pages, 13 figures. arXiv admin note: text overlap with arXiv:2401.09569

The scaling of neural networks with increasing data and model sizes necessitates more efficient deep learning algorithms. This paper addresses the memory footprint challenge in neural network training by proposing a modification to the handling of activation tensors in pointwise nonlinearity layers. Traditionally, these layers save the entire input tensor for the backward pass, leading to substantial memory use. Our method involves saving the output tensor instead, reducing the memory required when the subsequent layer also saves its input tensor. This approach is particularly beneficial for transformer-based architectures like GPT, BERT, Mistral, and Llama. Application of our method involves taken an inverse function of nonlinearity. To the best of our knowledge, that can not be done analitically and instead we buid an accurate approximations using simpler functions. Experimental results confirm that our method significantly reduces memory usage without affecting training accuracy. The implementation is available at https://github.com/PgLoLo/optiacts.

The friction force is derived using fractional calculus by considering the non-uniform flow of time in dissipative processes. The approach incorporates inhomogeneous velocity without unphysical approximations, resulting in a Lagrangian where the order of fractional derivatives measures time intervals. The fractional term in the Lagrangian provides correct Euler-Lagrange, and ultimately, the Hamilton equations, and vanishes during energy change measurements, like a ghost.

In the present work, an approach to the moment closure problem on the basis of orthogonal polynomials derived from Gram matrices is proposed. Its properties are studied in the context of the moment closure problem arising in gas kinetic theory, for which the proposed approach is proven to have multiple attractive mathematical properties. Numerical studies are carried out for model gas particle distributions and the approach is compared to other moment closure methods, such as Grad's closure and the maximum-entropy method. The proposed ``Gramian'' closure is shown to provide very accurate results for a wide range of distribution functions.

Ensuring the quality of black-box Deep Neural Networks (DNNs) has become ever more significant, especially in safety-critical domains such as automated driving. While global concept encodings generally enable a user to test a model for a specific concept, linking global concept encodings to the local processing of single network inputs reveals their strengths and limitations. Our proposed framework global-to-local Concept Attribution (glCA) uses approaches from local (why a specific prediction originates) and global (how a model works generally) eXplainable Artificial Intelligence (xAI) to test DNNs for a predefined semantical concept locally. The approach allows for conditioning local, post-hoc explanations on predefined semantic concepts encoded as linear directions in the model's latent space. Pixel-exact scoring concerning the global concept usage assists the tester in further understanding the model processing of single data points for the selected concept. Our approach has the advantage of fully covering the model-internal encoding of the semantic concept and allowing the localization of relevant concept-related information. The results show major differences in the local perception and usage of individual global concept encodings and demand for further investigations regarding obtaining thorough semantic concept encodings.

We present a concept for an indirect geometry crystal time-of-flight spectrometer, which we propose for a source similar to the FRM-II reactor in Garching. Recently, crystal analyzer spectrometers at modern spallation sources have been proposed and are under construction. The secondary spectrometers of these instruments are evolutions of the flat cone multi-analyzer for three-axis spectrometers (TAS). The instruments will provide exceptional reciprocal space coverage and intensity to map out the excitation landscape in novel materials. We will discuss the benefits of combining a time-of-flight primary spectrometer with a large crystal analyzer spectrometer at a continuous neutron source. The dynamical range can be very flexibly matched to the requirements of the experiment without sacrificing the neutron intensity. At the same time, the chopper system allows a quasi-continuous variation of the initial energy resolution. The neutron delivery system of the proposed instrument is based on the novel nested mirror optics, which images neutrons from the position of the pulse cutting chopper representing a bright virtual source onto the sample. The spot size of less than 1 cm x 1 cm at the virtual source allows the realization of very short neutron pulses by the choppers, while the small and well-defined spot size at the sample position provides an excellent energy resolution of the secondary spectrometer.

Electrical Impedance Tomography (EIT) is a non-invasive imaging modality that has earned significant attention for its potential in real-time monitoring of various physiological parameters. Despite its promise, the sensitivity and resolution of EIT remain areas of active research. This article presents a new way to analyse the sensitivity of EIT systems using the Cramer-Rao Lower Bound (CRLB). This statistical tool provides a theoretical lower bound on the variance of unbiased estimators. To simulate the EIT full cycle, we compared two forward models: standard Dirichlet-to-Neumann (DtN) and restricted DtN. By taking the CRLB over modelled with Finite Elements Method (FEM) 2D circular area with various conductivity patterns, we showed the influence of electrode configuration on each basic FEM element sensitivity. Also, the sensitivity on small perturbations for different conductivity patterns was offered. This article aims to bridge the gap between the research of widely used hardware implementations standard forward DtN model and theoretically approved restricted DtN. We conclude with a discussion on the motivation behind this research and the objectives our work introduces for the inverse restricted DtN model in practice., Comment: 12 pages, 7 figures

The expression for the higher temperature dependence of the mean squared displacement in proteins is obtained. The quantum multi-well model explains the dynamic transitions of the proteins and minimizes the amount of parameters to a single one leading to the few-state harmonic system at low-temperatures, and, thus, justifying the possibility of using proteins as atom traps to control qubits at a bit higher temperatures.

A framework for numerical evaluation of entropy-conservative volume fluxes in gas flows with internal energies is developed, for use with high-order discretization methods. The novelty of the approach lies in the ability to use arbitrary expressions for the internal degrees of freedom of the constituent gas species. The developed approach is implemented in an open-source discontinuous Galerkin code for solving hyperbolic equations. Numerical simulations are carried out for several model 2-D flows and the results are compared to those obtained with the finite volume-based solver DLR TAU.

Adversarial attacks (AAs) pose a significant threat to the reliability and robustness of deep neural networks. While the impact of these attacks on model predictions has been extensively studied, their effect on the learned representations and concepts within these models remains largely unexplored. In this work, we perform an in-depth analysis of the influence of AAs on the concepts learned by convolutional neural networks (CNNs) using eXplainable artificial intelligence (XAI) techniques. Through an extensive set of experiments across various network architectures and targeted AA techniques, we unveil several key findings. First, AAs induce substantial alterations in the concept composition within the feature space, introducing new concepts or modifying existing ones. Second, the adversarial perturbation itself can be linearly decomposed into a set of latent vector components, with a subset of these being responsible for the attack's success. Notably, we discover that these components are target-specific, i.e., are similar for a given target class throughout different AA techniques and starting classes. Our findings provide valuable insights into the nature of AAs and their impact on learned representations, paving the way for the development of more robust and interpretable deep learning models, as well as effective defenses against adversarial threats.

Aims. The X-ray luminous and radio-loud AGN SRGE J170245.3+130104 discovered at z $\sim$ 5.5 provides unique chances to probe the SMBH growth and evolution with powerful jets in the early Universe. Methods. We present 1.35 - 5.1 GHz Very Long Baseline Array (VLBA) results on the radio continuum emission and spectrum analysis for this quasar in a low flux density state. Results. This source is unresolved at three frequencies with the total flux densities of 8.35$\pm$0.09 mJy beam-1, 7.47$\pm$0.08 mJy beam-1, and 6.57$\pm$0.02 mJy beam-1 at 1.73 GHz, 2.26 GHz, and 4.87 GHz, respectively. Meanwhile, the brightness temperature is higher than 109 K. Conclusions. Compared with previous radio observations with arcsec-scale resolution, nearly all the radio emission from this source concentrates in the very central milli-arcsecond (mas) scale area. We confirm this source is a bright blazar at z > 5. This young AGN provide us the great chances to understand the first generation of strong jets in the early Universe., Comment: 5 pages, 2 figures, Accepted for publication in Astronomy & Astrophysics

To a subshift over a finite alphabet, one can naturally associate an infinite family of finite graphs, called its Rauzy graphs. We show that for a subshift of subexponential complexity the Rauzy graphs converge to the line $\mathbf{Z}$ in the sense of Benjamini-Schramm convergence if and only if its complexity function $p(n)$ is unbounded and satisfies $\lim_n\frac{p(n+1)}{p(n)} = 1$. We then apply this criterion to many examples of well-studied dynamical systems. If the subshift is moreover uniquely ergodic then we show that the limit of labelled Rauzy graphs if it exists can be identified with the unique invariant measure. In addition we consider an example of a non uniquely ergodic system recently studied by Cassaigne and Kabor\'e and identify a continuum of invariant measures with subsequential limits of labelled Rauzy graphs., Comment: V2 Theorem 1.1 has been improved. We added two new properties equivalent to the convergence of Rauzy graphs: convergence of the empirical spectral measures and convergence of the empirical spectral measures to a specified measure (that has density $\frac{1}{\pi\sqrt{4-x^2}}dx$ with respect to the Lebesgue measure on~$[-2, 2]$)

Numerous emerging deep-learning techniques have had a substantial impact on computer graphics. Among the most promising breakthroughs are the recent rise of Neural Radiance Fields (NeRFs) and Gaussian Splatting (GS). NeRFs encode the object's shape and color in neural network weights using a handful of images with known camera positions to generate novel views. In contrast, GS provides accelerated training and inference without a decrease in rendering quality by encoding the object's characteristics in a collection of Gaussian distributions. These two techniques have found many use cases in spatial computing and other domains. On the other hand, the emergence of deepfake methods has sparked considerable controversy. Such techniques can have a form of artificial intelligence-generated videos that closely mimic authentic footage. Using generative models, they can modify facial features, enabling the creation of altered identities or facial expressions that exhibit a remarkably realistic appearance to a real person. Despite these controversies, deepfake can offer a next-generation solution for avatar creation and gaming when of desirable quality. To that end, we show how to combine all these emerging technologies to obtain a more plausible outcome. Our ImplicitDeepfake1 uses the classical deepfake algorithm to modify all training images separately and then train NeRF and GS on modified faces. Such relatively simple strategies can produce plausible 3D deepfake-based avatars.

Consider a subset of positive integers $S$. In this paper, we reduce the upper bound on the length of a minimum program that enumerates $S$ in terms of the probability of $S$ being enumerated by a random program. So far, the best-known upper bound was given by Solovay. Solovay proved that the minimum length of a program enumerating $S$ is bounded by $3$ times minus binary logarithm of the probability that a random program enumerates $S$. Later, Vereshchagin showed that the constant can be improved from $3$ to $2$ for finite sets. By improving the method proposed by Solovay, we demonstrate that any bound for finite sets implies the same bound for infinite sets, modulo logarithmic factors. Thus, the constant can be replaced by $2$ for every set $S$ due to the result of Vereshchagin.

For debugging and verification of computer vision convolutional deep neural networks (CNNs) human inspection of the learned latent representations is imperative. Therefore, state-of-the-art eXplainable Artificial Intelligence (XAI) methods globally associate given natural language semantic concepts with representing vectors or regions in the CNN latent space supporting manual inspection. Yet, this approach comes with two major disadvantages: They are locally inaccurate when reconstructing a concept label and discard information about the distribution of concept instance representations. The latter, though, is of particular interest for debugging, like finding and understanding outliers, learned notions of sub-concepts, and concept confusion. Furthermore, current single-layer approaches neglect that information about a concept may be spread over the CNN depth. To overcome these shortcomings, we introduce the local-to-global Guided Concept Projection Vectors (GCPV) approach: It (1) generates local concept vectors that each precisely reconstruct a concept segmentation label, and then (2) generalizes these to global concept and even sub-concept vectors by means of hiearchical clustering. Our experiments on object detectors demonstrate improved performance compared to the state-of-the-art, the benefit of multi-layer concept vectors, and robustness against low-quality concept segmentation labels. Finally, we demonstrate that GCPVs can be applied to find root causes for confusion of concepts like bus and truck, and reveal interesting concept-level outliers. Thus, GCPVs pose a promising step towards interpretable model debugging and informed data improvement.

This paper is devoted to the construction of stochastic flows of measurable mappings in a locally compact separable metric space (M, $\rho$). We propose a new construction that produces strong measurable continuous modifications for certain stochastic flows of measurable mappings in metric graphs.

The present study focuses on experimental investigations of spin current across the interface of an iridate/manganite heterostructure (SrIrO3/La0.7Sr0.3MnO3) consisting of oxide epitaxial films with nanometer thickness. Pure spin current is induced by microwave irradiation in the GHz frequency band, specifically under conditions of ferromagnetic resonance. The detection of spin current is achieved through the inverse spin-Hall effect, which measures the charge current arising on the electrically conductive SrIrO3 film with strong spin-orbit interaction. To quantify the efficiency of spin current conversion to charge current, the angular dependences of spin magnetoresistance of the iridate/manganite interface are measured, thereby determining the spin- Hall angle., Comment: 13 pages, 7 figures

We present the results of our search for highly variable active galactic nuclei (AGNs) the X-ray flux from which changed by more than an order of magnitude during the SRG/eROSITA all-sky survey. Using the eROSITA data obtained in the period from December 2019 to February 2022, we have found 1325 sources the X-ray flux from which in the 0.3-2.3 keV energy band changed by more than a factor of 10 at a confidence level of at least 99.73 %. Of them, 635 objects have been classified as AGNs or AGN candidates. We describe the procedure of searching for highly variable sources and the selection of extragalactic objects among them and describe the statistical properties of the produced catalog. We provide a catalog of 49 sources for which a statistically significant flux in their low state was detected. For the latter we provide their light curves and X-ray spectra and discuss in detail the most interesting of them., Comment: 9 figures, 2 tables

Banks routinely use neural networks to make decisions. While these models offer higher accuracy, they are susceptible to adversarial attacks, a risk often overlooked in the context of event sequences, particularly sequences of financial transactions, as most works consider computer vision and NLP modalities. We propose a thorough approach to studying these risks: a novel type of competition that allows a realistic and detailed investigation of problems in financial transaction data. The participants directly oppose each other, proposing attacks and defenses -- so they are examined in close-to-real-life conditions. The paper outlines our unique competition structure with direct opposition of participants, presents results for several different top submissions, and analyzes the competition results. We also introduce a new open dataset featuring financial transactions with credit default labels, enhancing the scope for practical research and development.

We introduce and study a derived version $\mathbf L\mathrm{Bin}$ of the binomial monad on the unbounded derived category $\mathscr D(\mathbb Z)$ of $\mathbb Z$-modules. This monad acts naturally on singular cohomology of any topological space, and does so more efficiently than the more classical monad $\mathbf L\mathrm{Sym}_{\mathbb Z}$. We compute all free derived binomial rings on abelian groups concentrated in a single degree, in particular identifying $C_*^{\mathrm{sing}}(K(\mathbb Z,n),\mathbb Z)$ with $\mathbf L\mathrm{Bin}(\mathbb Z[-n])$ via a different argument than in works of To\"en and Horel. Using this we show that the singular cohomology functor $C_*^{\mathrm{sing}}(-,\mathbb Z)$ induces a fully faithful embedding of the category of connected nilpotent spaces of finite type to the category of derived binomial rings. We then also define a version $\mathbf L \mathcal Bin_X$ of the derived binomial monad on the $\infty$-category of $\mathscr D(\mathbb Z)$-valued sheaves on a sufficiently nice topological space $X$. As an application we give a closed formula for the singular cohomology of an fs log complex analytic space $(X,\mathcal M)$: namely we identify the pushforward $R\pi_*\underline{\mathbb Z}$ for the corresponding Kato-Nakayama space $\pi\colon X^{\mathrm{log}}\rightarrow X$ with the free coaugmented derived binomial ring on the 2-term exponential complex $\mathcal O_X\rightarrow \mathcal M^{\mathrm{gr}}$. This gives an extension of Steenbrink's formula and its generalization by the second author to $\mathbb Z$-coefficients., Comment: 61 pages, comments welcome

The Debye-Falkenhagen differential equation is commonly used as a mean-field macroscopic model for describing electrochemical ionic drift and diffusion in dilute binary electrolytes when subjected to a suddenly applied potential smaller than the thermal voltage. However, the ionic transport in most electrochemical systems, such as electrochemical capacitors, permeation through membranes, biosensors and capacitive desalination, the electrolytic medium is interfaced with porous, disordered, and fractal materials which makes the modeling of electrodiffusive transport with the simple planar electrode theory limited. Here we study a possible generalization of the traditional drift-diffusion equation of Debye and Falkenhagen by incorporating both fractional time and space derivatives for the charge density. The nonlocal (global) fractional time derivative takes into account the past dynamics of the variable such as charge trapping effects and thus subdiffusive transport, while the fractional space derivative allows to simulate superdiffusive transport., Comment: 12 pages, 6 figures

Purpose: Machine learning models can only be reliably evaluated if training, validation, and test data splits are representative and not affected by the absence of classes of interest. Surgical workflow and instrument recognition tasks are complicated in this manner, because of heavy data imbalances resulting from different lengths of phases and their erratic occurrences. Furthermore, the issue becomes difficult as sub-properties that help define phases, like instrument (co-)occurrence, are usually not considered when defining the split. We argue that such sub-properties must be equally considered. Methods: This work presents a publicly available data visualization tool that enables interactive exploration of dataset splits for surgical phase and instrument recognition. It focuses on the visualization of the occurrence of phases, phase transitions, instruments, and instrument combinations across sets. Particularly, it facilitates the assessment and identification of sub-optimal dataset splits. Results: We performed an analysis of common Cholec80 dataset splits using the proposed application and were able to uncover phase transitions and combinations of instruments that were not represented in one of the sets. Additionally, we outlined possible improvements to the splits. A user study with ten participants demonstrated the ability of participants to solve a selection of data exploration tasks using the proposed application. Conclusion: In highly unbalanced class distributions, special care should be taken with respect to the selection of an appropriate dataset split. Our interactive data visualization tool presents a promising approach for the assessment of dataset splits for surgical phase and instrument recognition. Evaluation results show that it can enhance the development of machine learning models. The application is available at https://cardio-ai.github.io/endovis-ml/ ., Comment: Accepted at IPCAI 2023 as long abstract; Submitted to IJCARS as original article; 21 pages, 10 figures, 3 tables

We present the results of our identification of 14 X-ray sources detected in the eastern Galactic sky ($010^{22}$ cm$^{-2}$ at a 90% confidence level, with one of them being probably heavily obscured ($N_{\rm H}>5\times 10^{22}$ cm$^{-2}$ with 90% confidence). This paper continues our series of publications on the identification of hard X-ray sources detected during the all-sky survey with the SRG orbital X-ray observatory., Comment: Published in Astronomy Letters, 2023, Vol. 49, No. 2. arXiv admin note: text overlap with arXiv:2208.10963

Large-scale transformer models have shown remarkable performance in language modelling tasks. However, such models feature billions of parameters, leading to difficulties in their deployment and prohibitive training costs from scratch. To reduce the number of the parameters in the GPT-2 architecture, we replace the matrices of fully-connected layers with the corresponding Tensor Train Matrix~(TTM) structure. Finally, we customize forward and backward operations through the TTM-based layer for simplicity and the stableness of further training. % The resulting GPT-2-based model stores up to 40% fewer parameters, showing the perplexity comparable to the original model. On the downstream tasks, including language understanding and text summarization, the model performs similarly to the original GPT-2 model. The proposed tensorized layers could be used to efficiently pre-training other Transformer models.

We examine a particular realization of derivative-free method as implemented on tensor train based optimization to the variational quantum eigensolver. As an example, we consider parametrized quantum circuits composed of a low-depth hardware-efficient ansatz and Hamiltonian variational ansatz for addressing the ground state of the transverse field Ising model. We further make a comparison with gradient-based optimization techniques and discuss on the advantage of using tensor train based optimization, especially in the presence of noise., Comment: 7 pages, 5 figures

The quantum-field renormalization group method is one of the most efficient and powerful tools for studying critical and scaling phenomena in interacting many-particle systems. The multiloop Feynman diagrams underpin the specific implementation of the renormalization group program. In recent years, multiloop computation has had a significant breakthrough in both static and dynamic models of critical behavior. In the paper, we focus on the state-of-the-art computational techniques for critical dynamic diagrams and the results obtained with their help. The generic nature of the evaluated physical observables in a wide class of field models is manifested in the asymptotic character of perturbation expansions. Thus, the Borel resummation of series is required to process multiloop results. Such a procedure also enables one to take high-order contributions into consideration properly. The paper outlines the resummation framework in dynamic models and the circumstances in which it can be useful. An important resummation criterion is the properties of the higher-order asymptotics of the perturbation theory. In static theories, these properties are determined by the method of instanton analysis. A similar approach is applicable in critical dynamics models. We describe the calculation of these asymptotics in dynamical models and present the results of the corresponding resummation.

This is the full version of a paper submitted to the Computability in Europe (CiE 2023) conference, with all proofs omitted there. In 2012 P. D. Azar and S. Micali introduced a new model of interactive proofs, called "Rational Interactive Proofs". In this model the prover is neither honest nor malicious, but rational in terms of maximizing his expected reward. In this article we explore the connection of this area with classic complexity results. In the first part of this article we revise the ties between the counting hierarchy and the hierarchy of constant-round rational proofs. We prove that a polynomial-time machine with oracle access to DRMA[k] decides exactly languages in DRMA[k], a coincidence unknown for levels of the counting hierarchy. In the second part we study communication complexity of single-round rational proofs. We show that the class defined by logarithmic-communication single-round rational proofs coincides with PP. We also show that single-round rational protocols that treat problems in Parity-P as black-box samplers of a random variable require at least a linear number of bits of communication.

Safety-critical applications require transparency in artificial intelligence (AI) components, but widely used convolutional neural networks (CNNs) widely used for perception tasks lack inherent interpretability. Hence, insights into what CNNs have learned are primarily based on performance metrics, because these allow, e.g., for cross-architecture CNN comparison. However, these neglect how knowledge is stored inside. To tackle this yet unsolved problem, our work proposes two methods for estimating the layer-wise similarity between semantic information inside CNN latent spaces. These allow insights into both the flow and likeness of semantic information within CNN layers, and into the degree of their similarity between different network architectures. As a basis, we use two renowned explainable artificial intelligence (XAI) techniques, which are used to obtain concept activation vectors, i.e., global vector representations in the latent space. These are compared with respect to their activation on test inputs. When applied to three diverse object detectors and two datasets, our methods reveal that (1) similar semantic concepts are learned regardless of the CNN architecture, and (2) similar concepts emerge in similar relative layer depth, independent of the total number of layers. Finally, our approach poses a promising step towards semantic model comparability and comprehension of how different CNNs process semantic information.

Analysis of how semantic concepts are represented within Convolutional Neural Networks (CNNs) is a widely used approach in Explainable Artificial Intelligence (XAI) for interpreting CNNs. A motivation is the need for transparency in safety-critical AI-based systems, as mandated in various domains like automated driving. However, to use the concept representations for safety-relevant purposes, like inspection or error retrieval, these must be of high quality and, in particular, stable. This paper focuses on two stability goals when working with concept representations in computer vision CNNs: stability of concept retrieval and of concept attribution. The guiding use-case is a post-hoc explainability framework for object detection (OD) CNNs, towards which existing concept analysis (CA) methods are successfully adapted. To address concept retrieval stability, we propose a novel metric that considers both concept separation and consistency, and is agnostic to layer and concept representation dimensionality. We then investigate impacts of concept abstraction level, number of concept training samples, CNN size, and concept representation dimensionality on stability. For concept attribution stability we explore the effect of gradient instability on gradient-based explainability methods. The results on various CNNs for classification and object detection yield the main findings that (1) the stability of concept retrieval can be enhanced through dimensionality reduction via data aggregation, and (2) in shallow layers where gradient instability is more pronounced, gradient smoothing techniques are advised. Finally, our approach provides valuable insights into selecting the appropriate layer and concept representation dimensionality, paving the way towards CA in safety-critical XAI applications.