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We propose a meta-learning method for semi-supervised learning that learns from multiple tasks with heterogeneous attribute spaces. The existing semi-supervised meta-learning methods assume that all tasks share the same attribute space, which prevents us from learning with a wide variety of tasks. With the proposed method, the expected test performance on tasks with a small amount of labeled data is improved with unlabeled data as well as data in various tasks, where the attribute spaces are different among tasks. The proposed method embeds labeled and unlabeled data simultaneously in a task-specific space using a neural network, and the unlabeled data's labels are estimated by adapting classification or regression models in the embedding space. For the neural network, we develop variable-feature self-attention layers, which enable us to find embeddings of data with different attribute spaces with a single neural network by considering interactions among examples, attributes, and labels. Our experiments on classification and regression datasets with heterogeneous attribute spaces demonstrate that our proposed method outperforms the existing meta-learning and semi-supervised learning methods.

We say that a Kripke model is a GL-model if the accessibility relation $\prec$ is transitive and converse well-founded. We say that a Kripke model is a D-model if it is obtained by attaching infinitely many worlds $t_1, t_2, \ldots$, and $t_\omega$ to a world $t_0$ of a GL-model so that $t_0 \succ t_1 \succ t_2 \succ \cdots \succ t_\omega$. A non-normal modal logic D, which was studied by Beklemishev (1999), is characterized as follows. A formula $\varphi$ is a theorem of D if and only if $\varphi$ is true at $t_\omega$ in any D-model. D is an intermediate logic between the provability logics GL and S. A Hilbert-style proof system for D is known, but there has been no sequent calculus. In this paper, we establish two sequent calculi for D, and show the cut-elimination theorem. We also introduce new Hilbert-style systems for D by interpreting the sequent calculi. Moreover, we show that D-models can be defined using an arbitrary limit ordinal as well as $\omega$. Finally, we show a general result as follows. Let $X$ and $X^+$ be arbitrary modal logics. If the relationship between semantics of $X$ and semantics of $X^+$ is equal to that of GL and D, then $X^+$ can be axiomatized based on $X$ in the same way as the new axiomatization of D based on GL.

We propose a neural network-based meta-learning method to efficiently solve partial differential equation (PDE) problems. The proposed method is designed to meta-learn how to solve a wide variety of PDE problems, and uses the knowledge for solving newly given PDE problems. We encode a PDE problem into a problem representation using neural networks, where governing equations are represented by coefficients of a polynomial function of partial derivatives, and boundary conditions are represented by a set of point-condition pairs. We use the problem representation as an input of a neural network for predicting solutions, which enables us to efficiently predict problem-specific solutions by the forwarding process of the neural network without updating model parameters. To train our model, we minimize the expected error when adapted to a PDE problem based on the physics-informed neural network framework, by which we can evaluate the error even when solutions are unknown. We demonstrate that our proposed method outperforms existing methods in predicting solutions of PDE problems.

The quality of explanations for the predictions made by complex machine learning predictors is often measured using insertion and deletion metrics, which assess the faithfulness of the explanations, i.e., how accurately the explanations reflect the predictor's behavior. To improve the faithfulness, we propose insertion/deletion metric-aware explanation-based optimization (ID-ExpO), which optimizes differentiable predictors to improve both the insertion and deletion scores of the explanations while maintaining their predictive accuracy. Because the original insertion and deletion metrics are non-differentiable with respect to the explanations and directly unavailable for gradient-based optimization, we extend the metrics so that they are differentiable and use them to formalize insertion and deletion metric-based regularizers. Our experimental results on image and tabular datasets show that the deep neural network-based predictors that are fine-tuned using ID-ExpO enable popular post-hoc explainers to produce more faithful and easier-to-interpret explanations while maintaining high predictive accuracy. The code is available at https://github.com/yuyay/idexpo., Comment: Accepted to AISTATS 2024

The topology method is an algorithm for accurate estimation of instantaneous heartbeat intervals using millimeter-wave radar signals. In this model, feature points are extracted from the skin displacement waveforms generated by heartbeats and a complex number is assigned to each feature point. However, these numbers have been assigned empirically and without solid justification. This study used a simplified model of displacement waveforms to predict the optimal choice of the complex number assignments to feature points corresponding to inflection points, and the validity of these numbers was confirmed using analysis of a publicly available dataset., Comment: 5 pages, 3 figures. This work is going to be published in IEEE Sensors Letters

A concept of finite-dimensional dynamical system representation is introduced. Since the solution trajectory of partial differential equations are usually represented within infinite-dimensional dynamical systems, the proposed finite-dimensional representation provides decomposed snapshots of time evolution. Here we focus on analyzing the breather solutions of nonlinear Klein-Gordon equations, and such a solution is shown to form a geometrical object within finite-dimensional dynamical systems. In this paper, based on high-precision numerical scheme, we represent the breather solutions of the nonlinear Klein-Gordon equation as the time evolving trajectory on a finite-dimensional dynamical system. Consequently, with respect to the evolution of finite-dimensional dynamical systems, we confirm that the rotational motion around multiple fixed points plays a role in realizing the breather solutions. Also, such a specific feature of breather solution provides us to understand mathematical mechanism of realizing the coexistence of positive and negative parts in nonlinear systems., Comment: to appear in AIP Conf. Proc. (ICNAAM 2023)

In this study, we calculate the nuclear matrix elements (NMEs) for the light neutrino-exchange mechanism of neutrinoless double beta $0\nu\beta\beta$) decay of $^{124}$Sn within the framework of the interacting nuclear shell model using the effective shell model Hamiltonian GCN5082. A novel method based on a nonclosure approach is employed, wherein for the intermediate nucleus $^{124}$Sb, effects of energy of 100 states for each $J_{k}^{\pi}$=$0^{+}$ to $11^{+}$ and $2^{-}$ to $9^{-}$ ($\Delta J_{k}$=1) are explicitly included in the NMEs calculation. Other common effects such as the finite size of nucleons, higher-order effects of nucleon currents, and short-range correlations (SRC) of nucleons are also taken into account. The extracted optimal closure energy is 2.9 MeV for a total NME of $^{124}$Sn $0\nu\beta\beta$ decay, which is independent of different forms of SRC parametrizations. A comparison of NMEs and half-lives with some of the recent calculations is presented. Further, to gain a comprehensive understanding of the role of nuclear structure on the $0\nu\beta\beta$ decay, the dependence of NMEs on spin-parity of the intermediate states, coupled spin-parity of neutrons and protons, and the number of intermediate states, is explored. It is observed that the inclusion of the effects of excitation energies of the intermediate nucleus yields more reliable NMEs. The present findings provide valuable insights for experimental investigations of $0\nu\beta\beta$ decay of $^{124}$Sn in India and elsewhere., Comment: 12 pages, 6 figures, submitted in the journal Physical Review C. arXiv admin note: text overlap with arXiv:2308.08216

The neutrinoless double beta decay is a pivotal weak nuclear process that holds the potential to unveil the Majorana nature of neutrinos and predict their absolute masses. In this study, we delve into examining the impact of spin-dependent short-range correlations (SRC) on the nuclear matrix elements (NMEs) for the light neutrino-exchange mechanism in neutrinoless double beta ($0\nu\beta\beta$) decay of $^{48}$Ca, employing an extensive interacting nuclear shell model. All computations are performed employing the effective shell model Hamiltonian GXPF1A, encompassing the entire $fp$ model space through the closure approximation. Our investigation examines the NMEs' dependencies on factors such as the number of intermediate states, coupled spin-parity attributes of neutrons and protons, neutrino momentum, inter-nucleon separation, and closure energy. This scrutiny is performed with respect to both the conventional Jastrow-type approach of SRC, employing various parameterizations, and the spin-dependent SRC paradigm. Our findings illuminate a discernible distinction in NMEs induced by spin-dependent SRC, differing by approximately 10-20\% from those computed through the conventional Jastrow-type SRC, incorporating distinct parameterizations., Comment: 13 pages, 5 figures, submitted in the journal Universe, MDPI

Drones are being used to assess the situation in various disasters. In this study, we investigate a method to automatically estimate the damage status of people based on their actions in aerial drone images in order to understand disaster sites faster and save labor. We constructed a new dataset of aerial images of human actions in a hypothetical disaster that occurred in an urban area, and classified the human damage status using 3D ResNet. The results showed that the status with characteristic human actions could be classified with a recall rate of more than 80%, while other statuses with similar human actions could only be classified with a recall rate of about 50%. In addition, a cloud-based VR presentation application suggested the effectiveness of using drones to understand the disaster site and estimate the human condition., Comment: In submission to the ICCV 2023 Artificial Intelligence for Humanitarian Assistance and Disaster Response Workshop

We discovered a simple regime where a near-critical plasma irradiated by a laser of experimentally available intensity can self-organize to produce positrons and accelerate them to ultra-relativistic energies. The laser pulse piles up electrons at its leading edge, producing a strong longitudinal plasma electric field. The field creates a moving gamma-ray collider that generates positrons via the linear Breit-Wheeler process -- annihilation of two gamma-rays into an electron-positron pair. At the same time, the plasma field, rather than the laser, serves as an accelerator for the positrons. The discovery of positron acceleration was enabled by a first-of-its-kind kinetic simulation that generates pairs via photon-photon collisions. Using available laser intensities of $10^{22}$$\ $$\rm W/cm^2$, the discovered regime can generate a GeV positron beam with divergence angle of $\sim10^{\circ}$ and total charge of 0.1$\ $pC. The result paves the way to experimental observation of the linear Breit-Wheeler process and to applications requiring positron beams.

Bayesian inference is often utilized for uncertainty quantification tasks. A recent analysis by Xu and Raginsky 2022 rigorously decomposed the predictive uncertainty in Bayesian inference into two uncertainties, called aleatoric and epistemic uncertainties, which represent the inherent randomness in the data-generating process and the variability due to insufficient data, respectively. They analyzed those uncertainties in an information-theoretic way, assuming that the model is well-specified and treating the model's parameters as latent variables. However, the existing information-theoretic analysis of uncertainty cannot explain the widely believed property of uncertainty, known as the sensitivity between the test and training data. It implies that when test data are similar to training data in some sense, the epistemic uncertainty should become small. In this work, we study such uncertainty sensitivity using our novel decomposition method for the predictive uncertainty. Our analysis successfully defines such sensitivity using information-theoretic quantities. Furthermore, we extend the existing analysis of Bayesian meta-learning and show the novel sensitivities among tasks for the first time.

This study proposes a method to determine the filter parameters required for the topology method, which is a radar-based noncontact method for measurement of heart inter-beat intervals. The effectiveness of the proposed method is evaluated by performing radar measurements involving both human participants and chimpanzee subjects. The proposed method is designed to enable setting of the filter cutoff frequency to eliminate respiratory components while maintaining the higher harmonics of the heartbeat components. Measurements using a millimeter-wave radar system and a reference contact-type electrocardiogram sensor demonstrate that the smallest errors that occur when measuring heart inter-beat intervals using the proposed method can be as small as 4.43 and 2.55 ms for humans and chimpanzees, respectively. These results indicate the possibility of using noncontact physiological measurements to monitor both humans and chimpanzees., Comment: 5 pages, 6 figures. This work is going to be submitted to the IEEE for possible publication

This study proposes an accurate method to estimate human body orientation using a millimeter-wave radar system. Body displacement is measured from the phase of the radar echo, which is analyzed to obtain features associated with the fundamental and higher-order harmonic components of the quasi-periodic respiratory motion. These features are used in body-orientation estimation invoking a novel hierarchical regression model in which a logistic regression model is adopted in the first step to determine whether the target person is facing forwards or backwards; a pair of ridge regression models are employed in the second step to estimate body-orientation angle. To evaluate the performance of the proposed method, respiratory motions of five participants were recorded using three millimeter-wave radar systems; cross-validation was also performed. The average error in estimating body orientation angle was 38.3$^\circ$ and 23.1$^\circ$ using respectively a conventional method with only the fundamental frequency component and our proposed method, indicating an improvement in accuracy by factor 1.7 when using the proposed method. In addition, the coefficient of correlation between the actual and estimated body-orientation angles using the conventional and proposed methods are 0.74 and 0.91, respectively. These results show that by combining the characteristic features of the fundamental and higher-order harmonics from the respiratory motion, the proposed method offers better accuracy., Comment: 5 pages, 4 figures. This work is going to be submitted to the IEEE for possible publication

We propose a method to measure the respiration of a rhesus monkey using a millimeter-wave radar system with an antenna array. Unlike humans, small animals are generally restless and hyperactive in nature, and suppression of their body motion components is thus necessary to realize accurate respiratory measurements. The proposed method detects and suppresses nonperiodic body motion components while also combining and emphasizing the periodic components from multiple echoes acquired from the target. Results indicate that the proposed method can measure respiration rate of the target monkey accurately, even with frequent body movements., Comment: 5 pages, 6 figures. This work is going to be submitted to the IEEE for possible publication

AIFV (almost instantaneous fixed-to-variable length) codes are noiseless source codes that can attain a shorter average codeword length than Huffman codes by allowing a time-variant encoder with two code tables and a decoding delay of at most 2 bits. First, we consider a general class of noiseless source codes, called k-bit delay decodable codes, in which one allows a finite number of code tables and a decoding delay of at most k bits for k >= 0. Then we prove that AIFV codes achieve the optimal average codeword length in the 2-bit delay decodable codes class., Comment: arXiv admin note: substantial text overlap with arXiv:2306.07563

The class of k-bit delay decodable codes, source codes allowing decoding delay of at most k bits for k >= 0, can attain a shorter average codeword length than Huffman codes. This paper discusses the general properties of the class of k-bit delay decodable codes with a finite number of code tables and proves two theorems which enable us to limit the scope of code-tuples to be considered when discussing optimal k-bit delay decodable code-tuples.