Miracle-dz/UniFAR-FTUs huggingface dataset:
TTN: A Domain-Shift Aware Batch Normalization in Test-Time Adaptation

This paper proposes a novel batch normalization strategy for test-time adaptation. Recent test-time adaptation methods heavily rely on the modified batch normalization, i.e., transductive batch normalization (TBN), which calculates the mean and the variance from the current test batch rather than using the running mean and variance obtained from the source data, i.e., conventional batch normalization (CBN). Adopting TBN that employs test batch statistics mitigates the performance degradation caused by the domain shift. However, re-estimating normalization statistics using test data depends on impractical assumptions that a test batch should be large enough and be drawn from i.i. d. stream, and we observed that the previous methods with TBN show critical performance drop without the assumptions. In this paper, we identify that CBN and TBN are in a trade-off relationship and present a new test-time normalization (TTN) method that interpolates the statistics by adjusting the importance between CBN and TBN according to the domain-shift sensitivity of each BN layer. Our proposed TTN improves model robustness to shifted domains across a wide range of batch sizes and in various realistic evaluation scenarios. TTN is widely applicable to other test-time adaptation methods that rely on updating model parameters via backpropagation. We demonstrate that adopting TTN further improves their performance and achieves state-of-the-art performance in various standard benchmarks.
Invariant Slot Attention: Object Discovery with Slot-Centric Reference Frames

Automatically discovering composable abstractions from raw perceptual data is a long-standing challenge in machine learning. Recent slot-based neural networks that learn about objects in a self-supervised manner have made exciting progress in this direction. However, they typically fall short at adequately capturing spatial symmetries present in the visual world, which leads to sample inefficiency, such as when entangling object appearance and pose. In this paper, we present a simple yet highly effective method for incorporating spatial symmetries via slot-centric reference frames. We incorporate equivariance to per-object pose transformations into the attention and generation mechanism of Slot Attention by translating, scaling, and rotating position encodings. These changes result in little computational overhead, are easy to implement, and can result in large gains in terms of data efficiency and overall improvements to object discovery. We evaluate our method on a wide range of synthetic object discovery benchmarks namely CLEVR, Tetrominoes, CLEVRTex, Objects Room and MultiShapeNet, and show promising improvements on the challenging real-world Waymo Open dataset.
A localisation theorem for singularity categories of proper dg algebras

Given a recollement of three proper dg algebras over a noetherian commutative ring, e.g. three algebras which are finitely generated over the base ring, which extends one step downwards, it is shown that there is a short exact sequence of their singularity categories. This allows us to recover and generalise some known results on singularity categories of finite-dimensional algebras.
A Practical Mixed Precision Algorithm for Post-Training Quantization

Neural network quantization is frequently used to optimize model size, latency and power consumption for on-device deployment of neural networks. In many cases, a target bit-width is set for an entire network, meaning every layer get quantized to the same number of bits. However, for many networks some layers are significantly more robust to quantization noise than others, leaving an important axis of improvement unused. As many hardware solutions provide multiple different bit-width settings, mixed-precision quantization has emerged as a promising solution to find a better performance-efficiency trade-off than homogeneous quantization. However, most existing mixed precision algorithms are rather difficult to use for practitioners as they require access to the training data, have many hyper-parameters to tune or even depend on end-to-end retraining of the entire model. In this work, we present a simple post-training mixed precision algorithm that only requires a small unlabeled calibration dataset to automatically select suitable bit-widths for each layer for desirable on-device performance. Our algorithm requires no hyper-parameter tuning, is robust to data variation and takes into account practical hardware deployment constraints making it a great candidate for practical use. We experimentally validate our proposed method on several computer vision tasks, natural language processing tasks and many different networks, and show that we can find mixed precision networks that provide a better trade-off between accuracy and efficiency than their homogeneous bit-width equivalents.
Nonemptiness of single affine Deligne-Lusztig varieties

Affine Deligne-Lusztig varieties with various level structures show up in the study of Shimura varieties and moduli spaces of shtukas. Among is the Iwahori level structure which is the most refined one. We study the nonemptiness problem of single affine Deligne-Lusztig varieties at Iwahori level in the basic case. Under a genericity condition (the ``shrunken Weyl chambers'' condition), an explicit criterion is known. However, no explicit criterion has been available without the condition even conjecturally. We conjecture a new criterion in full generality, and prove it except for finitely many cases. As an application, the nonemptiness problem for special cases and a new conjectural dimension formula are discussed.
Choose your tools carefully: a comparative evaluation of deterministic vs. stochastic and binary vs. analog neuron models for implementing emerging computing paradigms

Neuromorphic computing, commonly understood as a computing approach built upon neurons, synapses, and their dynamics, as opposed to Boolean gates, is gaining large mindshare due to its direct application in solving current and future computing technological problems, such as smart sensing, smart devices, self-hosted and self-contained devices, artificial intelligence (AI) applications, etc. In a largely software-defined implementation of neuromorphic computing, it is possible to throw enormous computational power or optimize models and networks depending on the specific nature of the computational tasks. However, a hardware-based approach needs the identification of well-suited neuronal and synaptic models to obtain high functional and energy efficiency, which is a prime concern in size, weight, and power (SWaP) constrained environments. In this work, we perform a study on the characteristics of hardware neuron models (namely, inference errors, generalizability and robustness, practical implementability, and memory capacity) that have been proposed and demonstrated using a plethora of emerging nano-materials technology-based physical devices, to quantify the performance of such neurons on certain classes of problems that are of great importance in real-time signal processing like tasks in the context of reservoir computing. We find that the answer on which neuron to use for what applications depends on the particulars of the application requirements and constraints themselves, i.e., we need not only a hammer but all sorts of tools in our tool chest for high efficiency and quality neuromorphic computing.
Fast Learnings of Coupled Nonnegative Tensor Decomposition Using Optimal Gradient and Low-rank Approximation

Nonnegative tensor decomposition has been widely applied in signal processing and neuroscience, etc. When it comes to group analysis of multi-block tensors, traditional tensor decomposition is insufficient to utilize the shared/similar information among tensors. In this study, we propose a coupled nonnegative CANDECOMP/PARAFAC decomposition algorithm optimized by the alternating proximal gradient method (CoNCPDAPG), which is capable of a simultaneous decomposition of tensors from different samples that are partially linked and a simultaneous extraction of common components, individual components and core tensors. Due to the low optimization efficiency brought by the nonnegative constraint and the high-dimensional nature of the data, we further propose the lraCoNCPD-APG algorithm by combining low-rank approximation and the proposed CoNCPD-APG method. When processing multi-block large-scale tensors, the proposed lraCoNCPD-APG algorithm can greatly reduce the computational load without compromising the decomposition quality. Experiment results of coupled nonnegative tensor decomposition problems designed for synthetic data, real-world face images and event-related potential data demonstrate the practicability and superiority of the proposed algorithms.
A Comprehensive Survey on Automatic Knowledge Graph Construction

Automatic knowledge graph construction aims at manufacturing structured human knowledge. To this end, much effort has historically been spent extracting informative fact patterns from different data sources. However, more recently, research interest has shifted to acquiring conceptualized structured knowledge beyond informative data. In addition, researchers have also been exploring new ways of handling sophisticated construction tasks in diversified scenarios. Thus, there is a demand for a systematic review of paradigms to organize knowledge structures beyond data-level mentions. To meet this demand, we comprehensively survey more than 300 methods to summarize the latest developments in knowledge graph construction. A knowledge graph is built in three steps: knowledge acquisition, knowledge refinement, and knowledge evolution. The processes of knowledge acquisition are reviewed in detail, including obtaining entities with fine-grained types and their conceptual linkages to knowledge graphs; resolving coreferences; and extracting entity relationships in complex scenarios. The survey covers models for knowledge refinement, including knowledge graph completion, and knowledge fusion. Methods to handle knowledge evolution are also systematically presented, including condition knowledge acquisition, condition knowledge graph completion, and knowledge dynamic. We present the paradigms to compare the distinction among these methods along the axis of the data environment, motivation, and architecture. Additionally, we also provide briefs on accessible resources that can help readers to develop practical knowledge graph systems. The survey concludes with discussions on the challenges and possible directions for future exploration.
Virtually increasing the measurement frequency of LIDAR sensor utilizing a single RGB camera

The frame rates of most 3D LIDAR sensors used in intelligent vehicles are substantially lower than current cameras installed in the same vehicle. This research suggests using a mono camera to virtually enhance the frame rate of LIDARs, allowing the more frequent monitoring of dynamic objects in the surroundings that move quickly. As a first step, dynamic object candidates are identified and tracked in the camera frames. Following that, the LIDAR measurement points of these items are found by clustering in the frustums of 2D bounding boxes. Projecting these to the camera and tracking them to the next camera frame can be used to create 3D-2D correspondences between different timesteps. These correspondences between the last LIDAR frame and the actual camera frame are used to solve the PnP (Perspective-n-Point) problem. Finally, the estimated transformations are applied to the previously measured points to generate virtual measurements. With the proposed estimation, if the ego movement is known, not just static object position can be determined at timesteps where camera measurement is available, but positions of dynamic objects as well. We achieve state-of-the-art performance on large public datasets in terms of accuracy and similarity to real measurements.
A Survey on Causal Reinforcement Learning

While Reinforcement Learning (RL) achieves tremendous success in sequential decision-making problems of many domains, it still faces key challenges of data inefficiency and the lack of interpretability. Interestingly, many researchers have leveraged insights from the causality literature recently, bringing forth flourishing works to unify the merits of causality and address well the challenges from RL. As such, it is of great necessity and significance to collate these Causal Reinforcement Learning (CRL) works, offer a review of CRL methods, and investigate the potential functionality from causality toward RL. In particular, we divide existing CRL approaches into two categories according to whether their causality-based information is given in advance or not. We further analyze each category in terms of the formalization of different models, ranging from the Markov Decision Process (MDP), Partially Observed Markov Decision Process (POMDP), Multi-Arm Bandits (MAB), and Dynamic Treatment Regime (DTR). Moreover, we summarize the evaluation matrices and open sources while we discuss emerging applications, along with promising prospects for the future development of CRL.
Bottom-up transient time models in coarse-graining molecular systems

This work presents a systematic methodology for describing the transient dynamics of coarse-grained molecular systems inferred from all-atom simulated data. We suggest Langevin-type dynamics where the coarse-grained interaction potential depends explicitly on time to efficiently approximate the transient coarse-grained dynamics. We apply the path-space force matching approach at the transient dynamics regime to learn the proposed model parameters. In particular, we parameterize the coarse-grained potential both with respect to the pair distance of the CG particles and the time, and we obtain an evolution model that is explicitly time-dependent. Moreover, we follow a data-driven approach to estimate the friction kernel, given by appropriate correlation functions directly from the underlying all-atom molecular dynamics simulations. To explore and validate the proposed methodology we study a benchmark system of a moving particle in a box. We examine the suggested model's effectiveness in terms of the system's correlation time and find that the model can approximate well the transient time regime of the system, depending on the correlation time of the system. As a result, in the less correlated case, it can represent the dynamics for a longer time interval. We present an extensive study of our approach to a realistic high-dimensional water molecular system. Posing the water system initially out of thermal equilibrium we collect trajectories of all-atom data for the, empirically estimated, transient time regime. Then, we infer the suggested model and strengthen the model's validity by comparing it with simplified Markovian models.
For the Metatheory of Type Theory, Internal Sconing Is Enough

Metatheorems about type theories are often proven by interpreting the syntax into models constructed using categorical gluing. We propose to use only sconing (gluing along a global section functor) instead of general gluing. The sconing is performed internally to a presheaf category, and we recover the original glued model by externalization. Our method relies on constructions involving two notions of models: first-order models (with explicit contexts) and higher-order models (without explicit contexts). Sconing turns a displayed higher-order model into a displayed first-order model. Using these, we derive specialized induction principles for the syntax of type theory. The input of such an induction principle is a boilerplate-free description of its motives and methods, not mentioning contexts. The output is a section with computation rules specified in the same internal language. We illustrate our framework by proofs of canonicity, normalization and syntactic parametricity for type theory.
Scale Reliant Inference

This article develops new tools and new statistical theory for a statistical problem we call Scale Reliant Inference (SRI). Many scientific fields collect multivariate data that lack scale: where the size, sum, or total of each measurement is arbitrary and is not representative of the scale of the underlying system being measured. For example, in the analysis of high-throughput sequencing data, it is well known that the number of sequencing reads (the sequencing depth) varies substantially due non-biological (technical) factors. This article develops a formal problem statement for SRI which unifies problems seen in multiple scientific fields. Informally, we define SRI as an estimation problem in which an estimand of interest cannot be uniquely identified due to the lack of scale information in the observed data. This problem statement represents a reformulation of the related field of Compositional Data Analysis and allows us to prove fundamental limits on SRI. For example, we prove that inferential criteria such as consistency, calibration, and bias are unattainable for common SRI tasks. Moreover, we show that common methods often applied to SRI implicitly assume infinite knowledge of the system scale and can lead to a troubling phenomena termed unacknowledged bias. Counter-intuitively, we show that this problem worsens with more data and can lead to substantially elevated Type-I and Type-II error rates. Still, we show that rigorous statistical inference is possible so long as models acknowledge the fundamental uncertainty in the system scale. We introduce a class of models we call Scale Simulation Random Variables (SSRVs) as flexible, rigorous, and computationally efficient approach to SRI.
A Review and Collation of Graphical Perception Knowledge for Visualization Recommendation

Selecting appropriate visual encodings is critical to designing effective visualization recommendation systems, yet few findings from graphical perception are typically applied within these systems. We observe two significant limitations in translating graphical perception knowledge into actionable visualization recommendation rules/constraints: inconsistent reporting of findings and a lack of shared data across studies. How can we translate the graphical perception literature into a knowledge base for visualization recommendation? We present a review of 59 papers that study user perception and performance across ten visual analysis tasks. Through this study, we contribute a JSON dataset that collates existing theoretical and experimental knowledge and summarizes key study outcomes in graphical perception. We illustrate how this dataset can inform automated encoding decisions with three representative visualization recommendation systems. Based on our findings, we highlight open challenges and opportunities for the community in collating graphical perception knowledge for a range of visualization recommendation scenarios.
A Second-Order Method for Stochastic Bandit Convex Optimisation

We introduce a simple and efficient algorithm for unconstrained zeroth-order stochastic convex bandits and prove its regret is at most $(1 + r/d)[d^{1.5} \sqrt{n} + d^3] polylog(n, d, r)$ where $n$ is the horizon, $d$ the dimension and $r$ is the radius of a known ball containing the minimiser of the loss.
Chapter IV: The Teaching of Mathematics in Grades I thru VIII

I N THE period covered by this review a number of significant summaries, bibliographies, and compilations have appeared. Altho some of these include or refer to articles which are not primarily reports of research, they are included here because of their preeminent usefulness to workers in the field. Fehr (32) , Beatty (5 ) , and Van Engen (95) summarized research in arithmetic and discussed implications of this research for the organization and learning of arithmetic. Beginning in December 1950, Kinsella (52) reported monthly a summary of research in mathematics. Subsequent issues of this journal continue this summary. Wilson (102) made an extensive revision of an earlier research review. Moser, Kinney, and Purdy (64) surveyed the literature pertaining to the aims and purposes in the teaching of mathematics. Spitzer and Burch (81) reviewed the discussions in the literature which dealt with methods and materials. Annual annotated bibliographies in arithmetic have been reported in each November issue of the Elementary School Journal by Hartung (46) . A selected list of references on arithmetic was provided by Van Engen (92) .
The Dantzig Discriminant Analysis with High Dimensional Data

It is well known that linear discriminant analysis (LDA) works well and is asymptotically optimal under fixed-p-large-n situations. But Bickel and Levina (2004) showed that the LDA is as bad as random guessing when p > n. This article studies the sparse discriminant analysis via Dantzig penalized least squares. Our method avoids estimating the high-dimensional covariance matrix and does not need the sparsity assumption on the inverse of the covariance matrix. We show that the new discriminant analysis is asymptotically optimal theoretically. Simulation and real data studies show that the classifier performs better than the existing sparse methods.
Stellar evolutionary tracks for low-mass stars

130 evolutionary tracks have been calculated for low-mass stars with updated input physics. The tracks have been evolved from the contracting Hayashi phase to the tip of the red giant branch. The mass range is 0.55 to 1.00 M0 in steps of 0.05 M0. The mixing length parameter IX is between 1.0 and 2.0 in steps of 0.25. The helium mass fraction Y is set to 0.24 - in addition, a few selected tracks have been computed with Y = 0.28. Values for the metallicity - solar scaled according to [Fe/H] - are Z = 0.0002,0.0005,0.001 and 0.004. Fourteen tracks have been computed with mass loss included through a Reimers mass-loss formula. We also provide parametrized formulae for T eJI, L, Me, and radius at the He-core flash, as well as for the zero-age main sequence. In addition, we parametrize the MS lifetime in terms of M, IX and Z. The grid has a range of physical parameters that covers the observed values for globular clusters, and is therefore well suited for'studies of them.
Experimentally probing the stability of thin-shell structures under pure bending

This paper studies the stability of space structures consisting of longitudinal, open-section thin-shells transversely connected by thin rods subjected to a pure bending moment. Localization of deformation, which plays a paramount role in the nonlinear post-buckling regime of these structures and is extremely sensitive to imperfections, is investigated through probing experiments. As the structures are bent, a probe locally displaces the edge of the thin shells, creating local dimple imperfections. The range of moments for which the early buckling of the structures can be triggered by this perturbation is determined, as well as the energy barrier separating the pre-buckling and post-buckling states. The stability of the local buckling mode is then illustrated by a stability landscape, and probing is extended to the entire structure to reveal alternate buckling modes disconnected from the structure’s fundamental path. These results can be used to formulate efficient buckling criteria and pave the way to operating these structures close to their buckling limits, and even in their post-buckling regime, therefore significantly reducing their mass. This article is part of the theme issue ‘Probing and dynamics of shock sensitive shells’.