Five-dimensional spacetimes of two orbifold 3-branes are studied, by assuming that {\em the two 3-branes are spatially homogeneous, isotropic, and independent of time}, following the so-called "bulk-based" approach. The most general form of the metric is obtained, and the corresponding field equations are divided into three groups, one is valid on each of the two 3-branes, and the third is valid in the bulk. The Einstein tensor on the 3-branes is expressed in terms of the discontinuities of the first-order derivatives of the metric coefficients. Thus, once the metric is known in the bulk, the distribution of the Einstein tensor on the two 3-branes is uniquely determined. As applications, we consider two different cases, one is in which the bulk is locally $AdS_{5}$, and the other is where it is vacuum. In some cases, it is shown that the universe is first decelerating and then accelerating. The global structure of the bulk as well as the 3-branes is also studied, and found that in some cases the solutions may represent the collision of two orbifold 3-branes. The applications of the formulas to the studies of the cyclic universe and the cosmological constant problem are also pointed out.
A vast majority of the current research in the field of Machine Learning is done using algorithms with strong arguments pointing to their biological implausibility such as Backpropagation, deviating the field's focus from understanding its original organic inspiration to a compulsive search for optimal performance. Yet, there have been a few proposed models that respect most of the biological constraints present in the human brain and are valid candidates for mimicking some of its properties and mechanisms. In this paper, we will focus on guiding the learning of a biologically plausible generative model called the Helmholtz Machine in complex search spaces using a heuristic based on the Human Image Perception mechanism. We hypothesize that this model's learning algorithm is not fit for Deep Networks due to its Hebbian-like local update rule, rendering it incapable of taking full advantage of the compositional properties that multi-layer networks provide. We propose to overcome this problem, by providing the network's hidden layers with visual queues at different resolutions using a Multi-level Data representation. The results on several image datasets showed the model was able to not only obtain better overall quality but also a wider diversity in the generated images, corroborating our intuition that using our proposed heuristic allows the model to take more advantage of the network's depth growth. More importantly, they show the unexplored possibilities underlying brain-inspired models and techniques.
A hallmark of chaotic dynamics is the loss of information with time. Although information loss is often expressed through a connection to Lyapunov exponents -- valid in the limit of high information about the system state -- this picture misses the rich spectrum of information decay across different levels of granularity. Here we show how machine learning presents new opportunities for the study of information loss in chaotic dynamics, with a double pendulum serving as a model system. We use the Information Bottleneck as a training objective for a neural network to extract information from the state of the system that is optimally predictive of the future state after a prescribed time horizon. We then decompose the optimally predictive information by distributing a bottleneck to each state variable, recovering the relative importance of the variables in determining future evolution. The framework we develop is broadly applicable to chaotic systems and pragmatic to apply, leveraging data and machine learning to monitor the limits of predictability and map out the loss of information.
In high-dimensional classification problems, a commonly used approach is to first project the high-dimensional features into a lower dimensional space, and base the classification on the resulting lower dimensional projections. In this paper, we formulate a latent-variable model with a hidden low-dimensional structure to justify this two-step procedure and to guide which projection to choose. We propose a computationally efficient classifier that takes certain principal components (PCs) of the observed features as projections, with the number of retained PCs selected in a data-driven way. A general theory is established for analyzing such two-step classifiers based on any projections. We derive explicit rates of convergence of the excess risk of the proposed PC-based classifier. The obtained rates are further shown to be optimal up to logarithmic factors in the minimax sense. Our theory allows the lower-dimension to grow with the sample size and is also valid even when the feature dimension (greatly) exceeds the sample size. Extensive simulations corroborate our theoretical findings. The proposed method also performs favorably relative to other existing discriminant methods on three real data examples.
Machine Translation (MT) is usually viewed as a one-shot process that generates the target language equivalent of some source text from scratch. We consider here a more general setting which assumes an initial target sequence, that must be transformed into a valid translation of the source, thereby restoring parallelism between source and target. For this bilingual synchronization task, we consider several architectures (both autoregressive and non-autoregressive) and training regimes, and experiment with multiple practical settings such as simulated interactive MT, translating with Translation Memory (TM) and TM cleaning. Our results suggest that one single generic edit-based system, once fine-tuned, can compare with, or even outperform, dedicated systems specifically trained for these tasks.
Several non-linear operators in stochastic analysis, such as solution maps to stochastic differential equations, depend on a temporal structure which is not leveraged by contemporary neural operators designed to approximate general maps between Banach space. This paper therefore proposes an operator learning solution to this open problem by introducing a deep learning model-design framework that takes suitable infinite-dimensional linear metric spaces, e.g. Banach spaces, as inputs and returns a universal \textit{sequential} deep learning model adapted to these linear geometries specialized for the approximation of operators encoding a temporal structure. We call these models \textit{Causal Neural Operators}. Our main result states that the models produced by our framework can uniformly approximate on compact sets and across arbitrarily finite-time horizons H\"older or smooth trace class operators, which causally map sequences between given linear metric spaces. Our analysis uncovers new quantitative relationships on the latent state-space dimension of Causal Neural Operators, which even have new implications for (classical) finite-dimensional Recurrent Neural Networks. In addition, our guarantees for recurrent neural networks are tighter than the available results inherited from feedforward neural networks when approximating dynamical systems between finite-dimensional spaces.
In machine learning, the selection of a promising model from a potentially large number of competing models and the assessment of its generalization performance are critical tasks that need careful consideration. Typically, model selection and evaluation are strictly separated endeavors, splitting the sample at hand into a training, validation, and evaluation set, and only compute a single confidence interval for the prediction performance of the final selected model. We however propose an algorithm how to compute valid lower confidence bounds for multiple models that have been selected based on their prediction performances in the evaluation set by interpreting the selection problem as a simultaneous inference problem. We use bootstrap tilting and a maxT-type multiplicity correction. The approach is universally applicable for any combination of prediction models, any model selection strategy, and any prediction performance measure that accepts weights. We conducted various simulation experiments which show that our proposed approach yields lower confidence bounds that are at least comparably good as bounds from standard approaches, and that reliably reach the nominal coverage probability. In addition, especially when sample size is small, our proposed approach yields better performing prediction models than the default selection of only one model for evaluation does.
We introduce a powerful deep classifier two-sample test for high-dimensional data based on E-values, called E-value Classifier Two-Sample Test (E-C2ST). Our test combines ideas from existing work on split likelihood ratio tests and predictive independence tests. The resulting E-values are suitable for anytime-valid sequential two-sample tests. This feature allows for more effective use of data in constructing test statistics. Through simulations and real data applications, we empirically demonstrate that E-C2ST achieves enhanced statistical power by partitioning datasets into multiple batches beyond the conventional two-split (training and testing) approach of standard classifier two-sample tests. This strategy increases the power of the test while keeping the type I error well below the desired significance level.
Fusing deep learning models trained on separately located clients into a global model in a one-shot communication round is a straightforward implementation of Federated Learning. Although current model fusion methods are shown experimentally valid in fusing neural networks with almost identical architectures, they are rarely theoretically analyzed. In this paper, we reveal the phenomenon of neuron disturbing, where neurons from heterogeneous local models interfere with each other mutually. We give detailed explanations from a Bayesian viewpoint combining the data heterogeneity among clients and properties of neural networks. Furthermore, to validate our findings, we propose an experimental method that excludes neuron disturbing and fuses neural networks via adaptively selecting a local model, called AMS, to execute the prediction according to the input. The experiments demonstrate that AMS is more robust in data heterogeneity than general model fusion and ensemble methods. This implies the necessity of considering neural disturbing in model fusion. Besides, AMS is available for fusing models with varying architectures as an experimental algorithm, and we also list several possible extensions of AMS for future work.
Assessing the validity of a real-world system with respect to given quality criteria is a common yet costly task in industrial applications due to the vast number of required real-world tests. Validating such systems by means of simulation offers a promising and less expensive alternative, but requires an assessment of the simulation accuracy and therefore end-to-end measurements. Additionally, covariate shifts between simulations and actual usage can cause difficulties for estimating the reliability of such systems. In this work, we present a validation method that propagates bounds on distributional discrepancy measures through a composite system, thereby allowing us to derive an upper bound on the failure probability of the real system from potentially inaccurate simulations. Each propagation step entails an optimization problem, where -- for measures such as maximum mean discrepancy (MMD) -- we develop tight convex relaxations based on semidefinite programs. We demonstrate that our propagation method yields valid and useful bounds for composite systems exhibiting a variety of realistic effects. In particular, we show that the proposed method can successfully account for data shifts within the experimental design as well as model inaccuracies within the simulation.
DNA has immense potential as an emerging data storage medium. The principle of DNA storage is the conversion and flow of digital information between binary code stream, quaternary base, and actual DNA fragments. This process will inevitably introduce errors, posing challenges to accurate data recovery. Sequence reconstruction consists of inferring the DNA reference from a cluster of erroneous copies. A common assumption in existing methods is that all the strands within a cluster are noisy copies originating from the same reference, thereby contributing equally to the reconstruction. However, this is not always valid considering the existence of contaminated sequences caused, for example, by DNA fragmentation and rearrangement during the DNA storage process.This paper proposed a robust multi-read reconstruction model using DNN, which is resilient to contaminated clusters with outlier sequences, as well as to noisy reads with IDS errors. The effectiveness and robustness of the method are validated on three next-generation sequencing datasets, where a series of comparative experiments are performed by simulating varying contamination levels that occurring during the process of DNA storage.
A confidence sequence (CS) is an anytime-valid sequential inference primitive which produces an adapted sequence of sets for a predictable parameter sequence with a time-uniform coverage guarantee. This work constructs a non-parametric non-asymptotic lower CS for the running average conditional expectation whose slack converges to zero given non-negative right heavy-tailed observations with bounded mean. Specifically, when the variance is finite the approach dominates the empirical Bernstein supermartingale of Howard et. al.; with infinite variance, can adapt to a known or unknown $(1 + \delta)$-th moment bound; and can be efficiently approximated using a sublinear number of sufficient statistics. In certain cases this lower CS can be converted into a closed-interval CS whose width converges to zero, e.g., any bounded realization, or post contextual-bandit inference with bounded rewards and unbounded importance weights. A reference implementation and example simulations demonstrate the technique.
Partial label learning (PLL) learns from training examples each associated with multiple candidate labels, among which only one is valid. In recent years, benefiting from the strong capability of dealing with ambiguous supervision and the impetus of modern data augmentation methods, consistency regularization-based PLL methods have achieved a series of successes and become mainstream. However, as the partial annotation becomes insufficient, their performances drop significantly. In this paper, we leverage easily accessible unlabeled examples to facilitate the partial label consistency regularization. In addition to a partial supervised loss, our method performs a controller-guided consistency regularization at both the label-level and representation-level with the help of unlabeled data. To minimize the disadvantages of insufficient capabilities of the initial supervised model, we use the controller to estimate the confidence of each current prediction to guide the subsequent consistency regularization. Furthermore, we dynamically adjust the confidence thresholds so that the number of samples of each class participating in consistency regularization remains roughly equal to alleviate the problem of class-imbalance. Experiments show that our method achieves satisfactory performances in more practical situations, and its modules can be applied to existing PLL methods to enhance their capabilities.
Small object detection for 3D point cloud is a challenging problem because of two limitations: (1) Perceiving small objects is much more diffcult than normal objects due to the lack of valid points. (2) Small objects are easily blocked which breaks the shape of their meshes in 3D point cloud. In this paper, we propose a pillar set abstraction (PSA) and foreground point compensation (FPC) and design a point-based detection network, PSA-Det3D, to improve the detection performance for small object. The PSA embeds a pillar query operation on the basis of set abstraction (SA) to expand its receptive field of the network, which can aggregate point-wise features effectively. To locate more occluded objects, we persent a proposal generation layer consisting of a foreground point segmentation and a FPC module. Both the foreground points and the estimated centers are finally fused together to generate the detection result. The experiments on the KITTI 3D detection benchmark show that our proposed PSA-Det3D outperforms other algorithms with high accuracy for small object detection.
Contextual bandit algorithms are ubiquitous tools for active sequential experimentation in healthcare and the tech industry. They involve online learning algorithms that adaptively learn policies over time to map observed contexts $X_t$ to actions $A_t$ in an attempt to maximize stochastic rewards $R_t$. This adaptivity raises interesting but hard statistical inference questions, especially counterfactual ones: for example, it is often of interest to estimate the properties of a hypothetical policy that is different from the logging policy that was used to collect the data -- a problem known as ``off-policy evaluation'' (OPE). Using modern martingale techniques, we present a comprehensive framework for OPE inference that relax unnecessary conditions made in some past works, significantly improving on them both theoretically and empirically. Importantly, our methods can be employed while the original experiment is still running (that is, not necessarily post-hoc), when the logging policy may be itself changing (due to learning), and even if the context distributions are a highly dependent time-series (such as if they are drifting over time). More concretely, we derive confidence sequences for various functionals of interest in OPE. These include doubly robust ones for time-varying off-policy mean reward values, but also confidence bands for the entire cumulative distribution function of the off-policy reward distribution. All of our methods (a) are valid at arbitrary stopping times (b) only make nonparametric assumptions, (c) do not require importance weights to be uniformly bounded and if they are, we do not need to know these bounds, and (d) adapt to the empirical variance of our estimators. In summary, our methods enable anytime-valid off-policy inference using adaptively collected contextual bandit data.
We describe findings of the third Nuanced Arabic Dialect Identification Shared Task (NADI 2022). NADI aims at advancing state of the art Arabic NLP, including on Arabic dialects. It does so by affording diverse datasets and modeling opportunities in a standardized context where meaningful comparisons between models and approaches are possible. NADI 2022 targeted both dialect identification (Subtask 1) and dialectal sentiment analysis (Subtask 2) at the country level. A total of 41 unique teams registered for the shared task, of whom 21 teams have actually participated (with 105 valid submissions). Among these, 19 teams participated in Subtask 1 and 10 participated in Subtask 2. The winning team achieved 27.06 F1 on Subtask 1 and F1=75.16 on Subtask 2, reflecting that the two subtasks remain challenging and motivating future work in this area. We describe methods employed by participating teams and offer an outlook for NADI.
Given independent samples from two univariate distributions, one-sided Wilcoxon-Mann-Whitney statistics may be used to conduct rank-based tests of stochastic dominance. We broaden the scope of applicability of such tests by showing that the bootstrap may be used to conduct valid inference in a matched pairs sampling framework permitting dependence between the two samples. Further, we show that a modified bootstrap incorporating an implicit estimate of a contact set may be used to improve power. Numerical simulations indicate that our test using the modified bootstrap effectively controls the null rejection rates and can deliver more or less power than that of the Donald-Hsu test. In the course of establishing our results we obtain a weak approximation to the empirical ordinance dominance curve permitting its population density to diverge to infinity at zero or one at arbitrary rates.
In the scope of drug discovery, the molecular design aims to identify novel compounds from the chemical space where the potential drug-like molecules are estimated to be in the order of 10^60 - 10^100. Since this search task is computationally intractable due to the unbounded search space, deep learning draws a lot of attention as a new way of generating unseen molecules. As we seek compounds with specific target proteins, we propose a Transformer-based deep model for de novo target-specific molecular design. The proposed method is capable of generating both drug-like compounds (without specified targets) and target-specific compounds. The latter are generated by enforcing different keys and values of the multi-head attention for each target. In this way, we allow the generation of SMILES strings to be conditional on the specified target. Experimental results demonstrate that our method is capable of generating both valid drug-like compounds and target-specific compounds. Moreover, the sampled compounds from conditional model largely occupy the real target-specific molecules' chemical space and also cover a significant fraction of novel compounds.
As ML models have increased in capabilities and accuracy, so has the complexity of their deployments. Increasingly, ML model consumers are turning to service providers to serve the ML models in the ML-as-a-service (MLaaS) paradigm. As MLaaS proliferates, a critical requirement emerges: how can model consumers verify that the correct predictions were served, in the face of malicious, lazy, or buggy service providers? In this work, we present the first practical ImageNet-scale method to verify ML model inference non-interactively, i.e., after the inference has been done. To do so, we leverage recent developments in ZK-SNARKs (zero-knowledge succinct non-interactive argument of knowledge), a form of zero-knowledge proofs. ZK-SNARKs allows us to verify ML model execution non-interactively and with only standard cryptographic hardness assumptions. In particular, we provide the first ZK-SNARK proof of valid inference for a full resolution ImageNet model, achieving 79\% top-5 accuracy. We further use these ZK-SNARKs to design protocols to verify ML model execution in a variety of scenarios, including for verifying MLaaS predictions, verifying MLaaS model accuracy, and using ML models for trustless retrieval. Together, our results show that ZK-SNARKs have the promise to make verified ML model inference practical.
RAW image datasets are more suitable than the standard RGB image datasets for the ill-posed inverse problems in low-level vision, but not common in the literature. There are also a few studies to focus on mapping sRGB images to RAW format. Mapping from sRGB to RAW format could be a relevant domain for reverse style transferring since the task is an ill-posed reversing problem. In this study, we seek an answer to the question: Can the ISP operations be modeled as the style factor in an end-to-end learning pipeline? To investigate this idea, we propose a novel architecture, namely RST-ISP-Net, for learning to reverse the ISP operations with the help of adaptive feature normalization. We formulate this problem as a reverse style transferring and mostly follow the practice used in the prior work. We have participated in the AIM Reversed ISP challenge with our proposed architecture. Results indicate that the idea of modeling disruptive or modifying factors as style is still valid, but further improvements are required to be competitive in such a challenge.