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Hidden Markov models (HMM) have been widely used by scientists to model stochastic systems: the underlying process is a discrete Markov chain and the observations are noisy realizations of the underlying process. Determining the number of hidden states for an HMM is a model selection problem, which is yet to be satisfactorily solved, especially for the popular Gaussian HMM with heterogeneous covariance. In this paper, we propose a consistent method for determining the number of hidden states of HMM based on the marginal likelihood, which is obtained by integrating out both the parameters and hidden states. Moreover, we show that the model selection problem of HMM includes the order selection problem of finite mixture models as a special case. We give rigorous proof of the consistency of the proposed marginal likelihood method and provide an efficient computation method for practical implementation. We numerically compare the proposed method with the Bayesian information criterion (BIC), demonstrating the effectiveness of the proposed marginal likelihood method.

Annotated datasets are an essential ingredient to train, evaluate, compare and productionalize supervised machine learning models. It is therefore imperative that annotations are of high quality. For their creation, good quality management and thereby reliable quality estimates are needed. Then, if quality is insufficient during the annotation process, rectifying measures can be taken to improve it. Quality estimation is often performed by having experts manually label instances as correct or incorrect. But checking all annotated instances tends to be expensive. Therefore, in practice, usually only subsets are inspected; sizes are chosen mostly without justification or regard to statistical power and more often than not, are relatively small. Basing estimates on small sample sizes, however, can lead to imprecise values for the error rate. Using unnecessarily large sample sizes costs money that could be better spent, for instance on more annotations. Therefore, we first describe in detail how to use confidence intervals for finding the minimal sample size needed to estimate the annotation error rate. Then, we propose applying acceptance sampling as an alternative to error rate estimation We show that acceptance sampling can reduce the required sample sizes up to 50% while providing the same statistical guarantees.

Huge memory consumption has been a major bottleneck for deploying high-throughput large language models in real-world applications. In addition to the large number of parameters, the key-value (KV) cache for the attention mechanism in the transformer architecture consumes a significant amount of memory, especially when the number of layers is large for deep language models. In this paper, we propose a novel method that only computes and caches the KVs of a small number of layers, thus significantly saving memory consumption and improving inference throughput. Our experiments on large language models show that our method achieves up to 26$\times$ higher throughput than standard transformers and competitive performance in language modeling and downstream tasks. In addition, our method is orthogonal to existing transformer memory-saving techniques, so it is straightforward to integrate them with our model, achieving further improvement in inference efficiency. Our code is available at //github.com/whyNLP/LCKV.

After coarse-graining a complex system, the dynamics of its macro-state may exhibit more pronounced causal effects than those of its micro-state. This phenomenon, known as causal emergence, is quantified by the indicator of effective information. However, two challenges confront this theory: the absence of well-developed frameworks in continuous stochastic dynamical systems and the reliance on coarse-graining methodologies. In this study, we introduce an exact theoretic framework for causal emergence within linear stochastic iteration systems featuring continuous state spaces and Gaussian noise. Building upon this foundation, we derive an analytical expression for effective information across general dynamics and identify optimal linear coarse-graining strategies that maximize the degree of causal emergence when the dimension averaged uncertainty eliminated by coarse-graining has an upper bound. Our investigation reveals that the maximal causal emergence and the optimal coarse-graining methods are primarily determined by the principal eigenvalues and eigenvectors of the dynamic system's parameter matrix, with the latter not being unique. To validate our propositions, we apply our analytical models to three simplified physical systems, comparing the outcomes with numerical simulations, and consistently achieve congruent results.

Large language models (LLMs) have become crucial for many generative downstream tasks, leading to an inevitable trend and significant challenge to deploy them efficiently on resource-constrained devices. Structured pruning is a widely used method to address this challenge. However, when dealing with the complex structure of the multiple decoder layers, general methods often employ common estimation approaches for pruning. These approaches lead to a decline in accuracy for specific downstream tasks. In this paper, we introduce a simple yet efficient method that adaptively models the importance of each substructure. Meanwhile, it can adaptively fuse coarse-grained and finegrained estimations based on the results from complex and multilayer structures. All aspects of our design seamlessly integrate into the endto-end pruning framework. Our experimental results, compared with state-of-the-art methods on mainstream datasets, demonstrate average accuracy improvements of 1.1%, 1.02%, 2.0%, and 1.2% for LLaMa-7B,Vicuna-7B, Baichuan-7B, and Bloom-7b1, respectively.

Earth observation (EO) applications involving complex and heterogeneous data sources are commonly approached with machine learning models. However, there is a common assumption that data sources will be persistently available. Different situations could affect the availability of EO sources, like noise, clouds, or satellite mission failures. In this work, we assess the impact of missing temporal and static EO sources in trained models across four datasets with classification and regression tasks. We compare the predictive quality of different methods and find that some are naturally more robust to missing data. The Ensemble strategy, in particular, achieves a prediction robustness up to 100%. We evidence that missing scenarios are significantly more challenging in regression than classification tasks. Finally, we find that the optical view is the most critical view when it is missing individually.

Discrete fracture models with reduced-dimensional treatment of conductive and blocking fractures are widely used to simulate fluid flow in fractured porous media. Among these, numerical methods based on interface models are intensively studied, where the fractures are treated as co-dimension one manifolds in a bulk matrix with low-dimensional governing equations. In this paper, we propose a simple yet effective treatment for modeling the fractures on fitted grids in the interior penalty discontinuous Galerkin (IPDG) methods without introducing any additional degrees of freedom or equations on the interfaces. We conduct stability and {\em hp}-analysis for the proposed IPDG method, deriving optimal a priori error bounds concerning mesh size ($h$) and sub-optimal bounds for polynomial degree ($k$) in both the energy norm and the $L^2$ norm. Numerical experiments involving published benchmarks validate our theoretical analysis and demonstrate the method's robust performance. Furthermore, we extend our method to two-phase flows and use numerical tests to confirm the algorithm's validity.

Answering questions that require reading texts in an image is challenging for current models. One key difficulty of this task is that rare, polysemous, and ambiguous words frequently appear in images, e.g., names of places, products, and sports teams. To overcome this difficulty, only resorting to pre-trained word embedding models is far from enough. A desired model should utilize the rich information in multiple modalities of the image to help understand the meaning of scene texts, e.g., the prominent text on a bottle is most likely to be the brand. Following this idea, we propose a novel VQA approach, Multi-Modal Graph Neural Network (MM-GNN). It first represents an image as a graph consisting of three sub-graphs, depicting visual, semantic, and numeric modalities respectively. Then, we introduce three aggregators which guide the message passing from one graph to another to utilize the contexts in various modalities, so as to refine the features of nodes. The updated nodes have better features for the downstream question answering module. Experimental evaluations show that our MM-GNN represents the scene texts better and obviously facilitates the performances on two VQA tasks that require reading scene texts.

Object detection typically assumes that training and test data are drawn from an identical distribution, which, however, does not always hold in practice. Such a distribution mismatch will lead to a significant performance drop. In this work, we aim to improve the cross-domain robustness of object detection. We tackle the domain shift on two levels: 1) the image-level shift, such as image style, illumination, etc, and 2) the instance-level shift, such as object appearance, size, etc. We build our approach based on the recent state-of-the-art Faster R-CNN model, and design two domain adaptation components, on image level and instance level, to reduce the domain discrepancy. The two domain adaptation components are based on H-divergence theory, and are implemented by learning a domain classifier in adversarial training manner. The domain classifiers on different levels are further reinforced with a consistency regularization to learn a domain-invariant region proposal network (RPN) in the Faster R-CNN model. We evaluate our newly proposed approach using multiple datasets including Cityscapes, KITTI, SIM10K, etc. The results demonstrate the effectiveness of our proposed approach for robust object detection in various domain shift scenarios.

Visual Question Answering (VQA) models have struggled with counting objects in natural images so far. We identify a fundamental problem due to soft attention in these models as a cause. To circumvent this problem, we propose a neural network component that allows robust counting from object proposals. Experiments on a toy task show the effectiveness of this component and we obtain state-of-the-art accuracy on the number category of the VQA v2 dataset without negatively affecting other categories, even outperforming ensemble models with our single model. On a difficult balanced pair metric, the component gives a substantial improvement in counting over a strong baseline by 6.6%.