Hamiltonian Monte Carlo (HMC) is a powerful tool for Bayesian statistical inference due to its potential to rapidly explore high dimensional state space, avoiding the random walk behavior typical of many Markov Chain Monte Carlo samplers. The proper choice of the integrator of the Hamiltonian dynamics is key to the efficiency of HMC. It is becoming increasingly clear that multi-stage splitting integrators are a good alternative to the Verlet method, traditionally used in HMC. Here we propose a principled way of finding optimal, problem-specific integration schemes (in terms of the best conservation of energy for harmonic forces/Gaussian targets) within the families of 2- and 3-stage splitting integrators. The method, which we call Adaptive Integration Approach for statistics, or s-AIA, uses a multivariate Gaussian model and simulation data obtained at the HMC burn-in stage to identify a system-specific dimensional stability interval and assigns the most appropriate 2-/3-stage integrator for any user-chosen simulation step size within that interval. s-AIA has been implemented in the in-house software package HaiCS without introducing computational overheads in the simulations. The efficiency of the s-AIA integrators and their impact on the HMC accuracy, sampling performance and convergence are discussed in comparison with known fixed-parameter multi-stage splitting integrators (including Verlet). Numerical experiments on well-known statistical models show that the adaptive schemes reach the best possible performance within the family of 2-, 3-stage splitting schemes.
Large Language Models (LLMs), benefiting from the auto-regressive modelling approach performed on massive unannotated texts corpora, demonstrates powerful perceptual and reasoning capabilities. However, as for extending auto-regressive modelling to multi-modal scenarios to build Large Multi-modal Models (LMMs), there lies a great difficulty that the image information is processed in the LMM as continuous visual embeddings, which cannot obtain discrete supervised labels for classification. In this paper, we successfully perform multi-modal auto-regressive modeling with a unified objective for the first time. Specifically, we propose the concept of visual words, which maps the visual features to probability distributions over LLM's vocabulary, providing supervision information for visual modelling. We further explore the distribution of visual features in the semantic space within LMM and the possibility of using text embeddings to represent visual information. Experimental results and ablation studies on 5 VQA tasks and 4 benchmark toolkits validate the powerful performance of our proposed approach.
We present ReCAT, a recursive composition augmented Transformer that is able to explicitly model hierarchical syntactic structures of raw texts without relying on gold trees during both learning and inference. Existing research along this line restricts data to follow a hierarchical tree structure and thus lacks inter-span communications. To overcome the problem, we propose a novel contextual inside-outside (CIO) layer that learns contextualized representations of spans through bottom-up and top-down passes, where a bottom-up pass forms representations of high-level spans by composing low-level spans, while a top-down pass combines information inside and outside a span. By stacking several CIO layers between the embedding layer and the attention layers in Transformer, the ReCAT model can perform both deep intra-span and deep inter-span interactions, and thus generate multi-grained representations fully contextualized with other spans. Moreover, the CIO layers can be jointly pre-trained with Transformers, making ReCAT enjoy scaling ability, strong performance, and interpretability at the same time. We conduct experiments on various sentence-level and span-level tasks. Evaluation results indicate that ReCAT can significantly outperform vanilla Transformer models on all span-level tasks and baselines that combine recursive networks with Transformers on natural language inference tasks. More interestingly, the hierarchical structures induced by ReCAT exhibit strong consistency with human-annotated syntactic trees, indicating good interpretability brought by the CIO layers.
Foundation models, such as Large language Models (LLMs), have attracted significant amount of interest due to their large number of applications. Existing works show that appropriate prompt design, such as Chain-of-Thoughts, can unlock LLM's powerful capacity in diverse areas. However, when handling tasks involving repetitive sub-tasks and/or deceptive contents, such as arithmetic calculation and article-level fake news detection, existing prompting strategies either suffers from insufficient expressive power or intermediate errors triggered by hallucination. To make LLM more discerning to such intermediate errors, we propose to guide LLM with a Divide-and-Conquer program that simultaneously ensures superior expressive power and disentangles task decomposition, sub-task resolution, and resolution assembly process. Theoretic analysis reveals that our strategy can guide LLM to extend the expressive power of fixed-depth Transformer. Experiments indicate that our proposed method can achieve better performance than typical prompting strategies in tasks bothered by intermediate errors and deceptive contents, such as large integer multiplication, hallucination detection and misinformation detection.
Proof-theoretic semantics (P-tS) is the approach to meaning in logic based on proof (as opposed to truth). There are two major approaches to P-tS: proof-theor\-etic validity (P-tV) and base-extension semantics (B-eS). The former is a semantics of arguments, and the latter is a semantics of logical constants. This paper demonstrates that the B-eS for intuitionistic propositional logic (IPL) encapsulates the declarative content of a basic version of P-tV. Such relationships have been considered before yielding incompleteness results. This paper diverges from these approaches by accounting for the constructive, hypothetical setup of P-tV. It explicates how the B-eS for IPL works.
Pre-trained models with large-scale training data, such as CLIP and Stable Diffusion, have demonstrated remarkable performance in various high-level computer vision tasks such as image understanding and generation from language descriptions. Yet, their potential for low-level tasks such as image restoration remains relatively unexplored. In this paper, we explore such models to enhance image restoration. As off-the-shelf features (OSF) from pre-trained models do not directly serve image restoration, we propose to learn an additional lightweight module called Pre-Train-Guided Refinement Module (PTG-RM) to refine restoration results of a target restoration network with OSF. PTG-RM consists of two components, Pre-Train-Guided Spatial-Varying Enhancement (PTG-SVE), and Pre-Train-Guided Channel-Spatial Attention (PTG-CSA). PTG-SVE enables optimal short- and long-range neural operations, while PTG-CSA enhances spatial-channel attention for restoration-related learning. Extensive experiments demonstrate that PTG-RM, with its compact size ($<$1M parameters), effectively enhances restoration performance of various models across different tasks, including low-light enhancement, deraining, deblurring, and denoising.
Few-shot anomaly detection (FSAD) is essential in industrial manufacturing. However, existing FSAD methods struggle to effectively leverage a limited number of normal samples, and they may fail to detect and locate inconspicuous anomalies in the spatial domain. We further discover that these subtle anomalies would be more noticeable in the frequency domain. In this paper, we propose a Dual-Path Frequency Discriminators (DFD) network from a frequency perspective to tackle these issues. Specifically, we generate anomalies at both image-level and feature-level. Differential frequency components are extracted by the multi-frequency information construction module and supplied into the fine-grained feature construction module to provide adapted features. We consider anomaly detection as a discriminative classification problem, wherefore the dual-path feature discrimination module is employed to detect and locate the image-level and feature-level anomalies in the feature space. The discriminators aim to learn a joint representation of anomalous features and normal features in the latent space. Extensive experiments conducted on MVTec AD and VisA benchmarks demonstrate that our DFD surpasses current state-of-the-art methods. Source code will be available.
Using Non-negative Matrix Factorization (NMF), the observed matrix can be approximated by the product of the basis and coefficient matrices. Moreover, if the coefficient vectors are explained by the covariates for each individual, the coefficient matrix can be written as the product of the parameter matrix and the covariate matrix, and additionally described in the framework of Non-negative Matrix tri-Factorization (tri-NMF) with covariates. Consequently, this is equal to the mean structure of the Growth Curve Model (GCM). The difference is that the basis matrix for GCM is given by the analyst, whereas that for NMF with covariates is unknown and optimized. In this study, we applied NMF with covariance to longitudinal data and compared it with GCM. We have also published an R package that implements this method, and we show how to use it through examples of data analyses including longitudinal measurement, spatiotemporal data and text data. In particular, we demonstrate the usefulness of Gaussian kernel functions as covariates.
In computational pathology, random sampling of patches during training of Multiple Instance Learning (MIL) methods is computationally efficient and serves as a regularization strategy. Despite its promising benefits, questions concerning performance trends for varying sample sizes and its influence on model interpretability remain. Addressing these, we reach an optimal performance enhancement of 1.7% using thirty percent of patches on the CAMELYON16 dataset, and 3.7% with only eight samples on the TUPAC16 dataset. We also find interpretability effects are strongly dataset-dependent, with interpretability impacted on CAMELYON16, while remaining unaffected on TUPAC16. This reinforces that both the performance and interpretability relationships with sampling are closely task-specific. End-to-end training with 1024 samples reveals improvements across both datasets compared to pre-extracted features, further highlighting the potential of this efficient approach.
Graph Neural Networks (GNNs) have recently become increasingly popular due to their ability to learn complex systems of relations or interactions arising in a broad spectrum of problems ranging from biology and particle physics to social networks and recommendation systems. Despite the plethora of different models for deep learning on graphs, few approaches have been proposed thus far for dealing with graphs that present some sort of dynamic nature (e.g. evolving features or connectivity over time). In this paper, we present Temporal Graph Networks (TGNs), a generic, efficient framework for deep learning on dynamic graphs represented as sequences of timed events. Thanks to a novel combination of memory modules and graph-based operators, TGNs are able to significantly outperform previous approaches being at the same time more computationally efficient. We furthermore show that several previous models for learning on dynamic graphs can be cast as specific instances of our framework. We perform a detailed ablation study of different components of our framework and devise the best configuration that achieves state-of-the-art performance on several transductive and inductive prediction tasks for dynamic graphs.
We introduce a new language representation model called BERT, which stands for Bidirectional Encoder Representations from Transformers. Unlike recent language representation models, BERT is designed to pre-train deep bidirectional representations from unlabeled text by jointly conditioning on both left and right context in all layers. As a result, the pre-trained BERT model can be fine-tuned with just one additional output layer to create state-of-the-art models for a wide range of tasks, such as question answering and language inference, without substantial task-specific architecture modifications. BERT is conceptually simple and empirically powerful. It obtains new state-of-the-art results on eleven natural language processing tasks, including pushing the GLUE score to 80.5% (7.7% point absolute improvement), MultiNLI accuracy to 86.7% (4.6% absolute improvement), SQuAD v1.1 question answering Test F1 to 93.2 (1.5 point absolute improvement) and SQuAD v2.0 Test F1 to 83.1 (5.1 point absolute improvement).