We study the bias of Stochastic Gradient Descent (SGD) to learn low-rank weight matrices when training deep ReLU neural networks. Our results show that training neural networks with mini-batch SGD and weight decay causes a bias towards rank minimization over the weight matrices. Specifically, we show, both theoretically and empirically, that this bias is more pronounced when using smaller batch sizes, higher learning rates, or increased weight decay. Additionally, we predict and observe empirically that weight decay is necessary to achieve this bias. In addition, we show that in the presence of intermediate neural collapse, the learned weights are particularly low-rank. Unlike previous literature, our analysis does not rely on assumptions about the data, convergence, or optimality of the weight matrices. Furthermore, it applies to a wide range of neural network architectures of any width or depth. Finally, we empirically investigate the connection between this bias and generalization, finding that it has a marginal effect on generalization.
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Bayesian inference for neural networks, or Bayesian deep learning, has the potential to provide well-calibrated predictions with quantified uncertainty and robustness. However, the main hurdle for Bayesian deep learning is its computational complexity due to the high dimensionality of the parameter space. In this work, we propose a novel scheme that addresses this limitation by constructing a low-dimensional subspace of the neural network parameters-referred to as an active subspace-by identifying the parameter directions that have the most significant influence on the output of the neural network. We demonstrate that the significantly reduced active subspace enables effective and scalable Bayesian inference via either Monte Carlo (MC) sampling methods, otherwise computationally intractable, or variational inference. Empirically, our approach provides reliable predictions with robust uncertainty estimates for various regression tasks.
Graph convolutional networks (GCNs) have achieved great success in graph representation learning by extracting high-level features from nodes and their topology. Since GCNs generally follow a message-passing mechanism, each node aggregates information from its first-order neighbour to update its representation. As a result, the representations of nodes with edges between them should be positively correlated and thus can be considered positive samples. However, there are more non-neighbour nodes in the whole graph, which provide diverse and useful information for the representation update. Two non-adjacent nodes usually have different representations, which can be seen as negative samples. Besides the node representations, the structural information of the graph is also crucial for learning. In this paper, we used quality-diversity decomposition in determinant point processes (DPP) to obtain diverse negative samples. When defining a distribution on diverse subsets of all non-neighbouring nodes, we incorporate both graph structure information and node representations. Since the DPP sampling process requires matrix eigenvalue decomposition, we propose a new shortest-path-base method to improve computational efficiency. Finally, we incorporate the obtained negative samples into the graph convolution operation. The ideas are evaluated empirically in experiments on node classification tasks. These experiments show that the newly proposed methods not only improve the overall performance of standard representation learning but also significantly alleviate over-smoothing problems.
A Lightweight, Rapid and Efficient Deep Convolutional Network for Chest X-Ray Tuberculosis Detection
Tuberculosis (TB) is still recognized as one of the leading causes of death worldwide. Recent advances in deep learning (DL) have shown to enhance radiologists' ability to interpret chest X-ray (CXR) images accurately and with fewer errors, leading to a better diagnosis of this disease. However, little work has been done to develop models capable of diagnosing TB that offer good performance while being efficient, fast and computationally inexpensive. In this work, we propose LightTBNet, a novel lightweight, fast and efficient deep convolutional network specially customized to detect TB from CXR images. Using a total of 800 frontal CXR images from two publicly available datasets, our solution yielded an accuracy, F1 and area under the ROC curve (AUC) of 0.906, 0.907 and 0.961, respectively, on an independent test subset. The proposed model demonstrates outstanding performance while delivering a rapid prediction, with minimal computational and memory requirements, making it highly suitable for deployment in handheld devices that can be used in low-resource areas with high TB prevalence. Code publicly available at //github.com/dani-capellan/LightTBNet.
The Potential Outcome Framework (POF) plays a prominent role in the field of causal inference. Most causal inference models based on the POF (CIMs-POF) are designed for eliminating confounding bias and default to an underlying assumption of Confounding Covariates. This assumption posits that the covariates consist solely of confounders. However, the assumption of Confounding Covariates is challenging to maintain in practice, particularly when dealing with high-dimensional covariates. While certain methods have been proposed to differentiate the distinct components of covariates prior to conducting causal inference, the consequences of treating non-confounding covariates as confounders remain unclear. This ambiguity poses a potential risk when conducting causal inference in practical scenarios. In this paper, we present a unified graphical framework for the CIMs-POF, which greatly enhances the comprehension of these models' underlying principles. Using this graphical framework, we quantitatively analyze the extent to which the inference performance of CIMs-POF is influenced when incorporating various types of non-confounding covariates, such as instrumental variables, mediators, colliders, and adjustment variables. The key findings are: in the task of eliminating confounding bias, the optimal scenario is for the covariates to exclusively encompass confounders; in the subsequent task of inferring counterfactual outcomes, the adjustment variables contribute to more accurate inferences. Furthermore, extensive experiments conducted on synthetic datasets consistently validate these theoretical conclusions.
In recent years, soft prompt learning methods have been proposed to fine-tune large-scale vision-language pre-trained models for various downstream tasks. These methods typically combine learnable textual tokens with class tokens as input for models with frozen parameters. However, they often employ a single prompt to describe class contexts, failing to capture categories' diverse attributes adequately. This study introduces the Partitioned Multi-modal Prompt (PMPO), a multi-modal prompting technique that extends the soft prompt from a single learnable prompt to multiple prompts. Our method divides the visual encoder depths and connects learnable prompts to the separated visual depths, enabling different prompts to capture the hierarchical contextual depths of visual representations. Furthermore, to maximize the advantages of multi-prompt learning, we incorporate prior information from manually designed templates and learnable multi-prompts, thus improving the generalization capabilities of our approach. We evaluate the effectiveness of our approach on three challenging tasks: new class generalization, cross-dataset evaluation, and domain generalization. For instance, our method achieves a $79.28$ harmonic mean, averaged over 11 diverse image recognition datasets ($+7.62$ compared to CoOp), demonstrating significant competitiveness compared to state-of-the-art prompting methods.
Reinforcement Learning (RL) methods are typically sample-inefficient, making it challenging to train and deploy RL-policies in real world robots. Even a robust policy trained in simulation, requires a real-world deployment to assess their performance. This paper proposes a new approach to evaluate the real-world performance of agent policies without deploying them in the real world. The proposed approach incorporates a simulator along with real-world offline data to evaluate the performance of any policy using the framework of Marginalized Importance Sampling (MIS). Existing MIS methods face two challenges: (1) large density ratios that deviate from a reasonable range and (2) indirect supervision, where the ratio needs to be inferred indirectly, thus exacerbating estimation error. Our approach addresses these challenges by introducing the target policy's occupancy in the simulator as an intermediate variable and learning the density ratio as the product of two terms that can be learned separately. The first term is learned with direct supervision and the second term has a small magnitude, thus making it easier to run. We analyze the sample complexity as well as error propagation of our two step-procedure. Furthermore, we empirically evaluate our approach on Sim2Sim environments such as Cartpole, Reacher and Half-Cheetah. Our results show that our method generalizes well across a variety of Sim2Sim gap, target policies and offline data collection policies. We also demonstrate the performance of our algorithm on a Sim2Real task of validating the performance of a 7 DOF robotic arm using offline data along with a gazebo based arm simulator.
With the rapid progress in Multi-Agent Path Finding (MAPF), researchers have studied how MAPF algorithms can be deployed to coordinate hundreds of robots in large automated warehouses. While most works try to improve the throughput of such warehouses by developing better MAPF algorithms, we focus on improving the throughput by optimizing the warehouse layout. We show that, even with state-of-the-art MAPF algorithms, commonly used human-designed layouts can lead to congestion for warehouses with large numbers of robots and thus have limited scalability. We extend existing automatic scenario generation methods to optimize warehouse layouts. Results show that our optimized warehouse layouts (1) reduce traffic congestion and thus improve throughput, (2) improve the scalability of the automated warehouses by doubling the number of robots in some cases, and (3) are capable of generating layouts with user-specified diversity measures. We include the source code at: //github.com/lunjohnzhang/warehouse_env_gen_public
Ensembles over neural network weights trained from different random initialization, known as deep ensembles, achieve state-of-the-art accuracy and calibration. The recently introduced batch ensembles provide a drop-in replacement that is more parameter efficient. In this paper, we design ensembles not only over weights, but over hyperparameters to improve the state of the art in both settings. For best performance independent of budget, we propose hyper-deep ensembles, a simple procedure that involves a random search over different hyperparameters, themselves stratified across multiple random initializations. Its strong performance highlights the benefit of combining models with both weight and hyperparameter diversity. We further propose a parameter efficient version, hyper-batch ensembles, which builds on the layer structure of batch ensembles and self-tuning networks. The computational and memory costs of our method are notably lower than typical ensembles. On image classification tasks, with MLP, LeNet, and Wide ResNet 28-10 architectures, our methodology improves upon both deep and batch ensembles.
Automatic KB completion for commonsense knowledge graphs (e.g., ATOMIC and ConceptNet) poses unique challenges compared to the much studied conventional knowledge bases (e.g., Freebase). Commonsense knowledge graphs use free-form text to represent nodes, resulting in orders of magnitude more nodes compared to conventional KBs (18x more nodes in ATOMIC compared to Freebase (FB15K-237)). Importantly, this implies significantly sparser graph structures - a major challenge for existing KB completion methods that assume densely connected graphs over a relatively smaller set of nodes. In this paper, we present novel KB completion models that can address these challenges by exploiting the structural and semantic context of nodes. Specifically, we investigate two key ideas: (1) learning from local graph structure, using graph convolutional networks and automatic graph densification and (2) transfer learning from pre-trained language models to knowledge graphs for enhanced contextual representation of knowledge. We describe our method to incorporate information from both these sources in a joint model and provide the first empirical results for KB completion on ATOMIC and evaluation with ranking metrics on ConceptNet. Our results demonstrate the effectiveness of language model representations in boosting link prediction performance and the advantages of learning from local graph structure (+1.5 points in MRR for ConceptNet) when training on subgraphs for computational efficiency. Further analysis on model predictions shines light on the types of commonsense knowledge that language models capture well.
Pre-trained deep neural network language models such as ELMo, GPT, BERT and XLNet have recently achieved state-of-the-art performance on a variety of language understanding tasks. However, their size makes them impractical for a number of scenarios, especially on mobile and edge devices. In particular, the input word embedding matrix accounts for a significant proportion of the model's memory footprint, due to the large input vocabulary and embedding dimensions. Knowledge distillation techniques have had success at compressing large neural network models, but they are ineffective at yielding student models with vocabularies different from the original teacher models. We introduce a novel knowledge distillation technique for training a student model with a significantly smaller vocabulary as well as lower embedding and hidden state dimensions. Specifically, we employ a dual-training mechanism that trains the teacher and student models simultaneously to obtain optimal word embeddings for the student vocabulary. We combine this approach with learning shared projection matrices that transfer layer-wise knowledge from the teacher model to the student model. Our method is able to compress the BERT_BASE model by more than 60x, with only a minor drop in downstream task metrics, resulting in a language model with a footprint of under 7MB. Experimental results also demonstrate higher compression efficiency and accuracy when compared with other state-of-the-art compression techniques.
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