CVMar 7, 2024Code
Disentangled Diffusion-Based 3D Human Pose Estimation with Hierarchical Spatial and Temporal DenoiserQingyuan Cai, Xuecai Hu, Saihui Hou et al.
Recently, diffusion-based methods for monocular 3D human pose estimation have achieved state-of-the-art (SOTA) performance by directly regressing the 3D joint coordinates from the 2D pose sequence. Although some methods decompose the task into bone length and bone direction prediction based on the human anatomical skeleton to explicitly incorporate more human body prior constraints, the performance of these methods is significantly lower than that of the SOTA diffusion-based methods. This can be attributed to the tree structure of the human skeleton. Direct application of the disentangled method could amplify the accumulation of hierarchical errors, propagating through each hierarchy. Meanwhile, the hierarchical information has not been fully explored by the previous methods. To address these problems, a Disentangled Diffusion-based 3D Human Pose Estimation method with Hierarchical Spatial and Temporal Denoiser is proposed, termed DDHPose. In our approach: (1) We disentangle the 3D pose and diffuse the bone length and bone direction during the forward process of the diffusion model to effectively model the human pose prior. A disentanglement loss is proposed to supervise diffusion model learning. (2) For the reverse process, we propose Hierarchical Spatial and Temporal Denoiser (HSTDenoiser) to improve the hierarchical modeling of each joint. Our HSTDenoiser comprises two components: the Hierarchical-Related Spatial Transformer (HRST) and the Hierarchical-Related Temporal Transformer (HRTT). HRST exploits joint spatial information and the influence of the parent joint on each joint for spatial modeling, while HRTT utilizes information from both the joint and its hierarchical adjacent joints to explore the hierarchical temporal correlations among joints. Code and models are available at https://github.com/Andyen512/DDHPose
82.6CVMar 29
MuSEAgent: A Multimodal Reasoning Agent with Stateful ExperiencesShijian Wang, Jiarui Jin, Runhao Fu et al.
Research agents have recently achieved significant progress in information seeking and synthesis across heterogeneous textual and visual sources. In this paper, we introduce MuSEAgent, a multimodal reasoning agent that enhances decision-making by extending the capabilities of research agents to discover and leverage stateful experiences. Rather than relying on trajectory-level retrieval, we propose a stateful experience learning paradigm that abstracts interaction data into atomic decision experiences through hindsight reasoning. These experiences are organized into a quality-filtered experience bank that supports policy-driven experience retrieval at inference time. Specifically, MuSEAgent enables adaptive experience exploitation through complementary wide- and deep-search strategies, allowing the agent to dynamically retrieve multimodal guidance across diverse compositional semantic viewpoints. Extensive experiments demonstrate that MuSEAgent consistently outperforms strong trajectory-level experience retrieval baselines on both fine-grained visual perception and complex multimodal reasoning tasks. These results validate the effectiveness of stateful experience modeling in improving multimodal agent reasoning.
CVMar 12, 2025Code
Incomplete Multi-view Clustering via Diffusion Contrastive GenerationYuanyang Zhang, Yijie Lin, Weiqing Yan et al.
Incomplete multi-view clustering (IMVC) has garnered increasing attention in recent years due to the common issue of missing data in multi-view datasets. The primary approach to address this challenge involves recovering the missing views before applying conventional multi-view clustering methods. Although imputation-based IMVC methods have achieved significant improvements, they still encounter notable limitations: 1) heavy reliance on paired data for training the data recovery module, which is impractical in real scenarios with high missing data rates; 2) the generated data often lacks diversity and discriminability, resulting in suboptimal clustering results. To address these shortcomings, we propose a novel IMVC method called Diffusion Contrastive Generation (DCG). Motivated by the consistency between the diffusion and clustering processes, DCG learns the distribution characteristics to enhance clustering by applying forward diffusion and reverse denoising processes to intra-view data. By performing contrastive learning on a limited set of paired multi-view samples, DCG can align the generated views with the real views, facilitating accurate recovery of views across arbitrary missing view scenarios. Additionally, DCG integrates instance-level and category-level interactive learning to exploit the consistent and complementary information available in multi-view data, achieving robust and end-to-end clustering. Extensive experiments demonstrate that our method outperforms state-of-the-art approaches. The code is available at https://github.com/zhangyuanyang21/2025-AAAI-DCG.
CVDec 11, 2024Code
Investigating the Scaling Effect of Instruction Templates for Training Multimodal Language ModelShijian Wang, Linxin Song, Jieyu Zhang et al.
Current multimodal language model (MLM) training approaches overlook the influence of instruction templates. Previous research deals with this problem by leveraging hand-crafted or model-generated templates, failing to investigate the scaling effect of instruction templates on MLM training. In this work, we propose a programmatic instruction template generator capable of producing over 15K unique instruction templates by filling randomly sampled positional synonyms into weighted sampled meta templates, enabling us to comprehensively explore MLM's performance across various template scales in the training process. Our investigation into scaling instruction templates for MLM training demonstrates that MLM capabilities do not consistently improve with increasing template scale. Instead, optimal performance is achieved at a medium template scale. Models trained with data augmented at the optimal template scale achieve performance gains of up to 10% over those trained on the original data and achieve the best overall performance compared with the similar-scale MLMs tuned on at most 75 times the scale of our augmented dataset. The code will be publicly available at https://github.com/shijian2001/TemplateScaling.
LGDec 4, 2024
AI-Driven Day-to-Day Route ChoiceLeizhen Wang, Peibo Duan, Zhengbing He et al.
Understanding travelers' route choices can help policymakers devise optimal operational and planning strategies for both normal and abnormal circumstances. However, existing choice modeling methods often rely on predefined assumptions and struggle to capture the dynamic and adaptive nature of travel behavior. Recently, Large Language Models (LLMs) have emerged as a promising alternative, demonstrating remarkable ability to replicate human-like behaviors across various fields. Despite this potential, their capacity to accurately simulate human route choice behavior in transportation contexts remains doubtful. To satisfy this curiosity, this paper investigates the potential of LLMs for route choice modeling by introducing an LLM-empowered agent, "LLMTraveler." This agent integrates an LLM as its core, equipped with a memory system that learns from past experiences and makes decisions by balancing retrieved data and personality traits. The study systematically evaluates the LLMTraveler's ability to replicate human-like decision-making through two stages of day-to-day (DTD) congestion games: (1) analyzing its route-switching behavior in single origin-destination (OD) pair scenarios, where it demonstrates patterns that align with laboratory data but cannot be fully explained by traditional models, and (2) testing its capacity to model adaptive learning behaviors in multi-OD scenarios on the Ortuzar and Willumsen (OW) network, producing results comparable to Multinomial Logit (MNL) and Reinforcement Learning (RL) models. These experiments demonstrate that the framework can partially replicate human-like decision-making in route choice while providing natural language explanations for its decisions. This capability offers valuable insights for transportation policymaking, such as simulating traveler responses to new policies or changes in the network.
CLDec 26, 2023
More than Correlation: Do Large Language Models Learn Causal Representations of Space?Yida Chen, Yixian Gan, Sijia Li et al. · harvard
Recent work found high mutual information between the learned representations of large language models (LLMs) and the geospatial property of its input, hinting an emergent internal model of space. However, whether this internal space model has any causal effects on the LLMs' behaviors was not answered by that work, led to criticism of these findings as mere statistical correlation. Our study focused on uncovering the causality of the spatial representations in LLMs. In particular, we discovered the potential spatial representations in DeBERTa, GPT-Neo using representational similarity analysis and linear and non-linear probing. Our casual intervention experiments showed that the spatial representations influenced the model's performance on next word prediction and a downstream task that relies on geospatial information. Our experiments suggested that the LLMs learn and use an internal model of space in solving geospatial related tasks.
CVApr 14, 2025
ESCT3D: Efficient and Selectively Controllable Text-Driven 3D Content Generation with Gaussian SplattingHuiqi Wu, Jianbo Mei, Yingjie Huang et al.
In recent years, significant advancements have been made in text-driven 3D content generation. However, several challenges remain. In practical applications, users often provide extremely simple text inputs while expecting high-quality 3D content. Generating optimal results from such minimal text is a difficult task due to the strong dependency of text-to-3D models on the quality of input prompts. Moreover, the generation process exhibits high variability, making it difficult to control. Consequently, multiple iterations are typically required to produce content that meets user expectations, reducing generation efficiency. To address this issue, we propose GPT-4V for self-optimization, which significantly enhances the efficiency of generating satisfactory content in a single attempt. Furthermore, the controllability of text-to-3D generation methods has not been fully explored. Our approach enables users to not only provide textual descriptions but also specify additional conditions, such as style, edges, scribbles, poses, or combinations of multiple conditions, allowing for more precise control over the generated 3D content. Additionally, during training, we effectively integrate multi-view information, including multi-view depth, masks, features, and images, to address the common Janus problem in 3D content generation. Extensive experiments demonstrate that our method achieves robust generalization, facilitating the efficient and controllable generation of high-quality 3D content.
CLOct 27, 2020
On the diminishing return of labeling clinical reportsJean-Baptiste Lamare, Tobi Olatunji, Li Yao
Ample evidence suggests that better machine learning models may be steadily obtained by training on increasingly larger datasets on natural language processing (NLP) problems from non-medical domains. Whether the same holds true for medical NLP has by far not been thoroughly investigated. This work shows that this is indeed not always the case. We reveal the somehow counter-intuitive observation that performant medical NLP models may be obtained with small amount of labeled data, quite the opposite to the common belief, most likely due to the domain specificity of the problem. We show quantitatively the effect of training data size on a fixed test set composed of two of the largest public chest x-ray radiology report datasets on the task of abnormality classification. The trained models not only make use of the training data efficiently, but also outperform the current state-of-the-art rule-based systems by a significant margin.
CLOct 1, 2019
Learning to estimate label uncertainty for automatic radiology report parsingTobi Olatunji, Li Yao
Bootstrapping labels from radiology reports has become the scalable alternative to provide inexpensive ground truth for medical imaging. Because of the domain specific nature, state-of-the-art report labeling tools are predominantly rule-based. These tools, however, typically yield a binary 0 or 1 prediction that indicates the presence or absence of abnormalities. These hard targets are then used as ground truth to train image models in the downstream, forcing models to express high degree of certainty even on cases where specificity is low. This could negatively impact the statistical efficiency of image models. We address such an issue by training a Bidirectional Long-Short Term Memory Network to augment heuristic-based discrete labels of X-ray reports from all body regions and achieve performance comparable or better than domain-specific NLP, but with additional uncertainty estimates which enable finer downstream image model training.
CLMay 6, 2019
Caveats in Generating Medical Imaging Labels from Radiology ReportsTobi Olatunji, Li Yao, Ben Covington et al.
Acquiring high-quality annotations in medical imaging is usually a costly process. Automatic label extraction with natural language processing (NLP) has emerged as a promising workaround to bypass the need of expert annotation. Despite the convenience, the limitation of such an approximation has not been carefully examined and is not well understood. With a challenging set of 1,000 chest X-ray studies and their corresponding radiology reports, we show that there exists a surprisingly large discrepancy between what radiologists visually perceive and what they clinically report. Furthermore, with inherently flawed report as ground truth, the state-of-the-art medical NLP fails to produce high-fidelity labels.
CVApr 2, 2019
A Strong Baseline for Domain Adaptation and Generalization in Medical ImagingLi Yao, Jordan Prosky, Ben Covington et al.
This work provides a strong baseline for the problem of multi-source multi-target domain adaptation and generalization in medical imaging. Using a diverse collection of ten chest X-ray datasets, we empirically demonstrate the benefits of training medical imaging deep learning models on varied patient populations for generalization to out-of-sample domains.
CLOct 1, 2018
Efficient and Accurate Abnormality Mining from Radiology Reports with Customized False Positive ReductionNithya Attaluri, Ahmed Nasir, Carolynne Powe et al.
Obtaining datasets labeled to facilitate model development is a challenge for most machine learning tasks. The difficulty is heightened for medical imaging, where data itself is limited in accessibility and labeling requires costly time and effort by trained medical specialists. Medical imaging studies, however, are often accompanied by a medical report produced by a radiologist, identifying important features on the corresponding scan for other physicians not specifically trained in radiology. We propose a methodology for approximating image-level labels for radiology studies from associated reports using a general purpose language processing tool for medical concept extraction and sentiment analysis, and simple manually crafted heuristics for false positive reduction. Using this approach, we label more than 175,000 Head CT studies for the presence of 33 features indicative of 11 clinically relevant conditions. For 27 of the 30 keywords that yielded positive results (3 had no occurrences), the lower bound of the confidence intervals created to estimate the percentage of accurately labeled reports was above 85%, with the average being above 95%. Though noisier then manual labeling, these results suggest this method to be a viable means of labeling medical images at scale.
CVMar 21, 2018
Weakly Supervised Medical Diagnosis and Localization from Multiple ResolutionsLi Yao, Jordan Prosky, Eric Poblenz et al.
Diagnostic imaging often requires the simultaneous identification of a multitude of findings of varied size and appearance. Beyond global indication of said findings, the prediction and display of localization information improves trust in and understanding of results when augmenting clinical workflow. Medical training data rarely includes more than global image-level labels as segmentations are time-consuming and expensive to collect. We introduce an approach to managing these practical constraints by applying a novel architecture which learns at multiple resolutions while generating saliency maps with weak supervision. Further, we parameterize the Log-Sum-Exp pooling function with a learnable lower-bounded adaptation (LSE-LBA) to build in a sharpness prior and better handle localizing abnormalities of different sizes using only image-level labels. Applying this approach to interpreting chest x-rays, we set the state of the art on 9 abnormalities in the NIH's CXR14 dataset while generating saliency maps with the highest resolution to date.
CVOct 28, 2017
Learning to diagnose from scratch by exploiting dependencies among labelsLi Yao, Eric Poblenz, Dmitry Dagunts et al.
The field of medical diagnostics contains a wealth of challenges which closely resemble classical machine learning problems; practical constraints, however, complicate the translation of these endpoints naively into classical architectures. Many tasks in radiology, for example, are largely problems of multi-label classification wherein medical images are interpreted to indicate multiple present or suspected pathologies. Clinical settings drive the necessity for high accuracy simultaneously across a multitude of pathological outcomes and greatly limit the utility of tools which consider only a subset. This issue is exacerbated by a general scarcity of training data and maximizes the need to extract clinically relevant features from available samples -- ideally without the use of pre-trained models which may carry forward undesirable biases from tangentially related tasks. We present and evaluate a partial solution to these constraints in using LSTMs to leverage interdependencies among target labels in predicting 14 pathologic patterns from chest x-rays and establish state of the art results on the largest publicly available chest x-ray dataset from the NIH without pre-training. Furthermore, we propose and discuss alternative evaluation metrics and their relevance in clinical practice.
SCMay 9, 2016
Theano: A Python framework for fast computation of mathematical expressionsThe Theano Development Team, Rami Al-Rfou, Guillaume Alain et al.
Theano is a Python library that allows to define, optimize, and evaluate mathematical expressions involving multi-dimensional arrays efficiently. Since its introduction, it has been one of the most used CPU and GPU mathematical compilers - especially in the machine learning community - and has shown steady performance improvements. Theano is being actively and continuously developed since 2008, multiple frameworks have been built on top of it and it has been used to produce many state-of-the-art machine learning models. The present article is structured as follows. Section I provides an overview of the Theano software and its community. Section II presents the principal features of Theano and how to use them, and compares them with other similar projects. Section III focuses on recently-introduced functionalities and improvements. Section IV compares the performance of Theano against Torch7 and TensorFlow on several machine learning models. Section V discusses current limitations of Theano and potential ways of improving it.
CVNov 19, 2015
Delving Deeper into Convolutional Networks for Learning Video RepresentationsNicolas Ballas, Li Yao, Chris Pal et al.
We propose an approach to learn spatio-temporal features in videos from intermediate visual representations we call "percepts" using Gated-Recurrent-Unit Recurrent Networks (GRUs).Our method relies on percepts that are extracted from all level of a deep convolutional network trained on the large ImageNet dataset. While high-level percepts contain highly discriminative information, they tend to have a low-spatial resolution. Low-level percepts, on the other hand, preserve a higher spatial resolution from which we can model finer motion patterns. Using low-level percepts can leads to high-dimensionality video representations. To mitigate this effect and control the model number of parameters, we introduce a variant of the GRU model that leverages the convolution operations to enforce sparse connectivity of the model units and share parameters across the input spatial locations. We empirically validate our approach on both Human Action Recognition and Video Captioning tasks. In particular, we achieve results equivalent to state-of-art on the YouTube2Text dataset using a simpler text-decoder model and without extra 3D CNN features.
CVNov 14, 2015
Oracle performance for visual captioningLi Yao, Nicolas Ballas, Kyunghyun Cho et al.
The task of associating images and videos with a natural language description has attracted a great amount of attention recently. Rapid progress has been made in terms of both developing novel algorithms and releasing new datasets. Indeed, the state-of-the-art results on some of the standard datasets have been pushed into the regime where it has become more and more difficult to make significant improvements. Instead of proposing new models, this work investigates the possibility of empirically establishing performance upper bounds on various visual captioning datasets without extra data labelling effort or human evaluation. In particular, it is assumed that visual captioning is decomposed into two steps: from visual inputs to visual concepts, and from visual concepts to natural language descriptions. One would be able to obtain an upper bound when assuming the first step is perfect and only requiring training a conditional language model for the second step. We demonstrate the construction of such bounds on MS-COCO, YouTube2Text and LSMDC (a combination of M-VAD and MPII-MD). Surprisingly, despite of the imperfect process we used for visual concept extraction in the first step and the simplicity of the language model for the second step, we show that current state-of-the-art models fall short when being compared with the learned upper bounds. Furthermore, with such a bound, we quantify several important factors concerning image and video captioning: the number of visual concepts captured by different models, the trade-off between the amount of visual elements captured and their accuracy, and the intrinsic difficulty and blessing of different datasets.
LGMar 18, 2015
GSNs : Generative Stochastic NetworksGuillaume Alain, Yoshua Bengio, Li Yao et al.
We introduce a novel training principle for probabilistic models that is an alternative to maximum likelihood. The proposed Generative Stochastic Networks (GSN) framework is based on learning the transition operator of a Markov chain whose stationary distribution estimates the data distribution. Because the transition distribution is a conditional distribution generally involving a small move, it has fewer dominant modes, being unimodal in the limit of small moves. Thus, it is easier to learn, more like learning to perform supervised function approximation, with gradients that can be obtained by back-propagation. The theorems provided here generalize recent work on the probabilistic interpretation of denoising auto-encoders and provide an interesting justification for dependency networks and generalized pseudolikelihood (along with defining an appropriate joint distribution and sampling mechanism, even when the conditionals are not consistent). We study how GSNs can be used with missing inputs and can be used to sample subsets of variables given the rest. Successful experiments are conducted, validating these theoretical results, on two image datasets and with a particular architecture that mimics the Deep Boltzmann Machine Gibbs sampler but allows training to proceed with backprop, without the need for layerwise pretraining.
MLFeb 27, 2015
Describing Videos by Exploiting Temporal StructureLi Yao, Atousa Torabi, Kyunghyun Cho et al.
Recent progress in using recurrent neural networks (RNNs) for image description has motivated the exploration of their application for video description. However, while images are static, working with videos requires modeling their dynamic temporal structure and then properly integrating that information into a natural language description. In this context, we propose an approach that successfully takes into account both the local and global temporal structure of videos to produce descriptions. First, our approach incorporates a spatial temporal 3-D convolutional neural network (3-D CNN) representation of the short temporal dynamics. The 3-D CNN representation is trained on video action recognition tasks, so as to produce a representation that is tuned to human motion and behavior. Second we propose a temporal attention mechanism that allows to go beyond local temporal modeling and learns to automatically select the most relevant temporal segments given the text-generating RNN. Our approach exceeds the current state-of-art for both BLEU and METEOR metrics on the Youtube2Text dataset. We also present results on a new, larger and more challenging dataset of paired video and natural language descriptions.
MLSep 2, 2014
On the Equivalence Between Deep NADE and Generative Stochastic NetworksLi Yao, Sherjil Ozair, Kyunghyun Cho et al.
Neural Autoregressive Distribution Estimators (NADEs) have recently been shown as successful alternatives for modeling high dimensional multimodal distributions. One issue associated with NADEs is that they rely on a particular order of factorization for $P(\mathbf{x})$. This issue has been recently addressed by a variant of NADE called Orderless NADEs and its deeper version, Deep Orderless NADE. Orderless NADEs are trained based on a criterion that stochastically maximizes $P(\mathbf{x})$ with all possible orders of factorizations. Unfortunately, ancestral sampling from deep NADE is very expensive, corresponding to running through a neural net separately predicting each of the visible variables given some others. This work makes a connection between this criterion and the training criterion for Generative Stochastic Networks (GSNs). It shows that training NADEs in this way also trains a GSN, which defines a Markov chain associated with the NADE model. Based on this connection, we show an alternative way to sample from a trained Orderless NADE that allows to trade-off computing time and quality of the samples: a 3 to 10-fold speedup (taking into account the waste due to correlations between consecutive samples of the chain) can be obtained without noticeably reducing the quality of the samples. This is achieved using a novel sampling procedure for GSNs called annealed GSN sampling, similar to tempering methods that combines fast mixing (obtained thanks to steps at high noise levels) with accurate samples (obtained thanks to steps at low noise levels).
MLJun 5, 2014
Iterative Neural Autoregressive Distribution Estimator (NADE-k)Tapani Raiko, Li Yao, Kyunghyun Cho et al.
Training of the neural autoregressive density estimator (NADE) can be viewed as doing one step of probabilistic inference on missing values in data. We propose a new model that extends this inference scheme to multiple steps, arguing that it is easier to learn to improve a reconstruction in $k$ steps rather than to learn to reconstruct in a single inference step. The proposed model is an unsupervised building block for deep learning that combines the desirable properties of NADE and multi-predictive training: (1) Its test likelihood can be computed analytically, (2) it is easy to generate independent samples from it, and (3) it uses an inference engine that is a superset of variational inference for Boltzmann machines. The proposed NADE-k is competitive with the state-of-the-art in density estimation on the two datasets tested.
LGDec 19, 2013
Multimodal Transitions for Generative Stochastic NetworksSherjil Ozair, Li Yao, Yoshua Bengio
Generative Stochastic Networks (GSNs) have been recently introduced as an alternative to traditional probabilistic modeling: instead of parametrizing the data distribution directly, one parametrizes a transition operator for a Markov chain whose stationary distribution is an estimator of the data generating distribution. The result of training is therefore a machine that generates samples through this Markov chain. However, the previously introduced GSN consistency theorems suggest that in order to capture a wide class of distributions, the transition operator in general should be multimodal, something that has not been done before this paper. We introduce for the first time multimodal transition distributions for GSNs, in particular using models in the NADE family (Neural Autoregressive Density Estimator) as output distributions of the transition operator. A NADE model is related to an RBM (and can thus model multimodal distributions) but its likelihood (and likelihood gradient) can be computed easily. The parameters of the NADE are obtained as a learned function of the previous state of the learned Markov chain. Experiments clearly illustrate the advantage of such multimodal transition distributions over unimodal GSNs.
LGNov 24, 2013
Bounding the Test Log-Likelihood of Generative ModelsYoshua Bengio, Li Yao, Kyunghyun Cho
Several interesting generative learning algorithms involve a complex probability distribution over many random variables, involving intractable normalization constants or latent variable normalization. Some of them may even not have an analytic expression for the unnormalized probability function and no tractable approximation. This makes it difficult to estimate the quality of these models, once they have been trained, or to monitor their quality (e.g. for early stopping) while training. A previously proposed method is based on constructing a non-parametric density estimator of the model's probability function from samples generated by the model. We revisit this idea, propose a more efficient estimator, and prove that it provides a lower bound on the true test log-likelihood, and an unbiased estimator as the number of generated samples goes to infinity, although one that incorporates the effect of poor mixing. We further propose a biased variant of the estimator that can be used reliably with a finite number of samples for the purpose of model comparison.
LGMay 29, 2013
Generalized Denoising Auto-Encoders as Generative ModelsYoshua Bengio, Li Yao, Guillaume Alain et al.
Recent work has shown how denoising and contractive autoencoders implicitly capture the structure of the data-generating density, in the case where the corruption noise is Gaussian, the reconstruction error is the squared error, and the data is continuous-valued. This has led to various proposals for sampling from this implicitly learned density function, using Langevin and Metropolis-Hastings MCMC. However, it remained unclear how to connect the training procedure of regularized auto-encoders to the implicit estimation of the underlying data-generating distribution when the data are discrete, or using other forms of corruption process and reconstruction errors. Another issue is the mathematical justification which is only valid in the limit of small corruption noise. We propose here a different attack on the problem, which deals with all these issues: arbitrary (but noisy enough) corruption, arbitrary reconstruction loss (seen as a log-likelihood), handling both discrete and continuous-valued variables, and removing the bias due to non-infinitesimal corruption noise (or non-infinitesimal contractive penalty).