Low-dimensional Latent Space Research Articles

Exploring the Hysteresis Properties of Nanocrystalline Permanent Magnets Using Deep Learning

We demonstrate the use of model order reduction and neural networks for estimating the hysteresis properties of nanocrystalline permanent magnets from microstructure. With a data-driven approach, we learn the demagnetization curve from data-sets created by grain growth and micromagnetic simulations. We show that the granular structure of a magnet can be encoded within a low-dimensional latent space. Latent codes are constructed using a variational autoencoder. The mapping of structure code to hysteresis properties is a multi-target regression problem. We apply deep neural network and use parameter sharing, in order to predict anchor points along the demagnetization curves from the magnet's structure code. The method is applied to study the magnetic properties of nanocrystalline permanent magnets. We show how new grain structures can be generated by interpolation between two points in the latent space and how the magnetic properties of the resulting magnets can be predicted.

Big-Hypergraph Factorization Neural Network for Survival Prediction From Whole Slide Image.

Survival prediction for patients based on histopa- thological whole-slide images (WSIs) has attracted increasing attention in recent years. Due to the massive pixel data in a single WSI, fully exploiting cell-level structural information (e.g., stromal/tumor microenvironment) from the gigapixel WSI is challenging. Most of the current studies resolve the problem by sampling limited image patches to construct a graph-based model (e.g., hypergraph). However, the sampling scale is a critical bottleneck since it is a fundamental obstacle of broadening samples for transductive learning. To overcome the limitation of the sampling scale for constructing a big hypergraph model, we propose a factorization neural network that embeds the correlation among large-scale vertices and hyperedges into two low-dimensional latent semantic spaces separately, empowering the dense sampling. Thanks to the compressed low-dimensional correlation embedding, the hypergraph convolutional layers generate the high-order global representation for each WSI. To minimize the effect of the uncertainty data as well as to achieve the metric-driven learning, we also propose a multi-level ranking supervision to enable the network learning by a queue of patients on the global horizon. Extensive experiments are conducted on three public carcinoma datasets (i.e., LUSC, GBM, and NLST), and the quantitative results demonstrate the proposed method outperforms state-of-the-art methods across-the-board.

Improving Multi-Label Learning by Correlation Embedding

In multi-label learning, each object is represented by a single instance and is associated with more than one class labels, where the labels might be correlated with each other. As we all know, exploiting label correlations can definitely improve the performance of a multi-label classification model. Existing methods mainly model label correlations in an indirect way, i.e., adding extra constraints on the coefficients or outputs of a model based on a pre-learned label correlation graph. Meanwhile, the high dimension of the feature space also poses great challenges to multi-label learning, such as high time and memory costs. To solve the above mentioned issues, in this paper, we propose a new approach for Multi-Label Learning by Correlation Embedding, namely MLLCE, where the feature space dimension reduction and the multi-label classification are integrated into a unified framework. Specifically, we project the original high-dimensional feature space to a low-dimensional latent space by a mapping matrix. To model label correlation, we learn an embedding matrix from the pre-defined label correlation graph by graph embedding. Then, we construct a multi-label classifier from the low-dimensional latent feature space to the label space, where the embedding matrix is utilized as the model coefficients. Finally, we extend the proposed method MLLCE to the nonlinear version, i.e., NL-MLLCE. The comparison experiment with the state-of-the-art approaches shows that the proposed method MLLCE has a competitive performance in multi-label learning.

Prediction of post transarterial chemoembolization MR images of hepatocellular carcinoma using spatio-temporal graph convolutional networks.

Magnetic resonance imaging (MRI) plays a critical role in the planning and monitoring of hepatocellular carcinomas (HCC) treated with locoregional therapies, in order to assess disease progression or recurrence. Dynamic contrast-enhanced (DCE)-MRI sequences offer temporal data on tumor enhancement characteristics which has strong prognostic value. Yet, predicting follow-up DCE-MR images from which tumor enhancement and viability can be measured, before treatment of HCC actually begins, remains an unsolved problem given the complexity of spatial and temporal information. We propose an approach to predict future DCE-MRI examinations following transarterial chemoembolization (TACE) by learning the spatio-temporal features related to HCC response from pre-TACE images. A novel Spatial-Temporal Discriminant Graph Neural Network (STDGNN) based on graph convolutional networks is presented. First, embeddings of viable, equivocal and non-viable HCCs are separated within a joint low-dimensional latent space, which is created using a discriminant neural network representing tumor-specific features. Spatial tumoral features from independent MRI volumes are then extracted with a structural branch, while dynamic features are extracted from the multi-phase sequence with a separate temporal branch. The model extracts spatio-temporal features by a joint minimization of the network branches. At testing, a pre-TACE diagnostic DCE-MRI is embedded on the discriminant spatio-temporal latent space, which is then translated to the follow-up domain space, thus allowing to predict the post-TACE DCE-MRI describing HCC treatment response. A dataset of 366 HCC's from liver cancer patients was used to train and test the model using DCE-MRI examinations with associated pathological outcomes, with the spatio-temporal framework yielding 93.5% classification accuracy in response identification, and generating follow-up images yielding insignificant differences in perfusion parameters compared to ground-truth post-TACE examinations.

Probabilistic Autoencoder Using Fisher Information.

Neural networks play a growing role in many scientific disciplines, including physics. Variational autoencoders (VAEs) are neural networks that are able to represent the essential information of a high dimensional data set in a low dimensional latent space, which have a probabilistic interpretation. In particular, the so-called encoder network, the first part of the VAE, which maps its input onto a position in latent space, additionally provides uncertainty information in terms of variance around this position. In this work, an extension to the autoencoder architecture is introduced, the FisherNet. In this architecture, the latent space uncertainty is not generated using an additional information channel in the encoder but derived from the decoder by means of the Fisher information metric. This architecture has advantages from a theoretical point of view as it provides a direct uncertainty quantification derived from the model and also accounts for uncertainty cross-correlations. We can show experimentally that the FisherNet produces more accurate data reconstructions than a comparable VAE and its learning performance also apparently scales better with the number of latent space dimensions.

Tracing individual trajectory of longitudinal tau spreading in deep latent space

AbstractBackgroundAlzheimer’s disease (AD) usually appears in mid‐60s (Late‐Onset AD, LOAD), but also rarely appears in patients younger than 65 (Early‐Onset AD, EOAD), while showing distinct features. Tau shows high correlation with AD prognosis and can be detected through positron emission tomography (PET) scan. Tau data mapped into a low dimensional latent space will help detect longitudinal change pattern along AD spectrum. Furthermore, fitting tensors using individual line segments will enable us to track individual tau trajectory in the latent space.MethodWe recruited 74 healthy controls, 75 mild cognitive impairment patients, and 38 AD patients with two PET scans ([18F]Flortaucipir for tau and [18F]Florbetaben for Aβ) with two‐year follow‐up. We used standardized uptake value ratios (SUVRs) for tau PET data. All patients’ tau data went through autoencoder and principal component analysis, pretrained using baseline (BL) tau data. Using only amyloid positive AD patients’ BL – follow‐up (FU) line segments, we fit tensors and tracked individual trajectories in the latent space using a tensor tracing algorithm.ResultIn the 2‐dimensional latent space the points dispersed toward the upper‐ and right‐side as the disease deteriorated. Reconstructed SUVR maps showed tau accumulation pattern of EOAD through x‐axis, such as tau spreading in temporal, prefrontal, and parietal lobes. Reconstructed map of 1st quartile group in y‐axis showed tau spreading dominance in parietal lobe and 4th quartile group showed dominance in prefrontal, temporal lobe. Each patient’s trajectory, predicted based on the latent space, showed reconstructed map following individual tau accumulation pattern. In addition, EOAD tau spreading trajectory tend to precede LOAD tau spreading trajectory.ConclusionWe decomposed high dimensional tau accumulation pattern into 2 independent components through deep‐learning methods. X‐axis showed EOAD tau accumulation pattern and y‐axis was divided into LOAD tau accumulation pattern and non‐prefrontal dominant pattern. In addition, tensor fitting of the longitudinal vector field enables us to find individual tau spreading trajectories which can be used to predict future and past spreading. Even though this study was done using only one factor, tau, it has the potential to be expanded to other factors such as amyloid or neurodegeneration data.

A Compact Representation of Measured BRDFs Using Neural Processes

In this article, we introduce a compact representation for measured BRDFs by leveraging Neural Processes (NPs). Unlike prior methods that express those BRDFs as discrete high-dimensional matrices or tensors, our technique considers measured BRDFs as continuous functions and works in corresponding function spaces . Specifically, provided the evaluations of a set of BRDFs, such as ones in MERL and EPFL datasets, our method learns a low-dimensional latent space as well as a few neural networks to encode and decode these measured BRDFs or new BRDFs into and from this space in a non-linear fashion. Leveraging this latent space and the flexibility offered by the NPs formulation, our encoded BRDFs are highly compact and offer a level of accuracy better than prior methods. We demonstrate the practical usefulness of our approach via two important applications, BRDF compression and editing. Additionally, we design two alternative post-trained decoders to, respectively, achieve better compression ratio for individual BRDFs and enable importance sampling of BRDFs.

Fusing multimodal neuroimaging data with a variational autoencoder.

Neuroimaging studies often collect multimodal data. These modalities contain both shared and mutually exclusive information about the brain. This work aims to find a scalable and interpretable method to fuse the information of multiple neuroimaging modalities into a lower-dimensional latent space using a variational autoencoder (VAE). To assess whether the encoder-decoder pair retains meaningful information, this work evaluates the representations using a schizophrenia classification task. The linear classifier, trained on the representations obtained through dimensionality reduction, achieves an area under the curve of the receiver operating characteristic (ROC-AUC) of 0.8609. Thus, training on a multimodal dataset with functional brain networks and a structural magnetic resonance imaging (sMRI) scan, leads to dimensionality reduction that retains meaningful information. The proposed dimensionality reduction outperforms both early and late fusion principal component analysis on the classification task.Clinical relevance - This work examines the interplay between neuroimaging modalities and their relation to mental disorders. This allows for more complex and rigorous analysis of multimodal neuroimaging data throughout clinical settings.

Link prediction by deep non-negative matrix factorization

Link prediction aims to predict missing links or eliminate spurious links and new links in future network by known network structure information. Most existing link prediction methods are shallow models and did not consider network noise. To address these issues, in this paper, we propose a novel link prediction model based on deep non-negative matrix factorization, which elegantly fuses topology and sparsity-constrained to perform link prediction tasks. Specifically, our model fully exploits the observed link information for each hidden layer by deep non-negative matrix factorization. Then, we utilize the common neighbor method to calculate the similarity scores and map it to multi-layer low-dimensional latent space to obtain the topological information of each hidden layer. Simultaneously, we employ the ℓ2,1-norm constrained factor matrix at each hidden layer to remove the random noise. Besides, we provide an effective the multiplicative updating rules to learn the parameter of this model with the convergence guarantees. Extensive experiments results on eight real-world datasets demonstrate that our proposed model significantly outperforms the state-of-the-art methods.

Multiscale Enhanced Sampling Using Machine Learning.

Multiscale enhanced sampling (MSES) allows for an enhanced sampling of all-atom protein structures by coupling with the accelerated dynamics of the associated coarse-grained (CG) model. In this paper, we propose an MSES extension to replace the CG model with the dynamics on the reduced subspace generated by a machine learning approach, the variational autoencoder (VAE). The molecular dynamic (MD) trajectories of the ribose-binding protein (RBP) in both the closed and open forms were used as the input by extracting the inter-residue distances as the structural features in order to train the VAE model, allowing the encoded latent layer to characterize the difference in the structural dynamics of the closed and open forms. The interpolated data characterizing the RBP structural change in between the closed and open forms were thus efficiently generated in the low-dimensional latent space of the VAE, which was then decoded into the time-series data of the inter-residue distances and was useful for driving the structural sampling at an atomistic resolution via the MSES scheme. The free energy surfaces on the latent space demonstrated the refinement of the generated data that had a single basin into the simulated data containing two closed and open basins, thus illustrating the usefulness of the MD simulation together with the molecular mechanics force field in recovering the correct structural ensemble.

TACN: A Topical Adversarial Capsule Network for textual network embedding

Combining topological information and attributed information of nodes in networks effectively is a valuable task in network embedding. Nevertheless, many prior network embedding methods regarded attributed information of nodes as simple attribute sets or ignored them totally. In some scenarios, the hidden information contained in vertex attributes are essential to network embedding. For instance, networks that contain vertexes with text information play an increasingly important role in our life, including citation networks, social networks, and entry networks. In these textual networks, the latent topic relevance information of different vertexes contained in textual attributes information are valuable in the network analysis process. Shared latent topics of nodes in networks may influence the interaction between them, which is critical to network embedding. However, much prior work for textual network embedding only regarded the text information as simple word sets while ignored the embedded topic information. In this paper, we develop a model named Topical Adversarial Capsule Network (TACN) for textual network embedding, which extracts a low-dimensional latent space of the original network from node structures, vertex attributes, and topic information contained in text of nodes. The proposed TACN contains three parts. The first part is an embedding model, which extracts the embedding representation from the topological structure, vertex attributes, and document-topic distributions. To ensure a consistent training process by back-propagation, we generate document-topic distributions by the neural topic model with Gaussian Softmax constructions. The second part is a prediction model, which is used to exploit labels of vertices. In the third part, an adversarial capsule model is used to help distinguish the latent representations from node structure domain, vertex attribute domain, or document-topic distribution domain. The latent representations, which may come from the three domains, are the output of the embedding model. We incorporate the adversarial idea into the adversarial capsule model to combine the information from these three domains, rather than to distinguish the representations conventionally. Experiments on seven real-world datasets validate the effectiveness of our method.

Adaptive machine learning for time-varying systems: low dimensional latent space tuning

Machine learning (ML) tools such as encoder-decoder convolutional neural networks (CNN) can represent incredibly complex nonlinear functions which map between combinations of images and scalars. For example, CNNs can be used to map combinations of accelerator parameters and images which are 2D projections of the 6D phase space distributions of charged particle beams as they are transported between various particle accelerator locations. Despite their strengths, applying ML to time-varying systems, or systems with shifting distributions, is an open problem, especially for large systems for which collecting new data for re-training is impractical or interrupts operations. Particle accelerators are one example of large time-varying systems for which collecting detailed training data requires lengthy dedicated beam measurements which may no longer be available during regular operations. We present a novel method of adaptive ML for time-varying systems. Our approach is to map very high (N ≈ 100k) dimensional inputs (a combination of scalar parameters and images) into the low dimensional (N ≈ 2) latent space at the output of the encoder section of an encoder-decoder CNN. We then actively tune the low dimensional latent space-based representation of complex system dynamics by the addition of an adaptively tuned feedback vector directly before the decoder sections builds back up to our image-based high-dimensional phase space density representations. This method allows us to learn correlations within and to quickly tune the characteristics of incredibly large parameter space systems and to track their evolution in real time based on feedback without massive new data sets for re-training. We demonstrate that our method can accurately predict and track the phase space of charged particle beams at various locations in a particle accelerator by adaptively adjusting in real-time while the unknown input beam distribution of the accelerator is changing in shape, charge, and offset and while the RF system of the accelerator itself is also changing in an unpredictable way. For FACET-II we demonstrate that such an approach has the potential to use transverse deflecting cavity and energy spread spectrum beam measurements to accurately predict 2D projections of the 6D phase space of the electron beam at the plasma wakefield acceleration interaction point where such diagnostics are unavailable.

Latent map Gaussian processes for mixed variable metamodeling

Gaussian processes (GPs) are ubiquitously used in sciences and engineering as metamodels. Standard GPs, however, can only handle numerical or quantitative variables. In this paper, we introduce latent map Gaussian processes (LMGPs) that inherit the attractive properties of GPs and are also applicable to mixed data which have both quantitative and qualitative inputs. The core idea behind LMGPs is to learn a continuous, low-dimensional latent space or manifold which encodes all qualitative inputs. To learn this manifold, we first assign a unique prior vector representation to each combination of qualitative inputs. We then use a low-rank linear map to project these priors on a manifold that characterizes the posterior representations. As the posteriors are quantitative, they can be directly used in any standard correlation function such as the Gaussian or Matern. Hence, the optimal map and the corresponding manifold, along with other hyperparameters of the correlation function, can be systematically learned via maximum likelihood estimation. Through a wide range of analytic and real-world examples, we demonstrate the advantages of LMGPs over state-of-the-art methods in terms of accuracy and versatility. In particular, we show that LMGPs can handle variable-length inputs, have an explainable neural network interpretation, and provide insights into how qualitative inputs affect the response or interact with each other. We also employ LMGPs in Bayesian optimization and illustrate that they can discover optimal compound compositions more efficiently than conventional methods that convert compositions to qualitative variables via manual featurization.

Dynamics on the manifold: Identifying computational dynamical activity from neural population recordings.

The question of how the collective activity of neural populations gives rise to complex behaviour is fundamental to neuroscience. At the core of this question lie considerations about how neural circuits can perform computations that enable sensory perception, decision making, and motor control. It is thought that such computations are implemented through the dynamical evolution of distributed activity in recurrent circuits. Thus, identifying dynamical structure in neural population activity is a key challenge towards a better understanding of neural computation. At the same time, interpreting this structure in light of the computation of interest is essential for linking the time-varying activity patterns of the neural population to ongoing computational processes. Here, we review methods that aim to quantify structure in neural population recordings through a dynamical system defined in a low-dimensional latent variable space. We discuss advantages and limitations of different modelling approaches and address future challenges for the field.

The most robust representations of flow trajectories are Lagrangian coherent structures

What is the most robust way to communicate flow trajectories? To answer this question, we employ two neural networks to respectively deconstruct (the encoder) and reconstruct (the decoder) trajectories, where information is passed between the two networks through a low-dimensional latent space in a set-up known as an autoencoder. To ensure that their communications are robust, we add noise to the coded information passed through this latent space. In the low-noise limit the latent space structures are non-spatial in nature, resembling modes of a principle component analysis (PCA). However, as the signal-to-noise ratio is decreased, we uncover Lagrangian coherent structures (LCS) as the most compact representations which still allow the decoder to accurately reconstruct trajectories. This relationship offers increased interpretability to both PCA and LCS analysis, and helps to bridge the gap between two methods of flow analysis.

Sparse identification of nonlinear dynamics with low-dimensionalized flow representations

We perform a sparse identification of nonlinear dynamics (SINDy) for low-dimensionalized complex flow phenomena. We first apply the SINDy with two regression methods, the thresholded least square algorithm and the adaptive least absolute shrinkage and selection operator which show reasonable ability with a wide range of sparsity constant in our preliminary tests, to a two-dimensional single cylinder wake at$Re_D=100$, its transient process and a wake of two-parallel cylinders, as examples of high-dimensional fluid data. To handle these high-dimensional data with SINDy whose library matrix is suitable for low-dimensional variable combinations, a convolutional neural network-based autoencoder (CNN-AE) is utilized. The CNN-AE is employed to map a high-dimensional dynamics into a low-dimensional latent space. The SINDy then seeks a governing equation of the mapped low-dimensional latent vector. Temporal evolution of high-dimensional dynamics can be provided by combining the predicted latent vector by SINDy with the CNN decoder which can remap the low-dimensional latent vector to the original dimension. The SINDy can provide a stable solution as the governing equation of the latent dynamics and the CNN-SINDy-based modelling can reproduce high-dimensional flow fields successfully, although more terms are required to represent the transient flow and the two-parallel cylinder wake than the periodic shedding. A nine-equation turbulent shear flow model is finally considered to examine the applicability of SINDy to turbulence, although without using CNN-AE. The present results suggest that the proposed scheme with an appropriate parameter choice enables us to analyse high-dimensional nonlinear dynamics with interpretable low-dimensional manifolds.

Discovering prerequisite relations from educational documents through word embeddings

Inferring prerequisite relations among educational documents, in terms of prior knowledge required to understand and complete assignments about certain topics, is a crucial task for instructional designers and teachers. Massive open online courses, electronic textbooks, public encyclopedias and repositories of learning objects and other forms of informative content create a huge availability of educational material, which can be exploited in online platforms for distance education, both for recommending specific resources and personalized learning paths. But public taxonomies of prerequisites, or learning object metadata useful to trace down prerequisites are not generally available.A description of a new approach for prerequisite discovering in educational documents is given. It is based on word embeddings, that is, statistical language models for the representation of text-based learning objects in low-dimensional latent spaces. It takes advantage of the latent representations to identify prerequisites in a binary classification setting. The accuracy of the approach is validated by means of an experimental benchmark covering multiple datasets of educational material.

Accelerating the training of deep reinforcement learning in autonomous driving

Deep reinforcement learning has been successful in solving common autonomous driving tasks such as lane-keeping by simply using pixel data from the front view camera as input. However, raw pixel data contains a very high-dimensional observation that affects the learning quality of the agent due to the complexity imposed by a 'realistic' urban environment. Ergo, we investigate how compressing the raw pixel data from high-dimensional state to low-dimensional latent space offline using a variational autoencoder can significantly improve the training of a deep reinforcement learning agent. We evaluated our method on a simulated autonomous vehicle in car learning to act and compared our results with many baselines including deep deterministic policy gradient, proximal policy optimization, and soft actorcritic. The result shows that the method greatly accelerates the training time and there was a remarkable improvement in the quality of the deep reinforcement learning agent.

Spontaneous and deliberate modes of creativity: Multitask eigen-connectivity analysis captures latent cognitive modes during creative thinking

Despite substantial progress in the quest of demystifying the brain basis of creativity, several questions remain open. One such issue concerns the relationship between two latent cognitive modes during creative thinking, i.e., deliberate goal-directed cognition and spontaneous thought generation. Although an interplay between deliberate and spontaneous thinking is often implicated in the creativity literature (e.g., dual-process models), a bottom-up data-driven validation of the cognitive processes associated with creative thinking is still lacking. Here, we attempted to capture the latent modes of creative thinking by utilizing a data-driven approach on a novel continuous multitask paradigm (CMP) that widely sampled a hypothetical two-dimensional cognitive plane of deliberate and spontaneous thinking in a single fMRI session. The CMP consisted of eight task blocks ranging from undirected mind wandering to goal-directed working memory task, while also included two widely-used creativity tasks, i.e., alternate uses task (AUT) and remote association task (RAT). Using eigen-connectivity (EC) analysis on the multitask whole-brain functional connectivity (FC) patterns, we embedded the multitask FCs into a low-dimensional latent space. The first two latent components, as revealed by the EC analysis, broadly mapped onto the two cognitive modes of deliberate and spontaneous thinking, respectively. Further, in this low-dimensional space, both creativity tasks were located in the upper right corner of high deliberate and spontaneous thinking (creative cognitive space). Neuroanatomically, the creative cognitive space was represented by not only increased intra-network connectivity within executive control and default mode network, but also by higher coupling between the two canonical brain networks. Further, individual differences reflected in the low-dimensional connectivity embeddings were related to differences in deliberate and spontaneous thinking abilities. Altogether, using a continuous multitask paradigm and a data-driven approach, we provide initial empirical evidence for the contribution of both deliberate and spontaneous modes of cognition during creative thinking.

An extended autoencoder model for reaction coordinate discovery in rare event molecular dynamics datasets.

The reaction coordinate (RC) is the principal collective variable or feature that determines the progress along an activated or reactive process. In a molecular simulation using enhanced sampling, a good description of the RC is crucial for generating sufficient statistics. Moreover, the RC provides invaluable atomistic insight into the process under study. The optimal RC is the committor, which represents the likelihood of a system to evolve toward a given state based on the coordinates of all its particles. As the interpretability of such a high dimensional function is low, a more practical approach is to describe the RC by some low-dimensional molecular collective variables or order parameters. While several methods can perform this dimensionality reduction, they usually require a preselection of these low-dimension collective variables (CVs). Here, we propose to automate this dimensionality reduction using an extended autoencoder, which maps the input (many CVs) onto a lower-dimensional latent space, which is subsequently used for the reconstruction of the input as well as the prediction of the committor function. As a consequence, the latent space is optimized for both reconstruction and committor prediction and is likely to yield the best non-linear low-dimensional representation of the committor. We test our extended autoencoder model on simple but nontrivial toy systems, as well as extensive molecular simulation data of methane hydrate nucleation. The extended autoencoder model can effectively extract the underlying mechanism of a reaction, make reliable predictions about the committor of a given configuration, and potentially even generate new paths representative for a reaction.