Many complex natural and cultural phenomena are well modelled by systems of simple interactions between particles. A number of architectures have been developed to articulate this kind of structure, both implicitly and explicitly. We consider an unsupervised explicit model, the NRI model, and make a series of representational adaptations and physically motivated changes. Most notably we factorise the inferred latent interaction graph into a multiplex graph, allowing each layer to encode for a different interaction-type. This fNRI model is smaller in size and significantly outperforms the original in both edge and trajectory prediction, establishing a new state-of-the-art. We also present a simplified variant of our model, which demonstrates the NRI's formulation as a variational auto-encoder is not necessary for good performance, and make an adaptation to the NRI's training routine, significantly improving its ability to model complex physical dynamical systems.
Many systems have been developed to model interactions implicitly with either single-layer fully connected graphs @cite_1 @cite_7 @cite_4 @cite_2 or with attention-based control mechanisms @cite_3 @cite_8 . However, to the end of developing an investigative or theorising machine assistant, modelling the interaction graph is more valuable than a high quality trajectory-reconstruction. The neural relational inference () model, introduced by Kipf2018NeuralSystemsb , is an unsupervised neural network that learns to predict the interactions and dynamics of a system of objects from observational data alone. When provided with the trajectories of a system of interacting objects, the model infers an explicit interaction graph for these objects which it uses to predict the evolution of the system. The model presents a strong foundation, answering key architectural questions and opening the door for further work dealing with explicit representations. In this work we identify two problems within the original formulation -- representational and experimental -- and in addressing these develop a model that significantly outperforms the original. We also present a variant of our model with greatly improved trajectory prediction that demonstrates the model's formulation as a variational auto-encoder () is not necessary for good performance.
@cite_4 @cite_7 @cite_8 @cite_1 @cite_3 @cite_2
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Interacting systems are prevalent in nature, from dynamical systems in physics to complex societ al dynamics. The interplay of components can give rise to complex behavior, which can often be explained using a simple model of the system's constituent parts. In this work, we introduce the neural relational inference (NRI) model: an unsupervised model that learns to infer interactions while simultaneously learning the dynamics purely from observational data. Our model takes the form of a variational auto-encoder, in which the latent code represents the underlying interaction graph and the reconstruction is based on graph neural networks. In experiments on simulated physical systems, we show that our NRI model can accurately recover ground-truth interactions in an unsupervised manner. We further demonstrate that we can find an interpretable structure and predict complex dynamics in real motion capture and sports tracking data. We develop a comprehensive Bayesian generative model for understanding indoor scenes. While it is common in this domain to approximate objects with 3D bounding boxes, we propose using strong representations with finer granularity. For example, we model a chair as a set of four legs, a seat and a backrest. We find that modeling detailed geometry improves recognition and reconstruction, and enables more refined use of appearance for scene understanding. We demonstrate this with a new likelihood function that rewards 3D object hypotheses whose 2D projection is more uniform in color distribution. Such a measure would be confused by background pixels if we used a bounding box to represent a concave object like a chair. Complex objects are modeled using a set or re-usable 3D parts, and we show that this representation captures much of the variation among object instances with relatively few parameters. We also designed specific data-driven inference mechanisms for each part that are shared by all objects containing that part, which helps make inference transparent to the modeler. Further, we show how to exploit contextual relationships to detect more objects, by, for example, proposing chairs around and underneath tables. We present results showing the benefits of each of these innovations. The performance of our approach often exceeds that of state-of-the-art methods on the two tasks of room layout estimation and object recognition, as evaluated on two bench mark data sets used in this domain. Building intelligent systems that are capable of extracting high-level representations from high-dimensional sensory data lies at the core of solving many AI related tasks, including object recognition, speech perception, and language understanding. Theoretical and biological arguments strongly suggest that building such systems requires models with deep architectures that involve many layers of nonlinear processing. The aim of the thesis is to demonstrate that deep generative models that contain many layers of latent variables and millions of parameters can be learned efficiently, and that the learned high-level feature representations can be successfully applied in a wide spectrum of application domains, including visual object recognition, information retrieval, and classification and regression tasks. In addition, similar methods can be used for nonlinear dimensionality reduction. The first part of the thesis focuses on analysis and applications of probabilistic generative models called Deep Belief Networks. We show that these deep hierarchical models can learn useful feature representations from a large supply of unlabeled sensory inputs. The learned high-level representations capture a lot of structure in the input data, which is useful for subsequent problem-specific tasks, such as classification, regression or information retrieval, even though these tasks are unknown when the generative model is being trained. In the second part of the thesis, we introduce a new learning algorithm for a different type of hierarchical probabilistic model, which we call a Deep Boltzmann Machine. Like Deep Belief Networks, Deep Boltzmann Machines have the potential of learning internal representations that become increasingly complex at higher layers, which is a promising way of solving object and speech recognition problems. Unlike Deep Belief Networks and many existing models with deep architectures, the approximate inference procedure, in addition to a fast bottom-up pass, can incorporate top-down feedback. This allows Deep Boltzmann Machines to better propagate uncertainty about ambiguous inputs. We present an architecture which lets us train deep, directed generative models with many layers of latent variables. We include deterministic paths between all latent variables and the generated output, and provide a richer set of connections between computations for inference and generation, which enables more effective communication of information throughout the model during training. To improve performance on natural images, we incorporate a lightweight autoregressive model in the reconstruction distribution. These techniques permit end-to-end training of models with 10+ layers of latent variables. Experiments show that our approach achieves state-of-the-art performance on standard image modelling benchmarks, can expose latent class structure in the absence of label information, and can provide convincing imputations of occluded regions in natural images.