nils-herrmann/clean_scirepeval huggingface dataset:
Wormholes Improve Contrastive Divergence

In models that define probabilities via energies, maximum likelihood learning typically involves using Markov Chain Monte Carlo to sample from the model's distribution. If the Markov chain is started at the data distribution, learning often works well even if the chain is only run for a few time steps . But if the data distribution contains modes separated by regions of very low density, brief MCMC will not ensure that different modes have the correct relative energies because it cannot move particles from one mode to another. We show how to improve brief MCMC by allowing long-range moves that are suggested by the data distribution. If the model is approximately correct, these long-range moves have a reasonable acceptance rate.
Energy-Based Models for Sparse Overcomplete Representations

We present a new way of extending independent components analysis (ICA) to overcomplete representations. In contrast to the causal generative extensions of ICA which maintain marginal independence of sources, we define features as deterministic (linear) functions of the inputs. This assumption results in marginal dependencies among the features, but conditional independence of the features given the inputs. By assigning energies to the features a probability distribution over the input states is defined through the Boltzmann distribution. Free parameters of this model are trained using the contrastive divergence objective (Hinton, 2002). When the number of features is equal to the number of input dimensions this energy-based model reduces to noiseless ICA and we show experimentally that the proposed learning algorithm is able to perform blind source separation on speech data. In additional experiments we train overcomplete energy-based models to extract features from various standard data-sets containing speech, natural images, hand-written digits and faces.
Efficient Parametric Projection Pursuit Density Estimation

Product models of low dimensional experts are a powerful way to avoid the curse of dimensionality. We present the "undercomplete product of experts" (UPoE), where each expert models a one dimensional projection of the data. The UPoE may be interpreted as a parametric probabilistic model for projection pursuit. Its ML learning rules are identical to the approximate learning rules proposed before for under-complete ICA. We also derive an efficient sequential learning algorithm and discuss its relationship to projection pursuit density estimation and feature induction algorithms for additive random field models.
Self Supervised Boosting

Boosting algorithms and successful applications thereof abound for classification and regression learning problems, but not for unsupervised learning. We propose a sequential approach to adding features to a random field model by training them to improve classification performance between the data and an equal-sized sample of "negative examples" generated from the model's current estimate of the data density. Training in each boosting round proceeds in three stages: first we sample negative examples from the model's current Boltzmann distribution. Next, a feature is trained to improve classification performance between data and negative examples. Finally, a coefficient is learned which determines the importance of this feature relative to ones already in the pool. Negative examples only need to be generated once to learn each new feature. The validity of the approach is demonstrated on binary digits and continuous synthetic data.
Learning Sparse Topographic Representations with Products of Student-t Distributions

We propose a model for natural images in which the probability of an image is proportional to the product of the probabilities of some filter outputs. We encourage the system to find sparse features by using a Student-t distribution to model each filter output. If the t-distribution is used to model the combined outputs of sets of neurally adjacent filters, the system learns a topographic map in which the orientation, spatial frequency and location of the filters change smoothly across the map. Even though maximum likelihood learning is intractable in our model, the product form allows a relatively efficient learning procedure that works well even for highly overcomplete sets of filters. Once the model has been learned it can be used as a prior to derive the "iterated Wiener filter" for the purpose of denoising images.
Stochastic Neighbor Embedding

We describe a probabilistic approach to the task of placing objects, described by high-dimensional vectors or by pairwise dissimilarities, in a low-dimensional space in a way that preserves neighbor identities. A Gaussian is centered on each object in the high-dimensional space and the densities under this Gaussian (or the given dissimilarities) are used to define a probability distribution over all the potential neighbors of the object. The aim of the embedding is to approximate this distribution as well as possible when the same operation is performed on the low-dimensional "images" of the objects. A natural cost function is a sum of Kullback-Leibler divergences, one per object, which leads to a simple gradient for adjusting the positions of the low-dimensional images. Unlike other dimensionality reduction methods, this probabilistic framework makes it easy to represent each object by a mixture of widely separated low-dimensional images. This allows ambiguous objects, like the document count vector for the word "bank", to have versions close to the images of both "river" and "finance" without forcing the images of outdoor concepts to be located close to those of corporate concepts.
A Desktop Input Device and Interface for Interactive 3D Character Animation

We present a novel input device and interface for interactively controlling the animation of graphical human character from a desktop environment. The trackers are embedded in a new physical design, which is both simple yet also provides significant benefits, and establishes a tangible interface with coordinate frames inherent to the character. A layered kinematic motion recording strategy accesses subsets of the total degrees of freedom of the character. We present the experiences of three novice users with the system, and that of a long-term user who has prior experience with other complex continuous interfaces.
Local Physical Models for Interactive Character Animation

Our goal is to design and build a tool for the creation of expressive character animation. Virtual puppetry, also known as performance animation, is a technique in which the user interactively controls a character's motion. In this paper we introduce local physical models for performance animation and describe how they can augment an existing kinematic method to achieve very effective animation control. These models approximate specific physically‐generated aspects of a character's motion. They automate certain behaviours, while still letting the user override such motion via a PD‐controller if he so desires. Furthermore, they can be tuned to ignore certain undesirable effects, such as the risk of having a character fall over, by ignoring corresponding components of the force. Although local physical models are a quite simple approximation to real physical behaviour, we show that they are extremely useful for interactive character control, and contribute positively to the expressiveness of the character's motion. In this paper, we develop such models at the knees and ankles of an interactively‐animated 3D anthropomorphic character, and demonstrate a resulting animation. This approach can be applied in a straight‐forward way to other joints.
Training Products of Experts by Minimizing Contrastive Divergence

It is possible to combine multiple latent-variable models of the same data by multiplying their probability distributions together and then renormalizing. This way of combining individual expert models makes it hard to generate samples from the combined model but easy to infer the values of the latent variables of each expert, because the combination rule ensures that the latent variables of different experts are conditionally independent when given the data. A product of experts (PoE) is therefore an interesting candidate for a perceptual system in which rapid inference is vital and generation is unnecessary. Training a PoE by maximizing the likelihood of the data is difficult because it is hard even to approximate the derivatives of the renormalization term in the combination rule. Fortunately, a PoE can be trained using a different objective function called contrastive divergence whose derivatives with regard to the parameters can be approximated accurately and efficiently. Examples are presented of contrastive divergence learning using several types of expert on several types of data.
A New Learning Algorithm for Mean Field Boltzmann Machines

We present a new learning algorithm for Mean Field Boltzmann Machines based on the contrastive divergence optimization criterion. In addition to minimizing the divergence between the data distribution and the equilibrium distribution, we maximize the divergence between one-step reconstructions of the data and the equilibrium distribution. This eliminates the need to estimate equilibrium statistics, so we do not need to approximate the multimodal probability distribution of the free network with the unimodal mean field distribution. We test the learning algorithm on the classification of digits.
Reinforcement learning for factored markov decision processes

Learning to act optimally in a complex, dynamic and noisy environment is a hard problem. Various threads of research from reinforcement learning, animal conditioning, operations research, machine learning, statistics and optimal control are beginning to come together to offer solutions to this problem. I present a thesis in which novel algorithms are presented for learning the dynamics, learning the value function, and selecting good actions for Markov decision processes. The problems considered have high-dimensional factored state and action spaces, and are either fully or partially observable. The approach I take is to recognize similarities between the problems being solved in the reinforcement learning and graphical models literature, and to use and combine techniques from the two fields in novel ways. 
In particular I present two new algorithms. First, the DBN algorithm learns a compact representation of the core process of a partially observable MDP. Because inference in the DBN is intractable, I use approximate inference to maintain the belief state. A belief state action-value function is learned using reinforcement learning. I show that this DBN algorithm can solve POMDPs with very large state spaces and useful hidden state. Second, the PoE algorithm learns an approximation to value functions over large factored state-action spaces. The algorithm approximates values as (negative) free energies in a product of experts model. The model parameters can be learned efficiently because inference is tractable in a product of experts. I show that good actions can be found even in large factored action spaces by the use of brief Gibbs sampling. 
These two new algorithms take techniques from the machine learning community and apply them in new ways to reinforcement learning problems. Simulation results show that these new methods can be used to solve very large problems. The DBN method is used to solve a POMDP with a hidden state space and an observation space of size greater than 2180. The DBN model of the core process has 232 states represented as 32 binary variables. The PoE method is used to find actions in action spaces of size 240 .
Learning Hierarchical Structures with Linear Relational Embedding

We present Linear Relational Embedding (LRE), a new method of learning a distributed representation of concepts from data consisting of instances of relations between given concepts. Its final goal is to be able to generalize, i.e. infer new instances of these relations among the concepts. On a task involving family relationships we show that LRE can generalize better than any previously published method. We then show how LRE can be used effectively to find compact distributed representations for variable-sized recursive data structures, such as trees and lists.
Approximate Contrastive Free Energies for Learning in Undirected Graphical Models

We present a novel class of learning algorithms for undirected graphical models, based on the contrastive free energy (CF). In particular we study the naive mean field, TAP and Bethe approximations to the contrastive free energy. The main advantage of CFlearning is the fact that it eliminates the need to infer equilibrium statistics for which mean field type approximations are particularly unsuitable. Instead, learning decreases the distance between the data distribution and the distribution with onestep reconstructions clamped on the visible nodes. We test the learning algorithm on the classification of digits.
TRAINING MANY SMALL HIDDEN MARKOV MODELS

This paper describes research in progress on two quite different ways of training systems that are composed of many small Hidden Markov Models (HMM’s). The first is a purely discriminative method in which all of the parameters of all the HMM’s are adjusted to optimize classification performance. The second is an unsupervised method in which many little HMM’s are used to model the probability density of a single set of sequences.
Developing Population Codes For Object Instantiation Parameters

An efficient and useful representation for an object viewed from different positions is in terms of its instantiation parameters. We show how the Minimum Description Length principle (MDL) can be used to train the hidden units of a neural network to develop a population code for the instantiation parameters of an object in an image. Each hidden unit has a location in a low-dimensional implicit space. If the hidden unit activities form a standard shape (a bump) in this space, they can be cheaply encoded by the center of this bump. So the weights from the input units to the hidden units in a self-supervised network are trained to make the activities form a bump. The coordinates of the hidden units in the implicit space are also learned, thus allowing flexibility, as the network develops separate population codes when presented with different objects.
Global Coordination of Local Linear Models

High dimensional data that lies on or near a low dimensional manifold can be described by a collection of local linear models. Such a description, however, does not provide a global parameterization of the manifold—arguably an important goal of unsupervised learning. In this paper, we show how to learn a collection of local linear models that solves this more difficult problem. Our local linear models are represented by a mixture of factor analyzers, and the "global coordination" of these models is achieved by adding a regularizing term to the standard maximum likelihood objective function. The regularizer breaks a degeneracy in the mixture model's parameter space, favoring models whose internal coordinate systems are aligned in a consistent way. As a result, the internal coordinates change smoothly and continuously as one traverses a connected path on the manifold—even when the path crosses the domains of many different local models. The regularizer takes the form of a Kullback-Leibler divergence and illustrates an unexpected application of variational methods: not to perform approximate inference in intractable probabilistic models, but to learn more useful internal representations in tractable ones.
Learning Distributed Representations of Concepts Using Linear Relational Embedding

We introduce linear relational embedding as a means of learning a distributed representation of concepts from data consisting of binary relations between these concepts. The key idea is to represent concepts as vectors, binary relations as matrices, and the operation of applying a relation to a concept as a matrix-vector multiplication that produces an approximation to the related concept. A representation for concepts and relations is learned by maximizing an appropriate discriminative goodness function using gradient ascent. On a task involving family relationships, learning is fast and leads to good generalization.
Relative Density Nets: A New Way to Combine Backpropagation with HMM's

Logistic units in the first hidden layer of a feedforward neural network compute the relative probability of a data point under two Gaussians. This leads us to consider substituting other density models. We present an architecture for performing discriminative learning of Hidden Markov Models using a network of many small HMM's. Experiments on speech data show it to be superior to the Standard method of discriminatively training HMM's.
Products of Hidden Markov Models

We present products of hidden Markov models (PoHMM's), a way of combining HMM's to form a distributed state time series model. Inference in a PoHMM is tractable and eAEcient. Learning of the parameters, although intractable, can be e ectively done using the Product of Experts learning rule. The distributed state helps the model to explain data which has multiple causes, and the fact that each model need only explain part of the data means a PoHMM can capture longer range structure than an HMM is capable of. We show some results on modelling character strings, a simple language task and the symbolic family trees problem, which highlight these advantages.
A New View of ICA

We present a new way of interpreting ICA as a probability density model and a new way of fitting this model to data. The advantage of our approach is that it suggests simple, novel extensions to overcomplete, undercomplete and multilayer non-linear versions of ICA. 1. ICA AS A CAUSAL GENERATIVE MODEL Factor analysis is based on a causal generative model in which an observation vector is generated in three stages. First, the activities of the factors (also known as latent or hidden variables) are chosen independently from one dimensional Gaussian priors. Next, these hidden activities are multiplied by a matrix of weights (the “factor loading” matrix) to produce a noise-free observation vector. Finally, independent Gaussian “sensor noise” is added to each component of the noise-free observation vector. Given an observation vector and a factor loading matrix, it is tractable to compute the posterior distribution of the hidden activities because this distribution is a Gaussian, though it generally has off-diagonal terms in the covariance matrix so it is not as simple as the prior distribution over hidden activities. ICA can also be viewed as a causal generative model [1, 2] that differs from factor analysis in two ways. First, the priors over the hidden activities remain independent but they are non-Gaussian. By itself, this modification would make it intractable to compute the posterior distribution over hidden activities. Tractability is restored by eliminating sensor noise and by using the same number of factors as input dimensions. This ensures that the posterior distribution over hidden activities collapses to a point. Interpreting ICA as a type of causal generative model suggests a number of ways in which it might be generalized, for instance to deal with more hidden units than input dimensions. Most of these generalizations retain marginal independence of the hidden activities and add sensor noise, but fail to preserve the property that the posterior distribution collapses to a point. As Funded by the Wellcome Trust and the Gatsby Charitable Foundation. a result inference is intractable and crude approximations are needed to model the posterior distribution, e.g., a MAP estimate in , a Laplace approximation in [4, 5] or more sophisticated variational approximations in . 2. ICA AS AN ENERGY-BASED DENSITY MODEL We now describe a very different way of interpreting ICA as a probability density model. In the next section we describe how we can fit the model to data. The advantage of our energy-based view is that it suggests different generalizations of the basic ICA algorithm which preserve the computationally attractive property that the hidden activities are a simple deterministic function of the observed data. Instead of viewing the hidden factors as stochastic latent variables in a causal generative model, we view them as deterministic functions of the data with parameters . The hidden factors are then used for assigning an energy , to each possible observation vector :
Learning Distributed Representations of Relational Data using Linear Relational Embedding

This thesis introduces new methods for solving the problem of generalizing from relational data. I consider a situation in which we have a set of concepts and a set of relations among these concepts, and the data consists of few instances of these relations that hold among the concepts; the aim is to infer other instances of these relations. My approach is to learn from the data a representation of the objects in terms of the features which are relevant for the set of relations at hand, together with the rules of how these features interact. I then use these distributed representations to infer how objects relate. 
Linear Relational Embedding (LRE) is a new method for learning distributed representations for objects and relations. It finds a mapping from the objects into a feature-space by imposing the constraint that relations in this feature-space are modelled by linear operations. Having learned such distributed representations, it becomes possible to learn a probabilistic model which can be used to infer both positive and negative instances of the relations. 
LRE shows excellent generalization performance. On a classical problem results are far better than those obtained by any previously published method. I also present results on other problems, which show that the generalization performance of LRE is excellent. Moreover, after learning a distributed representation for a set of objects and relations, LRE can easily modify these representations to incorporate new objects and relations. Learning is fast and LRE rarely converges to solutions with poor generalization. 
Due to its linearity LRE cannot represent some relations of arity greater than two. I therefore introduce Non-Linear Relational Embedding (NLRE), and show that it can represent relations that LRE cannot. A probabilistic model, which can be used to infer both positive and negative instances of the relations, can also be learned for NLRE. Hierarchical LRE and Hierarchical NLRE are modifications of the above methods for learning a distributed representation of variable-sized recursive data structures. Results show that these methods are able to extract semantic features from trees and use them to generalize correctly to novel trees.
November 21 , 2000 GCNU TR 2000 – 008 Products of Hidden Markov Models

We present products of hidden Markov models (PoHMM’s), a way of combining HMM’s to form a distributed state time series model. Inference in a PoHMM is tractable and efficient. Learning of the parameters, although intractable, can be effectively done using the Product of Experts learning rule. The distributed state helps the model to explain data which has multiple causes, and the fact that each model need only explain part of the data means a PoHMM can capture longer range structure than an HMM is capable of. We show some results on modelling character strings, a simple language task and the symbolic family trees problem, which highlight these advantages. Products of Hidden Markov Models Andrew D. Brown andy@gatsby.ucl.ac.uk Geoffrey E. Hinton hinton@gatsby.ucl.ac.uk