TASK DEFINITION: In this task, you are given the abstract of a research paper. Your task is to generate a summary of this abstract. Your summary should not be very short, but it's better if it's not more than 30 words.
PROBLEM: Statistical inference methods are fundamentally important in machine learning. Most state-of-the-art inference algorithms are 
 variants of Markov chain Monte Carlo (MCMC) or variational inference (VI). However, both methods struggle with limitations in practice: MCMC methods can be computationally demanding; VI methods may have large bias. 
 In this work, we aim to improve upon MCMC and VI by a novel hybrid method based on the idea of reducing simulation bias of finite-length MCMC chains using gradient-based optimisation. The proposed method can generate low-biased samples by increasing the length of MCMC simulation and optimising the MCMC hyper-parameters, which offers attractive balance between approximation bias and computational efficiency. We show that our method produces promising results on popular benchmarks when compared to recent hybrid methods of MCMC and VI.

SOLUTION: In this work, we aim to improve upon MCMC and VI by a novel hybrid method based on the idea of reducing simulation bias of finite-length MCMC chains using gradient-based optimisation.

PROBLEM: In recent years we have made significant progress identifying computational principles that underlie neural function. While not yet complete, we have sufficient evidence that a synthesis of these ideas could result in an understanding of how neural computation emerges from a combination of innate dynamics and plasticity, and which could potentially be used to construct new AI technologies with unique capabilities. I discuss the relevant principles, the advantages they have for computation, and how they can benefit AI. Limitations of current AI are generally recognized, but fewer people are aware that we understand enough about the brain to immediately offer novel AI formulations.


SOLUTION: Limitations of current AI are generally recognized, but fewer people are aware that we understand enough about the brain to immediately offer novel AI formulations.

PROBLEM: The goal of the paper is to propose an algorithm for learning the most generalizable solution from given training data. It is shown that Bayesian approach leads to a solution that dependent on statistics of training data and not on particular
 samples. The solution is stable under perturbations of training data because it is defined by an integral contribution of multiple maxima of the likelihood and not by a single global maximum. Specifically, the Bayesian probability distribution
 of parameters (weights) of a probabilistic model given by a neural network is estimated via recurrent variational approximations. Derived recurrent update rules correspond to SGD-type rules for finding a minimum of an effective loss that is an average of an original negative log-likelihood over the Gaussian distributions of weights, which makes it a function of means and variances. The effective loss is convex for large variances and non-convex in the limit of small variances. Among stationary solutions of the update rules there are trivial solutions with zero variances at local minima of the original loss and a single non-trivial solution with finite variances that is a critical point at the end of convexity of the effective loss
 in the mean-variance space. At the critical point both first- and second-order gradients of the effective loss w.r.t. means are zero. The empirical study confirms that the critical point represents the most generalizable solution. While the location of
 the critical point in the weight space depends on specifics of the used probabilistic model some properties at the critical point are universal and model independent.

SOLUTION:
Proposed method for finding the most generalizable solution that is stable w.r.t. perturbations of trainig data.