instruction:
In this task, you are given a part of an article. Your task is to generate headline (title) for this text. Preferred headlines are under fifteen words.
question:
This paper presents a theoretical, idealized model of the thinking process with the following characteristics: 1) the model can produce complex thought sequences and can be generalized to new inputs, 2) it can receive and maintain input information indefinitely for the generation of thoughts and later use, and 3) it supports learning while executing. The crux of the model lies within the concept of internal consistency, or the generated thoughts should always be consistent with the inputs from which they are created. Its merit, apart from the capability to generate new creative thoughts from an internal mechanism, depends on the potential to help training to generalize better. This is consequently enabled by separating input information into several parts to be handled by different processing components with a focus mechanism to fetch information for each. This modularized view with the focus binds the model with the computationally capable Turing machines. And as a final remark, this paper constructively shows that the computational complexity of the model is at least, if not surpass, that of a universal Turing machine.
answer:
(Yet) Another Theoretical Model of Thinking


question:
We start with an overview of a class of submodular functions called SCMMs (sums of concave composed with non-negative modular functions plus a final arbitrary modular). We then define a new class of submodular functions we call deep submodular functions or DSFs. We show that DSFs are a flexible parametric family of submodular functions that share many of the properties and advantages of deep neural networks (DNNs), including many-layered hierarchical topologies, representation learning, distributed representations, opportunities and strategies for training, and suitability to GPU-based matrix/vector computing. DSFs can be motivated by considering a hierarchy of descriptive concepts over ground elements and where one wishes to allow submodular interaction throughout this hierarchy. In machine learning and data science applications, where there is often either a natural or an automatically learnt hierarchy of concepts over data, DSFs therefore naturally apply. Results in this paper show that DSFs constitute a strictly larger class of submodular functions than SCMMs, thus justifying their mathematical and practical utility. Moreover, we show that, for any integer k > 0, there are k-layer DSFs that cannot be represented by a k′-layer DSF for any k′ < k. This implies that, like DNNs, there is a utility to depth, but unlike DNNs (which can be universally approximated by shallow networks), the family of DSFs strictly increase with depth. Despite this property, however, we show that DSFs, even with arbitrarily large k, do not comprise all submodular functions. We show this using a technique that “backpropagates” certain requirements if it was the case that DSFs comprised all submodular functions. In offering the above results, we also define the notion of an antitone superdifferential of a concave function and show how this relates to submodular functions (in general), DSFs (in particular), negative second-order partial derivatives, continuous submodularity, and concave extensions. To further motivate our analysis, we provide various special case results from matroid theory, comparing DSFs with forms of matroid rank, in particular the laminar matroid. Lastly, we discuss strategies to learn DSFs, and define the classes of deep supermodular functions, deep difference of submodular functions, and deep multivariate submodular functions, and discuss where these can be useful in applications.
answer:
Deep Submodular Functions


question:
Predictive coding (PDC) has recently attracted attention in the neuroscience and computing community as a candidate unifying paradigm for neuronal studies and artificial neural network implementations particularly targeted at unsupervised learning systems. The Mismatch Negativity (MMN) has also recently been studied in relation to PC and found to be a useful ingredient in neural predictive coding systems. Backed by the behavior of living organisms, such networks are particularly useful in forming spatio-temporal transitions and invariant representations of the input world. However, most neural systems still do not account for large number of synapses even though this has been shown by a few machine learning researchers as an effective and very important component of any neural system if such a system is to behave properly. Our major point here is that PDC systems with the MMN effect in addition to a large number of synapses can greatly improve any neural learning system's performance and ability to make decisions in the machine world. In this paper, we propose a novel bio-mimetic computational intelligence algorithm – the Deviant Learning Algorithm, inspired by these key ideas and functional properties of recent brain-cognitive discoveries and theories. We also show by numerical experiments guided by theoretical insights, how our invented bio-mimetic algorithm can achieve competitive predictions with even with very small problem specific data.
answer:

Deviant Learning Algorithm: Learning Sparse Mismatch Representations through Time and Space