Fractionally Predictive Spiking Neurons

Recent experimental work has suggested that the neural firing rate can be interpreted as a fractional derivative, at least when signal variation induces neural adaptation. Here, we show that the actual neural spike-train itself can be considered as the fractional derivative, provided that the neural signal is approximated by a sum of power-law kernels. A simple standard thresholding spiking neuron suffices to carry out such an approximation, given a suitable refractory response. Empirically, we find that the online approximation of signals with a sum of power-law kernels is beneficial for encoding signals with slowly varying components, like long-memory self-similar signals. For such signals, the online power-law kernel approximation typically required less than half the number of spikes for similar SNR as compared to sums of similar but exponentially decaying kernels. As power-law kernels can be accurately approximated using sums or cascades of weighted exponentials, we demonstrate that the corresponding decoding of spike-trains by a receiving neuron allows for natural and transparent temporal signal filtering by tuning the weights of the decoding kernel.Comment: 13 pages, 5 figures, in Advances in Neural Information Processing 201

Pricing options and computing implied volatilities using neural networks

This paper proposes a data-driven approach, by means of an Artificial Neural Network (ANN), to value financial options and to calculate implied volatilities with the aim of accelerating the corresponding numerical methods. With ANNs being universal function approximators, this method trains an optimized ANN on a data set generated by a sophisticated financial model, and runs the trained ANN as an agent of the original solver in a fast and efficient way. We test this approach on three different types of solvers, including the analytic solution for the Black-Scholes equation, the COS method for the Heston stochastic volatility model and Brent's iterative root-finding method for the calculation of implied volatilities. The numerical results show that the ANN solver can reduce the computing time significantly

Deep Gated Hebbian Predictive Coding Accounts for Emergence of Complex Neural Response Properties Along the Visual Cortical Hierarchy

Predictive coding provides a computational paradigm for modeling perceptual processing as the construction of representations accounting for causes of sensory inputs. Here, we developed a scalable, deep network architecture for predictive coding that is trained using a gated Hebbian learning rule and mimics the feedforward and feedback connectivity of the cortex. After training on image datasets, the models formed latent representations in higher areas that allowed reconstruction of the original images. We analyzed low- and high-level properties such as orientation selectivity, object selectivity and sparseness of neuronal populations in the model. As reported experimentally, image selectivity increased systematically across ascending areas in the model hierarchy. Depending on the strength of regularization factors, sparseness also increased from lower to higher areas. The results suggest a rationale as to why experimental results on sparseness across the cortical hierarchy have been inconsistent. Finally, representations for different object classes became more distinguishable from lower to higher areas. Thus, deep neural networks trained using a gated Hebbian formulation of predictive coding can reproduce several properties associated with neuronal responses along the visual cortical hierarchy

Visual pathways from the perspective of cost functions and multi-task deep neural networks

Vision research has been shaped by the seminal insight that we can understand the higher-tier visual cortex from the perspective of multiple functional pathways with different goals. In this paper, we try to give a computational account of the functional organization of this system by reasoning from the perspective of multi-task deep neural networks. Machine learning has shown that tasks become easier to solve when they are decomposed into subtasks with their own cost function. We hypothesize that the visual system optimizes multiple cost functions of unrelated tasks and this causes the emergence of a ventral pathway dedicated to vision for perception, and a dorsal pathway dedicated to vision for action. To evaluate the functional organization in multi-task deep neural networks, we propose a method that measures the contribution of a unit towards each task, applying it to two networks that have been trained on either two related or two unrelated tasks, using an identical stimulus set. Results show that the network trained on the unrelated tasks shows a decreasing degree of feature representation sharing towards higher-tier layers while the network trained on related tasks uniformly shows high degree of sharing. We conjecture that the method we propose can be used to analyze the anatomical and functional organization of the visual system and beyond. We predict that the degree to which tasks are related is a good descriptor of the degree to which they share downstream cortical-units.Comment: 16 pages, 5 figure

Predictive coding with spiking neurons and feedforward gist signaling

Predictive coding (PC) is an influential theory in neuroscience, which suggests the existence of a cortical architecture that is constantly generating and updating predictive representations of sensory inputs. Owing to its hierarchical and generative nature, PC has inspired many computational models of perception in the literature. However, the biological plausibility of existing models has not been sufficiently explored due to their use of artificial neurons that approximate neural activity with firing rates in the continuous time domain and propagate signals synchronously. Therefore, we developed a spiking neural network for predictive coding (SNN-PC), in which neurons communicate using event-driven and asynchronous spikes. Adopting the hierarchical structure and Hebbian learning algorithms from previous PC neural network models, SNN-PC introduces two novel features: (1) a fast feedforward sweep from the input to higher areas, which generates a spatially reduced and abstract representation of input (i.e., a neural code for the gist of a scene) and provides a neurobiological alternative to an arbitrary choice of priors; and (2) a separation of positive and negative error-computing neurons, which counters the biological implausibility of a bi-directional error neuron with a very high baseline firing rate. After training with the MNIST handwritten digit dataset, SNN-PC developed hierarchical internal representations and was able to reconstruct samples it had not seen during training. SNN-PC suggests biologically plausible mechanisms by which the brain may perform perceptual inference and learning in an unsupervised manner. In addition, it may be used in neuromorphic applications that can utilize its energy-efficient, event-driven, local learning, and parallel information processing nature

Flexible Working Memory Through Selective Gating and Attentional Tagging

Working memory is essential: it serves to guide intelligent behavior of humans and nonhuman primates when task-relevant stimuli are no longer present to the senses. Moreover, complex tasks often require that multiple working memory representations can be flexibly and independently maintained, prioritized, and updated according to changing task demands. Thus far, neural network models of working memory have been unable to offer an integrative account of how such control mechanisms can be acquired in a biologically plausible manner. Here, we present WorkMATe, a neural network architecture that models cognitive control over working memory content and learns the appropriate control operations needed to solve complex working memory tasks. Key components of the model include a gated memory circuit that is controlled by internal actions, encoding sensory information through untrained connections, and a neural circuit that matches sensory inputs to memory content. The network is trained by means of a biologically plausible reinforcement learning rule that relies on attentional feedback and reward prediction errors to guide synaptic updates. We demonstrate that the model successfully acquires policies to solve classical working memory tasks, such as delayed recognition and delayed pro-saccade/anti-saccade tasks. In addition, the model solves much more complex tasks, including the hierarchical 12-AX task or the ABAB ordered recognition task, both of which demand an agent to independently store and updated multiple items separately in memory. Furthermore, the control strategies that the model acquires for these tasks subsequently generalize to new task contexts with novel stimuli, thus bringing symbolic production rule qualities to a neural network architecture. As such, WorkMATe provides a new solution for the neural implementation of flexible memory control

On the data-driven COS method

In this paper, we present the data-driven COS method, ddCOS. It is a Fourier-based financial option valuation method which assumes the availability of asset data samples: a characteristic function of the underlying asset probability density function is not required. As such, the presented technique represents a generalization of the well-known COS method [1]. The convergence of the proposed method is in line with Monte Carlo methods for pricing financial derivatives. The ddCOS method is then particularly interesting for density recovery and also for the efficient computation of the option's sensitivities Delta and Gamma. These are often used in risk management, and can be obtained at a higher accuracy with ddCOS than with plain Monte Carlo methods

An image representation based convolutional network for DNA classification

The folding structure of the DNA molecule combined with helper molecules, also referred to as the chromatin, is highly relevant for the functional properties of DNA. The chromatin structure is largely determined by the underlying primary DNA sequence, though the interaction is not yet fully understood. In this paper we develop a convolutional neural network that takes an image-representation of primary DNA sequence as its input, and predicts key determinants of chromatin structure. The method is developed such that it is capable of detecting interactions between distal elements in the DNA sequence, which are known to be highly relevant. Our experiments show that the method outperforms several existing methods both in terms of prediction accuracy and training time