1. Methods Neural network Neural networks mimic biological processing by joining layers of artificial neurons in a meaningful way. The neural network employed in this project is a two-layer model that responds to spectrograms, frequency vs. time distributions of sound. This model utilizes time-delayed inputs to approximate temporal processing. The first layer of the neural network contains the information from three consecutive timesteps. The auditory information from the first layer gets relayed to the second layer through a network of weights. The value of a second layer artificial neuron is: where is the weight matrix, is the input from the current timestep, k is the timestep input that appeared 12 ms ago, and is the timestep input that appeared 24 ms ago. Animals can only hear a very limited range of frequencies. In this project, neural network artificially simulates a limited range of hearing between 0.172 and 5.512 kHz to more accurately match the real world. Unsupervised training The neural network was trained on a simple set of frequency-modulated (FM) sweeps and pure tones. The model modified its own weights according to Oja's rule after each presentation of a timestep in the training set. Only one or two artificial neurons were trained at one time depending on the initial frequency of the training stimulus. Moving ripples The moving ripple stimuli are complex, broadband noises that are used to determine the STRFs of artificial neurons. They are composed of hundreds of densely packed, log-spaced pure tones that are sinusoidally modulated in the spectral and temporal domains. The ripple equation is given as: where is intensity at frequency-time points, is modulation depth, is the ripple velocity (Hz), is the ripple frequency (cycles/octave), and is the phase shift (radians). These ripple stimuli were varied across two parameters separately, the ripple velocity (Hz) and the ripple frequency (cycles/octave). The transfer function (TF) is a broad characterization of an artificial neuron's response to the various ripple stimuli and is defined by: where, is the response phase (radians), and is the response magnitude. A two-dimensional inverse Fourier transform function was performed on the transfer function in order to generate the desired STRF. Purpose The aim of this project was to investigate receptive fields on a neural network to compare a computational model to the actual cortical-level auditory processing. The receptive fields are also analyzed against traditional methods of characterizing neural models such as tuning curves.Background Layout of the ear The ear is the earliest stage of auditory processing. The ear is divided into three main areas: the outer ear, the middle ear, and the inner ear. Transduction, the process of converting mechanical signals into electrical potentials, takes place in the inner ear. The vibrations in the inner ear selectively cause hair cells along the basilar membrane in the cochlea to move. The motion of the hair cells allows electrical potentials to travel to the auditory nerve and become processed by the brain. Hair cells are theorized to be frequency-selective: specific pitches excite specific areas of the basilar membrane. This layout of the ear makes it convenient to represent sound as a function of frequency and time, instead of a function of pressure and time. Spectro-temporal receptive fields (STRFs) STRFs represent the linear properties of primary auditory processing neurons and depict the neuronal impulse response characterizations at frequency-time. STRFs are generated by collecting a neuron's responses to different moving ripple stimuli. Since these stimuli are approximate components of complex sounds, the STRFs characterize the neuron response to spectro-temporally rich sound stimuli. Since STRFs describe the neuronal responses in both the spectral and temporal dimensions, they are hypothesized to be more useful than traditional methods of describing neurons such as tuning curves. Tuning curves Tuning curves have been used extensively in both biological and computational applications because they allow researchers to quantitatively analyze the frequencies at which a specific auditory neuron responds best. To generate these curves, the neuronal response to pure tones varied across the frequency domain are collected. The maximum response to each tone was plotted in a intensity vs. frequency plot, and the peak of the plotted curve denotes the best frequency (BF) of the artificial neuron. The neurons respond with the greatest intensity to tones that match their BF and with decreasing intensity to tones away from their BF. Oja's rule Unsupervised learning paradigms allow neural network models to dynamically modify their own weighted connections between nodes, analogous to the changes in synaptic plasticity between neurons. Oja's rule, one type of unsupervised learning algorithm, can be shown as: where represents weight change between two units, is the current weight, is the learning rate, and and are the activation values of the pre-synaptic and post-synaptic neurons, respectively. Figure 1. The basilar membrane and frequency-selectivity. Image taken from www.hearingaidcentral.com IN n IN n+1 Input units Output unit t AN IN n+1 IN n IN n+1 IN n IN n+1 IN n IN n+1 Weights t-αt-β Figure 3. Schematic of neural network Figure 2. STRFs from Mexican free-tailed bats. The image on the left shows the STRF from a neuron with blocked inhibition and the image on the right shows the STRF from a neuron with inhibition. Image taken from Spectrotemporal Receptive Fields in the Inferior Colliculus Revealing Selectivity for Spectral Motion in Conspecific Vocalizations by Andoni et al. Figure 4. Generation of STRFs through ripples.