Deep Learning With Asymmetric Connections and Hebbian Updates.
ABSTRACT: We show that deep networks can be trained using Hebbian updates yielding similar performance to ordinary back-propagation on challenging image datasets. To overcome the unrealistic symmetry in connections between layers, implicit in back-propagation, the feedback weights are separate from the feedforward weights. The feedback weights are also updated with a local rule, the same as the feedforward weights-a weight is updated solely based on the product of activity of the units it connects. With fixed feedback weights as proposed in Lillicrap et al. (2016) performance degrades quickly as the depth of the network increases. If the feedforward and feedback weights are initialized with the same values, as proposed in Zipser and Rumelhart (1990), they remain the same throughout training thus precisely implementing back-propagation. We show that even when the weights are initialized differently and at random, and the algorithm is no longer performing back-propagation, performance is comparable on challenging datasets. We also propose a cost function whose derivative can be represented as a local Hebbian update on the last layer. Convolutional layers are updated with tied weights across space, which is not biologically plausible. We show that similar performance is achieved with untied layers, also known as locally connected layers, corresponding to the connectivity implied by the convolutional layers, but where weights are untied and updated separately. In the linear case we show theoretically that the convergence of the error to zero is accelerated by the update of the feedback weights.
Project description:Using an asymmetrical set of vernier stimuli (-15?, -10?, -5?, +10?, +15?) together with reverse feedback on the small subthreshold offset stimulus (-5?) induces response bias in performance (Aberg & Herzog, 2012; Herzog, Eward, Hermens, & Fahle, 2006; Herzog & Fahle, 1999). These conditions are of interest for testing models of perceptual learning because the world does not always present balanced stimulus frequencies or accurate feedback. Here we provide a comprehensive model for the complex set of asymmetric training results using the augmented Hebbian reweighting model (Liu, Dosher, & Lu, 2014; Petrov, Dosher, & Lu, 2005, 2006) and the multilocation integrated reweighting theory (Dosher, Jeter, Liu, & Lu, 2013). The augmented Hebbian learning algorithm incorporates trial-by-trial feedback, when present, as another input to the decision unit and uses the observer's internal response to update the weights otherwise; block feedback alters the weights on bias correction (Liu et al., 2014). Asymmetric training with reversed feedback incorporates biases into the weights between representation and decision. The model correctly predicts the basic induction effect, its dependence on trial-by-trial feedback, and the specificity of bias to stimulus orientation and spatial location, extending the range of augmented Hebbian reweighting accounts of perceptual learning.
Project description:We follow up on a suggestion by Rolls and co-workers, that the effects of competitive learning should be assessed on the shape and number of spatial fields that dentate gyrus (DG) granule cells may form when receiving input from medial entorhinal cortex (mEC) grid units. We consider a simple non-dynamical model where DG units are described by a threshold-linear transfer function, and receive feedforward inputs from 1,000 mEC model grid units of various spacing, orientation and spatial phase. Feedforward weights are updated according to a Hebbian rule as the virtual rodent follows a long simulated trajectory through a single environment. Dentate activity is constrained to be very sparse. We find that indeed competitive Hebbian learning tends to result in a few active DG units with a single place field each, rounded in shape and made larger by iterative weight changes. These effects are more pronounced when produced with thousands of DG units and inputs per DG unit, which the realistic system has available, than with fewer units and inputs, in which case several DG units persists with multiple fields. The emergence of single-field units with learning is in contrast, however, to recent data indicating that most active DG units do have multiple fields. We show how multiple irregularly arranged fields can be produced by the addition of non-space selective lateral entorhinal cortex (lEC) units, which are modelled as simply providing an additional effective input specific to each DG unit. The mean number of such multiple DG fields is enhanced, in particular, when lEC and mEC inputs have overall similar variance across DG units. Finally, we show that in a restricted environment the mean size of the fields is unaltered, while their mean number is scaled down with the area of the environment.
Project description:Neuronal cortical circuitry comprises feedforward, lateral, and feedback projections, each of which terminates in distinct cortical layers [1-3]. In sensory systems, feedforward processing transmits signals from the external world into the cortex, whereas feedback pathways signal the brain's inference of the world [4-11]. However, the integration of feedforward, lateral, and feedback inputs within each cortical area impedes the investigation of feedback, and to date, no technique has isolated the feedback of visual scene information in distinct layers of healthy human cortex. We masked feedforward input to a region of V1 cortex and studied the remaining internal processing. Using high-resolution functional brain imaging (0.8 mm(3)) and multivoxel pattern information techniques, we demonstrate that during normal visual stimulation scene information peaks in mid-layers. Conversely, we found that contextual feedback information peaks in outer, superficial layers. Further, we found that shifting the position of the visual scene surrounding the mask parametrically modulates feedback in superficial layers of V1. Our results reveal the layered cortical organization of external versus internal visual processing streams during perception in healthy human subjects. We provide empirical support for theoretical feedback models such as predictive coding [10, 12] and coherent infomax  and reveal the potential of high-resolution fMRI to access internal processing in sub-millimeter human cortex.
Project description:Hebbian plasticity, a mechanism believed to be the substrate of learning and memory, detects and further enhances correlated neural activity. Because this constitutes an unstable positive feedback loop, it requires additional homeostatic control. Computational work suggests that in recurrent networks, the homeostatic mechanisms observed in experiments are too slow to compensate instabilities arising from Hebbian plasticity and need to be complemented by rapid compensatory processes. We suggest presynaptic inhibition as a candidate that rapidly provides stability by compensating recurrent excitation induced by Hebbian changes. Presynaptic inhibition is mediated by presynaptic GABA receptors that effectively and reversibly attenuate transmitter release. Activation of these receptors can be triggered by excess network activity, hence providing a stabilising negative feedback loop that weakens recurrent interactions on sub-second timescales. We study the stabilising effect of presynaptic inhibition in recurrent networks, in which presynaptic inhibition is implemented as a multiplicative reduction of recurrent synaptic weights in response to increasing inhibitory activity. We show that networks with presynaptic inhibition display a gradual increase of firing rates with growing excitatory weights, in contrast to traditional excitatory-inhibitory networks. This alleviates the positive feedback loop between Hebbian plasticity and network activity and thereby allows homeostasis to act on timescales similar to those observed in experiments. Our results generalise to spiking networks with a biophysically more detailed implementation of the presynaptic inhibition mechanism. In conclusion, presynaptic inhibition provides a powerful compensatory mechanism that rapidly reduces effective recurrent interactions and thereby stabilises Hebbian learning.
Project description:We introduce Equilibrium Propagation, a learning framework for energy-based models. It involves only one kind of neural computation, performed in both the first phase (when the prediction is made) and the second phase of training (after the target or prediction error is revealed). Although this algorithm computes the gradient of an objective function just like Backpropagation, it does not need a special computation or circuit for the second phase, where errors are implicitly propagated. Equilibrium Propagation shares similarities with Contrastive Hebbian Learning and Contrastive Divergence while solving the theoretical issues of both algorithms: our algorithm computes the gradient of a well-defined objective function. Because the objective function is defined in terms of local perturbations, the second phase of Equilibrium Propagation corresponds to only nudging the prediction (fixed point or stationary distribution) toward a configuration that reduces prediction error. In the case of a recurrent multi-layer supervised network, the output units are slightly nudged toward their target in the second phase, and the perturbation introduced at the output layer propagates backward in the hidden layers. We show that the signal "back-propagated" during this second phase corresponds to the propagation of error derivatives and encodes the gradient of the objective function, when the synaptic update corresponds to a standard form of spike-timing dependent plasticity. This work makes it more plausible that a mechanism similar to Backpropagation could be implemented by brains, since leaky integrator neural computation performs both inference and error back-propagation in our model. The only local difference between the two phases is whether synaptic changes are allowed or not. We also show experimentally that multi-layer recurrently connected networks with 1, 2, and 3 hidden layers can be trained by Equilibrium Propagation on the permutation-invariant MNIST task.
Project description:The spiking neural networks (SNNs) are the third generation of neural networks and perform remarkably well in cognitive tasks such as pattern recognition. The spike emitting and information processing mechanisms found in biological cognitive systems motivate the application of the hierarchical structure and temporal encoding mechanism in spiking neural networks, which have exhibited strong computational capability. However, the hierarchical structure and temporal encoding approach require neurons to process information serially in space and time respectively, which reduce the training efficiency significantly. For training the hierarchical SNNs, most existing methods are based on the traditional back-propagation algorithm, inheriting its drawbacks of the gradient diffusion and the sensitivity on parameters. To keep the powerful computation capability of the hierarchical structure and temporal encoding mechanism, but to overcome the low efficiency of the existing algorithms, a new training algorithm, the Normalized Spiking Error Back Propagation (NSEBP) is proposed in this paper. In the feedforward calculation, the output spike times are calculated by solving the quadratic function in the spike response model instead of detecting postsynaptic voltage states at all time points in traditional algorithms. Besides, in the feedback weight modification, the computational error is propagated to previous layers by the presynaptic spike jitter instead of the gradient decent rule, which realizes the layer-wised training. Furthermore, our algorithm investigates the mathematical relation between the weight variation and voltage error change, which makes the normalization in the weight modification applicable. Adopting these strategies, our algorithm outperforms the traditional SNN multi-layer algorithms in terms of learning efficiency and parameter sensitivity, that are also demonstrated by the comprehensive experimental results in this paper.
Project description:Cognitive functions rely on the coordinated activity of neurons in many brain regions, but the interactions between cortical areas are not yet well understood. Here we investigated whether low-frequency (?) and high-frequency (?) oscillations characterize different directions of information flow in monkey visual cortex. We recorded from all layers of the primary visual cortex (V1) and found that ?-waves are initiated in input layer 4 and propagate to the deep and superficial layers of cortex, whereas ?-waves propagate in the opposite direction. Simultaneous recordings from V1 and downstream area V4 confirmed that ?- and ?-waves propagate in the feedforward and feedback direction, respectively. Microstimulation in V1 elicited ?-oscillations in V4, whereas microstimulation in V4 elicited ?-oscillations in V1, thus providing causal evidence for the opposite propagation of these rhythms. Furthermore, blocking NMDA receptors, thought to be involved in feedback processing, suppressed ? while boosting ?. These results provide new insights into the relation between brain rhythms and cognition.
Project description:BACKGROUND:Impaired consciousness has been associated with impaired cortical signal propagation after transcranial magnetic stimulation (TMS). We hypothesised that the reduced current propagation under propofol-induced unresponsiveness is associated with changes in both feedforward and feedback connectivity across the cortical hierarchy. METHODS:Eight subjects underwent left occipital TMS coupled with high-density EEG recordings during wakefulness and propofol-induced unconsciousness. Spectral analysis was applied to responses recorded from sensors overlying six hierarchical cortical sources involved in visual processing. Dynamic causal modelling (DCM) of induced time-frequency responses and evoked response potentials were used to investigate propofol's effects on connectivity between regions. RESULTS:Sensor space analysis demonstrated that propofol reduced both induced and evoked power after TMS in occipital, parietal, and frontal electrodes. Bayesian model selection supported a DCM with hierarchical feedforward and feedback connections. DCM of induced EEG responses revealed that the primary effect of propofol was impaired feedforward responses in cross-frequency theta/alpha-gamma coupling and within frequency theta coupling (F contrast, family-wise error corrected P<0.05). An exploratory analysis (thresholded at uncorrected P<0.001) also suggested that propofol impaired feedforward and feedback beta band coupling. Post hoc analyses showed impairments in all feedforward connections and one feedback connection from parietal to occipital cortex. DCM of the evoked response potential showed impaired feedforward connectivity between left-sided occipital and parietal cortex (T contrast P=0.004, Bonferroni corrected). CONCLUSIONS:Propofol-induced loss of consciousness is associated with impaired hierarchical feedforward connectivity assessed by EEG after occipital TMS.
Project description:Spike-timing-dependent plasticity (STDP) has been well established between excitatory neurons and several computational functions have been proposed in various neural systems. Despite some recent efforts, however, there is a significant lack of functional understanding of inhibitory STDP (iSTDP) and its interplay with excitatory STDP (eSTDP). Here, we demonstrate by analytical and numerical methods that iSTDP contributes crucially to the balance of excitatory and inhibitory weights for the selection of a specific signaling pathway among other pathways in a feedforward circuit. This pathway selection is based on the high sensitivity of STDP to correlations in spike times, which complements a recent proposal for the role of iSTDP in firing-rate based selection. Our model predicts that asymmetric anti-Hebbian iSTDP exceeds asymmetric Hebbian iSTDP for supporting pathway-specific balance, which we show is useful for propagating transient neuronal responses. Furthermore, we demonstrate how STDPs at excitatory-excitatory, excitatory-inhibitory, and inhibitory-excitatory synapses cooperate to improve the pathway selection. We propose that iSTDP is crucial for shaping the network structure that achieves efficient processing of synchronous spikes.
Project description:Synaptic Plasticity, the foundation for learning and memory formation in the human brain, manifests in various forms. Here, we combine the standard spike timing correlation based Hebbian plasticity with a non-Hebbian synaptic decay mechanism for training a recurrent spiking neural model to generate sequences. We show that inclusion of the adaptive decay of synaptic weights with standard STDP helps learn stable contextual dependencies between temporal sequences, while reducing the strong attractor states that emerge in recurrent models due to feedback loops. Furthermore, we show that the combined learning scheme suppresses the chaotic activity in the recurrent model substantially, thereby enhancing its' ability to generate sequences consistently even in the presence of perturbations.