1. The effect of step changes in membrane potential on the end-plate conductance change produced ... more 1. The effect of step changes in membrane potential on the end-plate conductance change produced by bath-applied suberyldicholine was studied in voltage-clamped frog muscle fibres. 2. The suberyldicholine-induced conductance increased exponentially from its previous equilibrium level to a new equilibrium level following a step hyperpolarization. 3. For low suberyldicholine concentrations the time constant of this relaxation was independent of the concentration. 4. For low suberyldicholine concentrations the voltage dependence of equilibrium conductance and relaxation time constants was identical. 5. Bungarotoxin pretreatment did not affect the responses beyond a simple reduction in their amplitude. 6. The conductance evoked by high suberyldicholine concentrations was less voltage-sensitive than that evoked by low concentrations. 7. A new model for explaining noise and relaxation data is proposed. This postulates rate-limiting binding steps followed by a voltagedependent isomerization.
Proceedings of the National Academy of Sciences, 1990
Neurons of the cat's dorsal lateral geniculate nucleus were recorded intracellularly to study... more Neurons of the cat's dorsal lateral geniculate nucleus were recorded intracellularly to study the contribution of N-methyl-D-aspartate (NMDA) receptors to excitatory postsynaptic potentials (EPSPs) and low-threshold calcium spikes. EPSPs were evoked by stimulation of retinogeniculate axons in the optic tract and/or corticogeniculate axons in the optic radiations; EPSPs from both sources were similar. These EPSPs had one or two components, and the second component had several characteristics of NMDA receptor-mediated events. For example, EPSP amplitude decreased when neurons were hyperpolarized and increased when stimulus frequency was increased; these EPSPs could also be blocked reversibly by application of the selective NMDA receptor antagonist DL-2-amino-5-phosphonovaleric acid (APV). We also studied the influence of NMDA receptors on low-threshold calcium spikes, which are large, voltage- and calcium-dependent depolarizations that are often accompanied by high-frequency actio...
Purpose. We previously proposed that Hebbian adjustments that are incompletely synapse specific (... more Purpose. We previously proposed that Hebbian adjustments that are incompletely synapse specific ("crosstalk") might be analogous to genetic mutations. We analyze aspects of the effect of crosstalk in Hebbian learning using the classical Oja model. Methods. In previous work we showed that crosstalk leads to learning of the principal eigenvector of EC (the input covariance matrix pre-multiplied by an error matrix that describes the crosstalk pattern), and found that with positive input correlations increasing crosstalk smoothly degrades performance. However, the Oja model requires negative input correlations to account for biological ocular segregation. Although this assumption is biologically somewhat implausible, it captures features that are seen in more complex models. Here, we analyze how crosstalk would affect such segregation. Results. We show that for statistically unbiased inputs crosstalk induces a bifurcation from segregating to nonsegregating outcomes at a critical value which depends on correlations. We also investigate the behavior in the vicinity of this critical state and for weakly biased inputs. Conclusions. Our results show that crosstalk can induce a bifurcation under special conditions even in the simplest Hebbian models and that even the low levels of crosstalk observed in the brain could prevent normal development. However, during learning pairwise input statistics are more complex and crosstalk-induced bifurcations may not occur in the Oja model. Such bifurcations would be analogous to "error catastrophes" in genetic models, and we argue that they are usually absent for simple linear Hebbian learning because such learning is only driven by pairwise correlations.
Accurate 'synapses' and neocortex-like 'proofreading' may be required for future intelligent neur... more Accurate 'synapses' and neocortex-like 'proofreading' may be required for future intelligent neuromorphic devices.
et al., 2009). We found that useful learning is always still possible provided that Hebbian adjus... more et al., 2009). We found that useful learning is always still possible provided that Hebbian adjustments retain some connection specifi city, though it is degraded. However, there has been increasing realization that at least in the neocortex unsupervised learning must be sensitive to higher-than-pairwise correlations, which requires that the learning rule at individual connections be nonlinear. Since the number of possible higher-order correlations is, for high-dimensional input patterns, essentially unlimited, useful learning might require that the connection-level nonlinear learning rule be extremely accurate. To test this idea, we studied the effect of introducing Hebbian crosstalk in perhaps the simplest neural network model of nonlinear learning, independent components analysis (ICA) (Nadal
Background: Recent work on long term potentiation in brain slices shows that Hebb's rule is not c... more Background: Recent work on long term potentiation in brain slices shows that Hebb's rule is not completely synapse-specific, probably due to intersynapse diffusion of calcium or other factors. We previously suggested that such errors in Hebbian learning might be analogous to mutations in evolution. Methods and findings: We examine this proposal quantitatively, extending the classical Oja unsupervised model of learning by a single linear neuron to include Hebbian inspecificity. We introduce an error matrix E, which expresses possible crosstalk between updating at different connections. When there is no inspecificity, this gives the classical result of convergence to the first principal component of the input distribution (PC1). We show the modified algorithm converges to the leading eigenvector of the matrix EC, where C is the input covariance matrix. In the most biologically plausible case when there are no intrinsically privileged connections, E has diagonal elements Q and offdiagonal elements ð1 À Q Þ=ðn À 1Þ, where Q, the quality, is expected to decrease with the number of inputs n and with a synaptic parameter b that reflects synapse density, calcium diffusion, etc. We study the dependence of the learning accuracy on b, n and the amount of input activity or correlation (analytically and computationally). We find that accuracy increases (learning becomes gradually less useful) with increases in b, particularly for intermediate (i.e., biologically realistic) correlation strength, although some useful learning always occurs up to the trivial limit Q ¼ 1=n. Conclusions and significance: We discuss the relation of our results to Hebbian unsupervised learning in the brain. When the mechanism lacks specificity, the network fails to learn the expected, and typically most useful, result, especially when the input correlation is weak. Hebbian crosstalk would reflect the very high density of synapses along dendrites, and inevitably degrades learning.
1. The effect of step changes in membrane potential on the end-plate conductance change produced ... more 1. The effect of step changes in membrane potential on the end-plate conductance change produced by bath-applied suberyldicholine was studied in voltage-clamped frog muscle fibres. 2. The suberyldicholine-induced conductance increased exponentially from its previous equilibrium level to a new equilibrium level following a step hyperpolarization. 3. For low suberyldicholine concentrations the time constant of this relaxation was independent of the concentration. 4. For low suberyldicholine concentrations the voltage dependence of equilibrium conductance and relaxation time constants was identical. 5. Bungarotoxin pretreatment did not affect the responses beyond a simple reduction in their amplitude. 6. The conductance evoked by high suberyldicholine concentrations was less voltage-sensitive than that evoked by low concentrations. 7. A new model for explaining noise and relaxation data is proposed. This postulates rate-limiting binding steps followed by a voltagedependent isomerization.
Proceedings of the National Academy of Sciences, 1990
Neurons of the cat's dorsal lateral geniculate nucleus were recorded intracellularly to study... more Neurons of the cat's dorsal lateral geniculate nucleus were recorded intracellularly to study the contribution of N-methyl-D-aspartate (NMDA) receptors to excitatory postsynaptic potentials (EPSPs) and low-threshold calcium spikes. EPSPs were evoked by stimulation of retinogeniculate axons in the optic tract and/or corticogeniculate axons in the optic radiations; EPSPs from both sources were similar. These EPSPs had one or two components, and the second component had several characteristics of NMDA receptor-mediated events. For example, EPSP amplitude decreased when neurons were hyperpolarized and increased when stimulus frequency was increased; these EPSPs could also be blocked reversibly by application of the selective NMDA receptor antagonist DL-2-amino-5-phosphonovaleric acid (APV). We also studied the influence of NMDA receptors on low-threshold calcium spikes, which are large, voltage- and calcium-dependent depolarizations that are often accompanied by high-frequency actio...
Purpose. We previously proposed that Hebbian adjustments that are incompletely synapse specific (... more Purpose. We previously proposed that Hebbian adjustments that are incompletely synapse specific ("crosstalk") might be analogous to genetic mutations. We analyze aspects of the effect of crosstalk in Hebbian learning using the classical Oja model. Methods. In previous work we showed that crosstalk leads to learning of the principal eigenvector of EC (the input covariance matrix pre-multiplied by an error matrix that describes the crosstalk pattern), and found that with positive input correlations increasing crosstalk smoothly degrades performance. However, the Oja model requires negative input correlations to account for biological ocular segregation. Although this assumption is biologically somewhat implausible, it captures features that are seen in more complex models. Here, we analyze how crosstalk would affect such segregation. Results. We show that for statistically unbiased inputs crosstalk induces a bifurcation from segregating to nonsegregating outcomes at a critical value which depends on correlations. We also investigate the behavior in the vicinity of this critical state and for weakly biased inputs. Conclusions. Our results show that crosstalk can induce a bifurcation under special conditions even in the simplest Hebbian models and that even the low levels of crosstalk observed in the brain could prevent normal development. However, during learning pairwise input statistics are more complex and crosstalk-induced bifurcations may not occur in the Oja model. Such bifurcations would be analogous to "error catastrophes" in genetic models, and we argue that they are usually absent for simple linear Hebbian learning because such learning is only driven by pairwise correlations.
Accurate 'synapses' and neocortex-like 'proofreading' may be required for future intelligent neur... more Accurate 'synapses' and neocortex-like 'proofreading' may be required for future intelligent neuromorphic devices.
et al., 2009). We found that useful learning is always still possible provided that Hebbian adjus... more et al., 2009). We found that useful learning is always still possible provided that Hebbian adjustments retain some connection specifi city, though it is degraded. However, there has been increasing realization that at least in the neocortex unsupervised learning must be sensitive to higher-than-pairwise correlations, which requires that the learning rule at individual connections be nonlinear. Since the number of possible higher-order correlations is, for high-dimensional input patterns, essentially unlimited, useful learning might require that the connection-level nonlinear learning rule be extremely accurate. To test this idea, we studied the effect of introducing Hebbian crosstalk in perhaps the simplest neural network model of nonlinear learning, independent components analysis (ICA) (Nadal
Background: Recent work on long term potentiation in brain slices shows that Hebb's rule is not c... more Background: Recent work on long term potentiation in brain slices shows that Hebb's rule is not completely synapse-specific, probably due to intersynapse diffusion of calcium or other factors. We previously suggested that such errors in Hebbian learning might be analogous to mutations in evolution. Methods and findings: We examine this proposal quantitatively, extending the classical Oja unsupervised model of learning by a single linear neuron to include Hebbian inspecificity. We introduce an error matrix E, which expresses possible crosstalk between updating at different connections. When there is no inspecificity, this gives the classical result of convergence to the first principal component of the input distribution (PC1). We show the modified algorithm converges to the leading eigenvector of the matrix EC, where C is the input covariance matrix. In the most biologically plausible case when there are no intrinsically privileged connections, E has diagonal elements Q and offdiagonal elements ð1 À Q Þ=ðn À 1Þ, where Q, the quality, is expected to decrease with the number of inputs n and with a synaptic parameter b that reflects synapse density, calcium diffusion, etc. We study the dependence of the learning accuracy on b, n and the amount of input activity or correlation (analytically and computationally). We find that accuracy increases (learning becomes gradually less useful) with increases in b, particularly for intermediate (i.e., biologically realistic) correlation strength, although some useful learning always occurs up to the trivial limit Q ¼ 1=n. Conclusions and significance: We discuss the relation of our results to Hebbian unsupervised learning in the brain. When the mechanism lacks specificity, the network fails to learn the expected, and typically most useful, result, especially when the input correlation is weak. Hebbian crosstalk would reflect the very high density of synapses along dendrites, and inevitably degrades learning.
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Papers by Paul Adams