The hippocampus is able to rapidly learn incoming information, even if that information is only observed once. Furthermore, this information can be replayed in a compressed format in either forward or reverse modes during sharp wave–ripples (SPW–Rs). We leveraged state-of-the-art techniques in training recurrent spiking networks to demonstrate how primarily interneuron networks can achieve the following: (1) generate internal theta sequences to bind externally elicited spikes in the presence of inhibition from the medial septum; (2) compress learned spike sequences in the form of a SPW–R when septal inhibition is removed; (3) generate and refine high-frequency assemblies during SPW–R-mediated compression; and (4) regulate the inter-SPW interval timing between SPW–Rs in ripple clusters. From the fast timescale of neurons to the slow timescale of behaviors, interneuron networks serve as the scaffolding for one-shot learning by replaying, reversing, refining, and regulating spike sequences.
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The data that support the findings in this study are available from the corresponding author upon request.
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The authors thank F. Skinner for fruitful discussions. The authors acknowledge the support of the Natural Sciences and Engineering Research Council of Canada (NSERC), Postdoctoral Fellowship 487777 (to W.N.), and BBSRC BB/N013956/1, BB/N019008/1, Wellcome Trust 200790/Z/16/Z, Simons Foundation 564408, EPSRC EP/R035806/1, and NIH 1R01NS109994-01 (to C.C.).
The authors declare no competing interests.
Journal peer review information: Nature Neuroscience thanks György Buzsáki and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.
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Integrated supplementary information
A network consisting of 2000 Excitatory and 2000 Inhibitory LIF neurons was FORCE trained to oscillate at its own internal frequency, θINT . (A) A series of decoders is learned dynamically through Recursive Least Squares (RLS) minimization. The decoders are used to decode the signal cos(2πθINT t + χi) for χi drawn from a uniform distribution on [0, 2π] for i = 1, 2, . . . 100 components. The network receives INP-MS while it is trained. The decoders also function to stabilize the network dynamics through a learned feedback weight (see Materials and Methods for further details). The overlines denote the presence of INP-MS (gold) or RLS learning (pink). The evolution of 10 decoders is shown. (B) Voltage traces for 5 excitatory neurons (red) and 5 interneurons (blue) are shown for the epochs (i)-(ii) from (A). The excitatory neurons were kept sub- threshold by applying a low background current which was insufficient to induce spiking (ICA3E = −25 pA). The interneurons fire either bursts or single action potentials during a theta oscillation while the excitatory neurons display a sub-threshold interference pattern before and after training when INP-MS is present. (C) The intrinsic oscillator cos(2πθINT t + χi) can be decoded during training (i, bottom) and after training (ii, bottom) from the filtered spike times, r(t), of the interneurons. A subset of 5 decoded oscillators are shown. (D) A subset of 5 excitatory (red) and 5 inhibitory (blue) neurons at the start of FORCE training (top) and after FORCE training (bottom). No excitatory connection is present in this network either before or after training. The learned component of the inhibitory coupling is a perturbation to the initial random coupling. (E) Voltage trace (blue) for an interneuron along with the synaptic current the neuron receives (purple). The inhibitory population activity (grey) shows a strong theta modulation that is unaffected by the interference pattern from INP-MS and recurrent inhibitory oscillations (gold and red, respectively). The spike times for the interneurons (blue dots) precess in phase with respect to the population activity.
(A) A uniform distribution of phase preferences yields a flat population activity as neurons with opposing phase preferences cancel out. (B) As the uniform phase preferences yield a flat population activity, synchronized INP-MS yields a population activity with the same frequency. (C) The sum of INP-MS and the internal oscillation turns into a current that is described by the product of a carrier function (blue) and an envelope function (red). The envelope controls the spike rates while the carrier controls the spike times. Thus, the carrier causes phase precession. (D) The envelope phase, ψi/2 dictates the order of firing. This is inherited from the phase preferences in the internal oscillator, θINT (ψi).
Supplementary Figure 3 Sorting Neurons According to Theta Phase Preference Reveals a Banded Weight Structure.
(A) Both the excitatory and inhibitory neurons are sorted according to their phase preference in the internal theta oscillation, θINT. This preference is measured according to when the peak of the neurons’ inhibitory synaptic current occurs. (B) The unsorted I to I weight matrix appears largely structure-less, containing random elements with a perturbation due to FORCE training. Sorting the neurons according to their phase preference reveals diagonal bands of inhibition. This banding implies that an interneuron preferentially does not inhibit interneurons with slightly advanced phases, and is more likely to inhibit interneurons that have already fired. (C) Similar banding in 10 repetitions for FORCE training the recurrent inhibitory (I to I) weights. The parameters and training time are the same as in Supplementary Fig. 1, and the main figures in the manuscript. (D) This banding is also present in the inhibitory to excitatory weights. (E) As the weight matrices (I to I) are sorted according to phase preferences, averaging the phase sorted weight matrices after 10 iterations of FORCE training reveals the bands of inhibition more clearly. Thresholding the weights (>-1e-3) also reveals that inhibitory banding. This banding is off the primary diagonal indicating that interneurons preferentially do not inhibit interneurons with phases that advance the oscillation. (F) Same as in (D), only with I to E weights.
(A) The SHOT-CA3 network is successfully FORCE trained at a time step of dt = 0.01 ms with identical parameters as Supplementary Fig. 1. The network learns a compressible theta sequence, with compression triggered by removal of INP-MS. (B) The FORCE trained network considered in Supplementary Fig. 1 and the majority of this work, integrated with a time step of 0.05 ms. (C) The same network as in (B), only simulated at a smaller time step of 0.01 ms after FORCE training. FORCE training for the network in (B) and (C) occurred with a time step of 0.05 ms. The excitatory neurons received an extra background current of 20 pA to elicit burst firing ((A)-(C)).
(A) The distribution of phase preferences for the SHOT-CA3E under the normal conditions considered in the manuscript (first row), a proper re-sampled uniform distribution (second row), a unimodal distribution created from a Gaussian with mean π, and standard deviation 2, wrapped into the interval [0, 2π] with the mod function (third row), and a unimodal wrapped Gaussian with mean π and standard deviation 1. Here, the phases are re-sampled from the original phase distribution by generating a new phase variable, ψi for each excitatory neuron using the desired density function. The old phase preferences for the neurons, ψj correspond to rows in the FORCE trained I to E weight matrix. These rows are re-sampled such that the new weights to neuron i correspond to the weights that originally belonged to neuron i' such that |ψi – ψi’| is at a minimum. (B) The spike raster plot for the SHOT-CA3E (red dots) and RO-CA1 neurons (black dots). (C) A zoom of the compressed replay segment when INP-MS is off. For the phase densities considered, the local Fourier parameter was λ = 3.75 · 10−7 (pA2ms)−1 (first three rows), and 20 pA of extra current administered to the SHOT-CA3E to elicit spiking in [3.99,4.09]. A lower learning rate was used for the final row, λ = 2.5 · 10−7 (pA2ms)−1, with a larger administered current of 23 pA to elicit spiking. The background current to all excitatory neurons was ICA3E = −15 pA. (D) Here, we alter the neuronal parameters and FORCE train the network of neurons with heterogeneity. We consider three sources of heterogeneity separately: The refractory period of spiking τref, the membrane time constant, τm and the background current ICA3E, ICA3I. We consider uniform distributions in the refractory period ([1, 6] ms), and the membrane time constant ([10, 20]) ms, while we consider separate normal distribution for the background currents of the excitatory and inhibitory population. (E) The spike raster plot for the SHOT-CA3E (red dots) and RO-CA1 neurons (black dots). (F) A zoom of the compressed replay segment when INP-MS is off. (G) The recurrent inhibition (I to I) weight matrix after FORCE training and phase sorting of neurons. Note that in all cases, the light band indicating a lack of inhibition off the main diagonal remains. All FORCE training parameters were identical as in Supplementary Fig. 1. All other parameters were identical to those in Supplementary Fig. 1. The Fourier rule learning rates were 1.25 · 10−7 (pA2ms)−1, 8.75 · 10−7(pA2ms)−1, 6.5·10−7(pA2ms)−1. The extra current pulse used to activate the excitatory neurons was 27 pA (ICA3I/ICA3E), 28 pA (τref), and 25 pA (τm) delivered in the interval [3.99, 4.1]. The background current to the excitatory neurons in the τm and τref cases was ICA3E = −7 pA and ICA3E = −5 pA, respectively.
(A) A SHOT-CA3 network of 4500 excitatory neurons (red) and 500 interneurons (blue) was successfully FORCE trained on the internal oscillator θINT task while receiving INP-MS. The spike raster plot (left) is shown for 3.5 seconds of simulation time, with INP-MS is off on [3.97.4.09]s. The network learns the spike sequence of the 2000 RO-CA1 neurons. (Middle) Zoom of the spike raster plot for the RO-CA1 neurons when INP-MS is off and compressed replay is triggered. (Right) The θINT phase preference sorted weight matrix coupling the SHOT-CA3I to themselves. (B) Identical E/I ratio to (A), only with 9000 excitatory and 1000 interneurons, and 2000 RO-CA1 neurons. (C) A SHOT-CA3 network of 4000 excitatory neurons and 4000 interneurons was FORCE trained on the internal oscillator θINT task while receiving INP-MS. Left, Middle, and Right are as in (A). The RO-CA1 network consists of 2000 neurons. (D) A SHOT-CA3 network of 18000 excitatory neurons and 2000 interneurons was FORCE trained on the internal oscillator θINT task while receiving INP-MS. Left, Middle, and Right are as in (A). The RO-CA1 network consists of 2000 neurons. (E) A SHOT-CA3 network of 36000 excitatory neurons and 4000 interneurons was FORCE trained on the internal oscillator θINT task while receiving INP-MS. Left, Middle, and Right are as in (A). The RO-CA1 network consists of 2000 neurons. The FORCE q parameter was reduced to q = 2.5 (A)-(B), 1.5 (D), and 1.0 (E) to ensure convergence. The Fourier learning rates were λ = 5.2 · 10−7(pA2ms)−1 (A), 2.5 · 10−7(pA2ms)−1 (B), 2.8 · 10−7(pA2ms)−1 (C), 2.5 · 10−9(pA2ms)−1 (D), 5.0 · 10−8(pA2ms)−1 (E), with the extra current of 27 pA (A), 20 pA (B), 20 pA (C)-(E) delivered to the excitatory neurons when INP-MS is off to elicit spiking during a replay in the interval [3.97, 4.09] (A),(B), [3.99, 4.12] (C), [3.97, 4.11] (D)-(E). The background current to the excitatory neurons was ICA3E = −10 pA (A), ICA3E = −5 pA (B), ICA3E = −10 pA (C), ICA3E = −5 pA (D), and ICA3E = −8 pA (E).
(A) The SHOT-CA3 network of 2000 excitatory and 2000 inhibitory neurons (as in Fig. 1 of the main manuscript) is simulated with differing degrees of intra-SHOT-CA3 neuron synaptic failure, where the post- synaptic current randomly fails to occur at a synaptic connection between SHOT-CA3 neurons with probabilities 0.1,0.2,0.3,0.4, and 0.5 (descending rows). The network is not retrained and still generates sequential activity past 30% synaptic failure, but not 40%. Down-stream spike sequences in the RO-CA1 layer can still be learned in a single-trial for compressed replay past 30% spike failure but not 40%. Experimentally, inhibitory connections in hippocampal slices display a total of 3-7 connection sites, each with a probability of ≈ 0.5 of vesicle release  (see Supplementary Note Bibliography). Assuming independence of these sites, this implies a probability range of synaptic failure of 0.0078 = 0.57 < pfailure < 0.53 = 0.125. The SHOT-CA3 network still functions for failure rates well outside of this tolerance range. (B) A zoom of the compressed replay in the RO-CA1 layer upon deactivation of the INP-MS. The bias currents, ICA3E to the SHOT-CA3E were decreased slightly with increasing synaptic failure (as the background level of inhibition decreases with synaptic failure) with ICA3E = −6, −7, −7.5, −8, −8 pA, respectively. An extra 20 pA current was applied to all simulations when the INP-MS was turned off in the intervals [3.96, 4.08], [3.96, 4.07], [3.95, 4.05], [3.97, 4.08] and [3.97, 4.08], respectively. The local Fourier rule learning rate parameter was λ = 5 · 10−7(pA2ms)−1.
(A) The parameter θMs is swept from 2 Hz to 12 Hz over a 200-second interval using the MATLAB chip function. The spike raster plots of the SHOT-CA3E are sorted according to increasing phase preference. Note that the bottom axis corresponds to time while the top axis corresponds to θMS. The gold overline denotes the continuous presence of INP-MS. The three segments (i) (30, 40)s (ii) (50, 60)s and (iii) (110, 120)s are highlighted for subsequent analysis in (B)-(D). The firing fields flip in orientation near harmonics of the recurrent frequency θINT = 8.5 Hz. Note that neurons fire with slightly different rates within a firing field. This is likely due to errors in FORCE training not creating an exactly uniform distribution of phases. (B) The zoomed raster plots for the segments outlined in (i)-(iii). (C) The peak envelope (black) and the interference pattern (blue) generated by adding INP-MS to a perfect linear oscillator with a frequency of θINT for the segments (i)-(iii) outlined in (A). (D) The currents (blue) arriving at the excitatory neurons from the interneurons. Peak envelope of the currents (black). Note that the currents closely correspond to the expected ones with perfect linear oscillators in (C). The envelope is computed using the MATLAB envelope function for (C)-(D) using the peakfinder function (see MATLAB file exchange). (E) The period of the envelope for the SHOT-CA3 network (black) and the expected value (red) when the envelope is computed using the Hilbert transform. The envelope is computed for the input currents for one of the excitatory neurons. Peak to peak differences in the envelope are used to determine the periodicity of the envelope function. For θMS near θINT, this corresponds to the periodicity of the firing fields. A different formula is required near the harmonics. (F) The frequency of the SHOT-CA3 population activity as a function of θMS. The frequency is estimated using the inhibitory interneurons as they have faster firing rates distributed over the entire-theta interval, thereby generating a smoother estimate. The reciprocal of the peak to peak time interval is subsequently measured to compute the instantaneous frequency.
For (A)-(E), the background current to the SHOT-CA3I (ICA3I) was linearly ramped relative to the baseline amount over a 200-second interval. This corresponds to a range of [−25, 5] pA of applied current. For (F)-(J), the amplitude regulating term of the INP-MS signal (IGABA) was linearly ramped from 0.5× to 2.5× the baseline input amplitude (-5 pA to -25 pA) over a 100 second interval. (A) The current arriving at an excitatory SHOT-CA3 neuron (light blue) displays an interference pattern (envelope in black) for all current levels. (B) The population activity for the excitatory neurons (red, NCA3E = 2000) and interneurons (blue, NCA3I = 2000). As the background current increases, the excitatory neurons increase their firing through disinhibition. (C) A zoomed-in 4-second segment from (B). (D) The frequency of the theta oscillation was estimated by measuring the inter-peak interval. Linear regression revealed a small negative slope (−3.182·10−5, standard error = 2.375·10−4) that was not statistically significant (p = 0.89341, 1599 data points, F-test.). (E) Period of the interference pattern (black dot) as a function of time (blue line). Linear regression revealed a decreasing trend in the interference pattern periodicity with (slope of −0.00556, standard error 8.27010−4 that was significant (p = 1.22 · 10−9, 99 data points, F-test). (F) The current arriving at an excitatory neuron (blue) displays an interference pattern (envelope in black) for moderate levels of IGABA amplitude up to approximately 1.5×. (G) The population activity for the excitatory neurons (red) and interneurons (blue). As the GABAergic amplitude increases the excitatory neurons initially increase their firing through disinhibition. Past a critical point, the behaviour of the SHOT-CA3 network breaks down and the interneurons and excitatory neurons fire highly synchronized and pathological bursts. (H) A 4 second close up from (G). (I) The frequency of the theta oscillation in the population activity as a function of time. Linear regression revealed a small negative slope (−0.00186 · 10−5, standard error 7.90 · 10−4) that was statistically significant (p = 0.0186, 603 data points, F-test). Note that the pathological segments were removed (t > 80) in performing this analysis. (J) Period of the interference pattern (black dot), the least squares fit (blue line). Linear regression revealed an increasing trend in the interference pattern periodicity (slope of 0.036184, standard error 5.955 · 10−3) that was significant (p = 2.38 · 10−6, 27 observations, F-test). All analysis was conducted with the MATLAB function fitlm where the null-hypothesis under fitting conditions is a constant function.
(A) Uni-modal and multi-modal inter-sharp-wave-interval distributions in the SHOT-CA3 network emerge when excitatory connections as in Fig. 2 in the manuscript are incorporated into the network. As the background current (ICA3E) to the SHOT-CA3E increases, the distribution of inter-SPW intervals becomes less skewed, and the rate of SPW-Rs increases. Multi-modal distributions are elicited when the background current to all neurons is increased, with smaller amounts of noise applied to the neurons. The distributions were estimated after 1000 seconds of simulation. (B) SPWs generated in the population activity (computed for all SHOT-CA3E and SHOT-CA3I neurons, 1 ms binned spike times, 20 seconds). The colour corresponds to the parameter sets in (A). All other parameters are the same as in Fig. 2.
(A) The spike raster plot for SHOT-CA3E with the reversion interneurons receiving INP-MS. The firing fields reverse upon removal of INP-MS to all interneurons (SHOT-CA3 and reversion) and activation of the reversion interneurons. The reversion interneurons were activated by an extra 30 pA current after removal of INP-MS. The excitatory neurons received an extra 30 pA background current to induce spiking after removal of INP-MS. (B) The voltage trace for a reversion interneuron (left) and a zoom (right) when INP-MS is removed. (C) The currents impinging on the reversion interneuron from the SHOT-CA3 network (blue), INP- MS current (gold), and the background current (dark green). (D) Heterogeneity was added to the amplitude-phase relationship of inhibitory current from the reversion interneurons and the phase preference of the SHOT-CA3E. In particular, the functional relationship between the phase preference of the excitatory neurons (ψi, x-axis) was corrupted by adding a 0-mean normally distributed noise term with standard deviation σψ to ψi for 5 values σψ = 0, 0.1, 0, 5, 0.8, 1.5. (E) The raster plot for the SHOT-CA3E with INP-MS off at the corresponding distortion level on the left. The network was simulated for a 1-second transient before plotting. For increasing distortion levels, the reverse replay becomes corrupted by a forward replay, the default firing of the network.
Supplementary Figure 12 Learning Behavioral Trajectories Online with a Single Stimulus Presentation.
(A) A schematic for how decoders, φ(t) (green), can be learned online using the global Fourier rule applied to the SHOT-CA3 network. These decoders instantly bind the supervisor or quantity to be remembered to the SHOT-CA3 network activity, over the time period [t-τ, t] where τ is the period of the firing fields. As the firing fields repeat, the decoded memory replays the decoded representation (Xˆ (t)) of the memory, (X(t) = (x(t), y(t))). The decoder φ(t) in conjunction with the filtered spike trains, r(t) for the neurons in the SHOT-CA3 network, allows the network to replay its internal representation of x(t). The memory to be replayed is a simulated mouse trajectory. (B) A simulated mouse (blue) runs a loop around the maze. The SHOT-CA3 network learns online decoders and replays the trajectory in normal time (red) or compressed time (black). (C) The INP-MS is present for the first 11 seconds (gold overline) and absent for the remaining 2 seconds (brown overline). The global Fourier rule is turned on for the initial 2 seconds (green overline) so that the decoders can be learned using the supervisor (blue). The memory is replayed at a normal timescale when INP-MS is on (black, x component is solid, y is dashed) and replayed at a compressed timescale when INP-MS is removed (black). (D) A zoomed-in 1-second segment of the replays on a compressed timescale when INP-MS is removed (black x component is solid, y is dashed). A compressed and time aligned version of the memory (blue) is shown for reference. (E) The evolution of the decoders as they are learned by the global Fourier rule (first four seconds of (C)).
(A) The spike raster plot for the “X” example in Fig. 4g of the Manuscript. (B) The Gramian matrices are plotted for the SHOT-CA3E (when INP-MS is on), the RO-CA1 neurons (when INP-MS is on) and during compressed replay (INP-MS is off). For this example, the output supervisor is non-orthogonal. (C) The excitatory SHOT-CA3 network must learn two synchronous bursts, throughout RO-CA1. The model successfully replays the learned signal after INP-MS is removed and compressed replay is triggered. (D) The Gramian, as in (B). Note that for both (B) and (C), the Gramian for the SHOT-CA3E is not a diagonal matrix, indicating that orthogonality is only moderately satisfied by the SHOT-CA3E. The Gramian for the RO-CA1 populations is not diagonal, indicating that orthogonality is not a requirement for RO-CA1. The parameters considered were λ = 3.5 · 10−7 (pA2ms)−1. An additional 20 pA background current was used to elicit spiking in the interval [4.015, 4.095] in the SHOT-CA3E when INP-MS is off. The pair of bursts were elicited at 2 seconds, and 2.83 seconds, with a 50 pA current pulse to all RO-CA1 neuron. The pulse duration was 40 ms.
(A) The SHOT-CA3 and RO-CA1 network considered was trained identically as in Fig. 5, with the local Fourier rule. The spike raster plot is shown for the RO-CA1Is (teal), the RO-CA1Es (black), the SHOT-CA3I (blue) and the SHOT-CA3E (red). Here, INP-MS is kept on after learning and a small additional current (valued at 2 pA) is given to the SHOT-CA3E. This increases their activity rate, triggering high-frequency assemblies in RO-CA1. The assemblies are identical to those observed in the SPW-R state (Fig. 5), with only a subset of these assemblies expressed in each theta cycles. The subset of assemblies has a small inter-assembly-interval while the inter-subset-interval is θMS. Thus, these assemblies nest on the theta oscillation. The assemblies repeat on the same timescale as they were originally observed (see Fig. 5). (B) A zoomed view of the RO-CA1 population spike times demonstrating high-frequency assemblies in the excitatory neurons and high frequency firing in the interneurons. (C) The scaled (to unity) population activities for the RO-CA1 inhibitory (teal), the RO-CA1 excitatory (black), the SHOT-CA3 inhibitory (blue) and the SHOT-CA3 excitatory (red) populations. The population activity in all cases is computed as a histogram with 1 ms time bins. (D) A 200 ms zoom of the population activity from (C). The high-frequency activity is nested to the theta oscillation.
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Nicola, W., Clopath, C. A diversity of interneurons and Hebbian plasticity facilitate rapid compressible learning in the hippocampus. Nat Neurosci 22, 1168–1181 (2019) doi:10.1038/s41593-019-0415-2