Single-phase deep learning in cortico-cortical networks
Authors: Will Greedy
Heng Wei Zhu
Joseph Oliver Pemberton
Jack Mellor
Rui Ponte Costa
Venue: NeurIPS 2022 Accept (2022)
Keywords: cortical microcircuits
deep learning
synaptic plasticity
biologically plausible learning
neuroscience

Abstract: The error-backpropagation (backprop) algorithm remains the most common solution to the credit assignment problem in artificial neural networks. In neuroscience, it is unclear whether the brain could adopt a similar strategy to correctly modify its synapses. Recent models have attempted to bridge this gap while being consistent with a range of experimental observations. However, these models are either unable to effectively backpropagate error signals across multiple layers or require a multi-phase learning process, neither of which are reminiscent of learning in the brain. Here, we introduce a new model, Bursting Cortico-Cortical Networks (BurstCCN), which solves these issues by integrating known properties of cortical networks namely bursting activity, short-term plasticity (STP) and dendrite-targeting interneurons. BurstCCN relies on burst multiplexing via connection-type-specific STP to propagate backprop-like error signals within deep cortical networks. These error signals are encoded at distal dendrites and induce burst-dependent plasticity as a result of excitatory-inhibitory top-down inputs. First, we demonstrate that our model can effectively backpropagate errors through multiple layers using a single-phase learning process. Next, we show both empirically and analytically that learning in our model approximates backprop-derived gradients. Finally, we demonstrate that our model is capable of learning complex image classification tasks (MNIST and CIFAR-10). Overall, our results suggest that cortical features across sub-cellular, cellular, microcircuit and systems levels jointly underlie single-phase efficient deep learning in the brain.

Single-phase deep learning in cortico-cortical networks
Will Greedy*
Heng Wei Zhu'
Bristol Computational Neuroscience Unit Department of Computer Science, SCEEM University of Bristol, United Kingdom will. greedy@bristol.ac ac. uk
Bristol Computational Neuroscience Unit School of Phys., Pharm. and Neuroscience University of Bristol, United Kingdom hengwei zhu@bristol.... ac uk
Joseph Pemberton
Jack Mellor
Bristol Computational Neuroscience Unit Department of Computer Science, SCEEM University of Bristol, United Kingdom joe. wwwpppeettobbbssslllll...oom ac.uk
School of Phys., Pharm. and Neuroscience University of Bristol, United Kingdom jack www. mellor@bristol. ac... uk
Rui Ponte Costa
Bristol Computational Neuroscience Unit Department of Computer Science, SCEEM University of Bristol, United Kingdom rui wwwta@bristtto..e... uk
Abstract
The pror-bbackpropggation (backprop) algorithm remains the most common solu- tion to the credit assignment problem in artificial neural networks. In neuroscience, it is unclear whether the brain could adopt similar strategy to correctly modify its synapses. Recent models have attempted to bridge this gap while being consistent with range of experimental observations. However, these models to effectively backpropagate error signals across multiple layers or require a multi- phase learning process, neither of which reminiscent of learning in the brain. Here, we introduce a new model, Bursting Cortico-Cortical Cortical Networks (BurstCCN), which solves these issues by integrating known properties of cortical networks namely bursting activity, short-term plasticity (STP) and dendrite-targeting in- terneurons. BurstCCN relies burst multiplexing via coneectiontyype-seechn STP to propagate backprop-lic еттог signals within deep cortical networks. These error signals are encoded distal dendrites and induce burst-dependent plasticity as result of excitatory-inhibiue our model can effectively backpropagate errors through multiple layers using a single-phan phase learning process. Next, we show both empirically and analytically that learning our model approximates backprop-derived gradients. Finally, we demonstrate that our model is capable of learning complex image classification tasks (MNIST and CIFAR-10). Overall, our results suggest that cortical features across sub-cellular, cellular, microcircuit and systems levels jointly underlie single- phase efficient deep learning in the brain.
either unable
top-down inputs. First, we demonstrate that
Eqqual contributions
36th Conference on Neural Information Processing Systems (NcurIPS 2022).

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Introduction
For effective learning. synaptic modifications throughout the brain should result in improved be- havioural function. This requires process by which credit should be assigned to synapses given their contribution to behavioural output [1+3]. In multilayer networks, credit assignment is particularly challenging as the impact of changing a synaptic connection depends on its downstream brain areas. Classical local Hebbian plasticity rules, even when coupled with global neuromodulatory factors, are unable to communicate enough information for effective credit assignment through multiple (backprop) algorithm is
layers of processing [3. In machine learning, the srror-backroopggatio the most successful solution to the credit assignment problem. However, relies on a number of biologically implausible assumptions to compute gradient information used for synaptic updates. Previous work has attempted to address these implausibilities but important issues remain open when mapping backprop to the neuronal physiology. Earlier attempts relied using cinll--comarrtment neuron models 4 [ but this poses a problem as single-compartment neurons are unable to simulta- neously store the necessary inference and credit assignment signals. One solution is to model neurons with an apical dendritic compartment that separately stores credit information [5 6]. supported by the electrotonic separation of the soma and apical dendrites 77]. These distal credit signals can then be communicated to the soma through non-linear dendritic events that trigger bursting at the soma (8) thereby inducing long-term synaptic plasticity (9) In particular, two recent approaches, Error-encoding Dendritic Networks (EDNs) 6 and Burstprop [10], have demonstrated how such multi-compartment neuron models be used to construct networks capable of backprop-like credit assignment. EDNs encode credit signals at apical dendrites resulting from the mismatch between dendritic-targeting interneuron activity and downstream activity. Burstprop uses bursting, controlled by dendritic excitability, as a mechanism to communicate credit signals. However, these models still have major issues, such as the inability to effectively backpropagate error signals through many layers (EDNs) and the requirement for multi pulti learning process (Burstprop).
Here, we propose a new model called the Bursting Cortico-Cortical Network (BurstCCN) as a solution to the credit assignment problem which addresses several outstanding issues of current biologically plausible backprop research. Our model builds upon prior multi-compartment neuron models 10 it encodes credit signals in distal dendritic compartments which trigger bursting activity at the soma to drive backprop-like synaptic updates. We demonstrate that combining well-established properties of cortical neurons such as bursting activity, short-term plasticity (STP) and dendrite- targeting interneurons provides biologically plausible mechanism for performing credit assignment. In contrast to previous models, BurstCCN is highly effective at backpropagating credit signals in multi-layer architectures while only requiring a single-phase learning process. We implement multiple versions of the BurstCCN at different levels of abstraction in order to demonstrate some of its key properties and to empirically confirm our theoretically motivated claims.
First, we use a spike-based implementation of the BurstCCN to demonstrate its ability to learn without the need for multiple phases. We further show the importance of this single-phase learning by training a continuous-time rate-based version of the BursCCCN on a continuous-ting non-linear regression task. Next, we show both empirically and analytically that our model's dynamics result in learning that approximately follows backprop-derived gradients. Finally, we use a simplified discrete-time BurstCCN implementation to demonstrate that the model achieves good performance on non-trivial image classification tasks (MNIST and CIFAR-10), 10), even in the presence of random feedback synaptic weights.
2 Bursting Cortico-Cortical Networks
2.1 Burst Ensemble Multiplexing
Burst Ensemble Multiplexing (BEM) [1] refers to the idea that ensembles of cortical neurons are capable of simultaneously representing multiple distinct signals within the patterns of their spiking activity. Typically, pyramidal cells receive top-down and bottom-up signals into their apical and basal dendrites, respectively. Bottom-up basal inputs affect the rate of spiking and top-down apical inputs convert these somatically induced spikes into high-frequency bursts. Postsynaptic populations can then use STP to decode these distinct signals from the overall spiking activity.

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Figure 1: Bursting cortico-cortical networks (BurstCCN) for credit assignment through bursting
activity, (A) Network schematic consisting of neuron ensembles and comnectio-type-speiiin STP.
Events from the input are propagated forward through short-term depressing (STD) connections, W. Output event rates are compared to a target value which generates a teaching signal that is presented to the output layer apical dendrites. This acts as an error signal and appears deflection in the dendritic potential from its resting potential which causes changes to bursting activity from its baseline. The error-carrying bursting signals are propagated back through short-term facilitating connections, Y, which we interpret as being communicated by populations of dendrite-targetinn interneurons. Events are also propagated backwards via STD connections, Q, to provide means of cancelling baseline bursting activity. The difference in activity from these two feedback connections results in changes to dendritic excitability that lead to burst-dependent synaptic plasticity. (B) Burst-dependent plasticity rule. Simple setup of a single connection between a pre- and post-synaptic cell that are both modelled with Poisson spike trains with equal rates. As the firing rates increase, (top) plasticity the synaptic weight switches from long-term depression (LTD) to long-term potentiation (LTP) (middle) when the burst probability increases above the baseline value. (bottom) The magnitude of the weight change is scaled by the event rate. (C) Homeostatic plasticity rule for Q weights. The difference between the signals through Q and Y dictates the direction and magnitude of synaptic plasticity.
The BurstCCN uses the concept BEM in a similar way Burstprop [10] which ensembles of cells encode both feedforward inference signals and feedback error signals. The model encodes these signals as the rates of events and bursts, respectively, across the ensembles. Here, the specific definition of a burst is collection of spikes with interspike intervals less than 16ms and an event is either a burst or a single isolated spike (i.e. a spike not followed or preceded by another within 16ms). The burst probability of an ensemble is defined as the probability that an event at given time is burst and is computed as a ratio of the event rate (e) and burst rate (b): p = b/e.
2.2 Rate-basee BursiCCN
In our discrete-timee implementation of the rate- based BurstCCN, example input-output pairs are processed independently discrete timesteps. For each example, the event rates of the input layer, co. encode the input stimulus. The model then computes each subsequent layer's activities, equivalent to that a standard feedforward artificial neural network (Fig. [A). Specifically, somatic potentials are computed by integrating basal input as feedforward weights from layer [ - 1 to layer 1. The STD nature of these weights ensures that only event rate information propagates forwards. Each layer's event rates are then computed by applying non-line non-linear activation function, f. to the somatic potentials, e, = f(vi). These linear and nonlinear operations repeated for each layer in the network to ultimately obtain the output layer event rates, CL, where denotes the total number of layers.
W Wi where Wt are short-term depressing (STD)
The desired target output of the network, Starget, is compared to the output layer event rates to produce a signed error, etarget ey,, which is used as a teaching signal. This error information is then propagated backwards through each layer in the network by altering the apical dendritic compartment potential and, as a result, the burst probability of each pyramidal ensemble. the output layer, the burst probability is computed directly Pz- = P P2
(etorget ez) O h(ez) where @
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denotes the element-wise product, P represents the baseline burst probability in the absence of any teaching signal and h(er) = (v:) @ e.- These burst probabilities are used at the output layer (1 = L) to compute the burst rates as by = ot O Pi which are decoded and sent backwards to layer 1 - 1 apical dendrites by a set of short-term facilitating (STF) feedback weights, Y The STF feedback weights and STD feedforward weights are similarly used in Burstprop. However, the BurstCCN additionally includes novel set of apical sundrite-targeting STD feedback weights. Q1- which send event rates backwards. We interpret the STF feedback connections as being provided via a type of cendrite-targeting interneuron and STD feedback as direct connections in line with recent experimental studies [12 The signals through both sets of feedback weights lead to the apical potentials in the previous layer, u Qi-1e: Yt- These determine the layer's burst probabilities which are computed as Pt-1 = 0 @ h(e)-1)) where ā denotes the sigmoid function, o, with scaling and offset parameters, (xx) a(ox (3 (TTO; see SM, Section B). The same process is repeated backwards for each layer until the input layer to obtain their dendritic potentials and burst probabilities. Note that for all experiments, we set a = 4 (and 3 = to prevent this function from implicitly scaling down the errors propagating backwards through each layer by a dar ~ around x = 0).
factor of 4 (since
de
After the error information has been propagated backwards, feedforward synaptic weight changes are computed using burst-dependent synaptic plasticity rule:
AW = m (W) ((P: - pP) @ ef
(I)
where (W) is learning rate and .T is the transpose operation. Importantly, the learning rule depends on the change in burst probability from the predefined layer-wise baseline burst probability, p (1,..... 1)², which represents the signed error signal required for backprop-like learning.
Consequently, when we make both pre- and postsynaptic cells fire following Poisson statistics we obtain long-term depression and long-term potentiation for low and high firing rates, respectively (Fig. [B). This is in line with a large number of experimental studies of cortical synapses [18] 19]
can be shown that the updates produced by this learning rule approximate those obtained by the backpropagation algorithm in the weak-feedback case (see Section 3.3. and SM, Section B
In the absence of teaching signal, it is important for pyramidal ensembles to produce baseline level of bursting such that no weight changes occur (cf. [I. This holds true for the output layer other imputs onto the apical dendrites. However, for the hidden layers the event rate
as there signals through Q and the burst rate signals through Y need to exactly cancel each other out such that the apical dendritic potentials are at rest (i.e. set of Q weights that will produce this exact cancellation regardless of the event rates propagating through the network. Specifically, they must be set Q Y which we refer to the weights being in Q-Y symmetric state. However, it is not biologically plausible for the Q synapses to have direct knowledge of Y. Therefore, inspired by earlier work (6] 20 provide this cancellation:
0). For any Y weights, there is always an optimal
we use a learning rule for Q to
AQ -nt (Q) i 0
which explicitly aims to silence the apical potentials (Fig In the absence of a teaching signal at the output layer, all Q weights will eventually converge to their optimal values and achieve a symmetric state under reasonable assumptions (see SM, Section B.2). Note that we could similarly have added this learning rule on the Y feedback weights to cancel the activity through the Q weights, which produces similar results (Fig. ST).
When teaching signals are applied at the output layer, it is important to note that only the bursting activity propagated through the Y connections changes because the event rates through Q are unaffected by the dendritic activity. This enables single-phase learning as the symmetry in the two feedback connection types (Q and Y) can be exploited to directly compare without teacher signals (i.e. baseline) to with teacher signals.
Details of the continuous time implementation can be found in the Supplementary Materials.
2.3 Spiking BurstCCN
For our spiking implementation of the BurstCCN, we adapted the burst-dependent synaptic plasticity rule in Equation [ (see SM, Eq. [2]. Unlike the two rate-based implementations, the spiking BurstCCN more accurately models the internal neuron spiking dynamics instead of abstracting these

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Figure 2: Spiking BurstCCN does not require multi-phase learning to solve the XOR classifi- cation task. Schematic of the (A) two-phase and (B) single-phase learning settings. (A) For each input during two-phase learning, networks are given a 7.2s prediction period during which teaching signals and plasticity are turned OFF, followed by 0.8s learning period where both teaching signals and plasticity are turned back ON. (B) During single-phase learning, both the teaching signals and plasticity remain ON throughout training. (C, D) Top: event rate (e) of the output layer. Middle: burst probability (p) for the output layer and the baseline moving average of the burst probability (p' p) for BurstCCN and Burstprop, respectively. Bottom: the resulting weight updates for connections from hidden layer neurons. Model results represent mean + standard error 5).
details away and only considering the ensemble-level behaviour. Neurons are modelled with two compartments corresponding the soma and apical dendrites and spikes are generated when somatic threshold potential is met (see SM, Section A.2 for more details).
2.4 Related work
As previously mentioned, BursICCN takes inspiration from prior models: EDNs 66 and Burst- prop [10]. Similar to these models, the BurstCCN uses separate apical dendritic compartment to represent error signal. To silence this apical compartment and maintain correct error signals, the EDN uses a homeostatic plasticity rule from local interneurons to cancel the signals received from a separate feedback pathway. In the BursICCN, rule for learning of the novel Q weights. Unlike the EDN, we use a similar idea to Burstprop in which error signals are encoded as bursts in the neural activity and decoded by STP dynamics.
the same principle by adapting this plasticity
Within each layer, Burstprop includes a set of recurrent connections onto the apical compartments which aim to maintain the dendritic potential in the linear regime of the feedback non-linearity Updating the weights of these connections requires separate learning phases and it is unclear how the plasticity rule can be justified. In contrast, the BurstCCN does not require these connections. Instead, the novel set of STD feedback connections (Q) onto the apical dendrites provide a mechanism for single-phase learning and perform similar role of linearising the feedback. Additionally, burst- dependent plasticity in our model relies on a constant baseline burst probability instead of using a moving average of the burst probability (see SM, Section A.2 for more information).
3 Results
3.1 BurstCCN can learn with single learning phase
key motivation for developing the BurstCCN was to design a model capable of learning without the need for separate learning phases, while being consistent with a range of cortical features across
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multiple levels. To demonstrate that our model can perform single-phan learning, we trained the spiking version of our model on the XOR classification task and contrasted it with Burstprop. which requires two-phase learning process (Fig. 2). In both single- and two-phase learning regimes, the input stimulus is presented for a total of 8s before the next example is shown. The two-phase learning regime has an initial prediction phase, lasting 7.2s for each input presentation, where plasticity is switched off throughout the network and the output neurons do not receive any teaching sigmals (Fig. 2 This is followed by a teacher phase for the remaining 0.8s where plasticity is restored and teaching signals are delivered at the output. The single-phase regime removes the initial prediction phase and extends the teacher phase to the full duration of the input stimulus (Fig. 2B).
Our results show that both models were capable of successfully learning the task in the two-phase regime as indicated by the high output event rates in response to the (0, and (1.0) inputs and low event rates for the (0, 0) and (1, 1) inputs (Fig. D However, when training in the single-phase regime, only BurstCCN was able to learn the task Fig.(D). The inability of Burstprop to learn the task can be explained by comparing the moving average of the burst probability (p) with the actual burst probability (p) which determines the sign of synaptic weight updates Fig.(2). Burstprop failed to learn in the single-phase learning setup due to the teaching signal remaining on and preventing P from being able to provide stable representation of the without-teacher burst probability.
3.2 BurstCCN can learn with dynamic input-output
Typically, studies that have attempted to solve the credit assignment problem with biologically plausible implementations of backprop make implicit assumption that during learning there is a period where the continuous-time input stream is fixed [6] 10]. This is required in most cases to allow the network stabilise its activities before learning can take place. With single-phase learning, we can relax this assumption to enable learning in conditions where the inputs and their corresponding teaching signals are dynamically changing over time. We assessed this ability by training the continuous-ting
BurstCCN (see SM, Section A. on an online non-linear regression task (Fig. 3. This task consisted of three sinusoidal inputs, 24 (t) sin(a,t + 8.). with random frequencies ag ~ (0, 5) and phase offsets 3, ~ (0, 2T) (Fig. 3A). The network had a single output unit for which non-trivial target was obtained by passing the same inputs 3-25-1 artificial neural network (ANN). This approximates setting in which a given cortical area learns to regress its input onto the activity of another cortical area. The ANN weights were randomly initialised with w/y ~ U(- v3) for the first layer and w/y- ~ 4-0066, 0.6) for the second layer. Despite the BurstCCN initially producing outputs that were significantly different to the target (Fig. (C)) the results show that over training it learned to produce output patterns that closely matched the non-linear and dynamic target (Fig. B.D). This highlights that the BurstCCN is capable of adequately backpropagating useful error signals when both inputs and teaching signals are constantly changing.
3.3 Feedback plasticity rule faaillitates alignment to backprop updates
Next, we wanted to understand how well our model approximates backprop. As stated above, the purpose of the learning rule for the feedback STD Q connections (Eq, 2 is to silence the apical compartments in every ensemble by cancelling activity through the feedback STF Y connections. When a teaching signal is applied, this becomes important for computing the correct local error signal that is used for learning and backpropagated to previous layers. Here, we show both analytically and empirically using the discrete version of the model how the computed errors relate to backprop.
3.3.1 BurstCCN with weak feedback approximates backpropagation algorithm
Under some small assumptions, we analytically show that the feedback pathway of BurstCCN is approximately communicating the same error gradients that are computed by backprop. Specifically, we assume that the feedback weights are optimally aligned (i.e. Q: = r Yi) and focus on the change in burst rate, ōb, == (p: - -P²) @ eje we let Etask = |les - etarget|| 12 define the task error then, by construction, the change in burst rate at the output layer is equivalent to the negative error
gradient, åb,- ag For the hidden layers, we derive the following iterative relationship (see SM, Section B 8vz.
ōb: f (vi) @ (YY)) + +(u²).
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Figure 3: BurstCCN can learn a dynamic non-linear regression task. (A) Schematic of the task. Three sinusoidal waves with random frequencies are given as inputs. The task is to learn to match the target pattern which is obtained by passing the same inputs through a fixed, randomly initialised ANN. (B) Learning curve for the (continuous-time BurstCCN, (C, D) Example output traces for (C) before and (D) after training. Model results represent mean standard error (n = 5).
This upproximates the same relationship present in backprop up to third-orde term with respect to the apical potentials u, the feedback weights are set to be symmetric with the feedforward weights (i.c. Y; WW We refer to this as the W-Y symmetric state. The link between weight updates from simply performing gradient descent with backprop and the BurstCCN can be seen clearly:
WW BurstCNNN = TTi (W) 8b, e
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AW backprop = (W) DEaak
e
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Ov,
remains to be shown that the apical potentials, ur of every layer are indeed appropriately small (so that the approximation error, ||u,||, is small). Under the assumption u is small, we can derive the recursive relationship u, = f (V1+1) o (-Y;)u:+1 (see SM, Section B). We show that if f is bounded (as is the case for sigmoid and many activation functions) and the weights Y₁ are reasonably aginek
small then | < ||u ||. This means that the error gradient at the output layer, deN is small then, by induction, ||u/|| is small for every layer and A AW W BurstNN A WW backprop
3.3.2 Learning Q feedback connections better approximates backprop-derived gradients
We empirically evaluated our feedback plasticity rule by updating only the Q weights of randomly initialised 5-layer discrete-time BurstCCN with all other weight types (W and Y) fixed. We used multiple initialisations and training regimes understand how the plasticity rule behaves different scenarios. The network was either initialised in the W-Y symmetric state or with random feedback weights (where Y, * WW We computed the angle between the update that would have been made by the feedforward plasticity rule (Eq. [] and either backprop or feedback alignment [4] for the symmetric and random configurations, respectively. We examined both cases: in the theoretically ideal case for learning Q where no teaching signal is present (Fig. A-D) and with teaching signal at the output layer (Fig 4E-
In all cases, as the alignment between the Q and Y connections improved (Fig. AA.E), the apical potential decreased (Fig. 4B.F) and this resulted updates that more closely aligned to back- prop (Fig. 4C, and feedback alignment (Fig. (D.H). In the absence of a teaching signal, this
'erre use abuse of notation u² (ui,, 2i. )²² represent the element-wise cubic of u
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Figure Feedback learning rule enables a close alignment with backprop and feedback alignment. The network is a randomly initialised 5-layer discrete-time BursICCN with random (solid line) or symmetric (dashed line), fixed W and Y weights. The Q weights are updated in the presence of (A-D) no teaching signal or (E-H) teaching signal. (A.E) Alignment between Q and Y weights, (B,F) the mean absolute value of the apical potentials, (C,G) the alignment to backprop (BP) and (D.H) feedback alignment (FA) as the weights learn to silence apical dendrite potential. Updates below 90º marked by the black dashed line are considered useful as they still follow the direction of backprop average. Model results represent
+ standard error (n 5).
alignment angle to both backprop and feedback alignment eventually became very small which supports our analytical results that show our model approximates these methods (Fig, 4C-D). Despite producing less aligned feedforward updates in the presence of teaching signal, the updates computed were still informative since they were consistently well below 90" of the direction of steepest descent (Fig. 4G).
3.4
BurstCCN learns image classification tasks with multiple hidden layers
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Figure 5: BurstCCN learns to classify handwritten digits (MNIST) with deep networks. (A) Learning curve of 5-layer ANN (black), Burs(CCN (blue), BurstCCN (n/ = 0) (light blue), Burstprop (red) and EDN (green). (B) Test error with different numbers of hidden layers for all models. (C) Alignment to backprop (BP) over time for all 5-layer models. (D) Alignment to backprop with different numbers of hidden layers for all models. The black circle indicates that the hyperparameters for each model were optimised for 5-layer networks. Model results represent mean standard error (n= 5).
Next, to test whether our model can indeed perform backprop-like deep learning, we trained number of (discrete-time) BurstCCN architectures the MNIST handwritten digit classification task [21). We compared the BurstCCN with Burstprop 1Q] and EDNs 6 using similar architectures (see SM, Section C.3.3
We focused on the more biologically plausible case of using random fixed feedback

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weights (i.e. feedback alignment 4 see Fig. S2 for symmetric feedback weight case) with the remaining connection types of the different models updated using their respective plasticity rules. We also tested the BursICCN in its idealised case where the feedback STD weights (Q) were fixed in the Q-Y symmetric state (see Section
2.2p. We denote this model as "BurstCCN (Q-Y sym)".
Using 5-layer networks, the BurstCCN obtained a test error of 1.84 %. comparable to that of Burstprop with 1.75:10.01% and significantly outperforming the EDN with 10.65 (Fig. 55A As the network depth was increased, both Burs(CCN and Burstprop retained high performances but the EDN showed a substantial decay in performance with deeper networks (Fig. B). In an idealised case for the EDN, the disparity in performance and the effect of depth is less evident (Fig. [S3). We then compared the alignment between the models and backprop. For the 5-layer networks, Burstprop's 's updates were most closely aligned to backprop. followed by the two BurstCCN models which all vastly outperformed the EDN (Fig. 5C). As expected, the BurstCCN with Q-Y symmetry could better propagate error signals. By increasing the network depth, we demonstrate that it was more difficult to produce updates that were closely aligned to backprop. However, we show that the BursICCN was still capable of backpropagating useful error signals in relatively deep networks (Fig. PD).
3.4.2 CIFAR-10
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Figure 6: BurstCCN with convolutional layers learns to solve natural image classification task (CIFAR-10). (A) Schematic of BurstCCN architecture consisting of an input layer, three convolutional layers, fully-connected hidden layer and output layer. For the BurstCCN, each layer was connected with a set of feedforward weights, W, and feedback weights, Y and Q. (B) Learning curve and (C) alignment to backprop of the different models with random (solid lines) and symmetric (dashed lines) feedback weight regimes. Model results represent mean + standard error (n -0 5).
Finally, we wanted to investigate the capabilities of the BurstCCN on more challenging tasks that are commonly tested in deep learning. We constructed deep network consisting of three convolutional layers followed by a fully-connected hidden layer and output layer (Fig, (A). We trained ANN, BurstCCN and Burstprop models using this network architecture on the CIFAR-10 image classification task (22). BurstCCN (Q-Y sym) was trained in the Q-Y symmetric regime whereas BurstCCN was initialised in this state and Q weights were then updated using the corresponding plasticity rule. All model types were tested with two feedback weight regimes: W.Y symmetric and random fixed Y feedback weights (i.e. feedback alignment).
After training in the random feedback weight regime, we observed a test error of 38.99--0.188 for BurstCCN, similar to performances achieved by an ANN (36.30+-0. 16%) and Burstprop (41.32+-0. 14%) (Fig. (B). For the W-Y symmetric regime which most resembles backprop, BurstCCN 22.92+0.03% performed significantly better than all random feedback setups and, once

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again, obtained similar enror to the symmetric ANN (22.62+0.10%) and Burstprop (24.15=0.17%) models. In the symmetric setups, there was a large improvement in the alignment angles backprop compared to the random feedback setup (Fig. (P). This suggests that they were backpropagating errors more effectively which likely explains the increase in performance. However, as seen within the random feedback setups, improvement in this alignment does not guarantee an improvement to performance. This is because each model will traverse a different learning trajectory and converge to a different local minimum but the alignment angle remains good indicator of expected performance.
4 Conclusions and discussion
We have introduced a new model capable of backprop-like credit assignment by integrating known properties of cortical networks. We have shown that by combining specific biological mechanisms such as bursting, STP and dendrite-targeting inhibition it is possible to construct a model that learns effectively in continuous setting that is reminiscent of learning in the brain. Moreover, have demonstrated that such a model can learn complex image classification tasks with deep networks.
Our model proposes specific STP dynamics on the feedforward and feedback connections. It requires STD on cortico-cortical projections onto pyramidal cells line with experimental evidence [12] In addition, it suggests key role for dendrite dendrite-targeting interneurons such as SST-positiv Martinotti cells in the feedback pathway. There evidence that these interneurons receive STF top-down connections whereas top-down projections onto pyramidal cells exhibit STD dynamics as required by our model [7]. In future work, it would be interesting to model the specific neuron types for each connection satisfy Dale's law and further increase biological plausibility.
prediction from our model is that manipulations of interneurons with STF connections would lead to disruptions in burst decoding from the layer (brain area) above thereby obstructing learning in the brain area below. Additionally, as error signals alter the level of bursting in the network, the model predicts that the variance in bursting activity and the distal dendritic potentials would correlate with the severity of errors made by the network during learning.
Although our model captures a wide range of biological features, some biological implausibilities re- main. Currently, we use feedback alignment to provide solution to the weight transport problem [23] but this has substantial impact on performance, particularly in more challenging tasks. Therefore, would important to explore some of the recently introduced plausible feedback learning rules 26 which could be used in conjunction with our proposed learning rules to outperform feedback alignment
Overall, our work provides a novel solution to the credit assignment problem and suggests that range of cortical features from sub-cellular the systems level jointly underlie single-phase, efficient deep learning in the brain.
Acknowledgments and Disclosure of Funding
The authors would like to thank Alexandre Payeur, Jordan Guerguiev, Blake Richards, Richard Naud, Kevin Nejad, Jesper Sjostrom, Paul Anastasiades, Joao Sacramento, Adil Khan and Jasper Poort for useful discussions. This work made use of the supercomputer BluePebble. We would also like to thank Callum Wright and the rest of the High Performance Computing team at the University of Bristol for constant and quick help with BluePebble. This work has been supported by two EPSRC Doctoral Training Partnership PhD studentships to Will Greedy and Joseph Pemberton and Wellcome Trust Neural Dynamics PhD studentship to Heng Wei Zhu.
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References
[1] Pieter R Roelfsema and Anthony Holtmaat. Control of synaptic plasticity in deep cortical networks. Nature Reviews Neuroscience, 1963):166-180, 2018.
[2] Blake A Richards, Timothy P Lillierap, Philippe Beaudoin, Yoshua Bengio, Rafal Bogacz, Amelia Christensen, Claudia Clopath, Rui Ponte Costa, Archy de Berker, Surya Ganguli, et al. deep learning framework for neuroscience. Nature neuroscience, 22(11):1711-1770 2019.
[3] Timothy Lillicrap, Adam Santoro, Luke Marris, Colin Akerman, and Geoffrey Hinton. Backpropagation and the brain. Nature Reviews Neuroscience, 21(6):335-346, 2020.
[4] Timothy P Lillicrap, Daniel Cownden, Douglas B Tweed, and Colin J Akerman. Random synap- tie feedback weights support error backpropagation for deep learning. Nature communications, 7(1):1-10, 2016.
[5] Blake A Richards and Timothy P Lillicrap. Dendritic solutions the credit assignment problem. Current opinion in neurobiology, 54:28-300 2019.
[6] João Sacramento, Rui Ponte Costa, Yoshua Bengio, and Walter Senn. Dendritic cortical microcireuits approximate the backpropagation algorithm. In Advances in Neural Information Processing Systems, pages 8721-8732, 2018.
[7] Stephen R Williams and Greg Stuart. Dependence of epsp efficacy synapse location in neocortical pyramidal neurons. Science, 295($561):900--1990 2002.
[8] Ning-long Xu, Mark T Harnett, Stephen R Williams, Daniel Huber, Daniel H O' O'Connor, Karel Svoboda, and Jeffrey Magee. Nonlinear dendritic integration of sensory and motor input during an active sensing task. Nature, 42247429):247-251, 2012.
[9] P Jesper Sjostrom, Ede A Rancz, Arnd Roth, and Michael Hausser. Dendritic excitability and synaptic plasticity. Physiological reviews, 88(2):769-84)) 2008.
[10] Alexandre Payeur, Jordan Guerguiev, Friedemann Zenke, Blake A Richards, and Richard Naud. Burst-dependent synaptic plasticity can coordinate learning in hierarchical circuits. Nature neuroxcience, 24(7):0010-1099 2021.
[11] Richard Naud and Henning Sprekeler. Sparse bursts optimize information transmission in multiplexed neural code. Proceedings of the National Academy of Sciences, 115(27):E6329- E6338, 2018.
[12] Soohyun Lee, Illya Kruglikov, Z Josh Huang, Gord Fishell, and Bernardo Rudy. A disinhibitory circuit mediates motor integration the somatosensory cortex. Nature neuroscience, 16(11): 2013.
[13] Amanda K Kinnischtzke, Daniel J Simons, and Erika E Fanselow. Motor cortex broadly engages excitatory and inhibitory neurons in somatosensory barrel cortex. Cerebral cortex, 24 (8):2237-2248, 2014.
[14] Iraklis Petrof, Angela N Viaene, and S Murray Sherman. Properties of the primary somatosen- sory cortex projection to the primary motor cortex in the mouse. Journal of neurophysiology: 113(7):2400-2444 2015.
[15] Timothy A Zolnik, Julia Ledderose, Maria Toumazou, Thorsten Trimbuch, Tess Oram, Christian Rosenmund, Britta J Eickholt, Robert NS Sachdev, and Matthew E Larkum. Layer 6b is driven by intracortical long-range projection neurons. Cell reports, 30( 30(10):349233505 2020.
[16] Shovan Naskar, Jia Qi. Francisco Pereira, Charles R Gerfen, and Soohyun Lee. Cell-type- specific recruitment of gabaergic interneurons in the primary somatosensory cortex by long- range inputs. Cell reports, 3488)4008774, 2021.
[17] Luis E Martinetti, Kelly E Bonekamp, Dawn M Autio, Hye-Hyun Kim, and Shane R Crandall. Short-term facilitation long-range corticocortical synapses revealed by selective optical stimulation. Cerebral cortex, 193- 2022.

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[18] Elie L Bienenstock, Leon N Cooper, and Paul W Munro. Theory for the development of neuron selectivity; orientation specificity and binocular interaction in visual cortex. Journal of Neuroscience, 2(1):32-48, 48, 1982.
[19] Per Jesper Sjöström, Gina G Turrigiano, and Sacha B Nelson. Rate, timing, and cooperativity jointly determine cortical synaptic plasticity. Neuron, 32(6): 149-1164, 2001.
[20] Tim P Vogels, Henning Sprekeler, Friedemann Zenke, Claudia Clopath, and Wulfram Gerst- ner. Inhibitory plasticity balances excitation and inhibition in sensory pathways and memory networks. Science, 154660662 2011.
[21] Yann LeCun and Corinna Cortes. 7/yann.lecum www. http//xxdmmmii//////////
MNIST handwritten digit database. 2010. URL http:
[22] Alex Krizhevsky, Vinod Nair, and Geoffrey Hinton. Cifar- (canadian institute for advanced research).
cs. toronto........ edu/"kriz/cifar .html
[23] Francis Crick. The recent excitement about neural networks. Nature, 337 132, 1989.
[24] Houg-Hyun Lee, Saizheng Zhang, Asja Fischer, and Yoshua Bengio. Difference target propaga- tion. In Joint european conference on machine learning and knowledge discovery in databases, pages 498-515. Springer, 2015.
[25] Mohamed Akrout, Collin Wilson, Peter C Humphreys, Timothy Lillicrap, and Douglas Tweed. Using weight mirrors to improve feedback alignment. arXiv preprint 1904:55904 2019.
[26] Nasir Ahmad, Marcel A van Gerven, and Luca Ambrogioni. Gait-prop: A biologically plausible learning rule derived from backpropagation of error, Advances Neural Information Processing Systems, 19911-999991...--111111111111111 2020.
[27] Jordan Guerguiev, Timothy P Lillicraap and Blake A Richards. Towards deep learning with segregated dendrites. ELife, 6:e22901, 2017.
[28] Friedemann Zenke and Wulfram Gerstner. Limits to high-speed simulations of spiking neural
networks using general-purpose computers. Frontiers neuroinformatiis, 8:76, 2014.
[29] Lukas Biewald. Experiment tracking with weights and biases, 2020. URL https://www //www wandb. com// Software available from wandb.com.
[30] Chiayu Q Chiu, James S Martenson, Maya Yamazaki, Rie Natsume, Kenji Sakimura, Susumu Tomita, Steven Tavalin, and Michael J Higley. Input-specific nndar-dependent potentiation of dendritic gabaergic inhibition. Neuron, 97(2)366-377, 2018.
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Checklist
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Did you include the license the code and datasets? [Yes] See Section ??.
Did you include the license to the code and datasets? [No] The code and the data are proprictary.
Did you include the license to the code and datasets? [N/A]
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(a) Do the main claims made in the abstract and introduction accurately reflect the paper's contributions and scope? [Yes]
(b) Did you describe the limitations of your work? [Yes]
(c) Did you discuss any potential negative societal impacts of your work? [N/A]
(d) Have you read the ethics review guidelines and ensured that your paper conforms to them? [Yes]
2. If you are including theoretical results...
(a) Did you state the full set of assumptions of all theoretical results? [Yes] See SM and main text.
(b) Did you include complete proofs of all theoretical results? [Yes] See SM.
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(a) Did you include the code, data, and instructions needed to reproduce the main experi- mental results (either in the supplemental material or as URL)? [Yes] See SM. (b) Did you specify all the training details (e.g., data splits, hyperparameters, how they were chosen)? [Yes] See SM.
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(d) Did you include the total amount of compute and the type of resources used (e.g., type of GPUs, internal cluster, or cloud provider)? [Yes] See SM.
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Reviews:
[{"review_id": "fJtm-0D9Ekr", "reviewer": "Reviewer_BqpL", "summary": "This paper introduces a biological learning algorithm in multi-layer neural networks that uses information in neurons' spike trains (specifically, the distinction between overall firing rate and frequency of burst firing) to multiplex forward-propagated signals and backward-propagated error signals.  This approach relies heavily on short-term plasticity in feedforward and feedback signals to transmit firing rate and bursting information independently, and is shown to approximately implement backpropagation under certain conditions.  Unlike prior work, the model is capable of learning in a single phase, rather than separate inference and supervision phases, and can also handle learning from time-varying input.\n\n", "questions": "My main suggestion for the authors would be to more clearly delineate the contributions of their work relative to BurstProp (this is done somewhat in the Appendix, but I think it warrants more treatment in the main text).\n\nAlso, as mentioned above, it would be helpful to clarify the relationship between the spiking and rate-based model.  I would also suggest further empirical evaluation of the model on another (larger) dataset.\n\nI don't hold it against the paper for not including this, but it seems like it could be fairly straightforward to implement a version of the model with mechanisms to enforce weight symmetry (as mentioned in the conclusion section) that could improve performance.", "limitations": "The authors are clear and upfront about the limitations of the work.", "rating": 7, "confidence": 3, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "This paper addresses an important question -- how biological neural networks can usefully multiplex inference and learning signals without unrealistic switching between network phases.  As far as I know this work is the first to resolve this question in a reasonably biologically realistic way.  The presentation and derivations are clear, the mechanisms seem biologically plausible and have some grounding in evidence from neuroscience, and the experimental results are compelling.\n\nOne main potential weakness of this paper is that it is based heavily on a prior model, BurstProp.  Many of the key ideas of the model (multiplexing firing rate + burst probability information, short-term faciliation and depression to transmit signals independently) were present already in the BurstProp model.  The contributions of this paper enable single-phase learning, which I do believe is an important advance, but the paper would benefit from clarifying and emphasizing which features of the model are novel (and needed to enable single-phase learning) and which are derived from prior work.\n\nAnother concern I have is that the experiments are limited in scope and scale.  A variety of biologically plausible learning algorithms have been proposed in the literature that perform well on datasets like MNIST and CIFAR-10 but fail to scale to e.g. ImageNet, or to other non-image-classification tasks.\n\nFinally, I find it a bit unclear what the precise relationship is between the spiking and rate-based implementations.  Are they exactly equivalent in some limit?  I am aware that training spiking networks is generally more difficult than training rate networks, so I don't have a problem with the use of the rate model for the more complicated tasks, but it would help to clarify the link between the two models.", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "extra_scores": {"ethics_review_area": ""}, "extra_text": {}}, {"review_id": "cGCvtzzmk4", "reviewer": "Reviewer_niLx", "summary": "The authors proposed a bursting cortico-cortical network which can perform backprop-like credit assignment in deep cortical networks. By combining bursting, short-term plasticity and dendrite-targeting inhibition, they showed that the model can effectively learn with a single learning phase, as well as in a continuous-time way.  They carried out both empirical and theoretical analyses to show that the weight learning approximates backprop-derived gradients. They also demonstrated the mode performance on learning complex image classification tasks on two benchmarks. ", "questions": "Q1: why the feedforward weights are determiend in a short-term depression (STD) way while the feedback weights are determined in a joint way of STF and STD? Do these assumption have experimental support? STP are quite different across different brain regions and between different types of cell types (PC, PV SST, VIP, etc.). It seems there was a big assumption here.\n\nQ2: In the dynamic input-output task, is the sinusoidal input fed into the network in a stream way?\n\nQ3: When extending the model to a deep network (> 10 layers), how is the approximation of the weight update in the shallow layers with the proposed method? Does the approximation gradually become worse as the error signal propagates to the shallow layers?\n\nQ4: Does the brain learn in a back-prop way, is there any direct evidence? If not, since deep neural networks with back-prop have already shown great performance in many ML tasks, why is the 'biological plausible deep learning' a problem? ", "limitations": "Yes, the authors addressed the limitations of their work", "rating": 7, "confidence": 4, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "The paper is written clearly with a good logical flow. The question the authors tackled is instereting and may provide a solution for single-phase efficient deep learning in the brain (if the brain does learn in a back-prop way, see Q4 below). Both empirical and theoretical analyses are carried out to support the model. The model is a bit complex in its design but it seems novel.", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "extra_scores": {"ethics_review_area": ""}, "extra_text": {}}, {"review_id": "Tv97jDIEFF", "reviewer": "Reviewer_QqnL", "summary": "The paper proposes a novel framework for biologically-plausible hierarchical learning in deep feedforward neural networks. Notably, they present an algorithm for credit assignment, that can approximate backprop, by leveraging certain known properties of cortical networks. The proposed algorithm leverages the dendritic segregation of neurons to have a two-compartment neuron model coupled with burst-dependent synaptic plasticity to perform credit assignment in a single phase. The authors do a commendable job in presenting the key components of their model, both for updating the feedforward weights as well as updating the dendritic feedback projections from higher layer neurons. Furthermore, they demonstrate that under specific assumptions, the proposed credit assignment rule can approximate backprop-based weight update. Finally, the algorithm was able to learn the XOR task and a non-linear regression task as well as achieved competitive performance on image classification task on MNIST and CIFAR-10 datasets. Overall, this paper makes a significant contribution to biologically-plausible deep learning.", "questions": "1. Your derivation showing the equivalence of the learning rule to backprop assumes the sigmoid scaling factor to be 4 (Line 5 of equations on top of Page 3 in Supplementary Section B). Is there any specific reason to do so? Could you please elaborate in the text. If not, could you kindly add that this is a specific assumption. Also, it would be nice to comment whether the scaling factor adds a bias to the learning rule when it's not 4. \n2. What are the shaded lines in Fig 4. A & E? I initially thought they were stdev about mean or something. But if that's the case, why are they not centered about the mean line?\n3. Could the Q weights being plastic, as opposed to Y, be motivated by the fact that inhibitory weights exhibit lower plasticity than excitatory weights? I understand that the plasticity can be instead imposed on Y but just wondering if there is a specific reason to induce plasticity in only one of them as opposed to both?\n4. Doesn't having a full-rank Y matrix require the same number of interneurons as the number of pyramidal neurons in the layer? Is that biologically realistic?\n", "limitations": "The authors don't specifically mention any potential negative societal impact of their work but I don't think there are any straightforward implications either. ", "rating": 8, "confidence": 4, "soundness": 4, "presentation": 3, "contribution": 4, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "Strengths:\n1. The paper is generally well-written and addresses a very important topic in bio-plausible deep learning.\n2. The authors present convincing evidence from neurophysiology to demonstrate the biological plausibility of their model architecture. \n3. Along with the performance on image classification, the authors demonstrate how their algorithm solves toy tasks, specifically the XOR problem where the single-phase analog of burstprop fails. \n4. The alignment to the backpropagation updates has interesting trends, especially when the corresponding performance is taken into account. However, this probably needs more investigation and would come under the scope of future work to try and understand how the alignment could be improved and if doing so would yield better performance.\n5. The proposed model demonstrates impressive performance on image classification tasks (although it is unclear how this would scale to residual networks on big datasets) and incorporates a great deal of biological realism to make experimental predictions, thus contributing to the understanding of credit assignment in the brain.\n\nWeakness:\n1. I felt Section 3.3.1 could be better presented. It's a bit tedious to read right now and slightly unclear without looking into the derivations in the Appendix. It might be helpful if the authors could summarize the derivation as well as clarify the steps in the derivation in appendix to make this section more readable. \n2. It is slightly unclear why the algorithms achieve similar performance although there is a difference in the alignment angle for MNIST. Is the model able to achieve good performance despite the misalignment with the gradient due to dataset size? Or is it because of the size of the parameter space? This issue is slightly more pronounced for CIFAR-10 where burstprop achieves better alignment but worse performance. I am wondering if this has to do with the hyperparameters, specifically burstprop using a higher lr compared to BurstCCNs? \n3. Although the authors motivated the Q and Y matrices as feedback projections from higher layer pyramidal neurons and dendrite-targeting interneurons (inhibitory populations?), it is not necessarily imposed that weights in Q should be positive and Y should be negative. This is an issue that the authors already note in their Discusions section. I have another query related to this point which I have mentioned in the Questions section of the review (see Question #4 below).", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "extra_scores": {"ethics_review_area": ""}, "extra_text": {}}, {"review_id": "Nlat58cIlKX", "reviewer": "Reviewer_ChLd", "summary": "Backpropagation, while allowing ANNs to learn the statistical regularities of their inputs, is not a biologically plausible method for how biological networks learn.  Different methods have arisen recently to bridge the gap between local Hebbian rules that are biologically realistic but limited in performance, and non-local rules like backprop that are not biologically realizable but perform closer to brain-like levels (or better).  The authors add to this field, providing a learning method that utilizes different spiking patterns (\"events\" and \"bursts\") and electrotonically separated compartments (somas, basal and apical dendrites) that, in one phase, is able to approximate backprop and learn complex visual labeling tasks in a more biologically plausible manner.", "questions": " ", "limitations": "Yes", "rating": 8, "confidence": 4, "soundness": 4, "presentation": 3, "contribution": 4, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "**Originality:**\nAs far as I know, no previous, biologically plausible learning rule has allowed for an approximation to backprop that has only one phase of learning.\n\n**Quality:**\nThe authors pose their questions clearly and provide believable initial answers to these questions\n\n**Clarity:**\nThe question, methods, and results of the study are all quite clear.\n\n**Significance:**\nBy allowing for dynamic learning (see the sinusoid example) and biologically realistic modleing assumptions, the present work  of some of the most biologically realistic ANNs  The fact that they have been demonstrated to be able to learn in multiple layers in a single-phase makes a compelling case that the authors' setup may provide insight into a thorny biological problem\n", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "extra_scores": {"ethics_review_area": ""}, "extra_text": {}}]

Author rebuttal:

Decision: Accept