A Study of Biologically Plausible Neural Network: the Role and Interactions of Brain-Inspired Mechanisms in Continual Learning
Authors: Fahad Sarfraz
Elahe Arani
Bahram Zonooz
Venue: Submitted to ICLR 2023 (2023)
Keywords: Continual Learning
Catastrophic Forgetting
Brain-inspired Mechanisms
Active Dendrites
Dale's Principle
Hebbian Learning
Sparsity

Abstract: Humans excel at continually acquiring, consolidating, and retaining information from an ever-changing environment, whereas artificial neural networks (ANNs) exhibit catastrophic forgetting. There are considerable differences in the complexity of synapses, the processing of information, and the learning mechanisms in biological neural networks and their artificial counterpart, which may explain the mismatch in performance. We consider a biologically plausible framework that constitutes separate populations of exclusively excitatory and inhibitory neurons which adhere to Dale's principle and the excitatory pyramidal neurons are augmented with dendritic-like structures for context-dependent processing of stimuli. We then conduct a comprehensive study on the role and interactions of different mechanisms inspired by the brain including sparse non-overlapping representations, Hebbian learning, synaptic consolidation, and replay of past activations that accompanied the learning event. Our study suggests that employing multiple complementary mechanisms in a biologically plausible architecture, similar to the brain, can be effective in enabling continual learning in ANNs.

Under review as a conference paper at ICLR 2023
A STUDY OF BIOLOGICALLY PLAUSIBLE NEURAL NETWORK: THE ROLE AND INTERACTIONS OF BRAIN- INSPIRED MECHANISMS IN CONTINUAL LEARNING
Anonymous authors Paper under double-blind review
ABSTRACT
Humans excel at continually acquiring, consolidating, and retaining information from an ever-changing environment, whereas artificial neural networks (ANNs) exhibit catastrophic forgetting. There are considerable differences in the com- plexity of synapses, the processing of information, and the learning mechanisms in biological neural networks and their artificial counterpart, which may explain the mismatch in performance. We consider a biologically plausible framework that constitutes separate populations of exclusively excitatory and inhibitory neurons which adhere to Dale's principle, and the excitatory pyramidal neurons are aug- mented with dendritic-like structures for context- context-dependent processing of stimuli. We then conduct comprehensive study on the role and interactions of different mechanisms inspired by the brain including sparse non-overlapping representa- tions, Hebbian learning, synaptic consolidation, and replay of past activations that accompanied the learning event. Our study suggests that the employing of mul- tiple complementary mechanisms in biologically plausible architecture, similar to the brain, may be effective in enabling continual learning in ANNs.
TL;DR Keyword
INTRODUCTION
The human brain excels at continually learning from a dynamically changing environment whereas standard artificial neural networks (ANNs) are inherently designed for training from stationary i.i.d. data. Sequential learning of tasks continual learning (CL) violates this strong assumption, re- sulting in catastrophic forgetting. Although ANNs are inspired by biological neurons (Fukushima) 1980), they omit numerous details of design principles and learning mechanisms in the brain. These fundamental differences may account for the mismatch in performance and behavior.
Biological neural networks are characterized by considerably more complex synapses and dynamic context-dependent processing of information. Also, the individual neurons have specific role. Each presynaptic neuron has an exclusive excitatory or inhibitory impact on its postsynaptic part- ners, as postulated by Dale's principle (Strata al. 1999). Furthermore, distal dendritic segments in pyramidal neurons, which comprises the majority of excitatory cells in the neocortex, receive additional context information and enable context-dependent processing of information. This, in conjunction with inhibition, allows the network to learn task-specific patterns and avoid catastrophic forgetting (Yang et al.) 2014: Tyer et al., 202T: Barron et al., 2017). Furthermore, the replay of non- overlapping and sparse neural activities of previous experiences in the neocortex and hippocampus is considered to play a critical role in memory formation, consolidation, and retrieval (Walker & Stickgold 2004 McClelland et al. 1995). To protect information from erasure, the brain employs synaptic consolidation in which plasticity rates are selectively reduced in proportion to strengthened synapses (Cichon & Gan 2015).
Thus, we study the role and interactions of different mechanisms inspired by the brain in a bio- logically plausible framework in a CL setup. The underlying model constitutes separate popula-
We will make the code available upon acceptance.

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Context
(a)
W
WW
h
Wee
Dendrite Segments
(b)
inactive pyramidal cell
active pyramidal cell
inhibitory cell
Wei
Dropout
k-WTA
fully connected
Hebbian
Update
context vector
Wic
leamable weights
Figure I: Architecture one hidden layer in the biologically plausible framework. Each layer con- sists of separate populations of exclusively excitatory pyramidal cells and inhibitory neurons which adheres to Dale's principle. The shade indicates the strength weights or activations where darker shade indicating higher value. (a) The pyramidal cells are augmented with dendritic segments which receive an additional context signal c and the dendrite segment whose weights are most aligned with the context vector (bottom row) is selected to modulate the output activity of the feedforward neu- rons for context- context-dependent processing of information. (b) The Hebbian update step further strength- the association between the context and the winning dendritic segment with maximum absolute value (indicated with darker shade for bottom row). Finally, Heterogeneous dropout keeps the ac- tivation count of each pyramidal cell (indicated with the gray shade) and drops the neurons which were most active for the previous task (darkest shade dropped) to enforce non-overlapping represen- tations. The top-k remaining cells then project to the next layer (increased shade).
tions of exclusively excitatory and inhibitory neurons each layer which adheres to Dale's princi- ple (Cornford et al. 2020) and the excitatory neurons (mimicking pyramidal cells) augmented with dendrite- like structures for context- context-dependent processing of information (Iyer et al., (021]) Dendritic segments process additional context signal encoding task information and subsequently modulate the feedforward activity of the excitatory neuron (Figure []. We then systematically study the effect of controlling the overlap in representations, employing the "fire together, wire together" learning paradigm and employing experience replay and synaptic consolidation. Our empirical study shows that:
i. An ANN architecture equipped with context-dependent processing of information by den- drites and separate populations of excitatory pyramidal and inhibitory neurons adhering to Dale's principle can learn effectively in CL. setup.
ii Enforcing different levels of activation sparsity the hidden layers using k-winner-take-Bl activations and employing complementary dropout mechanism that encourages the model to use a different set of active neurons for each task can effectively control the overlap in representations, and hence reduce interference.
iii. Task similarities need to be considered when enforcing such constraints to allow for a balance between forwarding transfer and interference.
iv. Mimicking the ubiquitous "fire together, wire together" learning rule in the brain through a Hebbian update step the connection between context signal and dendritic segments, which further strengthens context gating and facilitates the formation of task-specific subnetworks.
Synaptic consolidation by utilizing Synaptic Intelligence (Zenke et al. (017)) with importance measures adjusted to take into account the discrepancy in the effect of weight changes in excitatory and inhibitory neurons further reduces forgetting.
vi. Replaying the activations previous tasks in a context-specific manner is critical for consol- idating information across different tasks, especially for the challenging Class-IL. setting.
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Our study suggests that employing multiple complementary mechanisms in a biologically plausible architecture, similar to what is believed to exist in the brain, can be effective in enabling CL in ANNs.
BIOLOGICALLY PLAUSIBLE FRAMEWORK FOR CL
We provide details of the biologically plausible framework within which conduct our study.
2.1 DALE'S PRINCIPLE
Biological neural networks differ from their artificial counterparts in the complexity of the synapses and the role of individual units. In particular, the majority of neurons in the brain adhere to Dale's principle, which posits that presynaptic neurons can only have an exclusive excitatory or inhibitory impact on their postsynaptic partners (Strata et al. 1999). Several studies show that the balanced dynamics (Murphy& & Miller, 2009: Van Vreeswijk & Sompolinsky 1996) of excitatory and in- hibitory populations provide functional advantages, including efficient predictive coding (Boerlin) et al. 2013) and pattern learning (Ingrosso & Abbott 2019). Furthermore. inhibition is hypoth- esized to play role in alleviating catastrophic forgetting (Barron et al.) 2017). Standard ANNs, however, lack adherence to Dale's principle, as neurons contain both positive and negative output weights, and signs can change while learning.
Corffor et al. (2020) incorporate Dale's principle into ANNs (referred to as DANNs), which take into account the distinct connectivity patterns of excitatory and inhibitory neurons (Tremllay et al, 2016) and perform comparable to standard ANNs in the benchmark object recognition task. Each layer/ / comprises of a separate population of excitatory, h E R4, and inhibitory hy E RT neurons, where ne >> Ti and synaptic weights strictly non-negative. Similar biological networks, while both populations receive excitatory projections from the previous layer (h,'),, only excitatory neurons project between layers. whereas inhibitory neurons inhibit the activity of excitatory units of the same layer. Cornford et al. (2020) characterized these properties by three sets of strictly positive weights: excitatory connections between layers W
ee E R X excitatory projection inhibitory units W in E RT:"", and inhibitory projections within the layer W E RRT The output of the excitatory units is impacted by the subtractive inhibition from the inhibitory units:
(W W W Mb- +
(1)
where 6' E R= is the bias term. Figure shows the interactions and connectivity between excitatory pyramidal cells (triangle symbol) and inhibitory neurons (denoted by i).
We aim to employ DANNs as feedforward neurons to show that they can also learn in a challenging CL setting and performance comparable standard ANNs and provide a biologically plausible framework for further studying the role of inhibition in alleviating catastrophic forgetting.
2.2 ACTIVE DENDRITES
The brain employs specific structures and mechanisms for context-dependent processing and routing of information. The prefrontal cortex, which plays an important role in cognitive control (Miller &
Cohen 2001), receives sensory inputs as well as contextual information, which allows it to choose the most relevant sensory features for the present task guide actions (Mante al., 2013 Fuster
2015 Siegel et al. 2015: Zeng et al., 2019). Of particular interest are pyramidal cells, which rep- resent the most populous members of the excitatory family of neurons the brain (Bekkers) 2011
The dendritic spines in pyramid cells exhibit highly nonlinear integrative properties which are con- sidered important for learning task-specific patterns (Yang et al. 2014). Pyramidal cells integrate range of diverse inputs into multiple independent dendritic segments, whereby contextual inputs in active dendrites can modulate a neuron's 's response, making it more likely to fire. However, stan- dard ANNs based point neuron model (Lapique) 1907) which is oversimplified model of biological computations and lacks the sophisticated nonlinear and context-dependent behavior of pyramidal cells.
Iyer et al. (002)) model these integrative properties of dendrites by augmenting each neuron with set of dendritic segments. Multiple dendritic segments receive additional contextual information,
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which is processed using separate set of weights. The resultant dendritic output modulates the feedforward activation which is computed by a linear weighted sum of the feedforward inputs. This computation results in a neuron where the magnitude of the response to given stimulus is highly depeedtte To enable task-specific processing of information, the prototype vector for task is evaluated by taking the element- wise mean of the tasks samples, DD at the beginning of the task and then subsequently provided as context during training.
1 Dr
Σ IED,
C,
During inference, the closest prototype vector to each test sample, x', selected the context using the Euclidean distance among all task prototypes, C, stored in memory.
c' = arg min |
Cr
Following Iyer et al. 2022), augment the excitatory units in each layer with dendritic segments (Figure (a)). The feedforward activity of excitatory units is modulated by the dendritic segments which receive context vector. Given the context vector, each dendritic segment, j computes uj c, given weight uy E Rd and the context vector e E Rd where d is the dimensions of the input image. For excitatory neurons, the dendritic segment with the highest response the context (maximum absolute value with the sign retained) is selected to modulate output activity,
h = k- &-WTA(21 y x ou c)),
where x = arg max luf cl
(4)
where a the sigmoid function (Han & Moraga
1995) and k- k-T))() the k- k-Winner-Take-Al
activation function (Ahmad & Scheinkman| 2019) which propagates only the top k neurons and sets the rest to zero. This provides us with a biologically plausible framework where, similar to biological networks, the feedforward neurons adheres to Dale's 'ss principle and the excitatory neurons mimic the integrative properties of active dendrties for context-dependent processing of stimulus.
3 CONTINUAL LEARNING SETTINGS
To study the role of different components inspired by the brain in biologically plausible NN for CL and gauge their roles in the performance and characteristics of the model, we conduct all our experiments under uniform settings. Implementation details and experimental setup are provided in the Appendix. We evaluate the models on two CL scenarios. Domain incremental learning (Domain-IL) refers to the CL scenario in which the classes remain the same in subsequent tasks but the input distribution changes, We consider Rot-MNIST which involves classifying the 10 digits in each task with each digit rotated by an angle between 0 and 180 degrees and Perm-MNIST which applies a fixed random permutation to the pixels for each task. Importantly, there are different vari- ants of Rot-MNIST with varying difficulties. We incrementally rotate the digits to a fixed degree, i.e. [0. 8, ... (N-1>*8) for task (21,72,-) 72, TN' which is substantially more challenging than random sampling rotations. Importantly, the MOI-T dataset captures the notion of similarity in subse- quent tasks where the similarity between two tasks is defined by the difference in their degree of rotation, whereas each task in Corm-NNISTIN is independent. We also consider the challenging Class incremental learning (Class-IL) scenario where new classes added with each subsequent task and the agent must learn to distinguish not only amongst the classes within the current task but also across all learned tasks. MeQ-M divides the MNIST classification into 5 tasks with 2 classes in each task.
4 EMPIRICAL EVALUATION
To investigate the impact of the different components inspired by the brain, use the aforemen- tioned biologically plausible framework and study the effect on the performance and characteristics of the model.
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Table I: Effect of each component of the biologically plausible framework different datasets with varying number of tasks. We first show the effect of utilizing feedforward neurons adhering to Dale's principle in conjunction with Active Dendrites form the framework within which we evaluate the individual effect of brain-inspired mechanisms before combining them all together (along with Heterogeneous Dropout) to forge Bio-ANN. For all the experiments, we set the percentage of active neurons to 5. We provide the average task performance and std of three runs.
NOI-MNIST
Perm-MNIST
Method
Seq-MNIST
5
10
20
5
10
20
Active Dendrites
92.72a031
71 18.48
48.13 13
95.53
94.37
91.76am.9
20.06
+ Dale's Principle
92.28
70.78
48.79
95.77
95.06
92.40sm.3
19.81
Hebbian Update
92.68
71.42.094
49.26.n.58
95.97
94.96x0.4
92.69aa.19
19. 19.85
+ SC
93.40a0s6
75.87
64.78
96.6720.3
96.36sa
95.61
20. 20.26
+ ERR
95. 1 150377
90.86s
43.42
96.75
96.01
94.50s0.16
86. 88
+ ER CR
96.67-o.6
93.85
89.38
97.34 .o:m
97.03+004
96.12 12000
89.23.004
Bio-ANN
96.82.o.14
94.64
91.32-o.5 0.76
97.33
97.07
96.51 .0.s
89.26.04:
Table 2: Effect of different levels of sparsity in activations on the performance the model.
Columns show the ratio of active neurons (k: in k-WTA activation), and the provide the number of tasks.
Rot-MNIST
MEIM-NNIST
#Tasks
0.05
0.10
0.20
0.50
0.05
0.10
0.20
0.50
92.28 28.28
92.26x0.1
92.7920.4
92,26
95.77
96.32a0.20
90.29 90.29.6.7
1
10
70.78
71.95a1.54
73.32
71.6
95.06.029
93.45
12.68:128
41.332672
20
48.79.0.77
47. 37.96+1.84
48.65
47.71
92.40
84.28+1.5
63.84-14s
20.804a.0
4.1
EFFECT OF INHIBITORY NEURONS
We first study whether feedforward networks with separate populations excitatory and inhibitory units can work well in the CL setting. Importantly, note that when learning sequence of tasks with inhibitory neurons, it is beneficial to take into account the disparities in the degree to which updates to different parameters affect the layer's output distribution (Cornford et al., (020)) and hence forgetting. Specifically, as W and W affect the output distribution to a higher degree than W reduce the learning rate for these weights after the first task (see Appendix).
Table T shows that models with feedforward neurons adhering to Dale's principle perform as well the standard neurons and can also further mitigate forgetting in some cases. Note that this gain comes with considerably fewer parameters and context-dependent processing, as we keep the num- ber of neurons in each layer the same, and only the excitatory neurons (~~90%) are augmented with dendritic segments. For 20 tasks, Active Dendrite with Dale's principle reduces the parameters from 70M less than ~64M parameters. We hypothesize that having separate populations within layer enables them to play specialized role. In particular, inhibitory neurons can selectively inhibit certain excitatory neurons based on stimulus, which can further facilitate the formation of task- specific subnetworks and complement the context-dependent processing of information by dendritic segments.
4.2 SPARSE ACTIVATIONS FACILITATE THE FORMATION OF SUBNETWORKS
Neocortical circuits are characterized by high levels of sparsity in neural connectivity and activa- tions (Barth Poulet 2012, Graham & Field 2006). This is in stark contrast to the dense and highly entangled connectivity in standard ANNs. Particularly for CL, sparsity provides several ad- vantages: sparse non-overlapping representations can reduce interference between tasks (Abbasi et al. 2022 Lyer et al.) 202I[Aljuma Aljundi et al.) 2018), lead to the natural emergence of task-specific modules (Hadsell et al. 2020). and sparse connectivity can further ensure fewer task-specific pa- rameters (Mallya al. 2018).
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w/o Hetrogeneous Dropout
w/ Hetrogeneous Dropout
Task
Activation Count (x) (x16P)
Task
Task
Task
Task
25
25
Total activation counts for the test set of each task (y-axis) for random set of 25 units in the second hidden layer of the model. Heterogeneous dropout reduces the overlap in activations and facilitates the formation of task-specific subnetworks.
Figure 2:
Table 3: Effect of Heterogeneous dropout with increasing values on different datasets with varying number of tasks.
w/o
Dropout parameter (p)
Dataset
# Tasks
Dropout
0.1
0.3
0.5
0.7
1.0
92.28+0.0
91.79+a.53
92.53-o.1
92.74+0.38
93. 19..39
93.42-m.s
Rot-MNIST
10
70.78
71.53+1.7
72.38
73.63-100
74.20ka.7
75.50+m.4
48. 48.79
48.5 48.57
48.91+065
49.8 49.84+0.59
51,03=031
51.11+0.6
20.77
95. 70
95,9720.48
96.40za2s
96.5820.17
96.482026
Perm-MNIST
10
95.0620.99
95. 23,20
95.65s0.20
95. 95.54.0.2
95. 25.74
95.94.0.1
20
92.40
92.83
93.20.0.32
92.82
93.09
91.77a0.0
We study the effect of different levels of activation sparsity by varying the ratio of active neurons in k-winner-take-all (k-WTA) activations (Ahmad & Scheinkman 2019). Each hidden layer of our model has constant sparsity in its connections (randomly 50% of weights are set to 0 at initial- ization) and propagates only the top-k activations (in Figure [ W-W layer). Table 2 shows that sparsity plays critical role in enabling CL in DNNs. Sparsity in activations effectively reduces interference by reducing the overlap in representations. Interestingly, the stark difference in the effect of different levels of sparse activations Rot-MNIST and Perm-MNIST highlights the im- portance of considering task similarity in the design of CL methods. As the tasks in Perm-MNIST are independent of each other, having fewer active neurons (5%) enables the network to learn non- overlapping representations for each task while the high task similarity in Rot-MNIST can benefit from overlapping representation, which allows for the reusability of features across the tasks. The number of tasks the agent has to learn also has an effect on the optimal sparsity level. In Appendix, we show that having different levels of sparsity in different layers can further improve performance. As the earlier layers learn general features, having a higher ratio of active neurons can enable higher resuability and forward transfer. For the later layers, a smaller ratio of active neurons can reduce interference between task-specific features.
4.3 HETEROGENEOUS DROPOUT FOR NON-OVERLAPPING ACTIVATIONS AND SUBNETWORKS
The information the brain is encoded by the strong activation of relatively small set of neurons, forming sparse coding. A different subset of neurons is utilized to represent different types of stimuli Graham & Field (2006). Furthermore, there is evidence of non-overlapping representations in the brain. To mimic this, we employ Heterogeneous dropout (Abbasi et al., (022) which in conjunction with context-dependent processing of information can effectively reduce the overlap of representations which leads to less interference between the tasks and thereby less forgetting. During training, we track the frequency of activations for each neuron in a layer for given task, and in the subsequent tasks, the probability of neuron being dropped is inversely proportional to its activation counts. This encourages the model to learn the new task by utilizing neurons that have been less active for previous tasks. Figure I shows that neurons that have been more active (darker

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Overiap in Representations
11.0
w/o Hebbian Update
Hebb
Up date
Symmetric KL-Div (1e.3)
10.5
-3.72
1:30
0:33
0:30
6:52
-3.71
3.55
0:33
6:36
Context Vecior
9.5
3.23
0.50
1.22
2.43
-2.33
0.39
8.5
3.72
0.33
0:41
0.31
2.13
-3.2
0.10
0.75
0.34
3.75
8.0
0.0
0.1
0.3
0.5
0.7
1.0
5.0
Dendrite Segments
Dendrite Segments
Heterogen Dropout
Figure 4: Dendritic segment activations of unit in layer I for the context vectors of each task for a model trained on Perm-MNIS with 5 tasks. Hebbian update strengthens the association between the context and the dendritic segments, increasing the magnitude of the modulating signal.
Figure 3: Effect of dropout on the overlap between the distributions of layer two activation counts for each task in Perm-MNIST with 2 tasks. Higher / reduces the overlap.
shade) are more likely be dropped before k-WTA is applied. Specifically, let [a'ly denote the activation counter for neuron j in layer after learning tasks. For learning task (+1, the probability of this neuron being retained is given by:
[all
1h+1h = exp(
(5)
max, [a]]
where p controls the strength of enforcement of non-overlapping representations with larger values leading to less overlap. This provides us with an efficient mechanism for controlling the degree of overlap between the representations of different tasks, and hence the degree of forward transfer and interference based on the task similarities.
Table shows that employing Heterogeneous dropout can further improve the performance of the model. We also analyze the effect of the parameter on the activation counts and the overlap in the representations. Figure 2 shows that Heterogeneous dropout can facilitate the formation of task- specific subnetworks and Figure B shows the symmetric KL-divergence between the distribution of activation counts on the test set of Task and Task 2 on the model trained with different values increase the P parameter, the activations in each layer become increasingly dissimilar. Similar to the sparsity in activations, in the Appendix, we show that having different dropout p for each layer (with lower p for earlier layers encourage resuability and higher for later layers to reduce interference between task representations) can further improve the performance. Heterogeneous dropout provides a simple mechanism for balancing the reusability and interference of features depending on the similarity of tasks.
Perm-MNIST with two tasks. As
4.4 HEBBIAN LEARNING STRENGTHENS CONTEXT GATING
For a biologically plausible ANN, it is important not only to incorporate the design elements of biological neurons but also the learning mechanisms it employs. Lifetime plasticity in the brain generally follows the Hebbian principle: a neuron that consistently contributes in making another neuron fire will build stronger connection to that neuron (Hebb 2005).
Therefore, we follow the approach in in/Flesch et al. (2022) to complement error-based learning with Hebbian update strengthen the connections between contextual information and dendritic seg- ments (Figure [b)). Each supervised parameter update with backpropagation followed by a Hebbian update step on the dendritic segments to strengthen the connections between the context input and the corresponding dendritic segment which is activated. To constrain the parameters, we Oja's rule which adds weight decay Hebbian learning (Oja 1982h.
Wy f- Wi + mpd(cc - du,)
where 7h, is the learning rate, A is the index of the winning dendrite with weight u, and modulating signal d = u e for the context signal c. Figure 4 shows that the Hebbian update step increases the

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magnitude of the modulating signal from the dendrites on the feedforward activity, which can further strengthen context-dependent gating and facilitate the formation of tis-ssicciiic subnetworks. Table I shows that this results in a consistent improvement in performance.
4.5 SYNAPTIC CONSOLIDATION FURTHER MITIGATES FORGETTING
In addition to their integrative properties, dendrites also play a key role in retaining information and
providing protection against erasure (Cichon & Gan 2015 Yang al. 2009). The new spines that are formed on different sets of dendritic branches in response to learning different tasks are protected from being eliminated through mediation of synaptic plasticity and structural changes that persist
when learning new task (Yang et al. 2009).
We employ synaptic consolidation by incorporating Synaptic Intelligence (Zenke et al. 2017) (de- tails in Appendix) which maintains an importance estimate of each synapse in an online manner during training and subsequently reduces the plasticity of synapses which are considered important for learned tasks. Notably, we adjust the importance estimate to account for the disparity in the degree to which updates to different parameters affect the output of the layer due to the inhibitory interneuron architecture in the DANN layers (Cornford et al. 2020). The importance estimate of the excitatory connections to the inhibitory units and the intra-layer inhibitory connections are upscaled to further penalize changes to these weights. Table [ shows that employing Synaptic Intelligence (+SC) in this manner further mitigates forgetting. Particularly for Rot-MNIST with 20 tasks, provides considerable performance improvement.
4.6 EXPERIENCE REPLAY IS ESSENTIAL FOR ENABLING CL IN CHALLENGING SCENARIOS
Replay of past neural activation patterns in the brain is considered to play a critical role in memory formation, consolidation, and retrieval (Walker & Stickgold 2004 McClelland et al. 1995). The replay mechanism in the hippocampus (Kumaran ct al. 2016 has inspired a series of schearsa-baaee approaches (Li & Hoiem 2017 Chaudhry et al. 2018 Lopez- & Ranzato 2017; Arani et al., 2022) which have proven to be effective in challenging continual learning scenarios (Farquhar & | Hadsell et al. 2020). Therefore, to replay samples from previous tasks, we utilize a small episodic memory buffer that is maintained through Reservoir sampling (Vitter 1985). It attempts to approximately match the distribution of the incoming stream by assigning equal probability to each new sample to be represented in the buffer. During training, samples from the current task, (Is, yb) ~ 'Dr, are interleaved with memory buffer samples, (Im. Vmn ~ .M to approximate the joint distribution of tasks seen so far. Furthermore, to mimic the replay of the activation patterns that accompanied the learning event in the brain, we also save the output logits, 2m, across the training trajectory and enforce a consistency loss when replaying the samples from the episodic memory. Concretely, the loss is given by:
-= Leta (f 9)) + (f Hm, + ((
((mm:)) -
2m
(7)
where f(: is the model parameterized by 0, Lata is the standard cross-entropy loss, and a and | controls the strength of interleaved training and consistency constraint, respectively.
Table shows that experience replay (+ER) complements the context-dependent processing of in- formation and enables the model to learn the joint distribution well in varying challenging settings. Particularly, the failure of the model to avoid forgetting in the Class-IL setting (Seq-MNIST) without experience replay suggests that context-dependent processing of information alone does not suffice. and experience replay might be essential. Adding consistency regularization (+CR) further improves performance as the model receives additional relational information about the structural similarity of classes, which facilitates the consolidation of information.
4.7 COMBINING THE INDIVIDUAL COMPONENTS
Having shown the individual effect of each of the brain-inspired components the biologically plausible framework, here we look at their combined effect. The resultant model is referred to as Bio-ANN. Table [ shows that the different components complement each other and consistently improve the performance of the model. The empirical results suggest that employing multiple com- plementary components and learning mechanisms, similar to the brain, can be an effective approach to enable continual learning in ANNs.
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5 DISCUSSION
We conducted a study on the effect of different brain-inspired mechanisms under a biologically plau- sible framework in the CL setting. The underlying model incorporates several key components of the design principles and learning mechanisms in the brain: each layer constitutes separate populations of exclusively excitatory and inhibitory units, which adheres Dale's principle, and the excita- tory pyramidal neurons are augmented with dendritic segments for context-dependent processing of information. We first showed that equipped with the integrative properties of dendrites, feedfor- ward network adhering to the Dale's principle not only performs as well as standard ANNs but also provides gains. Then we studied the individual role of different components. We showed that con- trolling the sparsity in activations using k-WTA activations and Heterogeneous dropout mechanism that encourages the model to use a different set of neurons for each task is an effective approach for maintaining a balance between reusability of features and interference, which is critical for en- abling CL. We further showed that complementing the error-based learning with the "fire together, wire together" learning paradigm nal and dendritic segments which process them and facilitate context- tetexxt-depeneet gating. To further mitigate forgetting, we incorporated synaptic consolidation in conjunction with experience replay and showed their effectiveness in challenging CL. settings. Finally, the combined effect of these components suggests that, similar to the brain, employing multiple complementary mechanisms in a biologically plausible architecture is an effective approach to enable CL in ANN. It also provides a framework for further study of the role of inhibition mitigating catastrophic forgetting.
further strengthen the association between the context sig-
However, there are several limitations and potential avenues for future research. In particular, as dendritic segments provide an effective mechanism for studying the effect of encoding different in- formation in the context signal, it provides an interesting research avenue as to what information is useful for the sequential learning of tasks and the effect of different context signals. Neuroscience studies suggest that multiple brain regions are involved in processing stimulus, and while there is evidence that active dendritic segments receive contextual information that is different from the input received by the proximal segments, it is unclear what information is encoded in the contex- tual information and how it is extracted. Here, we used the context signal as in (Iyer et al.] (02T). which aims to encode the identity of the task by taking the average input image of all samples in the task. Although this approach empirically works well in the Perm-MNIST setting, it is impor- tant consider its utility and limitations under different CL settings. Given the specific design of Perm-MNIST, binary centered digits, and the independent nature of the permutations in each task, the average input image can provide a good approximation of the applied permutation and hence efficiently encode the task identity. However, this is not straightforward for Rot-MNIST where the task similarities are higher and even more challenging for natural images where averaging the in- put image does not provide a meaningful signal. More importantly, it does not seem biologically plausible to encode task information alone as the context signal and ignore the similarity of classes occurring in different tasks. For instance, it seems more reasonable to process slight rotations of the same digits similarly (as Rot-MNIST) rather than processing them through different subnetworks. Ideally, we would want the context signal for different rotations of digit to be highly similar. It is, however, quite challenging to design context signals that can capture a wide range of complexities in sequential learning of tasks. Furthermore, instead of hand engineering the context signal to bias learning towards certain types of task, an effective approach for learning the context signal in an end-to-end training framework is an interesting direction for future search.
Overall, our study presents a compelling case for incorporating the design principles and learning machinery of the brain into ANNs and provides credence to the argument that distilling the details of the learning machinery of the brain can bring us closer to human intelligence (Hassabis et al.) 2017] Hayes al., 202I). Furthermore, deep learning increasingly being used in neuroscience research to model and analyze brain data (Richards et al., 2019). The utility of the model for such research depends on two critical aspects: the performance of the model and how close the architecture is to the brain (Cornford et al.) 2020; |Schrimpf et al. (020). The biologically plausible framework in our study incorporates several design components and learning mechanisms of the brain and performs well in (continual learning) task that is closer to human learning. Therefore, we believe that this work can also be useful for the neuroscience community to evaluate and guide computational neuroscience. Studying the properties of ANNs with higher similarity insight into the mechanisms of brain functions. We believe that the fields of artificial intelligence and neuroscience are intricately intertwined and progress in can drive the other well.
the brain may provide

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A APPENDIX
A.1 RELATED WORK- - BIOLOGICAL INSPIRED AI
The human brain has long been a source of inspiration for ANNs design (Hassabis et al. 2017 Kudithipudi et al. (2022). However, we have failed take full advantage of our enhanced understand- ing of the brain and there are fundamental differences between the design principles and learning mechanisms employed in the brain and ANNs. These differences may account for the huge gap in performance and behavior.
From an architecture design perspective, standard ANNs are predominantly based on the point neu- ron model [Lapique] [907] which is an outdated and oversimplified model of biological computa- tions which lacks the sophisticated and context dependent processing in the brain. Furthermore, the neurons in standard ANNs lack adherence to the Dale's principle (Strata et al. 1999) to which the majority of neurons in the brain adhere Unlike the brain where presynaptic neurons have an clusively excitatory or inhibitory impact on their postsynaptic partners, neurons in standard ANNs contain both positive and negative output weights, and signs can change while learning. These con- stitute as two of the major fundamental differences in the underlying design principle of ANNs and the brain.
Two recent studies attempt to address this gap. Cornford et al. 2020 incorporated Dale's principle into ANNs (DANNs) in a more biologically plausible manner and show that with certain initializa- tion and regularization considerations, DANNs can perform comparable to standard ANNs in object recognition task, which earlier attempts failed to do so. Our study extends DANNS to the more chal- lenging CL setting and show that accounting for the discrepancy in the effect of weight changes in excitatory and inhibitory neurons can further reduce forgetting CL.. [yer et al. (2021) propose an alternative to the point neuron model and provide algorithmic abstraction of pyramidal neurons in the neocortex. Each neuron is augmented with dendritic segments which receive an additional context signal and the output of the dendrite segment modulates the activity of the neuron, allowing context dependent processing of information. Our study builds upon their work and provides a bio- logically plausible architecture characterized with both adherence dale's principle and the context dependent processing of pyramidal neurons. This provides us with a framework to study the role of brain inspired mechanisms and allow for the studying the role of inhibition in the challenging continual learning setting which is more closer to human learning.
From learning perspective, several approaches have been inspired by the brain, particularly for CL (Kudithipudi et al. (022). The replay mechanism in the hippocampus (Kumaran et al. (016)
has inspired series of rehearsal- based approaches (Hayes et al. 202T Hadsell et al. (2020) which
have proven to be effective in challenging continual learning scenarios (Fargubar & Gall|201
An-
other popular approach for continual learning, regularization- based approaches/Zenke et al. (2017);
Kirkpatrick et al. (2017), have been inspired by neurobiological models which suggest that CL in the neocortex relies on a process of task-specific synaptic consolidation which involves rendering a proportion of synapses less plastic and therefore stable over long timescales (Benna & Fusi. 2016 Yang et al. 2009). While both these approaches are inspired by the brain, researches have mostly discounted the fact that the brain employs both of them in conjunction consolidate information rather than in isolation. Therefore, research in both of these methods have heen orthogonal. Further- more they have been applied on top of standard ANNs which are not representative of the complex- ities of the neuron in the brain. Our study employs replay and synaptic consolidation together in a more biologically plausible architecture and show that they complement each other improcve the performance.
Additionally, our frameworks employs several techniques to mimic the characteristics of the acti- vations in the brain. As the yyramidal neurons in the neocortex have highly sparse connectivity to each other (Hunter et al.) [20TT] Holmgren et al. 2003) and only a small percentage (<2% of neurons are active for given stimuli neurons (Barth & Poulet 2012), we apply k-winner-take-an (k-WTA) activations (Ahmad & Scheinkman 2019) to mimic activation sparsity. Several studies
have shown the benefits of sparsity in CL (Abbasi et al. 2022 Mallya et al. 2018 Aljundi et al.) 2018), they do not consider that the brain not only utilizes sparsity, it does so in an efficient man- ner to encode information. The information in the brain is encoded by the strong activation of relatively small set of neurons, forming sparse coding. A different subset of neurons is utilized to represent different types of stimuli (Foldiak 2003) and semantically similar stimuli activate similar
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set of neurons. Heterogeeoouss dropout (Abbasi al. 2022 coupled with k- L-WA activations aim to mimic these characteristics by encouraging the new task to utilize a new set neurons for learning. Finally argue that that it is important not only to incorporate the design elements of biological neurons but also the learning mechanisms it employs. Lifetime plasticity in the brain generally fol- lows the Hebbian principle (Hebb) 2005). Therefore, we follow the approach in [fllesch et al.) (2022) to complement error-based learning with Hebbian update to strengthen the connections between contextual information and dendritic segments and show that strengthens context gating.
Our study provides a biologically plausible framework with the the underlying architecture with the context dependent processing of information and adherence to dale's principle. Additionally employs the learning mechanisms (experience replay, synaptic consolidation and hebbian update) and characteristics (sparse non-overlapping activations and task specific subnetworks) of the brain. To the best of our knowledge, we are the first to provide comprehensive study of the integration of different brain-inspired mechanisms in a biologically plausible architecture in a CL. setting.
A.2 ADDITIONAL RESULTS
Additionally, we conducted experiments on Fashion-MNIST which more challenging than the MNIST datascts. We considered both the the Class-IL (Seq-FMNISTT and the Domain-IL (Rot- FMNIST) setting. Seq-FMNIST divides the classification into 5 tasks with 2 classes each while Rot-FMNIST involves classifying the 10 classes in each task with the samples rotated by i.e. (0, 8, (N-1)*8) for task [T1, T2, T
For brevity, refer to Active Dendrites Dale's principle as ActiveDANN. To show the effect of different components hetter (ActiveDANN without ER fail on the class-II. setting), we consider ActivelDann ER the baseline upon which add the other components. Empirical results in Table A.2 show that the findings on the MNIST settings also translate to Fashion-MNIST and each component leads to performance improvement.
Table 4: Effect of each component of the biologically plausible framework on different Seq- FMNIST and Rot-FMNIST. For all experiments, we use a memory budget of 500 samples. HD refers to heterogeneous dropout. We provide the average task performance and std of 5 runs.
Method
Seq-FMNIST Rot-FMNIST
Joint
94.331051
15.15.0.0
SGD
19.83
51.89
ActiveDANN + ER
77.56.0.7
80.99+0.33
Hebb
78.02+0.38
82. 144.26
+ SC
78.05-m.11
82.55+0.37
HD
78. 78.7410.8
83.9740.66
Bio-ANN
79.28
89.22sh.21
A.3 EXPERIMENTAL SETUP
To study the role of the different components inspired by the brain in a biologically plausible NN for CL and gauge their roles in the performance and characteristics of the model, we conduct all our experiments under uniform settings. Unless otherwise stated, we use multi-layer perception (MLP) with two hidden layers with 2048 units and k-WT activations. Each neuron is augmented with N dendritic segments where N corresponds to the number of tasks and the dimensions match the dimensions of the context vector which corresponds to the input image size (784 for all MNIST based settings). The model trained using an SGD optimizer with 0.3 learning rate and batch size of 128 for 3 epochs
each task. We set the weight sparsity to 0 and set the percentage of active neurons to 5%. For our experiments involving Dale's principle, we maintain the same number of total units in each layer divided into 1844 excitatory and 204 inhibitory units. Only the excitatory units are augmented with dendritic segments. Importantly, we use the initialization strategy and corrections for the SGD update as posited in Cornford et al. (2200) to account for the disparities in the degree to which updates to different parameters affect the layer output distribution. The inhibitory unit parameters updates are scaled down relative excitatory parameter update.
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Concretely, the gradient updates Wie were scaled by Vne and Wei by d' where ne the number of excitatory neurons in the layer and is the imput dimension to the layer. Furthermore, small validation set. Note, the goal
to select the hyperparameters for different settings was not to achieve the best possible accuracy, rather to show the effect of each component, we did not conduct extensive hyperparameter search. Table A.3 provides the selected hyperparameters for the effect of individual components experiments in Table [ and Table [A.3 provides the selected hyperparameter for Bio-ANN experiments. We report the mean accuracy over all tasks and std over three different random seeds.
Table 5: The selected hyperparamneters for the experiments showing the individual effect of each component (Table [. The base learning rate for the experiments 0.3 and the individual com- ponents use the same learning rates for Wie and Wer as (+ Dale's Principle). For SC experiments, we use Aw,.=10 and =w. For ER experiments, we use a memory budget of 500 samples.
Dataset
#Tasks
Dale's Principle
Hehbian Update
SC
ER
ER CR
nw. =3e-2. mW., =3e-3
n,=3e-10
A=0.25
a=1, 3-0
a=1, 3=0.50
Rot-MNIST
10
Tw. =3c-2, 33e-3
mx=3e-08
A=0.25
o=1, 8=0
o=1, 3=1,5= $=0.50
20
Tw. =30-3 1/,.,=3--
n,=3e-10 10
A=1.00
o=1, 8-0
e=1, 8=0.50
5
nw. =3e-2. =3e-2
n,=3e-09
A=0.10
a=1,
a=1, a=1,5= $=0.50
Perm-MNIST
10
ww. =3c-2, 13.2=33-22
n,=3c-06
A=0.25
o=1, 8-0
o=1, 3=0.50
20
nw., =3e-2. mW..=33-3
nx=3e-09
A=0.10
a=1,
a=1, 3=0.50
Seq-MNIST
nw,, =3e-2. m3..=33-3
ny=3e-07
A=0.25
a=1, 3=0
a=1. 3=0255
Table 6: The selected hyperparamneters for Bio-ANN experiments in Table learning rate for each setting as Dale's Principle (Table A.3).
We the same
Dataset
#Tasks
B
5
3e-8
0.25
0.1
0.5
Rot-MNIST
10
3e-8
0.1
0.3
0.5
20
3e-8
0.1
0.3
0.5
5
3e-6
0.1
0.1
0.5
Perm- -NIST
10
3e-8
0.1
0.3
0.5
20
3e-8
0.1
0.3
0.5
Seq-MNIST 5
3e-6
0.1
0.1
0.25
A.4 EFFECT OF ADJUSTING FOR THE INHIBITORY WEIGHTS
The inhibitory interneuron architccture of DANN layers introduces disparities in the degree which updates to different parameters affect the layer's s output distribution e.g. if a single element of Wie is updated, this has effect each element of the layer's output. An inhibitory weight update of to Wie changes the model distribution approximately nh times more than an excitatory weight update of 8 Wee (Cornford et al.) 2020). The effect of these disparities would be even more pronounced in CL setting as large changes to output distribution when learning a new task can cause more forgetting previous tasks. To account for these, we further reduce the learning rate of W,e and W.i after learning the first task. Table sh.sshows that accounting for the higher effect of inhibitory neurons can further improve the performance of the model in majority of the settings. It would be interesting to explore better approaches to account for the aforementioned disparities which are tailored for CL and consider the effect on forgetting.
A.5 EFFECT OF ADJUSTING FOR SCALING THE SI IMPORTANCE ESTIMATE FOR INHIBITORY WEIGHTS
Similar to adjusting the learning rate of inhibitory weights, we check whether scaling up the impor- tance estimate of inhibitory neurons further improve the effectiveness of synaptic consolidation
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Table 7: Effect of adjusting the learning rates of Wte and We the end of first task different datasets with varying number of tasks.
Rot-MNIST
Perm-MNIST
Tic
1/eii
5
10
20
10
20
3e-1
3--1
92. 12.122 2+0.34
70.86=044
46.30-103
95.78 19
94.73+a36
92.67-061
3e-2
3c-2
92.23
70.23
47.5321.79
95. 25.37
95.062029
91.6340.9
3c-2
3e-3
92.28x0.27
70.78
47.32.143
95.66 15.6820.14
94, 94.962a.19
92,4020.s
3e-3
3e-3
92.34.0.51
71.27
47.81
95. 7020.9
94.44
92.02.0.19
3e-3
3e-4
92.03
70.79
48.79
95,90
94.19
91.0420.34
in reducing forgetting. Table[A.5]shove shows that scaling the importance estimate in accordance with the degree to which the inhibitory weights affect the output distribution and hence forgetting further im- proves the performance majority of cases, especially for lower number of tasks. This suggest that regularization methods designed specifically for networks with inhibitory neurons is promising research direction.
Table 8: Effect of scaling the importance estimate for Wie and Wei to reduce the parameter shift in the inhibitory weights on Rot-MNIST and Perm-MNIST datasets with varying number of tasks.
Rot-MNIST
Perm-MNIST
A
AWa
AW..
5
10
20
5
10
20
1
92.924n.2
75.53s1.46
52.16.117
96.59
96.20aa.13
95.69s0.10
0.1
10
10
92. 20
74.70st.05
51.942108
96.57
96. 1
95.6420.15
10
100
92.50
74.67
52.55
96.67x023
96.26.0.26
95.61
92. 27..99
76.30
55.052247
96. 96.6220.2
96.07
95.36 95.362024
0.25
10
10
93.54
75.4420.11
54,93
96.54.0.2
96. 26.13
95.0320.13
100
03.40+0.66
75.87+1.35
55.06-1.7
96.65+0.2
96.36-b.10
95.18-0.2
93.2330.71
75.24.0.22
60.24.2002
96.2220.37
95.9710.06
92.9420.55
0.5
10
10
93. 13
75.95
59.35+1.53
96. s1
95.81 +0.10
92.86+087
10
100
92.8 92.85+142
75.85
58.94a215
96.36s042
96.02+a.77
93.48
w/o SC
92.28
70.78.0.23
48.79
95.77
95.0610.99
92.4020.8
A.6 LAYERWISE HETEROGENEOUS DROPOUT AND TASK SIMILARITY
For an effective CL agent, it is important to maintain a balance between the forward transfer and interference between the tasks. As the earlier layers learn general features, higher portion of the features can be reused to learn the new task which can facilitate forward transfer whereas the later layers learn more task specific features which can cause interference. Heterogeneous dropout provides us with an efficient mechanism for controlling the degree of overlap between the activations and hence the features of each layer. Here, investigate whether having different levels of sparsity (controlled with the parameter) in different layers can further improve performance. As the earlier layers learn general features, having higher overlap (smaller p) between the set of active neurons can enable higher resuability and forward transfer. For the later layers, lesser overlap between the activations (higher () can reduce the interference between task-specific features.
To study the effect of heterogeneous dropout in relation with task similarity, we vary the incremental rotation, Onne in each subsequent task for Rot-MNIST setting with tasks. The rotation for task is given by (r - 1)0 Table A.6 shows the performance of the model for different layerwise P values. Generally, heterogeneous dropout consistently improves the performance of the model, especially when the task similarity is low. For f.n 32, it provides ~55 improvement. As the task similarity reduces (#ine increases), higher values of p are more effective. Furthermore, we see that having different & values for each layer provide additional gains in performance.
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Under review as a conference paper at ICLR 2023
Table 9: Effect of layerwise dropout p on Rot-MNIST with 5 tasks with varying degrees of incre- mental rotation mme) in each subsequent task. Row 0 shows (p'), p²²) the p values for the first and second hidden layer respectively.
Task Similarity (0mcc)
p4, 1/2
4
8
16
24
32
0.1, 0.1
97. 97.60-0.1
96.74+0.16
91.79+m.53
74.99-116
63.33+1.15
57.39x2.96
0.1.
27.77
97.02aa.11
92.3920.3
75.56.1.66
64. 64.18at8 181.79
57.05a2.13
0.5
97. 97.88
97.22aa.11
92.74.0.38
76.73.101
14.18
58.35
0.5, 1.0
97.88=004
97.25
92.87
76.87=039
64, 84.84
59.40e2.51
1.0, 1.0
97.89=0.0
97.19
93.42s0.2
77.48
66,33+1.22
61.35
1.0, 2.0
97. 07.68
97.00aa.23
93.461078
79.07
68, 20,2.4
63.08
2.0, 2.0
17
97.00+a.11
93.53
80.03
69,99 19.99.1
65.74+1.21
2.0, 5.0
00.3
96.54+0.15
92.95+o.1
80.55+0.0
73.74+0.21
69 26.46...66
5.0, 5.0
96.8620.11
96. 12an.os
92.3320.18
79.5320.2
72.47a1.2
70.77
w/o Dropout 97.72-0.9
96.93+140
92.31+0.56
75.67-1.40
63.68+1.3
56.49+286
Table 10: Effect of different levels of sparsity in activations (ratio of active neurons, (k'1, k222 in 1 and 2nd hidden layer respectively) and connections (ratio of zero weights, Sw) on Rot-MNIST and Perm-MNNIST with increasing number of tasks. The best performance across the different sparsity levels for each task is in bold.
Activation Sparsity (Ad ,
#Tasks
Sw
(0.05, 0.05)
(0.1, 0.05)
(0.1, 0.1)
(0.2, 0.1)
(0.2, 0.2)
(0.5, 0.2)
(0.5, 0.5)
0.00
92.2
92.63.046
92.26ia3
92.25.001
92.79.04s
92.51.0.5
92.26.065
5
0.25
91.22a0.58
91.50
92.33
91.75
92,60aa.9
91.23au63
91.662046
Rot-MNIST
0.50
90. 40
91.15-0.3
91.25
91.25-09x
90.67
90.75.036
90.41-148
0.00
70. 70.78
71.16.0.51
71.95.154
72.22.0x3
73.32
71.8920.2
71.61
10
0.25
70.2 2007
71.4220.8
71.84
73.22a134
72.58
72.23am71
71.23=084
0.50
69.6 ao.50
70.59.0.s
70.94.a7i
72.05.a34
72.25.1.40
71.37an6s
70.85.067
0.00
48.79kh.7
48.01-0.58
47.96-184
48.33-122
48.65
48. 19-1.
47.71-091
20
0.25
47. 72203
18.61
48.4
48.53
48,30 30
48 18.2921.59
47.11-044
0.50
46. 16.20
47.15
48.02+1.1
48.17-142
48.30
47.6 47.66-15x
47.73-051
0.00
95. 77
95.55
96.43
95.85-119
90.29 19
88.18
74,51
0.25
a5.45.0.2
05.14.027
95.65.a22
95.75-0.2
93.73
87 87.49.2.3
75.97-561
Pem-MMNST
0.50
93. 95
19211
94,90
94,22a1.9
94.05
91.02a371
83,94
0.00
95.06
94.08
94.382ara
89.54_227
78.9 as
76.4427.5
35,862204
10
0.25
94.51 40.12
93.52-mor
93.62-404
88.58-2.17
84.94.1.
69.32-mm4
59.53.9.7
0.50
92. 220.2
90.3
92.29.ara
88.48-022
82.57x2.0
74.42.2a4
69.3
0.00
92.40aa.38
89,41
84.28.1.3
73.29
63.84.3.5
58.85a500
20.80
20
0.25
90.7 90.75
89.222094
84.29+a17
75.82=m.s
67. 07.26
63.96a1.19
41.60=204
0.50
87.31
84.90.1.9
83.72.as1
69.62.s9g
66.27
64.42.233
51.92.379
A.7 EFFECT OF SPARSITY
To further study the effect of different levels of sparsity in activations and connections, vary the number of weights set randomly to zero at initialization (Sw E {0, 0.25, 0.50}) and the ratio of active neurons (1,11 Rd22) in each hidden layer. Table A.7 shows that sparsity in activation plays a critical role in enabling CL in ANNs. Interestingly, sparsity in connections play a considerable role in Perm-MNIST with higher levels of active neurons (2 0.2). Furthermore, exploring finer differences in activation sparsity of different layers may further improve the performance. Similar heterogeneous dropout, we show the effect of activation sparsity in relation to the task similarity in Table A.7 Similar tasks (lower 9ine) benefits from higher number of active neurons which can increase the forward transfer whereas dissimilar tasks (higher 0,cc) performs better with higher activation sparsity which can reduce the overlap in representations.
17

---

Under review as a conference paper at ICLR 2023
Table 11: Effect of different levels of activation sparsity on Rot-MNIST with 5 tasks with varying degrees of incremental rotation (0mec) in each subsequent task. Row shows (k"1, k42) the ratio of active neurons in the s and 2nd hidden layer, respectively.
Task Similarity (Osnc)
(k4 1222
8
24
0.05, 0.05
97.54 77.04
96.56x0.14
91.95
75.13
63.1440.x
+0.01
0.1, 0.05
97.57.0.3
96.84.0.18
92.49.o.59
76.15
64.03a1.12
58.56+1.17
0.1,
97.81 10008
96.84+0.30
92.28.h.1
76.80
64.91
58.62+1.00
0.2, 0.1
97.44-074
96.882n.45
92.4720.69
75.79=1.26
64.3821.5
58.34
0,2, 0.2
97. 97.8820.11
97.27.0.15
92.7920.00
76.22.1.46
64.30a1.3
57. 57.22.1.06
0.5, 0.2
97.6 97.67
96.9220.8
92.61
75.66.095
63. 63.862061
56. 1
0.5, 0.5
27.67
97.03+a.5s
92.29tn.58
74.55=1.01
62.37
53.1
18

---

Under review as a conference paper at ICLR 2023
Algorithm Bio-ANN: A biologically plausible framework for CL.
Input:
Data stream D; Learning rates 7J, 1l. "W. Hebbian learning rate l)i Heterogeneous
dropout p: Synaptic consolidation weights X, Aw.e. Aw.. Experience replay weights a, B Initialize:
Model weights 0, Reference weights 0. = [}, Task prototypes C, = 0
Heterogeneous dropout: Overall activation counts A, 0, Keep probabilities P.
Memory buffer M + (
Synaptic Intelligence: w 0, =
Sample task from data stream
1: for D, E (D1, "D,,,''.., D do
Task context
2: Evaluate context vector (Eq. 2
C= ID-T ExED,
3: Update the of prototypes:
C, t (C+,c7
Train on task
4:
while Training do Sample data: (rb. yb) ~ D, and (Im: Um: 2m) ~ M
5:
Task specific loss
6:
Get the model output and activation counts on the current task batch:
Zb, G6 F( Cr; P.) Apply Heterogeneous dropout
7:
Calculate task loss:
C, Lots yb)
8:
Update overall activation counts:
A, + UppdaeecctivaionCounsss]]]
Experience replay
9:
Infer context for buffer samples (Eq. 3
arg min ||æ: Crll2
ez Get model output on buffer samples: # Disable Heterogeneous dropout
10:
F(Im, Cmi
11:
Calculate replay loss:
Per aLoto Vmn + B(z 2m)²
> Synaptic regularization
Calculate SI loss:
Csc= = 9 (0 0,)
Calculate overall loss and clip the gradient between and 1:
C C, Ler + Lec
Clip
b Update Models
14:
SGD update: 0 UpdateMModel( (V,,, 17. IJ... 17W..)
15:
Hebbian update dendritic segments: HebbianStep((c,, Cm U)
16:
Update small omega: w= + (ZLL) M + Reservoir[M, (Ib. yb. 26))
Update SI parameter
18:
Update memory buffer (Algorithm{)
19:
Task Boundary
20:
Update keep Probabilities (Eq 5): P, exp( max A.
21:
Update SI Omega and reference weights and reset small omega:
Ω + To- (.+
= 0.
22:
Scale up importance for inhibitory weights Radi ScaleUpInhib((I, Aw... Aw..)
return
19

---

Under review as a conference paper at ICLR 2023
Algorithm 2 Reservoir Sampling
Input: Memory Buffer M. Buffer Size B, Number of examples seen so far N, data points
(x, 2)
if N then
Check if memory is full
2: M[N] < 2x)
3: else
Select a sample to replace
4:
SumpeeRadmmntteeriii-- max=N)
5: if n < B then
6: M[n (x)
return M
20


Reviews:
[{"review_id": "eWpE60xEnx", "reviewer": "Reviewer_Bd22", "summary": "", "questions": "", "limitations": "", "rating": 6, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "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": "In this work the authors study the individual and combined effect of a range of biologically inspired mechanisms on continual learning. ", "summary_of_the_review": "Overall I think this is an important and interesting study, though interactions between mechanisms could be explored better and some controls are missing. ", "strength_and_weaknesses": "Strengths\n- Interesting and important research for both AI and neuroscience\n- Paper is well written and all approaches are clear and well described \n\nWeaknesses\n- No floor (e.g normal training) and ceiling (e.g. full replay) controls provided in the experiments.\n- Experiments limited to variants of MNIST. Unclear if active dendrites approach & prototypes/context will be as effective with datasets without an exemplar structure, like fashion mnist. \n- Unclear how the difference mechanisms interact with each other, but possibly beyond the scope of a conference paper. \n- Why do active dendrites fail with seq-mnist?\n- Is there biological evidence for context dependent dendritic processing of eq. (4). \n- Heterogeneous dropout does not seem to be biologically motivated. \n- Novelty appears limited to combining existing approaches, the authors could more clearly describe their specific novel contributions. \n", "limitations_and_societal_impact": "", "review_text": "", "extra_scores": {"correctness": "3: Some of the paper’s claims have minor issues. A few statements are not well-supported, or require small changes to be made correct.", "technical_novelty_and_significance": "2: The contributions are only marginally significant or novel.", "empirical_novelty_and_significance": "3: The contributions are significant and somewhat new. Aspects of the contributions exist in prior work."}, "extra_text": {}}, {"review_id": "ZyVZ5c3O62", "reviewer": "Reviewer_Ds8Z", "summary": "", "questions": "", "limitations": "", "rating": 3, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "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": "This paper evaluates previous work on biologically plausible DNNs in the setting of continual learning (CL). Namely, they evaluate ideas around Dale’s principle, Active Dendrites, heterogenous dropout, Hebbian learning, synaptic consolidation and experience replay. They present experimental evidence that these ideas can individually improve the performance on CL, or be combined to achieve greater improvement.", "summary_of_the_review": "While the paper presents an interesting discussion, it reuses ideas from other work and presents limited experimental evidence.", "strength_and_weaknesses": "+ This paper provided a useful list of biologically-inspired modifications to DNNs.\n+ I find the main idea interesting (investigating such modifications’ usefulness to CL).\n- The paper is a compilation of already published work.\n- Some of these insights (s.a. dropout being useful for CL) can be found in literature.\n- The experiments are exclusively done on MNIST-based datasets. While they provide evidence to support the claims of this paper, it would be useful to understand whether this translates into other image domains.", "limitations_and_societal_impact": "", "review_text": "", "extra_scores": {"correctness": "3: Some of the paper’s claims have minor issues. A few statements are not well-supported, or require small changes to be made correct.", "technical_novelty_and_significance": "2: The contributions are only marginally significant or novel.", "empirical_novelty_and_significance": "2: The contributions are only marginally significant or novel."}, "extra_text": {}}, {"review_id": "QHQHM3Z6Wi", "reviewer": "Reviewer_TqnH", "summary": "", "questions": "", "limitations": "", "rating": 8, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "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": "In this paper, the authors introduce a biologically inspired neural network architecture that combines a variety of learning and processing mechanisms, with the goal of studying whether the performance of artificial systems might be improved by increasing their computational realism. In particular, the authors explore the implementation of Dale’s principle, Hebbian updates, sparse coding, heterogeneous dropout, synaptic consolidation, and experience replay. The proposed model is tested in continual learning (CL) tasks derived from the popular MNIST benchmark, and results suggest significant performance gains.", "summary_of_the_review": "Overall, my judgment of this paper is positive. The research scope of this paper is broad enough to be of interest to the audience at ICLR and stimulate further interdisciplinary research work. At the same time, I believe that further simulations are required to make the paper stronger.", "strength_and_weaknesses": "One of the strengths of this paper is that it combines a remarkable number of recent ideas and biological processing mechanisms into a unified architecture. The proposed model is also tested in an incremental fashion, which allows to better understand the contribution of each mechanism / biological feature in final performance.\n\nA major weakness is the adoption of fairly “easy” tasks, since performance is almost at ceiling in most task variants (the only challenging one seems to be the Seq-MNIST). This might not allow to fully appreciate the gain associated with each model variants (e.g., Hebbian Update in Tab. 1). The latter issue is also amplified by the small number of runs (n=3) for each condition: increasing this number to at least 5 or 10 would allow to better clarify the actual gains, at least qualitatively; increasing it even more (maybe in some representative cases) would further allow to verify the gains through statistical testing. It would also be interesting to consider the full “Bio-ANN” model without Hebbian Update, to check whether the overall performance gain in the combined model really depends on the inclusion of such principle. Moreover, it might be useful to compare the proposed model with some other state-of-the-art approaches in continual learning to better highlight its potential (and possibly its limits).", "limitations_and_societal_impact": "", "review_text": "", "extra_scores": {"correctness": "3: Some of the paper’s claims have minor issues. A few statements are not well-supported, or require small changes to be made correct.", "technical_novelty_and_significance": "3: The contributions are significant and somewhat new. Aspects of the contributions exist in prior work.", "empirical_novelty_and_significance": "4: The contributions are significant, and do not exist in prior works."}, "extra_text": {}}, {"review_id": "FpYwnAT0vg", "reviewer": "Reviewer_jDQX", "summary": "", "questions": "", "limitations": "", "rating": 3, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "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": "The authors claim that including biological features in artificial neural networks can improve their performance on tasks such as continual learning. The authors propose to include four different biological features into their models and evaluate their relevance: 1) segregation of neurons into populations of excitatory and inhibitory neurons as in Dale's principle. 2) Dendritic-inspired structures as modulators and sparsifiers. 3) Hebbian plasticity rules. 4) Experience replay and regularization. \n\nThe different scenarios are evaluated based on variations of the famous MNIST dataset, showing the influence of the different parameters when considered together or separately. The authors claim that the results obtained offer compelling evidence. ", "summary_of_the_review": "This paper addresses the important question of the influence of biological inspiration on the design of artificial neural networks. \nThe paper falls short however in how the influence of the different features is evaluated and motivated. \nIt is a bit of a patchwork of biological components rather than a cohesive model. \n\nI greatly encourage the author to further this research as it can provide a great alternative to the blind study of artificial neural networks. ", "strength_and_weaknesses": "The paper addresses an important question on the importance of biological features for guiding the design principle of artificial neural networks. \n\nHowever, it is unclear how we can evaluate the importance of such features with the currently limited evaluation. How does it generalize to other datasets? What about synthetic datasets, where one can control for the different structures of the data that the features are supposed to be useful for?  \n\nThe influence of the different parameters is primarily measured in accuracy, but how is that the suitable proxy for measuring the impact of these features? Why are those features even relevant in this context? \n\nWhat is the rationale for combining Dale's principle, pyramidal-like cells, and Hebbian principles? Pyramidal cells are arguably not driven by the Hebbian principle. How is sparsity enforced without interneurons?  \nThe biological plausibility of those features is mostly in name but is vaguely plausible in their current implementation; as such, it cannot be one of the paper's main claims.\nMore rigor in how these concepts are handled would be greatly appreciated. \n", "limitations_and_societal_impact": "", "review_text": "", "extra_scores": {"correctness": "2: Several of the paper’s claims are incorrect or not well-supported.", "technical_novelty_and_significance": "2: The contributions are only marginally significant or novel.", "empirical_novelty_and_significance": "2: The contributions are only marginally significant or novel."}, "extra_text": {}}]

Author rebuttal:

Decision: Reject