Dynamical Signatures of Learning in Recurrent Networks
Authors: Marius Schneider
Andreea Lazar
Venue: Submitted to ICLR 2023 (2023)
Keywords: RNNs
self-organization
criticality
spatio-temporal dynamics

Abstract: Recurrent neural networks (RNNs) are powerful computational tools that operate best near the edge of chaos, where small perturbations in neuronal firing are transmitted between neurons with minimal amplification or loss. In this article, we depart from the observation that both stimulus and noise can be seen as perturbations to the intrinsic dynamics of a recurrent network, however stimulus information must be reliably preserved, while noise must be discarded. First, we show that self-organizing recurrent networks (SORNs) that learn the spatio-temporal structure of their inputs, increase their recurrent memory by preferentially propagating the relevant stimulus-specific structured signals, while becoming more robust to random perturbation. We find that the computational advantages gained through self-supervised learning are accompanied by a shift from critical to ordered dynamics, and that this dynamical shift varies with the structure of the stimulus. Next, we show that SORNs with subcritical dynamics can outperform their random RNNs counterparts with critical dynamics, on a range of tasks, including a temporal MNIST and a sequential shape-rotation task. Interestingly, when a shape is rotated, both the invariant (shape) and the variant (motion direction) aspects of the stimulus sequence are improved through learning in the subcritical SORNs. We propose that the shift in criticality is a signature of specialization and we expect it to be found in all cases in which general-purpose recurrent networks acquire self-correcting properties by internalizing the statistical structure of their inputs.

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DYNAMICAL SIGNATURES OF LEARNING IN RECURRENT NETWORKS
Anonymous authors Paper under double-blind review
ABSTRACT
Recurrent neural networks (RNNs) are powerful computational tools that oper- ate best near the edge of chaos, where small perturbations in neuronal firing are transmitted between neurons with minimal amplification or loss. In this article, we depart from the observation that both stimulus and noise can be seen as per- turbations to the intrinsic dynamics of a recurrent network, however stimulus information must be reliably preserved, while noise must be discarded. First, we show that self-organizing recurrent networks (SORNs) that learn the spatio- temporal structure of their inputs, increase their recurrent memory by preferentially propagating the relevant stimulus-specific structured signals, while becoming more robust to random perturbation. We find that the computational advantages gained through self-supervised learning are accompanied by a shift from critical to ordered dynamics, and that this dynamical shift varies with the structure of the stimulus. Next, show that SORNs with subcritical dynamics RNNs counterparts with critical dynamics, on a range of tasks, including a temporal MNIST and a sequential shape-rotation task. Interestingly, when shape is rotated, both the invariant (shape) and the variant (motion direction) aspects of the stimulus sequence are improved through learning the suberitical SORNs. We propose that the shift in criticality is signature of specialization and we expect it to be found in all cases in which general-purpose recurrent networks acquire self-correcting properties by internalizing the statistical structure of their inputs.
outperform their random
INTRODUCTION
Randomly-connecter recurrent neural networks (RNNs), often referred to as 'reservoir networks' Maass et al. (2002); y Jaeger & Haas 20044), are powerful computational tools that mimic the brain's 's mastery for sequential processing Buonomano & Maass 2009), while achieving impressive perfor- mance across a large variety of applications. As dynamical systems, RNNs exhibit fading memory of recent inputs which, in the limit, can be mapped through a simple readout to approximate any target function Maass & Markram (2004). In their seminal work, Bertschinger and Natschläger established a relationship between the computational power of recurrent networks and their dynamical properties Bertschinger Natschläger (2004). Specifically, they showed that randomly connected networks perform best when they operate at the critical edge between stability and chaos.
While random RNNs with critical dynamics exhibit a strong memory of recent inputs, for any arbitrary input sequences, they differ substantially from real cortical networks which are remarkably structured and specialized. Why did our brains evolve so as to contain so many specialized parts? ask Minsky and Papert in Perceptrons Minsky & Papert (1969). In order for a machine to learn to recognize or perform X, it a puttern or a process, that machine must in one sense or another learn represent embody X. Thus, it is sensible to believe that good model for, for example, visual processing is one that captures internally the common contingencies of features present in the natural visual environment. It is currently unknown how such learning or specialization impacts the dynamics of a RNN.
In this paper asked what is the relationship between network dynamics and performance, when RNNs learn the spatio-temports structure of their inputs. We contrast random RNNs, tuned close to criticality, to self-organizing recurrent networks (SORNs) that learn via unsupervised biologically-

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plausible plasticity mechanisms the sequential structure of their inputs Lazar et al. (2009); Hartmann et al. (015))
NETWORK MODEL AND DYNAMICS
2.1 RECURRENT NEURAL NETWORK
The network model consists of 80% excitatory units (N and 20% inhibitory units (N*). WIE W and W are dense connectivity matrices randomly drawn from the interval [0.1] and normalized so that the incoming connections each neuron sum up to constant (E, Way 1). The connections between excitatory units WEE are random and sparse Er is the probability of connection), with no self- self-recurrence.
For each discrete time step t, the network state is given by the two binary vectors x(t) E {0, 1),1, and ytt) E {0, 1] representing activity of the excitatory and inhibitory units, respectively. The network evolves using the following update functions:
1) o (WEB((()(())) W y()) + U())) T)))))
(1)
y(++1) O (()((())(()) w
The Heaviside step function constrains the network activation at time / to a binary representation: neuron fires if the total drive it receives is greater than its threshold. The threshold values for excitatory F) and inhibitory units (T') are drawn from a uniform distribution in the interval [0, The and [O. TI maz J. The initial values for excitatory weights (WEE) and thresholds (T stay constant for RNNs. These parameters have been chosen such that the dynamics of RNNs close to criticality and their memory performance is high. SORNs change their weights and thresholds during stimulation in an unsupervised fashion following the rules described in Section 2.3.
The input U(t) varies function of time and goes subset N of excitatory units.
2.2 PERTURBATION ANALYSIS
To define the chaotic and ordered phase of RNN we use the perturbation approach proposed by Derrida and Pomeau for autonomous systems Derrida & Pomeau (1986) and employed by Bertschinger and Natschläger for RNNs [Bertcchinger & Natschläger (2004). At each timestep i, we flip the activity of one the reservoir units (excitatory, non-input), giving us perturbed state vector x (t) with Hamming distance of from the original network xt). We map these two states rrt) and x' (t) to their corresponding successor states xtt + 1) and x' (t + 1), using the same weights and thresholds, and quantify the change in the Hamming distance. Distances that amplify are signature of chaos, whereas distances that decrease are signature of order.
2.3 SELF-ORGANIZING RECURRENT NETWORKS
For learning, we utilize simple model of spike-timing dependent plasticity STDP that strengthens (weakens) the synaptic weight W by fixed amount = 0.001 whenever unit i is active in the time step following (preceding) activation of unit
1j AW (1 nxTDr
1) ( ()))
In addition, synaptic normalization is used proportionally adjust the values of incoming connections to neuron so that they sum up to constant value.
Aw EE (t) E
EE (t)
Σ W WEE
(4)
To stabilize learning, we utilize a homeostatic intrinsic plasticity (IP) rule that spreads the activity evenly across units, by modulating their excitability using learning rate T)pp = 0.001. At each
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Figure Impact of self-organized learning on criticality Recurrent networks of randomly connected excitatory units exhibit ordered, critical and chaotic dynamics. In the upper row, examples of the temporal evolution of the network state for recurrent network with critical dynamics before and after the introduction of local plasticity rules. IP makes the dynamics of the network more chaotic (Hamming distance > 1), while SORN (STDP+IP) makes the dynamics more ordered (Hamming distance l). When plasticity is turned off, these recently acquired dynamical properties are preserved.
timestep, an active unit increases its threshold, while an inactive unit lowers its threshold by a small amount, such that on average each excitatory neuron will fire with the target firing rate jrp:
AT ())( pIP)
Learning is a source of stability for RNNs. We find that as SORNs learn the spatio-temporal structure of their inputs, the dynamical regime exhibited by the recurrent network becomes more ordered (illustration in Figure 1). In contrast, when used in isolation, IP is a source of variability for RNNs. As the activity is spread evenly across units, the dynamical regime of the IP-only networks becomes more chaotic (Figure 1).
The implementation of the model described above and the simulations presented in the following sections were performed in Matlab.
3 DYNAMICAL SIGNATURES OF LEARNING
In the following simulations, we select initial parameter settings that result in network dynamics close to criticality, which are known to result in a high memory performance. An example of network activity for reservoir composed of N 100 excitatory units, N 25, E 0.05, TE 0.5, T maz 0.3 is presented Figure 2. In order to understand the roles played by the homeostatic introduce them separately. Each plasticity interval (10000
and learning plasticity mechanisms, steps) is followed by no plasticity interval (10000 steps). Network performance and criticality are compared in the absence of plasticity.

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Figure (a) Activity of a network composed of 125 units over 60000 time steps (Top) and corresponding perturbation analysis (Bottom). Hamming distance is averaged across 500 consecutive time steps. The moments when IP and STDP+IP are introduced are marked by dotted lines. Networks with IP become more chaotic (Hamming distance>l). SORNs become more ordered (Hamming distance <1). In the absence of plasticity the networks retain their newly acquired dynamics. Shaded intervals are compared in (b) and (d). (b) IP-networks and SORNs have lower firing rates compared to random RNNs tuned to exhibit critical dynamics, because of their homeostatic IP. (c) Example of weight distributions before and after unsupervised learning with STDP. (d) Memory and prediction performance scores are compared between random RNNs, IP-networks and SORNs, after plasticity was turned off (shaded intervals (a), 20 runs). SORNs have an increased memory for the experienced stimuli compared to their counterparts.
In first learning task we randomly alternate input sequences of length (a1, ag.., a5i b1s bg.., by). Each symbol in sequence activates 2 input neurons, thus N 20 units out of the total 100 excitatory units receive input. Using the perturbation analysis described in Section 2.2, we observe shift in network dynamics towards a chaotic regime (Hamming>1) after IP is introduced (Figure 2a, average over 20 network runs). When STDP introduced in addition, network dynamics becomes ordered (Hamming<1).
Interestingly, while the firing rates of IP-networks and SORN-networks are similar (Figure 2b), due to the presence of IP, the dynamical regimes exhibited by these two types of networks are very different.
Through learning, SORNs change their synaptic weight distribution, with a subset of weights becoming stronger and subset of weights becoming weaker (example run in Figure 2c).
To quantify the computational power of the different recurrent networks under comparison, a simple Bayesian readout was trained to differentiate between the two sequences based in the reservoir state (cxcitatory non-input units) of the network at the present time plus or minus a time lag. k-fold validation procedure and I partition used for test. We found that after 10000 steps of unsupervised plasticity, SORNs learned the predictable structure of these simple sequential inputs and significantly outperformed both RNNs and [P-networks on this task (Figure 2d, 20 network runs, k = 4 partitions).
applied, that split data into & partitions, with k-1 partitions used for training
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Figure 3: Impact of learning a temPoral-MNIST on network dynamics. (a) Example stimuli from the original MNIST dataset and downsampled versions received by the network. 6000 stimuli were downsampled to 10x10 pixels and sectioned from top to bottom into 10 consecutive chunks, i.e. each digit became vector sequence length 10. (b) Activity of RNN, IP-network and SORN for 10000 steps and 10000 steps post plasstiiiic.ty. The comparison is made between non non-plastic networks, marked by shaded areas. RNNs are tuned to close to criticality, where their performance known to be high. Networks with IP become chaotic (Hamming distance>1) and remain chaotic when IP is turned off. SORNs become ordered after learning (Hamming distance<1) 1). (c) Impact of learning a large dataset (MNIST images) on network performance. RNNs have been tuned to be close to criticality, where their performance known to be high, but are outperformed by SORNs. (d) The dynamics of SORNs becomes ordered after learning. (e) Performance of SORNs is significantly higher for both memory and prediction compared to IP-networks and random RNNs (average over timelags 1 to 10).
SELF-ORGANIZED LEARNING OF MNIST DATASET
In second task, larger set of inputs was employed. 6000 independent examples of hand-written digits (10 digits, 600 examples per digit) from the MNIST dataset were downsampled as pictured in Figure and sectioned from top bottom into 10 consecutive chunks (each image became input sequence length 10). The resulting sequential input was 60000 time steps long and contained no overlapping data (each hand-writte digit was presented exactly once).
We selected initial parameter settings that resulted network dynamics close to criticality, Specifi- cally, the random recurrent networks composed of N 160 excitatory, N' 40 inhibitory

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units, with R 0.03, T maz 0.4 and T "ma =.3. An example of network activity and dynamics can be observed in Figure 3. As before, intrinsic and synaptic plasticity mechanisms were introduced separately and were followed by 10000 steps of no plasticity. Network performance and criticality were compared in the absence of plasticity (intervals marked yellow).
To assess the memory performance of recurrent network, simple Bayesian readouts trained to classify the current input digit based on network activity at time t plus or minus a time lag. Results were averaged over 20 network run. For each network run 4-fold validation procedure was employed: through rotation, three quarters of data were asigned for training, one quarter for test and the results were averaged. We found that the performance of SORNs was significantly higher than that of [P-networks and random RNNs for both memory and prediction (Figure 3c and e).
The dynamics of networks after learning was ordered, Hamming distance scores for SORNs were significantly lower than the Hamming distance scores of random RNNs (t-test, p < 0.0005, Figure 3d) and significantly lower than I (t-test, p x 10 10-9)
5 SELF-ORGANIZED LEARNING OF ROTATING SHAPES
In final task, we employed rotating shapes to differentiate between different aspects of sequential processing. Two shapes were rotated 90 degrees, either left or right, across seven individual image frames (Figure 4a). The network activity was split into individual trials, the rotating shapes alternated randomly across trials. Each trial consisted of 80 time-steps: 3 time-steps per image frame, time-steps blank between frames, and 40 steesseps of activity after the stimulus presentation, which allowed us to quantify the recurrent memory traces. Example trials for the three network types are shown in Figure 4b, in all three cases the networks respond strongly to example stimulus sequence and produce recurrent activity after the stimulus is extinguished.
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Figure Shape-rotation task. (a) Left and right rotating shapes. Each sequence is composed of 7 frames, each frame is 8x8 pixels. (b) Example single-trial network responses to sequence presentation for the three types networks.
The network activity of reservoir with N = 240 excitatory units, N' = E = 0.02, T mar 0.5, T T 0.3 is shown in Figure 5a. As the previous tasks, the Hamming distance increased for IP-networks and decreased for SORNs (Figure 5a bottom, 480 trials, 38400 timesteps).
We employed Bayesian classifiers to decode stimulus shape, irrespective of motion direction (Figure 5b) and motion direction, irrespective of stimulus shape (Figure 5c). In the first task, decoding of stimulus shape, maximum peak performance was reached for all three network types during stimulus presentation, though the Bayesian classifiers units were excluded). SORNs exhibited higher performance after the stimulus offset, compared to the other networks, with decoding performance being 70% the end of the trial (Figure 5b).
trained exclusively
reservoir units (input

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The second task, decoding of motion direction, more difficult, since it required an integration of information over time. We found that a strong memory trace of information about rotation direction was available in SORNs, 65%. at the end of the trial (Figure5c).
We conclude that the shift towards more orderly dynamics can be associated with enhancements in both variant and invariant aspects of sequential processing in self-organizing recurrent networks.
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Figure 5: (a) Activity of network composed of 300 units and corresponding perturbation analysis during the shape-rotation task over 480 trials (38400 time steps). Random RNNs become more chaotic after IP and more ordered after self-organization. Comparison of the memory performance of the three network types (yellow markings) in decoding the shape (b) and rotation direction (c) of the object. Negative times correspond the stimulus presentation, 0 marks the stimulus offset. After learning, SORNs exhibit a much stronger memory trace for both shape and direction compared to the other network types.
DISCUSSION
It makes no sense to seek the best network architecture or learning procedure because it makes no sense say that any network is efficient by itself: that makes sense only the context of some class of problems to be solved. Minsky & Paperi (1969)
We compared the dynamical properties of general-purpose recurrent networks to those of specialized recurrent networks that have learned the sequential structure of their inputs. We showed that local plasticity rules for learning and homeostasis can have opposing influences on network dynamics. Most importantly, we found that recurrent networks that learn the spatio-temporal structure of their inputs exhibit enhanced computational abilities and concomitantly shift their dynamics towards the ordered regime. The increased robustness to perturbation exhibited after learning provides with hints regarding the dynamical principles that enable biological systems to perform sophisticated information processing.
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Early theories of visual perception have suggested that the brain interprets its input signals the basis of an internal model of the visual world Von Helmholtz (1a (1867). Such a model can be learned through experience because the visual world is immensely rich, yet exquisitely structured, both across space and time. The ideal model, as it turns out, is not a general random machine, but a highly structured network that can accommodate large number of statistical contingencies, required for the interpretation of ever changing sensory input patterns. Here we have shown, in simple recurrent models, that the signatures of network specialization can be picked up from the network's 's dynamics. Future experimental work on cortical networks could investigate whether such a correspondence exists in real brain networks and what extent learning increases their robustness perturbation, or their ability to process noisy stimuli.
REFERENCES
Nils Bertschinger and Thomas Natschläger. Real-time computation the edge of chaos in recurrent neural networks. Neural computation, 16(7):1413-436, 2004.
Dean V Buonomano and Wolfgang Maass. State-dependent computations: spatiotemporal processing in cortical networks. Nature Reviews Neuroscience, 10(2):113 125, 2009.
Bernard Derrida and Yves Pomeau. Random networks of automata: simple annealed approximation. EPL (Europhysics Letters), 1(2):5,, 1986.
Christoph Hartmann, Andreea Lazar, Bernhard Nessler, and Jochen Triesch. Where's 's the noise? key features of spontaneous activity and neural variability arise through learning deterministic network. PLoS computational biology, 11(12)xe1006640, 2015.
Herbert Jaeger and Harald Haas. Harnessing nonlinearity: Predicting chaotic systems and saving energy in wireless communication. Science, 304(5667)77-880, 2004.
Andreea Lazar, Gordon Pipa, and Jochen Triesch. Sorn: self-organizing recurrent neural network. Frontiers in computational neuroscience, pp. 23, 2009.
Wolfgang Maass and Henry Markram. On the computational power of circuits of spiking neurons.
Journal of computer and system sciences, 69(4):593-616, 2004.
Wolfgang Maass, Thomas Natschläger, and Henry Markram. Real-time computing without stable states: A new framework for neural computation based on perturbations. Neural computation, 14 (11):2531 -2600, 2002.
Marvin Minsky and Scymour Papert. An introduction computational geometry. Cambridge tiass., HIT, 479:480, 1969.
Hermann Von Helmholtz. Handbuch der physiologischen Optik: mit 213 in den Text eingedruckten Holzschmitten und 11 Tafeln, volume 9. Voss, 1867.
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MODEL PARAMETERS
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DEPENDANCE OF CRITICALITY AND PERFORMANCE ON TASK DIFFICULTY
We use a learning task which randomly alternate two imput sequences length + (a, s.., c, I.., 2t, d), where input is common to sequences and repeated n times. The two input sequences alternate randomly during stimulation and are separated by up to 5 blanks. A linear readout is trained to separate between the two sequenees (hlanks removed). Each symbol in sequence activates 5 input neurons, thus total of 25 units receive input. The interesting aspect of this task is that the the length of the input sequences changing the ratio of input units to reservoir units. simulate networks The longer sequences require longer recurrent memory trace for correct classification. We find that the fading memory of SORNs improves through unsupervised learning over that of RNNs for both short and long sequenees. For very long sequenees (n 24, Figure I, right), the maintanance of long memory trace comes with cost for decoding recent and current stimuli.
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Figure 6: Contrast learning short (n 4, left panel) vs long sequences 24, right panel).
= RNNs with N=125 units, ===== 0.05, T (SORN). SORNs maintain longer input memory trace compared IP-networks and RNNs. Error
max 0.4, T maa 0.3 are shaped by IP or IP+STDP
bars indicate s.c.m.

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We compared the criticality values, estimated via perturbation analysis, for the three types of reservoirs considered here, to their memory performance on the task above (time lag = -15-55). The firing rates of IP- networks and SORNs are nearly identical, due to the presence of IP with a set target rate for all units, however the dynamical regimes exhibited by these two types of recurrent networks are quite different. IP IP-networks exhibit chaotic dynamics while SORNs exhibit ordered dynamics for all values of (Figure 2, left panel). While SORNs exhibit the most orderly dynamies for smaller n,, they outperform both IP-networks and RNNs the memory task by similar amounts for values of n. This interesting result suggests that, in SORNs, a perturbation start of an imput sequence is more likely to be corrected than perturbation at the end an input sequence. This type of stimulus dependance is less pronounced for IP (P-netwrrks and RNNs Prompted by this result we initiated analysis that compares outcomes of perturbations of the reservoir's state with respect their occurrence inside input sequence, which we plan to include in the final manuscript.
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Figure 7: Hamming distance for RNNs, IP-networks and SORNs in the presence of inputs of varying length. SORNs outperform the other networks and exhibit ordered dynamics (Hamming distance <1) for all values of n. Most orderly dynamics if observed for smaller n. Error bars indicate s.e.m.
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Reviews:
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They also showed that the SORN model with subcritical dynamics outperfrom random RNN counterparts with critical dynamics on a range of tasks. ", "summary_of_the_review": "This paper is lack of many details and contributes only in a limited way to the ICLR society. ", "strength_and_weaknesses": "Strength:\n\nThe idea is somehow interesting and the written is clear.\n\nWeaknesses:\n\n1, It is better to give an illustration of the network model, especially for those readers without comp. neuro. background. For the pertubabtion analysis, you can also give a illustration at somewhere. \n\n2, Many parts of the paper need to be explained more clearly. For instance, what does the input looks like when producing Figure 1?\n\n3, All the results are only verified with simulations, and theoretical analysis of why the network work is missing, making the paper more like a technical report.", "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": {}}, {"review_id": "rlSPwaxkQ7", "reviewer": "Reviewer_vp6e", "summary": "", "questions": "", "limitations": "", "rating": 3, "confidence": 5, "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 paper compares a RNN with step nonlinearities with randomly initialized parameters to ones in which parameters are trained by simple local updates inspired by biology. Namely, connections are changed to reinforce sequential structure (STDP) while the neuron thresholds change so as to keep activities small (IP). These RNN variants are evaluated in terms of their criticality via numerical perturbations and in terms of the ability of the network representations to carry information about sequential inputs to the network (using a separately trained decoder).", "summary_of_the_review": "Overall, a simple model analyzed with numerical means using methodology similar to past SORN work (Lazar, Triesch, etc), on a few toy tasks. The results show slight benefits from SORN learning over no learning (arguably, the minimal precondition for usefulness); I would not say that the mechanics of the process are much better understood as a result of the accompanying analysis and the relevance for the broader community seems minimal.", "strength_and_weaknesses": "+ Strength: SORNs involve purely local unsupervised updates; that endows them with some computational advantages relative to static reservoirs with randomly initialized parameters by exploiting statistical regularities in the inputs.\n- Weakness: the choice of model seems out of touch with the field, which invariably uses differentiable nonlinearities for the units, and which have lent itself to perhaps more interesting analytical investigation of the RNN dynamics after learning\n- W: the tasks are somewhat contrived to involve toy sequential structure\n- W: performance seems relatively poor overall\n- W: relevance of the work seems restricted to a small niche of computational neuroscience which focuses on criticality and reservoir computing, unclear what implications if any should this have on the wider comp neuro or machine learning field. ", "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": "1: The contributions are neither significant nor novel.", "empirical_novelty_and_significance": "2: The contributions are only marginally significant or novel."}, "extra_text": {}}, {"review_id": "rLRooDsUwjA", "reviewer": "Reviewer_B89g", "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": "In this paper, authors study the performance and properties of SORNs that have been exposed to the training dataset in terms of its ability to differentiate between task relevant and noise inputs. They show that these SORNs have sub-critical dynamics and can outperform RNNs at the edge of criticality in a couple of benchmarks.\n", "summary_of_the_review": "Overall, while the issue investigated and the results are interesting, the paper needs to improve on multiple fronts -- better and clearer writing, clearer statement of question being investigated, better justifications for various experiment details, more experiments to judge generality of results.", "strength_and_weaknesses": "## Strengths:\n\n- The properties of SORNs shown are very interesting in terms of such a sub-critical network performing better than RNNs at EOC.\n- Being able to get better performance than a standard reservoir on these tasks based on SORN training is nice.\n\n## Weaknesses:\n\n- A lot of the experimental setup seems very arbitrary, and there are no ablation studies to determine what's important. e.g. does IP always have to precede SORN?\n- The results of the study are hard to generalize due to very specific choices of plasticity and network setup.\n- Some parts of the experimental details are not clear.\n\n## Other questions\n\n- In Fig. 2, why is the performance above chance for both positive and negative time lags?\n- How's the bayesian readout trained?\n- More explanation needed for what variant and invariant aspects of processing are in Sec. 5.\n- How does SORN compare with self-supervised training using other optimization methods?", "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": "UcJM-j88-w", "reviewer": "Reviewer_RfJy", "summary": "", "questions": "", "limitations": "", "rating": 5, "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 compare the dynamical characteristics of recurrent neural networks before and after training. Specifically, the results presented in the paper suggest that training shifts RNNs toward subcriticality. The authors suggest that this subcriticality is a signature of specialization that can potentially be used to study specialization in biological neural networks.", "summary_of_the_review": "I believe this paper can make an important contribution to both machine learning and neuroscience by providing a dynamics-based metric for studying specialization in artificial and biological neural networks. However, I believe that the paper could benefit from more thorough examination of different learning rules and a few more control experiments, which I explained in my comments. I am willing to improve my score if the authors address my questions especially ones regarding different learning rules.  ", "strength_and_weaknesses": "$\\textbf{Strengths}$:\n\nStudying the connection between dynamical properties and learning in artificial neural networks (ANN) is novel, and can potentially build stronger link between the two common approaches of dynamical systems and deep learning in neuroscience. I found the approach presented in the paper very useful in that sense.\n\n$\\textbf{Weaknesses}$:\n\nI have some reservations about the main claim of the paper: namely “the shift in criticality is a signature of specialization.” I am not convinced that the data presented in the paper supports this general claim and is not specific to the learning rule and training sequences used in the experiments. I elaborate below:\n\n$\\textbf{Questions}$:\n\n1- All the results in this paper are produced with a learning rule that is a combination of a Hebbian plasticity and a homeostatic plasticity rule. If the main claim of the paper is that gaining specialization (regardless of the learning rule) leads to subcriticality in the dynamics of the RNN, I'd expect to see similar results with other learning rules, e.g. Oja’s rule, BCM rule, gradient descent rules, etc. \n\n2- The change in the Hamming distance after learning is different between different tasks. For example, in Figure 2a after applying the learning rule, the Hamming distance immediately starts going down, but in Figure 3b (the MNIST data), applying the learning rule actually causes a jump in the Hamming distance which gradually goes down but doesn’t get to below one (the subcriticality) until learning is turned off. This seems to suggest that there is an interaction between the effect of learning and the sequence statistics. How do the authors explain this apparent discrepancy between the two experiments? \n\n3- Although the effect of homeostatic plasticity on the dynamics is investigated separately (e.g Figure 1), the effect of STDP isn’t examined separately. Therefore, it is not clear whether the shift from criticality to subcriticality is due to the STDP rule or it is a combined effect of STDP and homeostatic plasticity. I suggest that the authors also include a comparison with STDP alone, or if it is not possible, please explain the reason. \n\n4- Related to comment # 2, the interaction between the statistics of the input sequence and the learning rule on shifting the dynamics of RNNs is not clear. How would the dynamical regime change if the input data was white noise? In a more systematic exploration, you could gradually increase the temporal (and even spatial) correlations (e.g. using an auto-regression process) and evaluate the shift in the dynamics as a function of the temporal/spatial correlation in the input sequence. \n\n5- In the introduction it is mentioned that “random RNNs with critical dynamics exhibit a strong memory of recent inputs for any arbitrary input sequences.” The results presented in the paper, however, show that learning improves the memory of the RNN for the training sequences. But, it is expected that it should decrease memory performance for other arbitrary sequences. It would be useful to explicitly show the underperformance of the RNN with other sequences compared to an RNN functioning at the edge of chaos. This would give a more balanced picture of the advantages and disadvantages of specialization. For example, in the context of continual learning (which might be beyond the scope of this paper), becoming too specialized might be a disadvantage for the neural network.  \n\n$\\textbf{Minor comments}$:\n\n1- In section 2.1, all inhibitory and excitatory synaptic weights are explained as being sampled from [0,1]. Is this only the magnitude of the synaptic connections, given that the inhibitory connections are expected to be sampled from a range of negative values.\n\n2- How are memory and prediction performance measured separately for the plots in Figure 3e?\n\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": "3: The contributions are significant and somewhat new. Aspects of the contributions exist in prior work.", "empirical_novelty_and_significance": "3: The contributions are significant and somewhat new. Aspects of the contributions exist in prior work."}, "extra_text": {}}]

Author rebuttal:

Decision: Reject