Title: The Simplicity Bias in Multi-Task RNNs: Shared Attractors, Reuse of Dynamics, and Geometric Representation
Venue: NeurIPS 2023
Accepted: yes
Keywords: Computational Neural Models; Recurrent Neural Networks; Multiple Tasks; Geometry;Dynamical Systems;Attractors;Neuroscience
Abstract: How does a single interconnected neural population perform multiple tasks, each with its own dynamical requirements? The relation between task requirements and neural dynamics in Recurrent Neural Networks (RNNs) has been investigated for single tasks. The forces shaping joint dynamics of multiple tasks, however, are largely unexplored. In this work, we first construct a systematic framework to study multiple tasks in RNNs, minimizing interference from input and output correlations with the hidden representation. This allows us to reveal how RNNs tend to share attractors and reuse dynamics, a tendency we define as the "simplicity bias".
We find that RNNs develop attractors sequentially during training, preferentially reusing existing dynamics and opting for simple solutions when possible. This sequenced emergence and preferential reuse encapsulate the simplicity bias. Through concrete examples, we demonstrate that new attractors primarily emerge due to task demands or architectural constraints, illustrating a balance between simplicity bias and external factors.
We examine the geometry of joint representations within a single attractor, by constructing a family of tasks from a set of functions. We show that the steepness of the associated functions controls their alignment within the attractor. This arrangement again highlights the simplicity bias, as points with similar input spacings undergo comparable transformations to reach the shared attractor.
Our findings propose compelling applications. The geometry of shared attractors might allow us to infer the nature of unknown tasks. Furthermore, the simplicity bias implies that without specific incentives, modularity in RNNs may not spontaneously emerge, providing insights into the conditions required for network specialization.

The Simplicity Bias in Multi-Task RNNs: Shared Attractors, Reuse of Dynamics, and Geometric Representation

Abstract

How does a single interconnected neural population perform multiple tasks, each with its own dynamical requirements? The relation between task requirements and neural dynamics in Recurrent Neural Networks (RNNs) has been investigated for single tasks. The forces shaping joint dynamics of multiple tasks, however, are largely unexplored. In this work, we first construct a systematic framework to study multiple tasks in RNNs, minimizing interference from input and output correlations with the hidden representation. This allows us to reveal how RNNs tend to share attractors and reuse dynamics, a tendency we define as the "simplicity bias". We find that RNNs develop attractors sequentially during training, preferentially reusing existing dynamics and opting for simple solutions when possible. This sequenced emergence and preferential reuse encapsulate the simplicity bias. Through concrete examples, we demonstrate that new attractors primarily emerge due to task demands or architectural constraints, illustrating a balance between simplicity bias and external factors. We examine the geometry of joint representations within a single attractor, by constructing a family of tasks from a set of functions. We show that the steepness of the associated functions controls their alignment within the attractor. This arrangement again highlights the simplicity bias, as points with similar input spacings undergo comparable transformations to reach the shared attractor. Our findings propose compelling applications. The geometry of shared attractors might allow us to infer the nature of unknown tasks. Furthermore, the simplicity bias implies that without specific incentives, modularity in RNNs may not spontaneously emerge, providing insights into the conditions required for network specialization.

1 Introduction

Consider the hand motions of a basketball player in a single game - dribbling, passing, receiving, and shooting. Each motion has its own dynamics, and yet all are orchestrated by the same area in the motor cortex. How can a single interconnected neural population give rise to a myriad of different actions? A recent body of work examined the link between task performance and neural dynamics by thinking of populations of neurons, especially in more cognitive and motor areas [5], as dynamical

systems (see [31] for a full review). Trained Recurrent Neural Networks (RNNs) provide a natural model for cortical areas [1, 12, 27]. Anatomically, the cortex is enriched with lateral connections, making feedback the default architecture. Functionally, RNNs are universal approximators and can thus be trained on tasks similar to those studied experimentally. The downside of trained RNNs is that, as with any machine learning tool, they are often seen as a black box. Nevertheless, many advances have been made on understanding both the dynamics of trained networks [3, 4, 5, 12, 19, 21, 23, 29] and how these dynamics emerge through training [7, 26].

Most (but not all) of these investigations have been focused on one controlled task at a time. This focus, although valuable, may not fully capture the complexity of an animal's behavioral repertoire which is dynamic, diverse, and often involves multiple simultaneous tasks [14]. Shifting the focus from single to multiple tasks is a natural evolution in the field, aligning more closely with the realities of an animal's environment which is characterized by symmetries, regularities, and structures. It is highly plausible that the neural circuits driving behavior have adapted to this structure by developing efficient mechanisms to perform multiple tasks. This perspective has led to several studies investigating the behavior of neural networks in multi-task settings [16, 17, 33]. Experimentally, [8] demonstrated that different muscle activity patterns can be explained by neural activity modes in M1 that are task-independent.

Recent studies have begun to address the complex issue of multi-task performance using RNNs. [35] trained single network models to perform an array of 20 cognitive tasks that encompass working memory, decision making, categorization, and inhibitory control. They discovered that after training, recurrent units can develop into clusters that are functionally specialized for different cognitive processes. [6] further extended this line of research by identifying an algorithmic neural substrate for compositional computation. They conducted dynamical systems analyses of networks and found computational strategies that mirrored the modular subtask structure of the task-set used for training. Key dynamical motifs, such as attractors, decision boundaries, and rotations, were reused across different task computations. Their work contributes to the understanding of compositional computation, presenting dynamical motifs as a fundamental unit of computation that allows for flexibility and generalization of previously learned computations.

Our work offers a complementary approach to these pioneering studies. Instead of working from common tasks towards their implementation, we take a step back to consider the most fundamental dynamical objects typically found in RNNs. We ask from first principles: How can a single neural population combine these disparate objects into a joint representation? And under what conditions do these representations become shared or separate?

To explore these questions, we use RNNs as our computational tool and introduce a novel framework that disentangles cognitive computation from sensory and motor processes. By ensuring that all tasks operate under identical input and output statistics, our approach simplifies the concept of tasksimilarity, rendering it amenable for systematic analysis. Our results reveal a bias toward developing shared representations, which we term "simplicity bias". This tendency persists regardless of the number of tasks or the nature of the dynamical objects involved, be they fixed points, limit cycles, line- or plane- attractors. We link this bias to the sequential emergence of attractors during training, and show how external factors can resist this bias and create more complex dynamical objects. We continue to explore the inner structure of these shared attractors. By limiting the discussion to tasks that require line attractors, and re-conceptualizing tasks as functions, we show that the steepness of the computation, and not the computation itself, are responsible for shaping the attractor itself.

Our results can be used to infer hidden capabilities of networks by observing their activity geometries. The results also shed light on the conditions for the emergence of modularity in RNNs, and more generally provide a framework for understanding complex tasks in terms of dynamical building blocks.

2 The systematic study of multiple tasks

To systematically study multiple tasks, it is critical to ensure that our experimental design does not artificially influence the divergence or convergence of the network's representations. Our methodology is twofold:

First, we standardize the input and output structure across all tasks and use a consistent network architecture. This approach ensures that any observed differences in representations can be attributed to intrinsic task complexities, rather than artificial variations in input-output structure or network design. This methodology is inspired by the discussion in [34], which highlights that single-layer RNNs, unlike the brain, simultaneously implement sensory, cognitive, and motor elements. This all-in-one implementation makes it challenging to attribute different parts of the computation to distinct elements. By standardizing the input-output structure and network design, we aim to sidestep this issue and gain a clearer understanding of the nature of task representations.

Secondly, to guard against artificial convergence in representations, we assign individual input and output channels for each task. This design choice ensures that any observed overlap or similarity in representations results from shared computational requirements or reused dynamics across tasks, rather than imposed sharing of input or output channels. Following these principles, we outline our experimental setup as detailed below.

2.1 Model description

We use a discrete-time recurrent neural network (RNN), with N hidden units. The state at each time step t is given by:

where W rec is the recurrent weight matrix, h t is the hidden state at time t, W in is the input weight matrix, and u t is the input at time t, and b rec is a bias term. The network output, y t , is:

where W out is the output weight matrix and b out is the bias term. For full details about the training process see supplementary 2.

2.2 Task structure

For more details see supplementary section 1.

We consider a set of tasks designed to elicit certain dynamical objects in the trained network [28]. The input sequence for each task consists of pulses with variable amplitude, interspersed with periods of no input. Tasks are defined based on the output during the intervals between inputs (Fig. 1A). For instance, requiring the network to maintain one of two discrete values (Fig. 1A, top) results in the network producing two fixed point (Fig. 1B, top). In a similar manner, different input-output demands result in limit cycles, line attractors, or plane attractors (second, third and fourth rows respectively).

Formally, the network receives a sequence of input values ( a 1 , ...a n -1 , a n , ... ) at corresponding times ( t 1 , ...t n -1 , t n , ... ) such that:

The output at time t maps the recent history ( a n , a n -1 , ..., t n , t n -1 , .., t ) onto the interval [ v min , v max ] . The specifics of this mapping influence the type and size of working memory required by the task, with any dependence on t determining the temporal structure of the output. In the neuroscience literature, line attractors are commonly associated with analog working memory [11, 20], fixed points with decision making [32], and limit cycles with motor patterns [22]. In general, however, there is more than one way to implement a given task [30].

2.3 Architecture and training procedure

For full details see supplementary section 2.

Our main objective in multi-task learning is to investigate the internal representations formed by the RNN. The choice of architecture can have a dramatic effect on these representations. For instance, if two tasks share a common output, then the internal state of the network has to be different for different tasks by construction. In contrast, if each task has an independent output, then the internal representation may utilize similar states and it may utilize different states. We focus on an architecture that maintains this freedom, but note that recognizing and characterizing these architectural biases is also an important research direction. Our setup includes separate input and output channels for each

input

channels

output

channels

task & loss regime

input A

input B

output A

output B

x

∅

⊥

∥

A

B

C

D

XX

task, so that W in ∈ R N × N tasks and W out ∈ R N tasks × N (Fig. 1C). We will denote by N the number of hidden units.

Apart from the network architecture, the trial structure of multi-task training also has several degrees of freedom. We consider three regimes: gated, orthogonal, and parallel (Fig. 1D, marked respectively with ∅ , ⊥ , ∥ ). In the gated scenario, every trial has inputs from only one task, and the loss is computed for the output of that task alone, ignoring (or gating) the other task outputs. For the orthogonal case, inputs are still separated in each trial but the output of the irrelevant tasks has to be zero. Finally, in the parallel setting, both tasks are presented simultaneously within the same trial.

3 RNNs representations show a simplicity bias

We trained 30 networks on pairs of tasks in the gated and orthogonal settings (Fig. 2, parallel settings were tested for some of the combinations, see supplementary 5) . For visualization purposes, we projected the states h t onto their leading two principal components. We found that in the gated setting, the attractors of the two tasks shared similar representations, whereas in the orthogonal case the attractors were much more separated. When the two tasks demanded similar objects (columns 1, 4, 6 and 7) the gated setting resulted in a complete overlap between the tasks. Even when the attractors differed qualitatively, we still observed that they reside in similar areas of phase space. To quantify this effect, we trained a linear classifier to separate the neural trajectories of one task from those of the other one. For the gated setting, classification failed in nearly all networks (Fig. 2B, see supplementary 3.3), suggesting that the networks generated a single attractor with parts of it serving each task. This was also evident in the ratio of variances between and within tasks (F-factor, Fig. 2C, see supplementary 3.4). In contrast, the orthogonal setting resulted in separate attractors for each task. Overall, we conclude that network dynamics evolve according to a "simplicity bias", where the simplest dynamical structure that is sufficient for the joint solution of all tasks is the one that will emerge. This bias is present even for attractors that might seem incongruent, such as limit cycles and

∅

⊥

A

B

C

D

X

X

X

#

fixed points. To demonstrate that a bias, and not a hard constraint, we used the orthogonal solutions as initial conditions for training in the gated setting. Retraining in the gated setting with added noise did not shift the solution from that of the orthogonal one.

Because dynamics stem from the recurrent connectivity, we hypothesized that the elaboration of the dynamics in the orthogonal setting is reflected in the spectrum of the connectivity matrix. Indeed, we found that the number of unstable eigenvalues was larger in the orthogonal setting for all tasks (Fig. 2D, see supplementary 3.5).

The above results lead to a simple hypothesis regarding the origin of the simplicity bias (Fig. 3). Consider a pair of tasks both requiring fixed points. Initially, only the origin is stable, and the inputs from both tasks lead to states that converge to the origin. The resulting loss modifies the recurrent connectivity and dynamics. Eventually, a stable fixed point will emerge away from the origin. Once this happens, the inputs from both tasks will lead to states that converge to this new fixed point. Crucially, the recurrent dynamics cause the states to mostly depend on the task-agnostic attractors, and less on the task-specific inputs. If the loss to both tasks can be reduced within this attractor, then learning is not expected to generate another one. Importantly, even if another attractor is needed (as in the fixed point and limit cycle combination), we expect it to emerge in the vicinity of the existing attractor. This is because gradient descent is proportional to the state of the network, modifications to the connectivity will be proportional to this state . In the orthogonal setting, the two attractors have to be orthogonal to each other, forcing the network to separate them.

We verify this hypothesis by following the attractor landscape of networks as they train. To better characterize the dynamics, we use a low-rank network [13]: W rec = mn T , where m,n ∈ R N × 2 are the only parameters trained via gradient descent, constraining connectivity to be of rank 2 . A consequence of this connectivity is that dynamics can be visualized in a two-dimensional space given by the projections κ i ( t ) = n T h t (the definition is slightly different from that of [13] because of the

Task A

State

Loss

Task B

Recurrent

Dynamics

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epoch 0

epoch 10

epoch 30

epoch 20

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differences in the definitions of the dynamics). See also supplementary 3.6. We follow the evolution of the dynamics for such a network trained on two fixed-point tasks in the parallel setting (Fig. 3D). Initially, only the origin is stable, as reflected in the two eigenvalues of W rec being inside the unit circle. Eventually, the origin destabilizes, and a single unstable eigenvalue emerges along with a pair of stable fixed points (due to symmetry of the dynamics). With more training, the second eigenvalue leaves the unit circle, and shortly after another pair of stable fixed points emerge, leading to the final attractor landscape with four basins of attraction.

We repeated this analysis for a two-task version (all fixed points) in all three settings (Fig. 3B). We show the loss for each task and the spectrum of eigenvalues. In the parallel and orthogonal settings, one can see the clear sequential emergence of two outliers, accompanied by decreases in loss for each sub-task. The gated setting is solved with a single outlier, as all tasks share a common attractor.

A systematic analysis of many such tasks (sets of fixed points, from 2 to 6 simultaneously) shows that the number of outliers is proportional to the number of tasks for the orthogonal and parallel, but not for the gated setting. We repeated this analysis for both GRU networks and Vanilla networks initialized with a rich output regime and obtained similar results. See supplementary 3.7 for details.

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4 Task similarity to representational similarity

Having established how RNNs tend to implement a shared attractor for all tasks, we aim to explore the principles that govern how multiple tasks will occupy the same attractor. In particular, how distances in task space translate to distances in representation space (Fig. 4A). To test this, we focus on a family of tasks that all require a line attractor.

4.1 Tasks as Functions

In line with our task structure (Section 2.2), the output of each task is a mapping ϕ : [ v min , v max ] → [ v min , v max ] , which operates on the most recently seen input a n . This form enables us to conceptualize a set of tasks as a family of 1D parametric functions ϕ i . An example for two such functions can be seen in 4B (left). Transitioning to a function space allows us to define measurable quantities mathematically and observe how they translate into representation.

4.2 Neural representation of tasks

To probe the relationship between task similarity and representation similarity, we trained rank-2 RNNs on six such tasks:

and generated the input similarly to what was explained in Section 2.2. Utilizing the rank-2 constraint, we are able to visualize the joint representation of all six tasks for two network realizations. The contour lines of Fig. 5A denote the velocity of the RNN dynamics ( q = | h t +1 -h t | , indicating the position of the line attractor. In both realizations, all of the tasks (colored dots) occupy the same attractor, consistent with the results of the previous section (illustrated in Fig. 4B).

4.3 Arc length parameterization of the attractor

To quantify the similarity of representations, we parameterize positions along the line attractor. For any given task i , we define its representation R i , as the ensemble of all achievable steady states. For each value v , uniformly spaced between v min and v max , we examine the corresponding steady state, denoted by R i ( v ) that belongs to R N . This results in a curve { R i ( v ) } v , a one-dimensional attractor embedded within an N-dimensional space. Because these are rank-2 networks, it is actually embedded in a 2-dimensional space, but we don't rely on it for this analysis.

Consider the entirety of points across all attractors { r j } i , which are sorted w.r.t. their distance to a given starting point r 0 . This arc length is determined as:

arc length (s)

arc length (s)

A

B

C

D

six-task training

two-task training

0.25

0.5

1

𝑞

level

curves

After this computation, the resultant arc lengths are normalized to fit within the [0 , 1] range. This normalization produces the arc length function s ( R i ( v )) which signifies the position of R i ( v ) on the unified one-dimensional curve.

In Fig. 5B we stack the 1D projection of the curves of each task, where on the left the corresponding functions appear. One can clearly see a gradual change in the functions, paralleling a gradual change in their representation.

4.4 Task distance

The functions in Fig. 5B seem to be ordered, but it is not immediately clear what is the metric underlying this ordering. A priori, there isn't one correct way to define the distance between tasks. When working with functions, the default way is to consider the l 2 distance between the corresponding functions:

Observing the ordering emerging from the networks, an alternative way is measuring the similarity between the steepness of the functions:

In practice, we approximate these integrals using Reimanns sum formula.

4.5 Representational distance

Representational distance quantifies the overlap between two distinct task representations. Leveraging the arc length function s , the distance is defined as:

𝑣 ↦ ℎ ↦ 𝑦

non-

linear

linear

(1 - 𝑣)

!

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1 - 𝑣

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ℎ

A

B

C

4.6 Function steepness shapes representations

To asses which task similarity correlates more with the representation similarity, we compute all pairwise distances between tasks - both in task space, and in representation space. The left columns of Fig. 5C,D show the relationship between either function-distance (C) or derivative distance (D) and the representation distance. The derivative distance is much more predictive, although not perfect. The existence of six simultaneous tasks could explain some of the spread in these graphs, so we also analyzed a simpler scenario. We trained full-rank networks on one pair of tasks at a time (right columns of Figure Fig. 5C,D). In this case the correlation between derivative distance is much stronger.

4.7 Symmetries in attractor representations

Why is it that steepness controls task alignment within attractors? A different perspective is to consider symmetries and invariances in task- and in representation- space [9]. Consider one specific function, y = v 4 , depicted in the center of Fig. 6A. One can apply two different symmetry operations on it to obtain different functions. We know from the results of Fig. 5C,D that only the vertical reflection will preserve steepness, and hence is expected to lead to a similar representation. To gain intuition on why this happens, consider the transformations from input to output (Fig. 6C). Input undergoes a nonlinear transformation to hidden state - both due to static nonlinearities and due to the dynamics leading to the corresponding fixed point. From the hidden state to the output, however, is a linear transformation. We ignore the different input and output directions, and the curvature of the attractor and encapsulate the entire transformation as some nonlinear function - for instance, the one in Fig. 6C. If we now replot the three functions in terms of their relation to the hidden state (Fig. 6B), we see why only transformations that respect steepness lead to similar representations.

5 Discussion

We showed that recurrent neural networks trained on multiple tasks exhibit a simplicity bias in terms of the dynamical objects formed during training. Unless prevented, networks will form the minimal number of objects needed to solve the task. We demonstrated that this bias is a consequence of recurrent dynamics and the sequential formation of attractors. First, attractors are generated one at a

time. Second, once an attractor forms, the recurrent dynamics will converge to this attractor for all tasks.

Our analysis focused on an architecture with separate input and output channels for each task, and without an explicit context channel. Furthermore, the input and output statistics were identical for all tasks. Several studies of multi-task learning used different architectures. [10] showed how modular representations can emerge from multi-task learning in feed forward networks. Their single input - many output configuration results in a joint representation of all tasks, with the nature of this representation being the object of study. Specifically, they showed that random classification tasks disentangle the representation. RNNs trained on many cognitive tasks with more complex input and output structures also show shared attractors [6, 35]. The task-set analyzed there is closer to neuroscience experiments, making it easier to compare to data. On the other hand, these tasks have a correlation between their input-output structure and their cognitive demands. Here, we opted for simpler tasks, using fundamental dynamical objects, and with identical input-output structure for all tasks. This allowed a systematic study of how dynamical objects arise during training and relate to one another.

Our choice for simple and systematic tasks also comes with several limitations. The tasks are not as close to biology as those in previous works [2, 35]. On the mahine learning side, the tasks and architectures are very far from state of the art. While we did examine GRU architectures and lazy vs rich initializations, the focus here was on the systematicity and to remain close to elementary dynamical objects.

The underlying mechanism for the simplicity bias is the sequential emergence of attractors, and the reduction of loss once enough attractors have emerged. This is reminiscent of several results showing the emergence of various network properties at different rates. Connectivity in deep linear networks is affected by leading modes of the data covariance faster than other modes [25]. RNNs trained on fixed point tasks develop rank-1 connectivity faster than higher ranks [26]. Gradient descent first learns low moments, and then high cumulants of the data [18]. In modular feed forward networks, different pathways through the network race with each other, leading to a reduced effective network [24].

The simplicity bias has several intriguing applications. First, reusing an existing representation leads to faster learning of tasks. This feature was most evident in the gated scenario, in which only one task is processed at a time. [15] highlighted a similar phenomenon as a possible normative reason for the limited capacity of cognitive control. Second, our results suggest that observing a modular representation is an indicator of some constraint on the architecture. Finally, an attractor shared between tasks is not identical to an attractor that was formed in response to a single task. For instance, if a task with constant output has an oscillatory component to its neural activity, it might suggest that the same circuit is also capable of generating such an oscillation in another context. One can imagine recording the neural activity of a subject dribbling a basketball, and being able to predict whether that subject also knows how to shoot.

Acknowledgments and Disclosure of Funding

This work was supported in part by the Israeli Science Foundation grant 1442/21 and an HFSP research grant (RGP0017/2021).

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Peer reviews:
comments: SUMMARY:
This paper studies how recurrent neural networks form shared attractors and reuse dynamics in the multitask setting. A simplicity bias is revealed, i.e., RNNs will not create new attractors unless necessary. The authors further investigate how task similarities (symmetry, gradients) can be translated to representation similarities. Finally, they discuss how their results are related to continual learning and modularity.

STRENGTHS:
This paper poses an interesting scientific question on the formation of attractors in recurrent neural networks in the multi-task setting. The simplicity bias, to the best of knowledge, is novel and investigated in details. The experiments are nicely controlled, and evidence are clear and convincing. The paper is in general well-written. Figure 1 & 2 are pleasure to read (although Figure 3-5 need improvement, see weaknesses).

WEAKNESSES:
The scope of the paper is a bit limited: it only did experiments on toy synthetic datasets. Although this is probably fine for a scientific paper when one tries to understand something deeply, I feel that the science part hasn't been pushed to the limit:

(1) How do you expect your conclusion scale to more complicated datasets (e.g., contains 1000 tasks)?

(2) Can your analysis generalize to auto-regressive models (e.g., transformer-like language models)?

I feel that the impact of this paper on engineering needs more discussion. 

(1) Is the simplicity bias a good or bad thing in practice?

(2) Once we understand the simplicity bias, what can we do to improve current RNNs?

QUESTIONS:
* Line 175, W_rec -> W_{rec}

* Figure 3, lack of axes make the plots hard to read. Figure 3D, I don't understand the difference between the 2nd and the 3rd subplot.

LIMITATIONS:
None
TITLE: Official Review
SOUNDNESS_CORRECTNESS: 3
DATE: 2023-06-30

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nWhile the relationship between task requirements and neural dynamics in Recurrent Neural Networks (RNNs) has been studied for individual tasks, the dynamics of multiple tasks working together remain largely unexplored. The study introduces a systematic framework to examine multiple tasks in RNNs, minimizing interference from input and output correlations. The findings reveal that RNNs tend to share attractors and reuse dynamics, which is referred to as the \"simplicity bias.\" It is observed that RNNs develop attractors sequentially during training, prioritizing the reuse of existing dynamics and opting for simple solutions whenever possible. Concrete examples demonstrate that new attractors primarily emerge due to task demands or architectural constraints, representing a balance between the simplicity bias and external factors. The geometry of joint representations along attractors is examined, and it is shown that task representations align based on their input strength, resulting in correlated projections. The research suggests potential applications, such as using the geometry of shared attractors to infer unknown tasks. Moreover, the simplicity bias implies that network modularity may not emerge spontaneously in RNNs without specific incentives, providing insights into the conditions necessary for network specialization.\n\nSTRENGTHS:\nThese suggestions are intended to improve the overall clarity and accessibility of the research.\n\nThe paper provides the logical progression in the field from studying single tasks to exploring multiple tasks. This shift is considered more in line with the environmental conditions animals face, which often exhibit symmetries, regularities, and structures.\n\nThe study standardized the input and output structure across all tasks and used a consistent network architecture. This helped attribute differences in representations to intrinsic task complexities rather than variations in structure or design. Individual input and output channels were assigned for each task to prevent artificial convergence in representations. This ensured that any overlap or similarity in representations reflected shared computational requirements or reused dynamics across tasks.\n\nThe simplicity bias results is very interesting and I would like to encourage the authors to further develop and refine this intriguing finding.  \n\nThe manuscript is overall clear and the relevant code was shared with the submission, permitting transparency of the results.\n\nWEAKNESSES:\nThese suggestions are intended to improve the overall clarity and accessibility of the research.\n\nThe paper lacks a clear outline of its limitations, contributions, and literature reviews, and would benefit from providing more references to position the work within the context of prior research. It is also important to include information about the computational cost associated with the proposed approach.\n\nThe limitations outlined below highlight some of the weaknesses of the paper.\n\nRegarding specific details:\n* The legend for Figure 3B is incomplete and does not provide essential information. Additionally, the functioning of the axes in plot 3B is unclear.\n\n* Figure 3C is not referenced or mentioned in the text, creating a discrepancy.\n\n* The paper does not make any reference to the supplementary material, which should be included.\n\n* Figure 5A is not properly referenced within the text, which may lead to confusion.\n\n* The definition of 5D is missing, and its context should be clarified.\n\n* Some typos and unclear sentences have been identified, which could benefit from clarification and proofreading.\n\n* The readability of Figure 3D is poor, and it would be advantageous to increase its size to improve understanding.\n\nTo enhance the quality and readability of the paper, it is crucial to address these issues and make the necessary revisions.\n\nQUESTIONS:\nDear authors, I would greatly appreciate it if you could respond to the following questions, as they would help improve my understanding of your work:\n\n* Why are the representations learned in the parallel setting not displayed in the first figure?\n\n* I am confused about how the two tasks are shown in the first setting, particularly with regards to \"\\0\". My understanding was that in this setting, the network was trained on only one task. Could you please clarify?\n\n* Line 277 suggests that the observed differences can be largely attributed to these architectures. I am unsure about the meaning of this statement. Could you elaborate further?\n\n* Based on the findings, what conclusions can be drawn about neuroscience? How does this work contribute to our understanding of neural processes?\n\n* Could you provide information about the color of the triangle in the figures?\n\nAdditionally, I find the results regarding the simplicity bias very interesting. I am curious to know if there could be a connection between this bias and the observed low rank bias in feedforward networks, where eigenvalues are learned sequentially when initialised with small random weights.\n\nLastly, I would like to know if you investigated the impact of different initializations in your experiments.\n\nAddressing these concerns would greatly influence my evaluation.\n\nLIMITATIONS:\nTo enhance the paper, it would be valuable to provide a clear outline of the limitations of the work. Some potential limitations to consider include:\n\n*  Lack of biological validation: While the paper proposes mechanisms and patterns observed in RNNs, it may lack direct biological validation. It would be beneficial to explore experimental evidence or connect the findings to known neurophysiological phenomena to strengthen the biological plausibility of the conclusions.\n\n* The other parameters of the network that could be looked at, I understand that for visualisation pursues and summarising  you look at subset of the information that could be looked at in this network. \n\n* Scope of external factors: The paper acknowledges the influence of external factors on the emergence and dynamics of multiple tasks but may not extensively explore the full range of potential external factors. Further investigations into the interplay between these factors and the simplicity bias in RNNs could provide a more comprehensive understanding. For example how initialisation changes the observed dynamics.\n\nClearly outlining these limitations would contribute to the transparency and credibility of the paper, encouraging further research and discussion in the field.", "TITLE": "Official Review", "RECOMMENDATION": 6, "REVIEWER_CONFIDENCE": 4, "SOUNDNESS_CORRECTNESS": 3, "DATE": "2023-07-04"}

comments: SUMMARY:
This paper uses a multi-task RNN setup and tries to make sense of what computations get shared, and how they get shared.

STRENGTHS:
A novel task set-up is used with gated, orthogonal, and parallel settings. The overall problem trying to be tackled is interesting.

WEAKNESSES:
1)	This paper is very confusingly presented. Section 2.2. is confusing. All the figures are extremely hard to parse and need much better annotation/labelling. I couldn’t make heads or tails what figure 3 was trying to say. Figure 4 suddenly has some triangles, pentagons, and diamonds. And they are different colours. Not explained why. 

2)	A main claim is that an understanding of a ‘simplicity bias’ is provided, but it’s not clear what understanding is provided beyond Yang et al 2017, or Driscoll et al 2022. Overall, it’s not clear how this paper furthers our understanding beyond those papers.

3)	Only one network structure was analysed, while Yang, Driscoll, and others, show interesting phenomena under different architectural constraints. 

4)	No reference is given to Saxe et al., 2022 which shows that shared representations are favoured as they are the ones which ‘see more data’ and so are learned fastest, thus explaining much of the phenomena from Yang, Driscoll, and your paper.

5)	(Reference [5] and [6] are the same paper.)

QUESTIONS:
See Weaknesses

LIMITATIONS:
Not clear that this clarifies anything over and above Yang or Driscoll. The paper is really hard to make sense of. Not because it is technically difficult, but because of its presentation. In particular, the figures are so under labelled that they may as well not be there.
TITLE: Official Review
SOUNDNESS_CORRECTNESS: 2
DATE: 2023-07-05

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThe paper proposes \"simplicity bias\" in RNNs when learning multiple tasks simultaneously. In particular, the paper focuses on investigating the formation of attractors in the dynamic system of RNN when tasks with variant difficulties are handled jointly. The RNN develop attractors sequentially, and simple attractors will emerge first, and new attractors may organize with task demands or architecture constrains. The authors conducted extensive, carefully-designed numerical experiments to demonstrate their ideas. The findings shed light on understanding the dynamics of artificial RNNs and also cortical functions in the brain.\n\n[post-rebuttal]\nI appreciate the authors' reply. I recommend an acceptance.\n\nSTRENGTHS:\n- The experiments are well-designed \n- Analysis is conducted from various perspective\n- The results are visualized and presented in an intriguing way\n- Too my knowledge, the insights about simplicity bias in RNNs is novel (while there are a few works about other kinds of models, but the not from a dynamical system perspective).\n\nWEAKNESSES:\nOverall, I think the paper did a good job on demonstrate the core concept of simplicity bias in RNNs. If there is something missing, I would say that it is unclear to what extend the conclusions apply. The tasks being tested are simple enough to understand, which contributes to more intuitive understanding for readers. However, the real-world tasks are usually much more complicated and it is hard to define or compare the diffulties of tasks.  One particular design about model architecture is that the input and output channels for individual tasks are distinguished, which may not be the case for the brain or many ANN models. In sum, there remians much to do to further validate and understand the conclusions made in this paper.\n\nQUESTIONS:\n- The abstract reads a bit too long and redundant, might it would be more concise to limit the absract to 200 words.\n- Reference 5 repeats with 6\n- Although I think it is reasonable to first consider the basic Elman-type RNN (eq. 1), I am also curious about whether other kinds of RNN such as LSTM and GRU features with similar simplicity bias, or there is something different.\n- Some figures (e.g., Fig.2) is too cotmpact which makes it hard to read when printed on paper.\n\nLIMITATIONS:\nThis work is foundamental and rather like a proof of concept. Future work should try to clarify how much the conclusions can extend to broader model architectures and task properties.", "TITLE": "Official Review", "RECOMMENDATION": 7, "REVIEWER_CONFIDENCE": 3, "SOUNDNESS_CORRECTNESS": 4, "DATE": "2023-07-08"}