Geometry of naturalistic object representations in recurrent neural network models of working memory
Authors: Xiaoxuan Lei
Takuya Ito
Pouya Bashivan
Venue: NeurIPS 2024 poster (2024)
Keywords: Working memory
geometry
recurrent neural networks
Primary area: neuroscience_and_cognitive_science
TL;DR: We found that multi-task RNN models of working memory maintain both task-relevant and irrelevant information in orthogonalized subspaces and use rotational dynamics to track past information amidst new inputs.

Abstract: Working memory is a central cognitive ability crucial for intelligent decision-making. Recent experimental and computational work studying working memory has primarily used categorical (i.e., one-hot) inputs, rather than ecologically-relevant, multidimensional naturalistic ones. Moreover, studies have primarily investigated working memory during single or few number of cognitive tasks. As a result, an understanding of how naturalistic object information is maintained in working memory in neural networks is still lacking. To bridge this gap, we developed sensory-cognitive models, comprising of a convolutional neural network (CNN) coupled with a recurrent neural network (RNN), and trained them on nine distinct N-back tasks using naturalistic stimuli. By examining the RNN’s latent space, we found that: 1) Multi-task RNNs represent both task-relevant and irrelevant information simultaneously while performing tasks; 2) While the latent subspaces used to maintain specific object properties in vanilla RNNs are largely shared across tasks, they are highly task-specific in gated RNNs such as GRU and LSTM; 3) Surprisingly, RNNs embed objects in new representational spaces in which individual object features are less orthogonalized relative to the perceptual space; 4) Interestingly, the transformation of WM encodings (i.e., embedding of visual inputs in the RNN latent space) into memory was shared across stimuli, yet the transformations governing the retention of a memory in the face of incoming distractor stimuli were distinct across time. Our findings indicate that goal-driven RNNs employ chronological memory subspaces to track information over short time spans, enabling testable predictions with neural data.

Geometry of naturalistic object representations in recurrent neural network models of working memory
Xiaoxuan Lei
Takuya Ito
Pouya Bashivan
Department of Physiology, McGill University, Montreal, Canada 2 Mila, Université de Montréal, Montreal, Canada
3 IBM Research, Yorktown Heights, NY, USA
Abstract
Working memory is a central cognitive ability crucial for intelligent decision- making. Recent experimental and computational work studying working mem- ory has primarily used categorical (i.e., one-hot) inputs, rather than ecologically- relevant, multidimensional naturalistic ones. Moreover, studies have primarily investigated working memory during single or few number of cognitive tasks. As result, an understanding of how naturalistic object information is maintained in working memory in neural networks is still lacking. To bridge this gap, we developed sensory-cognitive models, comprising of convolutional neural net- work (CNN) coupled with recurrent neural network (RNN), and trained them on nine distinct N-back tasks using naturalistic stimuli. By examining the RNN's s latent space, we found that: 1) Multi-task RNNs represent both task-relevant and irrelevant information simultaneously while performing tasks; 2) While the latent subspaces used to maintain specific object properties in vanilla RNNs are largely shared across tasks, they are highly task-specific in gated RNNs such as GRU and LSTM; 3) Surprisingly, RNNs embed objects in new representational spaces in which individual object features are less orthogonalized relative to the perceptual space; 4) Interestingly, the transformation of WM encodings (i.e., embedding of visual inputs in the RNN latent space) into memory was shared across stimuli, yet the transformations governing the retention of memory in the face of incoming distractor stimuli were distinct across time. Our findings indicate that goal-drives RNNs employ chronological memory subspaces track information over short time spans, enabling testable predictions with neural data.
Introduction
Working memory (WM) the ability to store and manipulate information over short periods is a central cognitive capability that enables a wide spectrum of behaviors [Baddeley] 1992]. Over the past few decades, various experimental, computational, and theoretical techniques have been adopted to study WM from both cognitive and neural perspectives. However, several fundamental issues remain unresolved, including the key question of how high-dimensional sensory information is encoded, maintained, and modulated according to specific task demands.
A significant body of work has been dedicated to modelling the computations underlying WM. These include many classic models from cognitive science [Meyer and Kieras, 1997a Ritter al. 2019
38th Conference on Neural Information Processing Systems (NcurIPS 2024).

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Baddeley et al. 2021], neuroscience Miller et al., 1996. Wang
1999 Emrich et al. 2013]. and
more recently deep learning (Yang et al. 2019 Ehrlic and Murray 2022] Recent approaches have focused on using artificial neural networks, such as recurrent neural networks (RNNs), to understand and model WM due to their ability to learn the complex cognitive tasks that are commonly used to study WM in humans. However, prior studies were limited in three aspects. First, most works used abstract categorical inputs, such as color and location of moving dots that are represented as binary (or one-hot vector) inputs [Panichello and Buschman 202 Yang et al. 2019 Piwek et al. 2023 While training models with such categorical inputs is easier in practice, the resulting models offer limited insights into how real world, naturalistic stimuli (which are embedded in high-dimensional spaces) are processed. Second, most prior work has considered single or a few cognitive tasks [Xie et al. 2022 Mante et al.] 2013 Piwek et al. 2023]. limiting the generality of these models in explaining the neural computations underlying working memory. Lastly, while some prior work has explored how object features are encoded into population activity (Xie al. 2022]. it remains unclear how information in working memory is sustained across time to support concurrent encoding, retention, and retrieval during a dynamic task and how these processes might align with classic cognitive theories [Luck and Vogei
1997 Alvarez and Cavanagh 2004 Franconeri et al.) 2013].
To address these limitations, we investigated how task-optimized RNNs manipulate the multidimen- sional properties of naturalistic visual inputs during different stages of WM (Figure [d]. Specifically, examined: 1) How do task-opti RNNs select task-relevan properties of naturalistic objects during WM? 2) What computational strategies do RNNs employ to dynamically maintain object properties in the face of incoming (distractor) information? To address these questions, trained multi-takk models on a collection of N-back tasks using naturalistic stimuli, and analyzed the RNNs' latent space during concurrent encoding, retention, and retrieval of information. We specifically chose the N-back task, given that it requires the dynamic encoding, retention, and retrieval of information in the face of incoming distractor information. This is in contrast prior studies, which primarily studied WM tasks such as saayeeddmmach-t--s-aae stable fixation periods. The nature of the N-back task makes it an excellent testbed evaluate how naturalistic object features are maintained in dynamic environment that requires on-the on-the-fly WM updates and -maiin..............
tasks, which focus on WM maintenance during
Our main contributions are as follows:
We trained different classes of gated and gateless RNN models on a suite of WM tasks and developed decoder- based analyses to study the geometry of naturalistic object representations during different stages of WM.
We found that task-relevant and -irrelevant object properties are simultaneously encoded in multi-task RNN models, while only gateless RNNs produced shared and reusable represen- tations across tasks.
We found that object features are less orthogonalized in the RNNs' hidden dynamics compared to perceptual representations.
We found that RNNs solve the N-back task by using chronological memory subspaces to separate object representations presented across time, This finding supports resource-based models of working memory [Alvarez and Cavanagh, 2004 Franconeri et al. 2013 and challenges the classic slot-based model [Luck and Vogel 1997
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Related Works
Models of working memory. Originally rooted in cognitive science, the notion of WM was first formally defined and popularized by Baddeley [1922 who proposed cognitive system consisting of modality-specifff buffers and a shared executive module to control the information flow in and out of the memory buffers. This initial work, along with most early models, portrayed WM as a memory system with three key features: flexibility of information representation, limited capacity, and limited temporal span.
Subsequent models based on this perspective were largely akin to the architecture of the Von- Neumann computers, comprising of input and output channels, volatile memory components, and central processing system that continuously executed pre-specified computer code according to task goals Cowan 1988 Meyer and Kieras 1997b] Anderson, 2013). However, experimental work in

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neuroscience has showed that the underlying biological circuitry of WM consists of wide network of brain areas with diverse roles that do not adhere the clean-cut modules specified in those previous models [Sreenivasan and D Esposito 2019].
Compte al. 2000 was one of the first studies that showed RNNs with closely matched connection parameters to those measured from the brain can reliably store information in the presence of distractors. Later work showed that these networks are not only capable of performing many classic WM tasks but also replicate neural signatures that were previously observed in animals' brains during
these tasks, indicating that similar neural computations may be used by both systems (O'Reilly and
Frank] 2006, |Manee et al. [2013] Xie et al. [203] Finkelstein et al. 2021 Masse et al. 2019]. More
recent work proposed various neural network architectures that combine linear attention mechanisms
with slot-based memory modules and feedback mechanisms as models of working memory (Hwang
et al.
2024
Loynd et al. 2020).
Neural network models in neuroscience. Neural network models have been increasingly used in computational neuroscience to model neural computations during different behaviors. These models are valuable tools that incorporate ideas from a diverse range of cognitive architectures, while also making testable behavioral or neural predictions. Various classes of neural network models have now been used to simulate neural activity in sensory brain regions (Schrimpf et al.
2018 Kell et al.)
2018, Khaligh-Razavi and Kriegeskorte, [2014] Yamins et al. 2014 Bashivan et al. 2019 language
comprehension [Hasoon et al. [020] Schrimpf et al. [022]]. and decision making [Mante et al. 2013
Yang et al. 2019]. Furthermore, others have used RNNs to study the dynamical motifs that underlic various behavioral signatures such as memorization, integration and selection of information, and attention. For example, Mante et al. [2013) used goal-directed RNNs to simulate the dynamics of neural populations in the macaque prefrontal cortex during a context-dependent decision making task and found specific dynamical mechanisms for the selection and integration of task-relevant inputs. Yang et al. [219)] identified specialized functional clusters, mixed selectivity, and compositional representation in multi-task RNNs. The shared dynamic motifs across tasks were further extended and described mathematically in Driscoll et al. [022]
3 Methods
Tasks. We considered N-back tasks (N E (1,2,3) based on one of three distinct object properties (i.e. feature; F' E (Location, Idnttity Category) (denoted as L, 1, C)), resulting total of N-back task variants (Figure Naturalistic stimuli were generated using 3D object models from the ShapeNet dataset (rendered examples in Figure A [Chang al. 2015), comprising 4 object categories. each with 2 unique identities rendered from various view angles, and presented at 1 of 4 possible locations. We consider two validation approaches: validating on novel view angles, and validating on novel identities. The training and validation novel angle datasets differed in their viewing angles, necessitating view-invariant processing by the model. In contrast, the validation novel identity includes unseen identity sampled from categories same as the training dataset.
Model Architecture. We considered a two-stage model that delineates perceptual and cognitive processes (Figure Te). At the first stage, the model processes sequences of images, utilizing an Ima- geNet [Deng et al. 2009) pre-trained ResNet50 (He et al. 2016) model to derive visual embeddings from each image input. All object features including category, identity, and location were highly decodable from these activations (category: 100.00%, identity: 99.57% location: 100.00%; 2-fold cross-validation.. A point-wise convolutional layer reduces the dimensionality of the 2048-chanma feature map from ResNet's penultimate layer (layer 4.2 ReLU) to match the RNN's hidden size. Next, the vectorized embeddings are concatenated with a task index vector and processed by a fully connected layer (matching the RNN's latent size) with layer normalization [Ba 2016), serving as input to the RNN. The RNN's 's output is then fed through another fully connected layer and projected to one of three possible responses: match, non non-match, or action.
or multiple tasks (multi-feature or multi-task or both). After training, we analyzed activations from the penultimate layer of ResNet50 (i.e. the perceptual space), as well as the RNN activations during the stimulus presentation and subsequent timesteps (i.e. encoding and memory space respectively, denoted as E and M as shown
Each network is trained to perform one Säingle-askk-single---
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Figure 1: Tasks and Models: a) Example of a 2-back category task. Each object's category is two frames prior. b) The suite of n-back tasks
compared with the category of the object considered in the study. e) The sensory-cognitive model architecture. d) A schematic showing the latent subspaces for category, identity, and locations in the perceptual, encoding, and memory subspaces. Left: Stimuli are encoded in high dimensional latent space of the vision model (CNN). Each object property encoded high dimensional latent subspace of this model; Right: RNN model represents each object property in its encoding latent subspace and retains some or all of the properties within its memory subspaces later time points.
in Figure 44). We considered three recurrent architectures for the second stage of the model including the vanilla RNN, GRU [Chung et al.) 2014), and LSTM [Hochreiter and Schmidhuber, 1997
Model Training training diet:
Each model architecture was trained within three scenarios that differed in their
Dangle-Task--Sinle--Feaaae (STSF): trained on single n-back task based on single
object feature (e.g. -back location).
Single-Tasie Baaple-Tassk-MultFFFFeaaaa (STMF): trained on single choice of N for all three feature variations (e.g. I-back L, or C' or T).
(MTMF): encompassing all choices of N (1,2,3) and features
I.)
Model parameters were trained using Adam [Loshchilov and Hutter 2017 optimizer with initial learning rate of 3e and Multi-step learning rate decay with 7 0.T for every 100 iterations. Batch size 256 and all trials were generated on-the-fly using the iWISDM package [Lei et al.

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2024]. Hidden layers of RNN modules are initialized with Kaiming Initialization He et al. 2015].
For details of decoding analysis and Procrustes analysis, please refer to Appendix
4 Experiments
All models reached > 95% accuracy on train and > 90% on validation set with novel object angles. Generalization to novel object instances was substantially weaker (Figure Alp, p. c). Model performance increased with the number of model parameters, and with identical parameter count, vanilla RNNs aceuracy was lower compared to their gated counterparts (Figure The ensuing analyses utilized data collected from models with 512 units for vanilla RNNs, and 256 units for GRUs and LSSMs, to ensure comparable model performance as well as comparable model parameters.
4.1 Encoding of task-relevant and -irrelevant object properties in task-optimized RNNs
We first examined how RNN modules represent various object properties such as location, identity and category in their latent space. In particular, we investigated the following two questions:
1) Do recurrent networks preserve object properties that are not necessary for the task? In order to perform a task, recurrent networks must maintain information about the task-relevant object properties. However, maintaining information about the task-irrelevant factors is not necessary from the perspective of the task objective. Therefore, RNNs may either selectively maintain task- relevant information maintain full object representations, recalling task-relevant information when prompted.
We trained decoders (i.e. classifiers) to predict each object property from the RNN hidden state activity from the first timestep of each trial (e.g. F L; vs. F Li decoders, total 4 location decoders). Cross-validated validated decoding accuracies are shown in Figure 2p for STSF, STMF, and MTMF GRU models. Unsurprisingly, the task-relevant object properties are fully retrievable all models. Further tests revealed a causal relationship between the subspaces encoding task-relevant information and the network's generated response (Fig. [A7] see section [T for details.) However, while task- irrelevant object features are not generally well-preserved in STSF models (Figure 2b, left), they are much better preserved in STMF and MTMF models (i.c. decoding accuracy > 85%; Figure 2p middle and right). This finding was consistent across all three RNN architectures (Figure A2a) and across time points (Fig. A5 These results suggested that all RNNs maintained full representation of objects in their latent spaces regardless of which object properties were required for performing the task.
2) Are object properties encoded within a subspace that is shared across different tasks or distinct ones within each task? Having observed that both task-relevant and -irrelevant information are retained by multi-feature RNNs, we next asked whether RNN encoding of object properties is task-dependent or -independent. To probe this, trained decoders predict object properties from the RNNs' activations during one task, and tested the decoder on RNN activations when performing another task (i.e., cross-task decoding). We quantified the generalization performance of MTMF models across all three architectures (Figure 2h.. We found that gated RNNs (GRU and LSTM, Figure A2p) utilized highly task-specific subspaces for encoding object properties, while vanilla RNN encoded object properties within a subspace that was shared across all task- variatiiss (Figure 2c). This suggests that gated RNNs tend learn task-specific representations that do not generalize across tasks, potentially impacting their ability to generalize to new tasks.
4.2 Representational orthogonalization in task-optimized RNNs.
To improve their performance, RNN weights might form structured and separable representations for each task-relevant feature. For this be true, the RNN latent space may orthogonalize feature representations beyond their perceptual representation (see schematics in Figure To quantify orthogonalization, we calculated the angles between all pairs of decision hyperplanes using cosine similarity (bootstrapped 10 times). We then summarized these angles into a single orthogonality mea- sure by computing the Frobenius norm of the difference between this matrix and the identity matrix (which represents complete orthogonalization).. We defined this measure as the orthogonalization
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Figure 2: Representation of task-releannt-irreeeaan object properties: (a) Decoding generaliza-
tion accuracy for each object property is displayed across tasks and operating modes for vanilla RNN and GRU. Rows and columns of 3 matrices correspond to the N --bcck task on which the decoders fitted and tested respectively. Matrix columns correspond to particular decoders denoted by D (k E {1, 2, 3), F {L, (.)) (indicating which task and decoding feature the decoder was fitted on), while matrix rows correspond to the object property of the task the decoder (b) Validation accuracy of decoders trained on RNN latent space activations from the first time step of each trial predict different object properties. Each column represents the object property the decoder was trained on, while each row corresponds to a model. c) Quantification of the validation accuracy (within the same task, indicated in purple) and generalization accuracy (across tasks with different resk-relevant features, indicated in yellow) across all model architectures.
tested on.
index (0):
Wi 1 abs (cos(W,, W2))
O E ((rii(()))
where W; is the normal vector of the decision hyperplane that separates points assigned with feature value from the rest, cos(W, W,) the cosine similarity between the two normal vectors. We take the absolute value since the relative direction does not matter. triu(.) is the upper triangle operator.
We evaluated the degree of representation orthogonalization within the perceptual and encoding spaces. Contrary to our hypothesis, we observed that relative to the perceptual space, the RNN latent space slightly de-orthogonalize the axes along which distinct object features are represented (Figure 33)). Similar results were found when PCA was used to equalize dimensionality between the two spaces (Figure A3 Although more orthogonalized representations generally facilitate structured and enhanced separation of task-relevant features, our behavioral results still indicate optimal performance. One possible interpretation these results that the reduced orthogonalization in the RNN latent space produces more efficient (lower dimensional) representation. (In contrast, increased orthgonalization in the representational space would increase the overall dimensionality of the object representations.) In practice, only a subset of dimensions need to contain orthogonalized representations for successful task performance. turn, this would make easier to train the read out weights of the RNN to produce the correct task responses.

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Figure 3: Orthogonalization: a) A schematic of two hypothetical object spaces in 3D. ri, represents the angle formed by the decision hyperplanes that separate feature value and from each other. Top: non-orthogonalized representation; Bottom: orthogonalized representation. b) Upper panel: Normalized orthogonalization index, for both perceptual and encoding spaces respectively (denoted as O(Perceptual) and O EEcoding)). In most models, less orthogonalized representation of feature values emerges in the RNN encoding space compared to the perceptual space (CNN output). Lower panel: Statistical comparison of the relative orthogonalization levels between the perceptual and encoding spaces. A two-sample t-test was performed to assess differences between the distributions of orthogonalization indices in the perceptual space and the encoding space.
4.3 Neural mechanisms concurrent encoding, maintenance, and retrieval in RNN models of WM
Having examined the encoding of objects in the RNN's latent space, we next investigated how RNN dynamics enable simultaneous encoding. maintenance, and retrieval of information. Performing our N-back task suite required the RNN to keep track of prior objects' properties while simultaneously encoding incoming stimuli with minimal interference.
We reasoned that the RNN may implement one of three possible mechanisms to perform the N-back working memory task suite (Figure 4b):
HI: Slot-based memory subspaces [Luck and Vogel, 1997]. Where the RNN latent space is divided into separate subspaces that are indexed in time within the sequence. Each object is encoded into its corresponding subspace (i.e. slot) and is maintained there until retrieved. By definition, the subspace assigned to each memory slot distinct and "sustained" in time.
H2: Relative chronological memory subspaces. Where the RNN latent space is divided into separate subspaces that each maintains object information according to their age (i.c. how long ago they were encoded). Such mechanism will require dynamic process for updating the content of each memory space at each time step during the task.
H3: Stimulus-specifiic relative chronological memory subspaces. This is similar to the relative chronological memory hypothesis but with independent subspaces assigned to each object. Each observation in the sequence is thus encoded into distinct subspace and encoding of each stimulus is in turn distinctly transformed into associated memory representations.
To identify the hypothesis that best matches the computations performed by the RNN, we analyzed how the RNN latent subspace encodes and transforms each object property (Fi(sTT) across time into memory (M())T) (Fig. I.).
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We first tested whether object information is maintained in a temporally stable subspace (i.e. sustained working memory representation) which aligns with H1 prediction (i.e. E(smiiT=1) & M(s E (2, 4...]: Fig. Fp). For this, we trained decoders to predict the value of each object property using the RNN unit activity during the encoding phase (i.e. Encoding Space) and evaluated its gencralization performance in consecutive steps (i.c. Memory Spaces). We reasoned that if the object information is encoded in subspace that is stable across time (as in a memory slot), the decoders' generalization performance should be high and comparable to its performance during the encoding phase. Contrary to H1's 's prediction, found that the decoders do not generalize well (Figure Ap), suggesting that the object information is not stably encoded in a temporally
RNN latent space.
However, we observed that in STMF and MTMF models, the cross-time decoding accuracy is consistently higher during recall (Figure 4p and c). Interestingly, this suggests that the object representation is partially realigned with its original encoding representation when it is retrieved (Fig. AD).
Next, we examined whether the object encoding space is shared between incoming stimuli, irre-
spective of the specific object or time (H2 vs. H3; i.c E(s=i,T==) - thus fitted classifiers to decode each object property using the hidden activity from the encoding space of each stimulus within the sequence (i.e. decoding = i from E(s=),==)) testing it on the stimuli appearing other time steps (i.e. decoding S = j from E(S=j.T=))). We performed this analysis for all object properties and for all models and all tasks. The validation and general- ization accuracies were almost identical (Figure 4it), suggesting stable encoding representation (E(s-i,,T (,)))) = T( consistent with H2. In other words, each object in the sequence was encoded according to its chronological age (i.e., when was placed into memory), regardless of the object property.
E(s=g.==)) for + j). We
Having examined how the RNN latent space allows concurrent encoding, retention, and retrieval of information, we next investigated what transformations underlie the conversion of information from one subspace to another. Specifically, we inquired whether the transformation of feature subspaces across timesteps is stable with respect to the same encoded stimulus (i.e. Ti = Ti+ see Fig. 4 As detailed in Appendix [ adopted the orthogonal Procrustes analysis obtain rotation matrix Rs.r to characterize the transformation. The orthogonal Procrustes analysis is a statistical shape analysis which discovers simple rigid transformations that superimpose set of vectors/points onto another. We used this analysis to inquire whether each set of object feature decoders can be rotated to align with the set of decoders for the same object properties, but across time. Thus, the above test can be reformulated as
R(S=(T=))) _ ((S=AT==++1)
Additionally, we also tested if the transformation is consistent across stimuli within the sequence:
R(S=iT==)) _ R(S=
We first checked whether the feature representation subspace transformation across timesteps are structured (Figure left). In other words, we evaluated how well the Procrustes analysis can capture the rotation transformation of feature representation subspaces. The reconstructed decision hyperplanes resulting from rotating the original decoders by the Procrustes transformation matrix were highly accurate (Fig. rigght, indicating that rotation was able to capture the transformation performed by the RNN across time (also see Figure A4).
Next, we tested Eqs. 2 and 3 by swapping the rotation matrix at R(s=i,T=)) with R(s=;T==++)) or R(s=i+**T=+++) respectively, and plotted the accuracy of reconstructed decision hyperplane for MTMF models in Figure Ag.. We reasoned that if these rotation operations were shared across time steps and stimuli, swapping them would not significantly affect the decoding accuracy. Across all model architectures and tasks, we found that replacing R(S consistently yields good accuracy, whereas replacing R(s=(T==++1) does not. Similar results were obtained models trained on larger N (N=1-4), stimuli with naturalistic texture backgrounds, and more number of categories and identities (Fig. (A).. These results suggest that while the transformation remains consistent across different stimuli, it not stable over time.
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Figure 4: RNN dynamics during n-back task schematic of the 3-back task for a trial of 6 inputs. Model encodes each observed object in its respective Encoding Space denoted as E(i,) (diagonal frames with yellow borders). For each stimulus, various object properties their respective Memory Space denoted as MS. On executive steps (frames with red borders) model produces response according to the memory of the stimulus and the newly observed stimulus that time. b) Decoding accuracy for predicting object identity at different time steps where the decoder is fit data from the encoding step of MTMF GRU during 1/2/3-back identity tasks. Red box indicates the executive steps. c) For each model type, we measured the generalization accuracy on executive (left boxplot) and non-executive (right boxplot) steps. d) Decoding accuracy for decoders trained and tested on the same F2, space (validation) or tested on other Ey...j * i spaces. e) Left: Schematic of the two latent space transformations.
retained over time in
Schematic of the three hypotheses. Structured transformation preserves the topology (i.e. the transformation can be captured solely by common scaling factor and rotation matrix). Unstructured transformation: does not preserve the topology. Right: Decoding accuracy for fitted decoders (solid line) and reconstructed decoders (dotted line) using the rotation matrix Ri..yfrom the Procrustes analysis. The small accuracy gap between fitted and reconstructed decoders suggests a structured transformation. g) Decoding accuracy of the reconstructed decoder when the original rotation matrix substituted with another (indicated by the x-axis labels). Rows and columns corresponds to object properties and MTMF network architectures respectively.

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5 Discussion and Conclusions
We investigated how naturalistic objects represented in recurrett models during dynamic and difficult WM task. In contrast to most prior work that build computational models of WM using abstract categorical stimuli, which typically study WM during a stable fixation/delay period, we trained range of sensory-cognitive models to perform N-back tasks using naturalistic stimuli. We found that models trained on multiple features and multiple tasks retained object information regardless of their task-relevande While prior studies investigating WM tasks using RNNs have identified shared representations and dynamical motifs across related tasks (Yan et al. 2019 Driscoll et al. 2022]. we found that representations were largely task-specific in gated RNNs such as GRUs and MSTMss The representational differences between gated and gateless RNNs provides an opportunity for future work to adjudicate between these recurrent architectures and their cognitive significance (i.e., gated vs. gateless) with empirical neural data.
While increased orthogonalization could in theory enable better task performance through the formation of increased separation of object representations in the recurrent module, we found the opposite. Despite reduced orthogonalization of task-relevant features in the RNN, this did not appear influence task generalization behavior. One possible interpretation of this is that the reduced orthogonalization in the RNN latent space produces more efficient (lower dimensional) representation. In practice, only a subset of latent need to contain orthogonalized task-relevant representations representations for successful task performance. Having fewer latent dimensions that orthogonalize task-relevant representations could make it easier to decode/read out the correct response information from this latent subspace. Clarifying this distinction further will be important for future work.
Lastly, we found that RNNs solve the N-back task by leveraging chronological memory subspaces to maintain information about different objects distinct. This finding is consistent with the "resource" model of working memory [Alvarez and Cavanagh [004]] FFanconeri et al., 2013). which proposes that memory resources are flexibly distributed across all items. This contrast to the "slot-based" model [Luck and Vogel 1997], which suggests that memory is composed of discrete, independent slots for each item. Furthermore, the observed dynamics align with the conceptual framework in Whittington et al. (2023), where different memory slots can transfer information between each other during working memory. Our experiments reveal that similar slot-like subspaces naturally emerge in task-optimized RNNs, with information transfer between them guided by RNN transformations based on task demands. However, as these subspaces are carved out of a shared neural space defined by the RNN units and dependent on chronology. they are not necessarily non-overlapping (unlike that assumed in Whittington et al. 2023)). ). Such possible overlaps may account for previous findings on the influence of memory load on working memory performance [Ma et al. 2014). Altogether, these
results provide testable predictions to evaluate the neural basis of WM in humans in future work.
Limitations
Our study has several limitations:
1. Task-Specific Findings: Our results are specific to the N-back task structure, and it remains uncertain whether similar computational strategies would emerge in other working memory tasks.
2. Analysis for Novel Objects: While we observed reduced performance with novel objects, we did not analyze the representational geometry associated with these stimuli or investigate the reasons for diminished performance. Our use of naturalistic stimuli was intended to avoid imposing the representational geometry typical of abstract inputs, as seen previous studies (Pwee et al. 2023), Yang et al. [2019)).
3. Architectural Constraints: Our findings are restricted to commonly used RNN architec- tures, such vanilla RNNs and LSTMs. Therefore, we cannot make definitive claims about how different neural network architectures might affect representational geometry. Further research could explore whether other architectures yield similar or distinct patterns.
4. Impact of Network Scaling: We did not explore how scaling the network size might influence the results. is possible that increasing the network size could alter the strategies employed by models to perform dynamic WM tasks.
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Acknowledgments
This research was supported by the Healthy-Braing Brains-Healthy-Live startup supplement grant, the NSERC Discovery grant RGP05-2021-03035, and CIHR Project Grant PJT-191957. P.B. was supported by FRQ-S Research Scholars Junior grant 310924, and the William Dawson Scholar award. All analyses were executed using resourees provided by the Digital Research Alliance of Canada (Compute Canada) and funding from Canada Foundation for Innovation project number 42730.
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Appendix
10
Plceil
RIM
2.
b
Accuracy
0.5
26-
Duta bot
Tuin
Veiddttn
dlundtty
L.beck
Sancc Soretion
catopoory
Validttion new chjects
Model/Model Operating Modes
Number trainsble (log
Sigge-ask Single feature
Single-task Muttifeature
MuRi-aak Muliifetture
Figure A1: Stimuli and Model performance rendered stimuli examples from Shapenet. b) task variations of N-back constructed from different choices of task-relevant features (L, C*) and N (1,2,3) index. c) Model performance on train, validation novel angle and validation novel object datasets. Three architectures are tested with various number of hidden size, with the number of trainable parameters indicated on x-axis.
.1 Methods
Model training We used cross-entropy loss for training, and the identity of the task was encoded in 6-digit binary format: the first 3 digits represented the one-hot encoding of the feature (e.g.. stimulus location, category, or identity), and the second 3 digits represented the one-hot encoding of the n-back choice of n. For the single-task single-featurs model, used the same task identity vector as in the multi-task models. The multi-task multi-feature model typically takes around 4-8k iterations with batch size of 256, and we cut off training 14k iterations. The sequence length is fixed at 6 for both the training and validation sets.
Causal test To establish the causal relevance between the decoder-defined subspace and the network's behavioral performance, we perturbed the network's representations by shifting them along the direction of the normal vector given decision hyperplane. By passing the resulting hidden states through consecutive timesteps, we computed the probabilities the three possible actions. We subsampled matched trials and perturbed the hidden states various magnitudes in the direction of the corresponding decision hyperplane. As shown in Figure A7 the probability of obtaining a match action dropped significantly as the hidden states traversed the hyperplane, while the probability of no action increased. The probability of non-match action remained largely unaffected, except for an increase in variance the hidden states crossed the boundary. These results support the causal relationship, indicating that the subspace defined by the decoding analysis is actively utilized by the network in solving the task.
Decoding analyses We consider the latent space of the RNN as a D-dimensional space R where D is the number of units in the RNN model. We used support vector classifiers (SVC) to perform all the decoding analysis. The decoder should be able to classify one feature value from the rest, for example, location bottom left to all the other locations. Each decoder was fitted with activations from either perceptual, encoding, or memory spaces and labels from one of the three possible features (I,, T, C) of the stimuli from current previous time steps]] We adopted 10-fold cross-validation as well as grid search to find the best regularization values from (0.001, 0.01, 1, 103. All the classifiers reached cross- cross-validee validated accuracy of > 85%.
Each classifier is then described by its normal vector w to its decision hyperplane dannd a bias term b.
We used Seikit-Learn's implementation of SVC for fitting the classifier parameters.
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a
Multi-task Multi-Fcature
Model Operating Mode
RNN
LSTM hidden
LSTM cell
Location
Identity
Category
Location
Identity
Category
Location
Identity
Category
Decoding Feature
b
LSTM hidden states
LSTM cell states
Model Operating Mode (Test)
Model Operating Mode (Test)
1-bakk
2-back
3-back
1-back
2-back
3-back
00.
D., D2, D
D, Dr P
D, D, Dic
D, D. Dig
D D Dic
D D
00.
Da, Du Dac
Da, Dy Dic
Da, Dy
Da, Da Dac
Dy, Dar Dac
Dyr Dy Dzc
-0.2
Da Day Dac
D2 Du Dac
Da, Da, Dgo
D.u Day Dac
Dr, Dau Dac
D5, D.u Dag
0.0
Figure A2: Object representation efficiency: a) Similar Figure 2p, right panel, but for RNN and LSTM trained on MFMT. b) Similar to Figure 2a but for LSTM hidden and cell states (model trained on MFMT)
a
Location
Identity
Category
b
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Identity
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O(Percepiual)
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Sceek
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00
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OxPoroppual)
OhEnending)
0 05
O(Percpuual)
O(Encoding)
OpPercepuual)
Offnnsading)
O(Encoding)
O(Eacoding)
O(Encoding)
Figure A3: Orthogonalization: Similar to Figure 3p, but with PCA to reduce the dimensionality to the same level of the perceptual and encoding space.
= data +
In the Procrustes analyses (see the Procrustes analysis section below), the vector w is derived by rotating the original decoder using the Procrustes transformation and the bias is obtained from the original decoder. When O, the corresponding data point is assigned to one class, and to the alternative class when
The set of vectors (W1. W2, W in D-dimensional space RD, represent decoders that space. These vectors span subspace of D that is the set of all possible linear combinations of these vectors. Mathematically. the subspace S spanned by these vectors is defined as: S = span(wi, W2. w.) = [ N a,w, a; E R]...
Procrustes analysis Procrustes analysis Ross 2004 is powerful method for identifying shape correspondence that relies on the orthogonality of the rotation matrix. Here, we consider shape spanned by vertices specified by the normal vectors of decision hyperplanes obtained by classifying
16

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one feature value from the rest. For example, for four possible locations, the shape is defined by four vertices each corresponding to classifier that discriminates one location from the rest. We calculate such descriptions of shapes at each time step, for each feature, and across all possible tasks for each model. The goal of our analysis to transform decision hyperplanes obtained under one condition to target decision hyperplanes obtained under another condition. In other words, we want to align source shape with the target shape. To do so, we take the following steps:
Train the decoders, obtain the normal vectors of the source and target shape, denoted as
Wsource and Wiarree
Standardise Wsouree and Wttrrget
w source
Wsouree Wsouree
(5)
Usuuree
Wsource
Wharget
Wtarget
target
Wtarget
Wtarget
We denote Wtarget as b and |target
Wtarget 2 S.
Perform Orthogonal Procrustes Analysis [Gower and Dijksterhuis 2004 to align w gourre with w/ Wargett which returns a rotation matrix (Rsource-targel) and global scaling factor (s)
Transform Wsouree to Warrget by
Wreconstructed (w gource Rsoarce-ttarget)
Apply the inverted standardization to get the final reconstructed weights:
Wreconstructed Wreoonstructed S B
(8)
The obtained Weeconstrrcttd be used to reconstruct SVC, and the decoding accuracy of the reconstructed SVC can be used as measure of the alignment quality. In future analysis, we swap Rargret by rotation matrix obtained by aligning other pairs of shapes, evaluate the resulting reconstructed SVC's performance and use it to quantify the similarity between two rotation matrices.
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RNN
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t t= 4
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t=
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t t= 5
t = 6
Figure A4:
Validation of Procrustes Analysis: Similar to Figure but for RNN and LSTM
trained on MFMT
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Within Timestep Decoding Task-Relevant Features
Within Timestep Decoding for
Task-Irrelevant Features
1.10
back
Decoding Accuracy
Decoding Accuracy
back
1.05
back
1.00
1.00
0.95
0.95
0.90
0.90
Time
Time
Figure A5: Within-timestep Decoding Analysis: At each timestep, trained SVMs activations from the recurrent module for task-relevant features (left) and task iire-intelevant features (right), plotting the validation accuracies averaged across different feature values. The results shown are for an example GRU model trained on a multi-task, multi-feature task set. As expected, both task-relevant and task-irrelevant features well represented their corresponding encoding times. In addition, task-relevant features were more robustly encoded and distinctly separated compared to iasevitrleeaant
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C.
Location
1.0
Accuracy
0.8
0.8
0.6
0.6
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Identity
Catogory
0.2
Bidd) de Rasksad)
Beah de Baist))
MiSut E(5ad.7
(w2)
Miswirra))
Mesial
d.
RNN
GRU
Model Operating Mode (Test)
Model Operating Mode (Test)
1-back
2-back
3-back
1-back
2-back
3-back
L
1-back
C
D D D, DI D D, D, D, D
2-back
C
Da Da Dac
Du Da
Da, Dap
D,, Dac
Da,
D., D.
3-back
DaL Dac
D5 Dac
D2LDs1 D3,
Du, D3
D3 Dac
D3 D3.
Figure A6: a) Frames with different natural backgrounds: We overlaid our original 3D object stimuli on synthesized natural background textures [Efros and Freeman 2023 (https://githiie WewDDeashi-hhouuie
TTexture- Teexture-Syttheiss) Three examples of the resulting frames are shown. b) Task performance for models trained on different datasets: Accuracies were calculated on the validation set with novel object angles. Multi-task multi-feature models were trained on more N-back tasks (1/2/3/4-back), visual frames with naturalistic texture backgrounds (texture bg), or tasks generated with a larger stimulus dataset (8 categories with 4 identities each; larger dataset). c) Rotation transformation analysis: We identified consistent patterns in the model's response to rotation transformations across various tasks, similar to the results in Figures 4i-g Left side plot shows an example for the MTMF model performing 4-back tasks. d) Cross-task decoding analysis: Consistent decoding results, with higher generalization accuracy for vanilla RNN models compared to gated models.
Nor.Match Action
MatchAAction
No-Action
3.0
Mean
0.06
Standard Deviation
3.04
0.3
0-1
3.00
0.2
0.00
0.6
1.0
Dikinioc Miros Moros (1n1))
Diatnce Moxca turill
Figure A7: Causality test: We subsampled trials with matched actions and trained feature-based two-way decoders. We then perturbed the hidden states, obtained during the presentation of the first stimulus, along the direction of the corresponding decision hyperplane. The distance moved is proportional to the normalized norm vector (x-axis, distance moved in units). The perturbed hidden states were passed through the recurrent module along with the paired stimulus compute the probabilities of the three possible actions.
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Reviews:
[{"review_id": "Zw56kJ7QyH", "reviewer": "Reviewer_VPbf", "summary": "This work involves training RNNs on the n-back task with naturalistic images fed into the RNN through a CNN front-end. Through a large number of permutations comprising different task requirements, different combinations of tasks and different architectures, the authors study how task relevant and task irrelevant information is processed in the RNN back-end.", "questions": "There seems to be a lack of details in the methods. For example, are the models only trained/tested on 6 time steps?", "limitations": "In the checklist, the authors claim that \"We point out the limitations of our model and analysis methods in the discussion.\" But I really cannot find any sentence in Section 5 that describes any limitation of this work at all.", "rating": 5, "confidence": 4, "soundness": 2, "presentation": 1, "contribution": 3, "strengths": "The analysis is principled and rigorous. A large number of model-task permutations have been trained, which all support the same conclusions.", "weaknesses": "This work is critically lacking the control experiment of simply training an RNN without natural images or CNNs. The aim of this work is to understand how RNNs process natural images in working memory, but I feel that these results (such as representational orthogonalization) can be reproduced if you simply use randomly generated vectors as inputs. I foresee that this would be a logical doubt from many readers, including myself.\n\nOne reason to think this way is that the output of the final layer of a pretrained CNN is essentially uninterpretable (and hence no different from being a random vector of numbers) beyond how it can be clustered according to its softmax boundaries. This is especially so when CNNs have location invariance due to their shared convolution across space, and produce very similar outputs at the final layer (from which the RNN is connected to) for images from the same category.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "We thank the reviewer’s recognition of the strengths of our manuscript, particularly noting the principled and rigorous nature of the approach. We are glad that the extensive training across various model-task permutations robustly supported our conclusions. In response to the weaknesses and limitations the reviewer highlighted, we carefully provide detailed responses addressing each point:\n* __Lack of control experiments and whether naturalistic stimuli can be replaced by random vectors.__ \nWe used a pretrained CNN (on ImageNet), which was trained to categorize objects. This suggests that the output layer of the CNN is, overall, lower-dimensional than its inputs (given that the number of objects classified is fewer than the number of total samples in ImageNet). Nevertheless, to verify this intuition on images sampled from our dataset, we measured the dimensionality of the inputs relative to the dimensionality of the CNN output layer, and the dimensionality of the RNN space. As the Reviewer suggested, we also used randomly sampled vectors (the same number as the number of images in our dataset), and measured the dimensionality of the stimulus vectors in the  input space, CNN output layer, and RNN layer. We then compared the dimensionality of our stimulus set vs. randomly sampled vectors for each of these embeddings. We found that the dimensionality of randomly sampled vectors is significantly higher than the dimensionality of the stimuli used in our experiments, suggesting that our results are unique to our specific chosen stimuli and task, and cannot be replaced by using randomly sampled vectors (see fig 1a in the attached 1-page PDF). **Importantly, to directly address the Reviewer’s comment, what this control analysis shows is that the output of the final layer of the pretrained CNN is different from being a random vector of numbers, since the dimensionality of random vectors is higher-dimensional than input vectors from our stimulus set.** Since dimensionality measures the orthogonality between pairs of vectors (stimuli), our analysis shows that the degree of orthogonalization differs (and cannot be directly reproduced) with random vectors.\n* __Lack of details in the Methods.__\nWe thank the reviewer for bringing this point to our attention. All models were trained and tested on trials of the same length (6 time steps). Moreover, we have included additional methodological (e.g., training details) in our general response to all reviewers. In the revised version of our manuscript, we include those details, in addition to other missing method details.\n* __Limitations in the discussion.__\nThank you for bringing this issue to our attention. We have substantially revised the Discussion and Conclusion sections of the paper, expanding on the current study’s limitations and likely future directions. Since updating the submission is not allowed during this period, we provide a brief summary as follows: 1) our findings are limited to the N-back task structure and it’s unclear whether similar computational strategies will emerge in other tasks requiring working memory. However, we provide specific predictions and further experiments that may lead to the discovery of more general principles used by RNNs for different WM tasks (e.g., in a simple delayed-match-to-sample task with only a fixation for the delay, we hypothesize that there will not be a rotation of representations through time); 2) we haven’t considered novel objects in our analyses. We reported reduced performance for novel objects but did not examine the representational geometry with those stimuli or the possible reasons for the diminished performance. We welcome any further suggestions from the reviewer; 3) Our findings are limited to the commonly-used RNN architectures, and we cannot make definitive claims about the representational geometry resulting from other neural network architectural choices. Additionally, we have not examined how scaling the network affects the results; 4) Our results suggest a possible hypothesis about working memory, but further investigation with real neural data is needed to validate this. It would also be valuable to explore the relationship between architectural choices and experimental outcomes.", "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": "", "extra_scores": {}}, {"review_id": "hdZKMaZyGX", "reviewer": "Reviewer_YsNL", "summary": "This paper examines the mechanisms of working memory in recurrent neural networks (RNNs) trained with naturalistic objects and N-back tasks, a classic task in cognitive and neuroscience. The aim is to study more complex, ecologically valid stimuli than the abstract categorical input that previous studies of working memory in RNNs have used. Additionally, the choice of N-back tasks provides a setting in which encoding of new memories, maintenance of prior ones in the face of distracting stimuli, and retrieval must all be balanced. For example, in a 2-back task, I must maintain a memory of the stimulus I saw 1 trial ago, and protect it from interference, as I encode the current stimulus and retrieve the stimulus from 2 trials ago to compare them. Here, the authors investigate what strategies RNNs use to dynamically maintain this object information. Moreover, they investigate RNNs' ability to flexibly switch between multiple tasks (1-, 2-, or 3-back tasks) as well as multiple object properties (identity, category and location). \nThe findings can be summarized as follows:\n1. Information about both task-relevant and task-irrelevant object properties (as measured through a linear classifier's decoding accuracy from the latent vector) is present in multi-task RNNs, but not in single-task RNNs, where only the single property that is relevant for the task is decodable.\n2. Information about object properties is orthogonalized in the RNNs' latent space, meaning that the normal vectors of the hyperplanes separating different values of the features used in the task (identity, category and location) are close to orthogonal.\n3. In multi-task settings, a vanilla RNN encodes object properties in a subspace that is shared across tasks, while gated RNNs (LSTM and GRU) keep separate subspaces for different tasks.\n4. In N-back tasks that require to simultaneously encode, maintain, and retrieve information in working memory, RNNs implement a shared encoding space for all stimuli that appear for the first time, and they do not maintain consistent codes for different objects across time.\n5. The transformations of feature subspaces across time can be well-approximated by a rotation matrix, and they are consistent across stimuli, but not stable over time. In other words, the rotation matrix that predicts the transformation of one stimulus from one timepoint to the next can predict the transformation of another stimulus at equivalent processing stages (e.g. between the initial encoding of the stimulus and the next timestep) but it cannot generalize to other processing stages.\n\nOverall, this paper is a thorough investigation of the mechanisms underlying working memory in RNNs in a complex, ecologically valid task setting.", "questions": "No questions, aside from those mentioned in the \"weaknesses\" section.", "limitations": "The paper does not explicitly address the limitations of the current approach. In particular, to what extent the current findings generalize to other working memory tasks, and to what extent they reflect working memory operations in biological systems, is not clarified.", "rating": 7, "confidence": 4, "soundness": 3, "presentation": 2, "contribution": 3, "strengths": "- The paper studies a class of tasks (N-back tasks) that elegantly combines different requirements of working memory. It thus allows to study several simultaneous operations, providing a considerably more complete picture relative to previous work. It also uses realistic stimuli, providing a closer approximation to complex tasks used to study working memory in humans and animals.\n- The \"related works\" section provides a concise but informative overview of previous work, including the study of working memory in both biological and artificial systems.\n- The experiments are creative and sound, and provide a detailed picture of the computational solutions found by RNNs to solve N-back tasks.", "weaknesses": "- The paper contains several typos: for example, at line 106 \"dynamical dynamics\", lines 238-240 \"We thus fit classifiers to decode each object property using the hidden activity from Encoding Space of the stimuli first appears at one timestep testing it on stimuli first appears other time steps.\", line 244 \"we next investigated how what transformations underlied the conversion of information\", line 258: \"architecutre\". I would recommend the authors to go through the manuscript and correct these errors, as they make reading the paper unnecessarily harder.\n- Several details of the model and training are left out: for example, figure 1c shows a hidden layer between the RNN's latent space and the output. What is the size of this layer? What is the training loss? I imagine it is cross-entropy, but this information should be made explicit. Also, how was the identity of the task encoded? Was a dummy (constant, or random) task identity vector also provided to the single-task single-feature model? How many iterations was the model trained for? How long were the sequences in the training and validation sets?\n- The generalization to novel object views and novel object instances is briefly mentioned, but not developed any further. The authors should add an explanation of what can be inferred from these results, and how they related to other findings in the paper. Otherwise, I see little reason for including them.\n- I am not sure what conclusions can be drawn from the orthogonalization found in the RNNs' latent space. The authors seem to attribute it to the dynamical encoding of stimulus information implemented by the RNNs, but the comparison between the perceptual space (penultimate layer of ResNet) and the latent space of the RNN does not seem appropriate, especially since the RNN is trained, while the ResNet (if I understand correctly) is frozen. It seems natural then that any network (even an additional feedforward layer) explicitly trained for a task would represent stimuli along orthogonal dimensions that corresponds to the task-relevant features. It becomes hard then to interpret the finding of orthogonalized representations.\n- While the paper convincingly characterize the subspaces used by the RNNs to perform the N-back tasks, it does not directly test their causal relevance. This seems like it would be relatively straightforward: by shifting the network's representation along the direction of the normal vector to a given hyperplane, it should be possible to \"push it\" towards giving a specific answer. For example, once the hyperplane separating \"car\" from other categories has been computed, the RNN's hidden state can be shifted along the normal vector's direction to (falsely) make it output \"match\" if the object seen N timesteps ago was a car (in a category N-back task). A similar analysis would validate the notion that the subspaces found by the decoding analysis are actually used by the networks in solving the task. \n- While the paper contains several analyses looking at _cross_-decoding, in which a classifier trained on a timestep in the sequence is evaluated on another timestep, there is no plot showing the _within-timestep_ decoding accuracy. Such an analysis would be helpful for characterizing the dynamics of the information contained in the representation: for example, is the representation of an object simply maintained in memory, iteratively enhanced, or does it degrade in time? Looking at decoding accuracy over time, or also at the orthogonalization index over time, would help to adjudicate between these possibilities. The fact that representation transformations across timesteps are well approximated by rotation matrices suggests that stimulus discriminability is roughly constant (at least until recall, as shown in fig. 4f) but measuring this discriminability directly as decoding accuracy would help to interpret the finding of rotation-like dynamics in functional terms. As decoding accuracy seems to be in general close to 100%, perhaps a continuous measure such as distance from the classification hyperplane would be more sensitive in revealing these dynamics.\n- In general, I feel that the paper does not provide a cohesive story to bind the different results together and interpret them. I think the findings are really interesting, but it is not clear what the take-home message is in terms of what they teach us about working memory in humans, animals or artificial systems. For example, what does the relative chronological memory subspace proposed in H2 (and confirmed by the results) mean in functional terms? What is the functional usefulness of having an encoding-specific subspace shared across stimuli, for example? Or what does the finding of rotation-like dynamics tell us in functional terms? One possible interpretation that I take away from this is that _protection against interference_ is a major principle determining RNNs' dynamical codes. For example, having an encoding-specific subspace can help to maintain the current stimulus separate from the ones being held in memory. Is this also your interpretation of the results? The results, as I said, are very interesting by themselves, but providing your own (even if speculative, that is completely fine) interpretation of what principles underlie these results would substantially strengthen the paper. Relatedly, what is the link between the present results and the broader literature on working memory in neuro- and cognitive science? Do these results allow us to distinguish between theories that have been previously proposed, or do they require a new explanatory framework? I appreciated the \"Related works\" section, which gave a nice overview of research in this field, but I felt the Discussion was not as thorough in placing the current findings in context.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "We thank the reviewer for recognizing the importance of our study. We have carefully considered the reviewer's comments and have provided the following response:\n* __Typos.__\nWe sincerely thank the reviewer for carefully listing all of the typos in our original draft. We will fix them and more thoroughly review the revised manuscript to ensure clarity. \n\n* __Missing details about model training.__\nThank you for highlighting this. We have included additional methodological (e.g., training details) in our general response to all reviewers. In the revised version of our manuscript, we will include those details, in addition to other missing method details.\n\n* __Discussion on the relevance of generalization to novel object/view angle.__\nThe primary reason for our evaluation of novel view/angle generalization was to highlight that the mechanisms of working memory learned by the model were not strictly limited to the specific set of visual features used during training. Hence, we used the same stimuli but with novel views/angles. Nevertheless, we agree with the reviewer that it will be potentially interesting to further examine the representational dynamics of RNNs when considering alternative stimuli (e.g. novel objects). (Note, however, that novel objects would prevent us from evaluating on the n-back identity task, since this requires the same stimulus.) Given the limited time at our disposal for providing a response to the reviews we were unable to perform further analyses in this direction. However, we have added this suggestion as an important future direction in our discussion section. \n\n* __Interpretation of the orthogonalization results.__\nRegarding the update of the orthogonalization analysis and interpretation, we kindly ask the reviewer to refer to our general reply for a detailed explanation due to the limited character count for individual rebuttals.\n* __Causal relevance test.__\nWe thank the reviewer for their suggestion. We performed a new analysis to address this point. Specifically, we considered trials from the 1-back location task where two objects had matching location property. We then manually adjusted the hidden state of the network in the direction normal to the decoder’s decision boundary. We then calculated the network’s generated output probabilities as a result of this hidden state adjustment. This analysis revealed that when adjusting the hidden state such that the decoder judges the object location to be different from its original value, the probability of match output is reduced while the probability of non-match and no-action outputs increase (Fig 1c in the attached 1-page PDF). This result thus supports the causal role of the particular encoding of object properties on the network’s generated behavioral output. \n\n* __Within time-step decoding analysis.__\nFollowing the reviewer’s suggestion, we performed the decoding analyses for each time step separately. The results qualitatively mirrored those we had reported in our Procrustes analysis that showed near perfect decodability up the time step where the object information was necessary for performing the task. Please see Fig. 1b in the attached 1-page PDF.  In addition, as suggested by the reviewer, we acknowledge that given the near-perfect decoding accuracies, using a continuous measure like distance from the decoding hyperplane could provide more nuanced insights into the representation dynamics. We will include the results of this analysis in the final revised version of the manuscript.\n* __Interpretation and relationship to previous literatures.__\nOur goal from the present work was to characterize the way multidimensional object properties are represented in the RNN models of WM and to reveal the mechanisms employed by these models for concurrent encoding, retention, and recall of information according to task demands. We will revise the abstract and the main paper to more clearly reflect these aims and to highlight its importance and distinctness from prior work. Furthermore, our findings in section 4.3 provide evidence against one of the prominent models of working memory, the slot-based model of working memory (Luck and Vogel 1997, Whittington et al. 2023). Relatedly, our results further show that within the family of n-back tasks, the memory representation is not “sustained” as is commonly suggested by prior studies. We expect that a sustained or dynamic memory representation will largely depend on the task structure (e.g., n-back task vs. a working memory delay with a static fixation).\n\nLuck, S. J., & Vogel, E. K. (1997). The capacity of visual working memory for features and conjunctions. Nature, 390(6657), 279-281.\n\nWhittington, J. C., Dorrell, W., Behrens, T. E., Ganguli, S., & El-Gaby, M. (2023). On prefrontal working memory and hippocampal episodic memory: Unifying memories stored in weights and activity slots. bioRxiv, 2023-11.\n\n* __Limited discussion.__\nWe agree that the discussion on the limitations of our work was largely incomplete. To address the reviewer’s concern, we substantially revised the Discussion and Conclusion sections, and included a list of limitations and future directions. This includes additional experiments,  including the reviewer’s suggestion on studying other working memory tasks. In particular, we are planning to perform an additional analysis using a simple delayed match-to-sample task to compare how working memory representations are maintained in the absence of incoming stimuli (i.e., the N-back task has incoming stimuli at every ‘delay’ period). If indeed the rotation-like dynamics are employed to protect against interference in the N-back task, we hypothesize that there may be the lack of rotation-like dynamics across time in a delayed match-to-sample (in which the delay is just a fixation). Though we could not perform this analysis during this rebuttal period, we are aiming to include this analysis in the final version of this paper.", "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": "", "extra_scores": {}}, {"review_id": "K7L6ukVnfN", "reviewer": "Reviewer_8PnP", "summary": "The manuscript uses various RNN architectures as \"model animals\" to study the representation and processing of naturalistic stimulus during several working memory (K-back) tasks. Unlike prior work, the current study considers various contexts for the cues, making the representation by the RNNs inherently higher dimensional. They find that when RNNs are required to perform a task with multiple contexts, all RNNs kept track of irrelevant stimuli; yet only vanilla (not gated) RNNs used shared representations across tasks. Moreover, the authors find distinct features are stored in orthogonal subspaces, a finding consistent with the prior experimental literature. They conclude with a study of temporal stability in the face of incoming distractors.", "questions": "I believe the manuscript is novel, convincing, and impactful. Some methodological details are missing, but I am sure the authors can add them during the revisions. Please find my comments/questions below:\n\n- Could you please define what is meant by a latent space, preferably in mathematical terms? I think the authors refer to subspaces defined by the decoder weights, but this should be stated more clearly since latent subspace has different meanings in neuroscience.\n\n- I believe there are at least two seminal works that need to be cited. Please see [1] and [2]; and several citations therein. Specifically, the claim \"This is in contrast to prior studies, which primarily studied WM tasks such as delayed-match-to-sample tasks, which don’t evaluate WM maintenance in the face of incoming (and distracting) information.\" is not correct as both of these works considered attractors. There are more works that should be cited. I believe the authors can find them through a short search, anchoring on these two papers.\n\n- \"For this, we trained decoders to predict the value of each object property using the RNN unit activity during the Encoding Space and evaluated its generalization performance in consecutive Memory Spaces.\" I am wondering if this is a fair test, since the representation may settle into a steady-state after a few time steps. I am not exactly sure how to test this in a way that can account for transient response to die out, so I will leave it to the authors if you wish to address this or not.\n\nOverall, I ended with more exciting questions after reading the manuscript than I started with, which is a mark of a paper that I believe deserves a publication in NeurIPS. I would kindly ask the authors to perform *substantial* edits to improve the presentation so that it is easier to follow the details of Section 4.3.\n\nCitations:\n\n[1] Masse, N. Y., Yang, G. R., Song, H. F., Wang, X. J., & Freedman, D. J. (2019). Circuit mechanisms for the maintenance and manipulation of information in working memory. Nature neuroscience, 22(7), 1159-1167.\n\n[2] Finkelstein, A., Fontolan, L., Economo, M. N., Li, N., Romani, S., & Svoboda, K. (2021). Attractor dynamics gate cortical information flow during decision-making. Nature neuroscience, 24(6), 843-850.", "limitations": "NA", "rating": 7, "confidence": 4, "soundness": 3, "presentation": 2, "contribution": 4, "strengths": "- The memory task is complex and requires the RNNs to learn the context.  \n\n- The use of naturalistic inputs is in direct contrast and a welcome addition to traditional studies where categorical inputs are used. Though please see [1].\n\n- The observation \"These observations challenge the generality of prior studies using vanilla RNNs and categorical inputs in which shared representations and dynamical motifs across related tasks were found [35, 9].\" is rather intriguing and very timely, given that [9] just got published as a high-impact publication.", "weaknesses": "- Some relevant citations are missing, please see below.\n- The presentation, for me, was a bit dense. I was not fully able to follow Section 4.3, though I believe I understood the general takeaways. The authors should work significantly on the presentation.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "We thank the reviewer for their thoughtful response. We also appreciate the acknowledgment of the potentially conflicting results our study highlights in relation to prior works. Below, we respond to individual questions the reviewer raised:\n* __Presentation styles__\nWe significantly revised the text in section 4.3 to improve its clarity as the reviewer suggested. Since updating the submission is not allowed during this period, we provide a brief summary of changes: 1) expanding the definition of hypotheses 1-3, adding references to prior related work to each hypothesis; 2) functional interpretation of each hypothesis (Hypothesis 1: sustained WM; Hypothesis 2: dynamic updating; Hypothesis 3: dynamic updating of stimulus-specific memory spaces); 2) adding more references to relevant figures containing definitions; 3) further methodological clarification (time steps and labels used for fitting and testing each decoder); 4) clarified the goal of several analyses (e.g., why did we use the Procrustes analysis, and how was it implemented); 5) added geometric interpretation for each result. We believe that these changes have substantially improved the readability and clarity of the results presented in section 4.3 and hope that will address the reviewer’s concern.\n* __Mathematical definition of latent space__\nThe latent space of the RNN refers to a D-dimensional space $\\mathbb{R}^D$ where $D$ is the number of units in the RNN model. Consider a set of $N$ vectors $\\{\\mathbf{v}_1, \\mathbf{v}_2, \\ldots, \\mathbf{v}_N\\}$ in D-dimensional space $\\mathbb{R}^D$, that represent $N$ decoders in that space. These vectors span a subspace of $\\mathbb{R}^D$ that is the set of all possible linear combinations of these vectors. Mathematically, the subspace $S$ spanned by these vectors ( $\\text{span} \\{ \\mathbf{v}_1, \\mathbf{v}_2, \\ldots, \\mathbf{v}_N \\}$) is defined as:  $$S = \\left\\{ \\sum_{i=1}^N \\alpha_i \\mathbf{v}_i \\mid \\alpha_i \\in \\mathbb{R} \\right\\}$$. We will revise the text to make this information and the relation between the decoder weights and the RNN subspace more explicit. \n* __Relevant citations__\nWe thank the reviewer for pointing us to these papers. We agree that these two references are highly relevant and we will add them to the updated manuscript and adjust the text accordingly. We also identify the following references relevant to our studies. \n\n* __Questions regarding cross-time generalization analysis__\nWe like to first clarify that in our experiments, each model executes exactly one step of computation per input observation and in that sense is different from many prior RNN models used in the literature that involve hundreds of steps within each trial to investigate attractor dynamics in high temporal resolution. For that reason, our experiments do not face the issue of transient responses between two consecutive inputs. In our experiments, we tested the generalization of the decoders up to five steps (the duration of the trial) after observing a stimulus. Thus, if any transient response fades during the trial, our analysis would be able to capture that phenomenon. \n\n\n\n\n\n## References\n1. Kozachkov, Leo, John Tauber, Mikael Lundqvist, Scott L. Brincat, Jean-Jacques Slotine, and Earl K. Miller. “Robust and Brain-like Working Memory through Short-Term Synaptic Plasticity.” PLOS Computational Biology 18, no. 12 (December 27, 2022): e1010776.\n2. Curtis, Clayton E., and Thomas C. Sprague. “Persistent Activity During Working Memory From Front to Back.” Frontiers in Neural Circuits 15 (2021). \n3. Mejías, Jorge F, and Xiao-Jing Wang. “Mechanisms of Distributed Working Memory in a Large-Scale Network of Macaque Neocortex.” Edited by Tatiana Pasternak and Tirin Moore. eLife 11 (February 24, 2022): e72136. \n4. Murray, John D., Alberto Bernacchia, Nicholas A. Roy, Christos Constantinidis, Ranulfo Romo, and Xiao-Jing Wang. “Stable Population Coding for Working Memory Coexists with Heterogeneous Neural Dynamics in Prefrontal Cortex.” Proceedings of the National Academy of Sciences 114, no. 2 (January 10, 2017): 394–99.", "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": "", "extra_scores": {}}, {"review_id": "5V3tALeMoU", "reviewer": "Reviewer_CRdT", "summary": "The paper presents a study of Working Memory (WM) in Recurrent Neural Network (RNN) models.\nThe main contribution is the study of the latent space dynamics of RNNs during WM-related tasks with respect to naturalistic stimuli, instead of abstract categorical stimuli that are commonly used. The paper analyses gated and non-gated RNNs, and characterises how the geometric properties of their latent spaces change during the trials, as new stimuli are integrated in the WM.", "questions": "* Does the training from ImageNet transfer to this dataset?\n* The normal vectors to the decision boundaries can be taken to be unit norm. In a high dimensional space, however, unit-normed vectors are, with high probability, orthogonal to each other. How does this impact the validity of the orthogonality index?\n* It is unclear to this reviewer the reasoning behind the usage of Procrustes analysis for studying the evolution of the decision boundaries.", "limitations": "The dataset and the task extent seem to be undersized with respect to what seems reasonably possible. Including larger N-back windows and more objects could be beneficial.", "rating": 6, "confidence": 3, "soundness": 2, "presentation": 2, "contribution": 2, "strengths": "* The paper focuses on a more realistic setup than what usually done. It incorporates a “perceptual backbone” given by a CNN, and a “WM backbone” given by a RNN.\n* The paper clearly states the tasks (particularly via the plots) and the architectural choices\n* The results, being obtained in a more realistic setup that previous works, serve as a basis to formulate testable predictions on biological entities", "weaknesses": "* Very small dataset (4 categories, 2 identities per category, 4 possible locations). The N back window also seems limited (how does WM scale for N>3?)\n* Stimuli are more realistic, but there is space for improvement (i.e., realistic backgrounds instead of pitch black?)\n* The discussion of the three hypotheses in subsection 4.3 is unclear to this reviewer.\n\nIf these weaknesses are addressed, the rating may be increased.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "We appreciate the reviewer's positive assessment and their suggestions. We address their specific questions and weaknesses below:\n* __Small dataset and limited N-back window__\nWe appreciate the reviewer highlighting the limited size of our stimuli and task sets. We would like to clarify that our stimuli dataset includes 4 categories, each with 2 identities. For each identity, there are approximately 20 view angles in the training set and 4 view angles in the validation set. Additionally, we include 2 additional identities for each category in the validation novel object dataset, resulting in a total of 192 stimuli. Despite this dataset size, the model is capable of generalizing to identities with novel angles and novel identities, suggesting that the model is indeed learning (and generalizing) the task. We argue that with larger datasets, the model should retain the same representation geometry as discovered with the given dataset.  \nTo directly address the reviewer's concerns, we ran several additional experiments. In particular, we trained models on a relatively larger dataset containing 8 categories and 4 identities per category. Due to rendering quality restrictions, we obtained models with comparable training and validation accuracy (~80%), suggesting that the models still captured the task dynamics. We performed a cross-condition decoding analysis (similar to Fig. 2a) and found consistent results, indicating shared representation for vanilla RNNs but not gated RNNs. The relatively low decoding accuracy is a direct consequence of the lower saturation accuracy of the model that will likely be ameliorated with additional training time. Additionally, we further trained models to perform 1-4 back tasks across all 3 features (adding the additional 4-back task setting). Models achieved comparable performance to our original 9-task model, and we were able to replicate the findings from Fig. 4f and g (see attached 1-page PDF Fig 2a). Together, these new results suggested that our findings generalize to broader settings including more diverse object categories and broader task settings. \n* __Suggestion to add realistic background__\nWe thank the reviewer for their suggestion and acknowledge that more natural experimental settings are desired and may be important for proper analysis of the neural computations underlying working memory. To address the reviewer’s concern, we ran an additional experiment using stimuli overlaid on synthetically generated natural textures. For this, we synthesized textures as stimulus background using the method from [Texture Synthesis](https://github.com/Devashi-Choudhary/Texture-Synthesis) and overlaid the 3D objects on them to create each frame (see attached 1-page PDF Fig 1c). We then trained models to perform n-back tasks with these new stimuli. We found that models achieved equally well performance levels with comparable speed (see attached 1-page PDF  Fig 1d). In other words, we found that the choice of background does not affect our main results. We plan to include a more detailed analysis of this model in the revised submission (with the full set of analyses).\n* __Interpretation of subsection 4.3__\nPlease refer to the general reply for an updated interpretation. \n* __Does the training transfer from Imagenet to Shapenet?__\nAs mentioned on line 122-123, our vision backbone consisted of an Imagenet-trained ResNet50 model with fixed parameters. In all our experiments, we used the unit activations of this model as the input to the RNN models. All object features including category, identity, and location were highly decodable from these activations (category: 100.00%, identity: 99.57%, location: 100.00%; 2-fold cross-validation), confirming that the Imagenet trained ResNet50 model generalized to our stimulus set from ShapeNet. \n* __Orthogonalization index interpretation__\nWe agree with the reviewer that the high dimensionality of the latent space, specially the perceptual space, could make the comparison potentially invalid. To address the reviewer’s concern, we repeated this analysis by first applying PCA on the activations within perceptual and RNN spaces and equalized the number of dimensions in both. We then calculated the orthogonality measure on the dimensionality matched spaces (perceptual and RNN encoding). This analysis replicated the same findings from the original analysis done without dimensionality matching (see Fig. 1e in the attached 1-page PDF). Lastly, we want to emphasize that the point made in our orthogonality analysis experiments is the difference in orthogonality between the two spaces and we do not directly examine the absolute value of orthogonality, which as the reviewer suggested may be affected by the dimensionality of the latent space. \n* __Rationale behind using the Procrustes analysis__\nWe were interested in investigating whether the geometry of object representations is unchanged across different time steps (e.g. between encoding representation and 1st, 2nd, or 3rd memory representations). For this we needed to analyze the likeness of the representational geometry across time steps and for encoding and memory representations. The orthogonal Procrustes analysis is a statistical shape analysis which enables discovering simple rotation transformations that superimpose a set of vectors/points onto another set. We used this analysis to inquire whether each set of object feature decoders can be rotated to align with the set of same decoders at a different time or for a different stimulus.", "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": "", "extra_scores": {}}]

Author rebuttal:
We sincerely thank the reviewers for their insightful and positive feedback. We are encouraged by the reviewers’ acknowledgement of the rigorousness and thoroughness of our work (*reviewer VPbf and YsNL*), creativity and soundness of our experiments (*reviewer YsNL*), and novelty and impactfulness of our results (*reviewer YsNL and 8PnP*), while identifying its questions and limitations. Here we point out several common questions raised in the reviews. (We respond to all inquiries in individual responses.)
* **Updated results in Fig. 3b.** We would like to first acknowledge an error in producing the plots in Fig 3b. The measure we used in the original manuscript was $O = \| \text{abs}(\cos(w_i, w_j)) - I\|_F$ with $I$ as the identity matrix. This measure however produced an inverted measure of orthogonality as we should have used $O = \|\text{abs}(\cos(w_i, w_j)) - \mathbf{1}\|_F$ and only considered the upper (or lower) triangle (thus the higher the orthogonalization index, the more orthogonalized the representation). When correcting the measure, our results and interpretation of them were reversed (see fig 2e in the attached 1-page PDF). Both space are highly orthogonalized, however, even when equalizing the dimensionality of the perceptual and RNN space with PCA, the results demonstrated significant reduction in orthogonalization of the latent space in the RNN. We revised our description of the method and results related to this section accordingly. Our current hypothesis for this counter-intuitive result is that the high-dimensional perceptual space may not have been fully captured by PCA. Specifically, PCA might not have adequately represented the relative dimensional differences between the two spaces under comparison. We kindly ask for the reviewers' opinions and insights regarding this updated result.
* **Missing details in Methods.** We appreciate the reviewers’ suggestions and for pointing out the lack of details in some places. There is only one feedforward layer with a softmax activation that projects the hidden state to one of the three possible output actions. We understand that the visualization may have caused confusion, and we will update it accordingly in the revised manuscript. We used cross-entropy loss for training, and the identity of the task was encoded in a 6-digit binary format: the first 3 digits represented the one-hot encoding of the feature (e.g., stimulus location, category, or identity), and the second 3 digits represented the one-hot encoding of the n-back choice of n. For the single-task single-feature model, we used the same task identity vector as in the multi-task models. The multi-task multi-feature model typically takes around 4-8k iterations with a batch size of 256, and we cut off training at 14k iterations. The sequence length is fixed at 6 for both the training and validation sets. In the revised version of the paper, we will include all necessary training details in the supplementary materials. In addition, we will make the code and trained models publicly available.
* **Interpretation of subsection 4.3**. To address the reviewer’s comment, we revised the portion of the text that details the three hypotheses. Since updating the manuscript is not allowed during this period, we present the revised text below:  
**H1**: Slot-based memory subspaces (Luck and Vogel 1997, Whittington et al. 2023). Where the RNN latent space is divided into separate subspaces that are indexed by time within the sequence. Each object is encoded into its corresponding subspace (i.e. slot) and is maintained there until retrieved. By definition, the subspace assigned to each memory slot is distinct and “sustained” in time.   
**H2**: Relative chronological memory subspaces. Where the RNN latent space is divided into separate subspaces that each maintains object information according to their age (i.e. how long ago they were observed, for example memory of observation from one, two or three time steps ago). Such a mechanism will require a dynamic process for updating the content of each memory space at each time step during the task.   
**H3**: Stimulus-specific relative chronological memory subspaces. Which is similar to the relative chronological memory hypothesis but with independent subspaces assigned to each object. Each observation in the sequence is encoded into a distinct subspace and encoding of each stimulus is in turn distinctly transformed into associated memory representations.

Meta-review: In this study, the authors developed sensory-cognitive models, comprising of a convolutional neural network (CNN) coupled with a recurrent neural network (RNN), and trained them on nine distinct N-back tasks using naturalistic stimuli. The representational geometry and dynamics were investigated using latent subspace analysis. The reviewers had several concerns about the motivation/task design/writing. In particular, the reviewers asked for additional control experiments to strengthen the claims here. The rebuttal went very well and all reviewers gave positive comments. I am inclined to accept the paper.
Decision: Accept (poster)