Multi-task Learning yields Disentangled World Models: Impact and Implications

Authors: pantelis  vafidis
aman  bhargava
antonio  rangel
Venue: NeurIPS_cc_2024_Workshop_UniReps
Published: 2024-09-23 20:20:18

Abstract: Intelligent perception and interaction with the world hinges on internal representations that capture its underlying geometry ("disentangled" or "abstract" representations). The ability to form these disentangled representations from high-dimensional, noisy observations is a hallmark of intelligence, observed in both biological and artificial systems. In this opinion paper we highlight unpublished experimental and theoretical results guaranteeing the emergence of disentangled representations in agents that optimally solve multi-task evidence aggregation classification tasks, canonical in the cognitive neuroscience literature. The key conceptual finding is that, by producing accurate multi-task classification estimates, a system implicitly represents a set of coordinates specifying a disentangled, topology-preserving representation of the underlying latent space. Since the theory relies only on the system accurately computing the classification probabilities, we are able to derive a closed-form solution for extracting disentangled representations from any multi-task classification system. The theory provides conditions for the emergence of these representations in terms of noise, number of tasks, and evidence aggregation time, and we experimentally validate the theoretical predictions on RNNs and GPT-2 transformers solving such canonical evidence-aggregation decision-making neuroscience tasks. We find that transformers are particularly suited for disentangling representations, which might explain their unique world understanding abilities. Overall, our opinion paper puts forth parallel processing as a general principle for the formation of cognitive maps that capture the structure of the world and that are shared across both biological and artificial systems, and helps explain why ANNs often arrive at human-interpretable concepts, and how they both may acquire exceptional zero-shot generalization capabilities. We discuss implications of these findings, for machine learning and neuroscience alike.

Main paper: 
 introduction: 
 Humans and animals can generalize to new settings effortlessly, leveraging a combination of past experiences and world models [Lake et al., 2015 [Lake et al., , 2016]] . Modern foundation models also display emergent out-of-distribution (OOD) generalization abilities, in the form of zero-or few-shot learning [Brown et al., 2020 , Pham et al., 2021 , Oquab et al., 2023] .One mechanism for generalization is through abstract, or disentangled, representations [Higgins et al., 2017 , Kim and Mnih, 2018 , Johnston and Fusi, 2023] . These two concepts are interrelated yet somewhat distinct [Ostojic and Fusi, 2024 ]. An abstract representation of x 1 , . . . , x n represents each x i linearly and approximately mutually orthogonally. Disentangled representations encode each x i orthogonally, without the necessity of linearity. When a representation is abstract, a linear decoder (i.e. downstream neuron) trained to discriminate between two categories can readily generalize to stimuli not observed in training, due to the structure of the representation. Furthermore, the more disentangled the representation is, the lower the interference from other variables and hence the better the performance. This corresponds to decomposing a novel stimulus into its familiar features, and performing feature-based generalization. For instance, imagine you are at a grocery store, deciding whether a fruit is ripe or not. If the brain's internal representation of food attributes (ripeness, caloric content, etc.) is disentangled, then learning to perform this task for bananas would lead to zero-shot generalization to other fruit (e.g. mangos, Figure 1a ). Crucially, the visual representation of a mango is high-dimensional, non-linear and noisy, making it particularly challenging to extract a low dimensional latent like "ripeness".Several brain areas including the amygdala, prefrontal cortex and hippocampus have been found to encode variables of interest in an abstract format [Saez et al., 2015 , Bernardi et al., 2020 , Boyle et al., 2022 , Nogueira et al., 2023 , Courellis et al., 2024] . This raises the question of under which conditions do such representations emerge in biological and artificial agents alike. Here we argue that multi-task learning is crucial to get the kind of topology-preserving representations that yield generalization in biological systems, and that a parallel processing view of the brain, in line with the cortical architecture, is naturally conducive to that framework. To do so, we first summarize findings from Vafidis et al. [2024] which proves mathematical conditions for disentanglement and experimentally confirms them in autoregressive architectures (RNNs, LSTMs, transformers) that can deal with noisy sequential real-world data, and then discuss the implications of the work for machine learning and neuroscience alike. 
problem formulation: 
 In Vafidis et al. [2024] we are considered with canonical cognitive neuroscience tasks that involve evidence aggregation over time, mirroring decision-making under uncertainty. The tasks have a trial structure. In each trial, a ground truth vector x * ∈ R D (x * i ∼ Uniform(-0.5, 0.5)) is sampled (Figure 1b ). Each element x * i of x * corresponds to different options a decision-maker might have, or to different attributes of the same item. The target output for the trial y(x * ) ∈ {-1, +1} Ntask is a vector of N task +1s and -1s, depending on whether x * is above or below each of N task classification boundaries (Figure 1b ). The boundaries are fixed, and reflect criteria based on which decisions will be made. Imagine for example that x 1 corresponds to food and x 2 to water reward. Depending on the agent's internal state, one could take precedence over the other, and the degree of preference is reflected in the slope of the line.We train RNNs and GPT-2 transformers to output the target labels y(x * ) (Figure 1c ). The networks do not have access to the ground truth x * but rather a noised-up, non-linearly transformed version of it. Specifically, the input is X(t) ∈ R D where X(t) = x * +σ N (0, I D ), σ being the input noise standard deviation. The network should integrate noisy samples X(t) over time, viewed through an static, injective observation map (encoder) f , to estimate Ŷi (t) = Pr{y i (x * ) = 1|f (X(1)), . . . , f (X(t))}. 
contributions: 
 We here summarize the main contributions of Vafidis et al. [2024] :• We that any optimal multi-task classifier is guaranteed to learn an abstract representation of the ground truth contained in the noisy measurements in its latent state, if the classification boundary normal vectors span the input space. Furthermore, the representations are guaranteed to be disentangled if N task ≫ D. Intriguingly, noise in the observations is necessary to guarantee the latent state would compute an optimal, disentangled representation of the ground truth (for proofs, see Appendix B of included paper).• We confirm that RNNs trained to multitask develop abstract representations that generalize OOD as quantified by regression generalization [Johnston and Fusi, 2023] when N task ≥ D (Figure 1f ), and that the latent factors are approximately orthogonal when N task ≫ D (disentanglement, Figure 1g ). The substrate of these representations are continuous attractors [Amari, 1977] storing an estimate of x * in a product space of the latent factors (Figure 1d ). Furthermore, these representations preserve the topology of the real world in their structure, where a latent factor (e.g. x 1 , x 2 ) corresponds to a direction in PC space of RNN hidden layer activity, and nearby trials get mapped to nearby trajectories in PC space (Figure 1d ).• We show that the setting is robust to a number of manipulations, including interleaved learning of linear and non-linear tasks and free reaction time decisions.• We reproduce these findings in GPT-2 transformers, which generalize better due to them learning orthogonal representations for lower N task , confirming their appropriateness for constructing world models.• Finally, we demonstrate the strong advantage of multi-task learning, which scales linearly with D and leads to representations that can be used for any task that involves the same latent variables, over previously proposed mechanisms of representation learning in the brain ("context-dependent computation") [Mante et al., 2013 , Yang et al., 2019] , which scale linearly with N task and exponentially with D.Despite being framed in the context of canonical decision-making neuroscience tasks, these results are general; they apply to any system aggregating noisy evidence over time. 
implications for representation learning: 
 Topology-preserving representation learning These results have implications for the learning of representations that inherit the topological structure of the world. They suggests that this naturally happens, as long as there are enough tasks to uniquely identify the location of the ground truth x * when solving these classifications (see Appendix B of Vafidis et al. [2024] ). Crucially, the constraints from different tasks need to be placed simultaneously on the representation, which explains why representations emerging from context-dependent computation are typically not disentangled. An example from neurobiology is the fly head-direction system [Vafidis et al., 2022 , Wilson, 2023] , where a ring-like topology-preserving representation of head direction might be enforced exactly because of it's functional role in driving many downstream circuits for navigation.Potentially even more far reaching, this work implies guarantees about representational alignment across individuals or neural networks. It suggests that as long as we are faced and solve similar problems in the day-to-day world, we are bound to arrive at similar, disentangled representations of latent factors governing these decisions. This is reminiscent of the Platonic representation hypothesis [Huh et al., 2024] , which suggests that the convergence in deep neural network representations is driven by a shared statistical model of reality, like Plato's concept of an ideal reality. This could explain why for example modern LLMs come to encode high-level, human-interpretable concepts [Templeton et al., 2024] .Manifold hypothesis While our problem is framed in terms of arbitrary injective observation map f , the formulation encompasses many scenarios relevant to the manifold hypothesis [Fefferman et al., 2013] . The function f can represent a smooth manifold embedded in a high dimensional space, directly modelling the manifold hypothesis of deep learning. In neuroscience, f could be a non-linear encoding of stimuli in a neural population response, connecting our work to neural manifold research [Langdon et al., 2023] . By developing and testing theoretical guarantees for the emergence of disentangled representations in this multi-task problem formulation, we provide insight on how neural networks can inherently discover and linearize low-dimensional manifolds within high-dimensional, non-linear observations, enhancing our understanding of how complex data structures are captured and represented in deep learning models and biological systems alike.Interplay between number of tasks and fine-grainness of representations Intriguingly, this work reveals a fundamental interplay between richness of tasks performed and complexity/detail of the representation learned. If only a small number of tasks are performed, the resulting representations will be fundamentally limited to lie within the space spanned by these tasks. However, as more tasks are added, finer details could be discerned. Therefore, the theorem and experimental results provided are not a one-way-street from dimensionality D of the latent factors to how many tasks N task are required to uncover such latents. Rather, in a complicated and high-dimensional world, the richness of the tasks at hand directly affects the dimensionality D of the latents that can be extracted, allowing for "ground truths" x * at different levels of granularity to be explored. The richer the label information available, the more fine-grained the resulting world model will be.Disentanglement and axis-alignment Axis-alignment is the property by which individual neurons encode distinct latent factors, or equivalently factors are encoded across standard axis of the representation. Computer science [Higgins et al., 2017 , Kim and Mnih, 2018 , Chen et al., 2018 , Hsu et al., 2023 , Eastwood et al., 2022] and some recent neuroscience [Whittington et al., 2022] work has incorporated axis-alignment in the definition of disentanglement. However, under our definition above axis-alignment is not a requirement for disentanglement (also see Higgins et al. [2018] ). Instead, we suggest that the computer science and computational neuroscience communities should adopt this broader definition of disentanglement, because otherwise we might be missing cases where the factors are not axis-aligned, but they are still orthogonal and can still be isolated by a linear decoder. Our argument is that there is nothing special about individual factors being encoded by individual neurons. Rather, we think that allowing for mixed representations within the definition of disentanglement leads to a more holistic view of disentanglement. A contribution of our work, along with others [Johnston and Fusi, 2023] , is to bring this argument to the forefront.5 Connections to neuroscience and machine learning 
correspondence to brain processes: 
 The brain encodes variables of interest in a disentangled format, in processes as disparate as memory [Boyle et al., 2022] , emotion [Saez et al., 2015] , and decision making [Bongioanni et al., 2021] . Furthermore, performance in tasks has been shown to degrade once said neural representations collapse [Saez et al., 2015] , supporting the role of abstract representations in guiding generalizable behavior. Given our findings, and that the cortical architecture is uniquely suited for parallel processing [Hawkins et al., 2019] , the cortex is a prime candidate area for the construction of disentangled world models. Another such area is the thalamus; it is posited that thalamocortical loops operate in parallel, and combined with internal state-dependent mechanisms lead to statedependent action selection (e.g. prioritizing water when thirsty), while evidence integration occurs in corticostriatal circuits [Rubin et al., 2020] . The algorithmic efficiency of multi-task learning compared to alternatives ("context-dependent computation", Mante et al. [2013] , Yang et al. [2019] ), makes us think that it is no coincidence that the cortex is built for parallel processing; all the pieces are there, and we feel that the brain has to leverage this feature to construct faithful models of the world, as it does.While our theory stems from parallel processing, i.e. multi-task learning, it is not contingent upon the parallel execution of multiple tasks, i.e. multitasking. Behaviorally, the agent need only perform one action, the one most appropriate to it's current internal state (e.g. thirst vs. hunger in the example above). What we posit is that tasks that have been performed by the agent before and rely on the same input are still resolved somewhere in the brain, by the brain circuits (e.g. cortical columns Hawkins et al. [2019] ) previously responsible for them, instead of the entire decision-making brain area focusing only on the current task [Mante et al., 2013] . We feel that this is a more natural way of thinking about how the brain manages different tasks, with older tasks still leaving traces somewhere in the brain [Losey et al., 2024] , and this theory is closely related to the widely observed phenomenon of memory replay [Foster and Wilson, 2006] .The experiments in Vafidis et al. [2024] are inspired by canonical cognitive neuroscience tasks, rather than state-of-the-art ML paradigms. Yet, the conclusions concern the fundamental nature of generalization. For instance, why do foundation models generalize well in various domains?We suggest that parallel processing forces learning of generalizable world models, and our setting directly applies to settings where neural networks predict a rich representation of the world from partial observations. Some examples are predictive coding where high-dimensional next states have to be predicted [Gornet and Thomson, 2024] , which is equivalent to the classification objective of predicting which objects are going to be in the field of view (and where), and self-supervised learning, where multiple missing image patches have to filled up at once [Dosovitskiy et al., 2020] .Finally, an alternative to multi-task learning that we explore is slow interleaved learning. This allows the weights of a neural network to be effectively conditioned to solve all the tasks simultaneously.The relation between multi-task and interleaved learning is a promising topic for future research.Another interesting future direction would be to extend our work to CRNN and vision transformer architectures [Bertasius et al., 2021] that can extract latents from high-dimensional, dynamic observations e.g. video. That would require a naturalistic dataset that affords multiple views of the same object under different angles, lighting conditions etc., but still simple enough to extract useful insight. Something like a dynamic extension of dSprites [Matthey et al., 2017] would be ideally suited, however we are not currently aware of such a dataset.Preprint. 
 
 Appendix:  


Decision: In light of the positive reviewers' feedback and relevancy of the submission, we are pleased to accept this paper for presentation at UniReps 2024. We kindly ask the authors to incorporate the reviewers' suggestions and feedback in the final camera-ready version of the manuscript.

Reviews: review: title: title: Good paper very relevant to the audience
main_review: main_review: In this work, the author’s present an insightful hypothesis: multitasking (parallel processing). Specifically, that abstract representations result from the need to use the same feature representations to solve a multitude of tasks. Following from this hypothesis, the author’s derive conditions that guarantee the emergence of abstract representations: namely the number of simultaneous tasks being performed and show that their theory holds up in three classes of sequence models RNNs, LSTMs and Transformers.

I think this work is quite strong and the results are both clear and impactful. As the author’s mentioned in this paper, their theory provides guarantees on when two people, or a model and a person will form the same representations. This alone is an important finding that already suggests a myriad of future experiments. Yet, the author’s also point out an equally interesting observation: that is that Transformers seem to have an implicit bias leading them to naturally develop abstract representations at least in comparison to RNNs. Understanding the source of this bias (is it architectural? Is it due to the attention mechanism?) will be particularly insightful for developing learning theories and broadly interesting to the machine learning community as a whole.

That all of these results stem from the assumption that brain or the model must simultaneously perform multiple tasks is interesting and has broad implications to neuroscience. However, I think more could be done to strengthen this connection. Namely, a key assumption for this theory is the simultaneity of tasks. Many experimental tasks are sequential – sometimes interleaved or blocked. In the full paper, the author’s show that their theory generalizes to the interleaved training regime, but in my experience blocked training is much easier for animals and probably humans. Relatedly, work from Anne Collin’s group has shown that whether animals are trained with interleaved or blocked trial designs has strong implications for which strategies they develop and the generalization properties of those strategies. I would be curious to see how the blocked training regime can be encapsulated in this model and what kind of results emerge. Another key assumption is that the representations are disentangled. Can the authors say anything more about which tasks this is likely to hold for (e.g. sensory discrimination tasks but not motor learning tasks)? Could these results be generalized and extended to meta-learning as well? For instance, does training networks to perform the Harlo task bias them towards learning abstract representations in future tasks? 

But these are just more examples of interesting questions spawned by this work.

All said, this is an excellent and thought provoking paper, and anyone interested in how the brain or neural networks in general develop their representations, or which representations lead to generalization would benefit from hearing about this work.
title: title: Revision of UniReps '24 — #38
main_review: main_review: **Paper summary**

In this paper, the authors argue that disentangled representations emerge in agents that optimally solve multi-task evidence aggregation classification tasks, canonical in the cognitive neuroscience literature. The key conceptual finding is that, by producing accurate multi-task classification estimates, a system implicitly represents a set of coordinates specifying a disentangled, topology-preserving representation of the underlying latent space. The proposed theory provides conditions for the emergence of these representations in terms of noise, number of tasks, and evidence aggregation time, and they experimentally validate the theoretical predictions on RNNs and GPT-2 models solving such canonical evidence-aggregation decision-making neuroscience tasks.

**Paper strengths**

The argument posed in this paper is interesting, and the application in the neuroscience research field is quite novel.
The authors present results using both traditional RNNs and more recent models like GPT-2.

**Paper weaknesses**

This paper is a condensed version of the full article, "Disentangling Representations through Multi-task Learning", which is provided as supplementary material. Therefore, it does not contain any significant improvements/new claims compared to the extended version, but is only a summary of it.

**Suggestions**

To expand and improve this work further, the authors should check the literature in other research fields in which several works have already been presented regarding the relationship between disentanglement and MTL.
For example:
* Meng et al. [1] highlight a link between disentangled representations and MTL, demonstrating that disentangled features can enhance multi-task network performance, particularly on datasets with novel properties.
* Yang et al. [2] introduce the concept of "Knowledge Factorization", where the knowledge from a pre-trained multi-task network (the teacher) is leveraged to train disentangled single-task networks (the students), optimizing computational efficiency for the final single-task network. Their factorization approach is twofold: structural factorization, which separates the network into a shared knowledge network and a task-specific network, and representation factorization, which is driven by mutual information.
* Maziarka et al. [3] conducted a disentanglement analysis of MTL models using a semi-synthetic dataset derived from latent information in simple datasets.
* Skenderi et al. [4] demonstrate that disentangling the representation space can be a general prior for MTL. By leveraging disentanglement to identify auxiliary tasks, an MTL model can extract a model-specific embedding that incorporates both the primary task and the newly discovered labels, ultimately enhancing performance on the primary task.

**References**

[1] Meng, Qingjie, et al. "Representation disentanglement for multi-task learning with application to fetal ultrasound". Smart Ultrasound Imaging and Perinatal, Preterm and Paediatric Image Analysis: First International Workshop, SUSI 2019, and 4th International Workshop, PIPPI 2019, Held in Conjunction with MICCAI 2019, Shenzhen, China, October 13 and 17, 2019, Proceedings 4. Springer International Publishing, 2019.

[2] Yang, Xingyi, Jingwen Ye, and Xinchao Wang. "Factorizing knowledge in neural networks". European Conference on Computer Vision. Cham: Springer Nature Switzerland, 2022.

[3] Maziarka, Łukasz, et al. "On the relationship between disentanglement and multi-task learning". Joint European Conference on Machine Learning and Knowledge Discovery in Databases. Cham: Springer International Publishing, 2022.

[4] Skenderi, Geri, et al. "Disentangled Latent Spaces Facilitate Data-Driven Auxiliary Learning". arXiv preprint arXiv:2310.09278 (2023).
title: title: Interesting findings about the impact of multi-task learning on the learned latent space
main_review: main_review: Summary:
The work analyzes how training RNN models and GPT-2 models on multiple tasks ($N_{tasks}$) can cause disentanglement of the latent space of dimension ($D$). The authors discuss and conclude that when $N_{tasks} \gg D$, the disentanglement is pronounced. This entanglement is further correlated with OOD generalization of the trained model through an independent series of experiments.

Pros:
1. The paper provides rigorous theoretical guarantees for disentangled representations in multi-task classification
2. The authors validate their theoretical results across various neural architectures (RNNs, transformers) and tasks. The experiments demonstrate that abstract, disentangled representations lead to zero-shot out-of-distribution (OOD) generalization​
3. The paper connects neuroscience and machine learning by drawing parallels between cognitive processes (e.g., decision-making) and neural networks. This link could be insightful for both fields
4. The paper comprehensively discusses connections to existing theories in neuroscience and AI, making the findings applicable to both biological and artificial systems

Cons:
1. While the paper presents detailed experiments, most are neuroscience-based. It lacks results on standard ML benchmarks, such as dSprites, which could have made the results more directly comparable to existing methods.
2. The findings indicate that noise is essential for achieving disentangled representations, but do not address limitations associated with having noise in the labels, such as slow convergence and instability of training.
3. Search space is limited to RNNs and GPT-2-like models to perform classification tasks and the extension of the findings to other types of neural networks such as CNNs is not tested or discussed, limiting the direct extension to vision-related applications
title: title: Review of Multi-task Learning yields Disentangled World Models: Impact and Implications
main_review: main_review: Quality:
The work provides a detailed exploration of the emergence of disentangled representations in multi-task learning, backed by theoretical results and experimental validation.

Clarity:
The paper is well-structured and presents its findings in a clear and organized manner. It effectively communicates complex concepts related to disentangled representations, multi-task learning, and their implications for both machine learning and neuroscience. The figure of learning disentangled representations helps readers grasp the core concept of paper quickly.

Originality:
The work showcases originality by highlighting the emergence of disentangled representations in agents solving multi-task evidence aggregation and classification tasks. It also emphasizes the role of parallel processing in constructing cognitive maps shared across biological and artificial systems, contributing to the originality of the findings.

Significance:
The work holds significant implications for both machine learning and neuroscience. It sheds light on the generalization abilities of biological and artificial systems, as well as their exceptional zero-shot generalization capabilities. The implications for representation learning and topology-preserving representation learning are also noteworthy. The findings that transformers are particularly suited for disentangling representations could lead to better explanation of unique world.

Pros:

1. Clear and organized presentation of findings

2. Original insights into disentangled representations and multi-task learning

Cons:

1. Need more explicit discussion of the potential practical applications of the findings.

Comments: title: Reply to reviewer
Reply to reviewer
Reply to reviewer
comment: We would like to thank the reviewer for their detailed comments. In regards to the specific points raised:

1. While we agree that our study focuses on neuroscience tasks, as we emphasize in the limitations in the highlighted work there are no ML benchmarks such as dSprites for the kind of dynamical, noisy tasks that we are dealing with here. Future work could address this shortcoming by creating new datasets that extend dSprites in more dynamic, real world settings e.g. where items are viewed from different angles and light conditions in a grocery store. An alternative would be to apply our framework to online retailer data where sequential decisions like the ones we study are made; however no datasets of this nature are publicly available to our knowledge.

2. While noise is bound to slow down the pre-training process, it is a limitation that agents operating in the real world would have to face anyway. In terms of the post-training usage of the representation by linear decoders, this is a convex optimization problem with convergence guarantees.

3. While we agree that an extension to vision architectures would be interesting, that would require a considerable overhaul of our approach including data and architecture, where more naturalistic data and deep CRNN-types of architectures might have to be used. For this reason, this would constitute an entire new study on its own, and future work could endeavor to do this. In the noise-free regime on the other hand, things are more straightforward and models that are using convolutional feedforward architectures have been shown to disentangle (Maziarka et al 2022).
We would like to thank the reviewer for their comments, and for pointing these references to us. 

Most of these references are on disentanglement in feedforward architectures, and we focus in recurrent architectures; yet we found [3] particularly useful since it seems that its approach and results are very similar to Johnston & Fusi (2023) which we discuss extensively, and while we focus on the Multi-task Learning -> Disentanglement connection [4] shows that the opposite direction is also possible. Therefore, we plan to include these references in future versions of the highlighted work where we discuss connections to the literature in detail.

On that note, we would like to remind the reviewer that these results have not been presented before, as this constitutes an opinion paper based on unpublished results.
We thank the reviewer for their in depth comments and for acknowledging the implications of this work. In regards to the specific comments:

### Motor learning

As an output-driven process, motor learning involves the learning of highly specialized trajectories that are specific to the task being executed. We could, however, see our framework leading to the learning of motor primitives, if several such motor executions are vicariously planned in parallel (efferent copy etc.). Then the motor primitives could be combined to form motor plans, the same way features are combined to form objects.

### Meta-learning

Our work can be though as already implementing meta learning, since the learned representation can be used for *any* downstream task involving the same latent variables.

### Interleaved and blocked training

The reviewer makes an insightful observation that humans and animals excel at blocked learning. On the other hand, neural networks generally perform best at interleaved learning, which allows their weights to be gradually conditioned to solve all tasks. Some recent work has attempted to bridge the two (Flesch, T., Nagy, D. G., Saxe, A., & Summerfield, C. (2023). Modelling continual learning in humans with Hebbian context gating and exponentially decaying task signals. PLoS computational biology, 19(1)), but the setting is quite simplified. Our intuition is that this difference in performance across different learning regimes rests upon high-level learning biases that living organisms have, related to their allocation of attention etc., for which phenomena neural networks might not be the most appropriate level of explanation. Yet, we think that relaxing the simultaneity assumption in our work for interleaved and even blocked training settings would be a very promising area for future work.