Learning cortical representations through perturbed and adversarial dreaming

Humans and other animals learn to extract general concepts from sensory experience without extensive teaching. This ability is thought to be facilitated by offline states like sleep where previous experiences are systemically replayed. However, the characteristic creative nature of dreams suggests that learning semantic representations may go beyond merely replaying previous experiences. We support this hypothesis by implementing a cortical architecture inspired by generative adversarial networks (GANs). Learning in our model is organized across three different global brain states mimicking wakefulness, non-rapid eye movement (NREM), and REM sleep, optimizing different, but complementary, objective functions. We train the model on standard datasets of natural images and evaluate the quality of the learned representations. Our results suggest that generating new, virtual sensory inputs via adversarial dreaming during REM sleep is essential for extracting semantic concepts, while replaying episodic memories via perturbed dreaming during NREM sleep improves the robustness of latent representations. The model provides a new computational perspective on sleep states, memory replay, and dreams, and suggests a cortical implementation of GANs.


Introduction
After just a single night of bad sleep, we are acutely aware of the importance of sleep for orderly body and brain function.In fact, it has become clear that sleep serves multiple crucial physiological functions (Siegel, 2009;Xie et al., 2013), and growing evidence highlights its impact on cognitive processes (Walker, 2009).Yet, a lot remains unknown about the precise contribution of sleep, and in particular dreams, on normal brain function.
One remarkable cognitive ability of humans and other animals lies in the extraction of general concepts and statistical regularities from sensory experience without extensive teaching (Bergelson and Swingley, 2012).Such regularities in the sensorium are reflected on the neuronal level in invariant object-specific representations in high-level areas of the visual cortex (Grill-Spector et al., 2001;Hung et al., 2005;DiCarlo et al., 2012) on which downstreams areas can operate.These so called semantic representations are progressively constructed and enriched over an organism's lifetime (Tenenbaum et al., 2011;Yee et al., 2013) and their emergence is hypothesized to be facilitated by offline states such as sleep (Dudai et al., 2015).
Previously, several cortical models have been proposed to explain how offline states could contribute to the emergence of high-level, semantic representations.Stochastic hierarchical models which learn to maximize the likelihood of observed data under a generative model such as the Helmholtz machine (Dayan et al., 1995) and the closely related Wake-Sleep algorithm (Hinton et al., 1995;Bornschein and Bengio, 2015) have demonstrated the potential of combining online and offline states to learn semantic representations.However, these models do not leverage offline states to improve their generative model activities, our cortical model trained on natural images develops rich latent representations along with the capacity to generate plausible early sensory activities.We demonstrate that adversarial dreaming during REM sleep is essential for learning representations organized according to object semantics, which are improved and robustified by perturbed dreaming during NREM sleep.Together, our results demonstrate a potential role of dreams and suggest complementary functions of REM and NREM sleep in cortical representation learning.

Complementary objectives for wakefulness, NREM and REM sleep
We consider an abstract model of the visual ventral pathway consisting of multiple, hierarchically organized cortical areas, with a feedforward pathway, or encoder, transforming neuronal activities from lower to higher areas (Fig. 2, E).These high-level activities are compressed representations of lowlevel activities and are called latent representations, here denoted by z.In addition to this feedforward pathway, we similarly model a feedback pathway, or generator, projecting from higher to lower areas (Fig. 2, G).These two pathways are supported by a simple hippocampal module which can store and replay latent representations.Three different global brain states are considered: wakefulness (Wake), non-REM sleep (NREM) and REM sleep (REM).We focus on the functional role of these phases while abstracting away dynamical features such as bursts, spindles or slow waves (Léger et al., 2018), in line with previous approaches based on goal-driven modeling which successfully predict physiological features along the ventral stream (Yamins et al., 2014;Zhuang et al., 2021).
In our model, the three brain states only differ in their objective function and the presence or absence of external input.Synaptic plasticity performs stochastic gradient descent on state-specific objective functions via error backpropagation (LeCun et al., 2015).We assume that efficient credit assignment is realized in the cortex, and focus on the functional consequences of our specific architecture.For potential implementations of biophysically plausible backpropagation in cortical circuits, we refer to previous work (e.g., Whittington and Bogacz, 2019;Lillicrap et al., 2020).
During Wake (Fig. 2a), sensory inputs evoke activities x in lower sensory cortex which are trans- formed via the feedforward pathway E into latent representations z in higher sensory cortex.The hippocampal module stores these latent representations, mimicking the formation of episodic memories.Simultaneously, the feedback pathway G generates low-level activities x from these representations.Synaptic plasticity adapts the encoding and generative pathways (E and G) to minimize the mismatch between externally-driven and internally-generated activities (Fig. 2a).Thus, the network learns to reproduce low-level activity from abstract high-level representations.Simultaneously, E also acts as a 'discriminator' with output d that is trained to become active, reflecting that the low-level activity was driven by an external stimuli.The discriminator learning during Wake is essential to drive adversarial learning during REM.Note that computationally the classification of low-level cortical activities into "externally driven" and "internally generated" is not different from classification into, for example, different object categories, even though conceptually they serve different purposes.The dual use of E reflects a view of cortical information processing in which several network functions are preferentially shared among a single network mimicking the ventral visual stream (DiCarlo et al., 2012).This approach has been previously successfully employed in machine learning models (Huang et al., 2018;Brock et al., 2017;Ulyanov et al., 2017;Munjal et al., 2019;Bang et al., 2020).
For the subsequent sleep phases, the system is disconnected from the external environment, and activity in lower sensory cortex is driven by top-down signals originating from higher areas, as previously suggested (Nir and Tononi, 2010;Aru et al., 2020).During NREM (Fig. 2b), latent representations z are recalled from the hippocampal module, corresponding to the replay of episodic memories.These representations generate low-level activities which are perturbed by suppressing early sensory neurons, modeling the observed differences between replayed and waking activities (Ji and Wilson, 2007).The encoder reconstructs latent representations from these activity patterns, and synaptic plasticity adjusts the feedforward pathway to make the latent representation of the perturbed generated activity similar to the original episodic memory.This process defines perturbed dreaming.
During REM (Fig. 2c), sleep is characterized by creative dreams generating realistic virtual sensory experiences out of the combination of episodic memories (Fosse et al., 2003;Lewis et al., 2018).In PAD, multiple random episodic memories from the hippocampal module are linearly combined and projected to cortex.Reflecting the decreased coupling (Wierzynski et al., 2009;Lewis et al., 2018) between hippocampus and cortex during REM sleep, these mixed representations are diluted with spontaneous cortical activity, here abstracted as Gaussian noise with zero mean and unit variance.From this new high-level cortical representation, activity in lower sensory cortex is generated and finally passed through the feedforward pathway.Synaptic plasticity adjusts feedforward connections E to silence the activity of the discriminator output as it should learn to distinguish it from externallyevoked sensory activity.Simultaneously, feedback connections are adjusted adversarially to generate activity patterns which appear externally-driven and thereby trick the discriminator into believing that the low-level activity was externally-driven.This is achieved by inverting the sign of the errors that determine synaptic weight changes in the generative network.This process defines adversarial dreaming.
The functional differences between our proposed NREM and REM sleep phases are motivated by experimental data describing a reactivation of hippocampal memories during NREM sleep and the occurrence of creative dreams during REM sleep.In particular, hippocampal replay has been reported during NREM sleep within sharp-wave-ripples (O'Neill et al., 2010), also observed in the visual cortex (Ji and Wilson, 2007), which resembles activity from wakefulness.Our REM sleep phase is built upon cognitive theories of REM dreams (Llewellyn, 2016b;Lewis et al., 2018) postulating that they emerge from random combinations between episodic memory elements, sometimes remote from each other, which appear realistic for the dreamer.This random coactivation could be caused by theta oscillations in the hippocampus during REM sleep (Buzsáki, 2002).The addition of cortical noise is motivated by experimental work showing reduced correlations between hippocampal and cortical activity during REM sleep (Wierzynski et al., 2009), and the occurence of ponto-geniculo-occipital (PGO) waves (Nelson et al., 1983) in the visual cortex often associated with generation of novel visual imagery in dreams (Hobson et al., 2000(Hobson et al., , 2014)).Furthermore, the cortical contribution in REM dreaming is supported by experimental evidence that dreaming still occurs with hippocampal damage, while reported to be less episodic-like in nature (Spanò et al., 2020).
Within our suggested framework, 'dreams' arise as early sensory activity that is internally-generated via feedback pathways during offline states, and subsequently processed by feedforward pathways.In particular, this implies that besides REM dreams, NREM dreams exist.However, in contrast to REM dreams, which are significantly different from waking experiences (Fosse et al., 2003), our model implies that NREM dreams are more similar to waking experiences since they are driven by single episodic memories, in contrast to REM dreams which are generated from a mixture of episodic memories.Furthermore, the implementation of adversarial dreaming requires an internal representation of whether early sensory activity is externally or internally generated, i.e., a distinction whether a sensory experience is real or imagined.

Dreams become more realistic over the course of learning
Dreams in our model arise from both NREM (perturbed dreaming) and REM (adversarial dreaming) phases.In both cases, they are characterized by activity in early sensory areas generated via feedback pathways.To illustrate learning in PAD, we consider these low-level activities during NREM and during REM for a model with little learning experience ("early training") and a model which has experienced many wake-sleep cycles ("late training"; Fig. 3).A single wake-sleep cycle consists of Wake, NREM and REM phases.As an example, we train our model on a dataset of natural images (CIFAR-10; Krizhevsky et al., 2013) and a dataset of images of house numbers (SVHN; Netzer et al., 2011).Initially, internally-generated low-level activities during sleep do not share significant similarities with sensory-evoked activities from Wake (Fig. 3a); for example, no obvious object shapes are represented (Fig. 3b).After plasticity has organized network connectivity over many wake-sleep cycles (50 training epochs), low-level internally-generated activity patterns resemble sensory-evoked activity (Fig. 3c).NREM-generated activities reflect the sensory content of the episodic memory (sensory input from the previous day).REM-generated activities are different from the sensory activities corresponding to the original episodic memories underlying them as they recombine features of sensory activities from the two previous days, but still exhibit a realistic structure.This increase in similarity between externally-driven and internally-generated low-level activity patterns is also reflected in a decreasing Fréchet inception distance (Fig. 3d), a metric used to quantify the realism of generated images (Heusel et al., 2018).The increase of dreams realism, here mostly driven by a combination of reconstruction learning (Wake) and adversarial learning (Wake and REM), correlates with the development of dreams in children, that are initially plain and fail to represent objects, people, but become more realistic and structured over time (Foulkes, 1999;Nir and Tononi, 2010).
The PAD training paradigm hence leads to internally-generated low-level activity patterns that become more difficult to discern from externally-driven activities, whether they originate from single episodic memories during NREM or from noisy random combinations thereof during REM.We will next demonstrate that the same learning process leads to the emergence of robust semantic representations.

Adversarial dreaming during REM facilitates the emergence of semantic representations
Semantic knowledge is fundamental for animals to learn quickly, adapt to new environments and communicate, and is hypothesized to be held by so-called semantic representations in cortex (DiCarlo et al., 2012)

2015).
Here we demonstrate that PAD, due to the specific combination of plasticity mechanisms during Wake, NREM and REM, develops such semantic representations in higher visual areas.Similarly as in the previous section, we train our model on the CIFAR-10 and SVHN datasets.To quantify the quality of inferred latent representations, we measure how easily downstream neurons can read out object identity from these.For a simple linear read-out, its classification accuracy reflects the linear separability of different contents represented in a given dataset.Technically, we train a linear classifier that distinguishes object categories based on their latent representations z after different numbers of wake-sleep cycles ('epochs', Fig. 4a) and report its accuracy on data not used during training of the model and classifier ("test data").While training the classifier, the connectivity of the network (E and G) is fixed.
The latent representation (z) emerging from the trained network (Fig. 4b, full model) shows increasing linear separability reaching around 59% test accuracy on CIFAR-10 (Fig. 4c, black line, for details see Supplements Table 1) and 79% on SVHN (Fig. 4d, black line), comparable to less biologically plausible machine-learning models (Berthelot et al., 2018).These results show the ability of PAD to discover semantic concepts across wake-sleep cycles in an unsupervised fashion.
Within our computational framework, we can easily consider sleep pathologies by directly interfering with the sleep phases.To highlight the importance of REM in learning semantic representations, we consider a reduced model (P d d AD) in which the REM phase with adversarial dreaming is suppressed and only perturbed dreaming during NREM remains (Fig. 4b, pink cross).Without REM sleep, linear separability increases much slower and even after a large number of epochs remains significantly below the PAD (see also Supplements Fig. 12c,d).This suggests that adversarial dreaming during REM, here modeled by an adversarial game between feedforward and feedback pathways, is essential for the emergence of easily readable, semantic representations in the cortex.From a computational point of view, this result is in line with previous work showing that learning to generate virtual inputs via adversarial learning (GANs variants) forms better representations than simply learning to reproduce external inputs (Radford et al., 2015;Donahue et al., 2016;Berthelot et al., 2018).
Finally, we consider a different pathology in which REM is not driven by randomly combined episodic memories and noise, but by single episodic memories without noise, as during NREM (Fig. 4b, purple cross).Similarly to removing REM, linear separability increases much slower across epochs, leading to worse performance of the readout (Fig. 4c,d, purple lines).For the SVHN dataset, the performance does not reach the level of the PAD even after many wake-sleep cycles (see also Supplements Fig. 12d).This suggests that combining different, possibly non-related episodic memories, together with spontaneous cortical activity, as reported during REM dreaming (Fosse et al., 2003), leads to significantly faster representation learning.
Our results suggest that generating virtual sensory inputs during REM dreaming, via a high-level combination of hippocampal memories and spontaneous cortical activity and subsequent adversarial learning, allow animals to extract semantic concepts from their sensorium.Our model provides hypotheses about the effects of REM deprivation, complementing pharmacological and optogenetic studies reporting impairments in the learning of complex rules and spatial object recognition (Boyce et al., 2016).For example, our model predicts that object identity would be less easily decodable from recordings of neuronal activity in the Inferior-Temporal (IT) cortex in animal models with chronically impaired REM sleep.

Perturbed dreaming during NREM improves robustness of semantic representations.
Generalizing beyond previously experienced stimuli is essential for an animal's survival.This generalization is required due to natural perturbations of sensory inputs, for example partial occlusions, noise, or varying viewing angles.These alter the stimulation pattern, but in general should not change its latent representation subsequently used to make decisions.
Here, we model such sensory perturbations by silencing patches of neurons in early sensory areas during the stimulus presentation (Fig. 5a).As before, linear separability is measured via a linear classifier that has been trained on latent representations of un-occluded images and we use stimuli which were not used during training.Adding occlusions hence directly tests the out-of-distribution generalization capabilities of the learned representations.For the model trained with all phases (Fig. 5b, full model), the linear separability of latent representations decreases as occlusion intensity increases, until reaching chance level for fully occluded images (Fig. 5c,d; black line).
We next consider a sleep pathology in which we suppress perturbed dreaming during the NREM phase while keeping adversarial dreaming during REM ( PAD, Fig. 5B, orange cross).In PAD, linear separability of partially occluded images is significantly decreased for identical occlusion levels (Fig. 5c,  d; compare black and orange lines).In particular, performance degrades much faster with increasing occlusion levels.Note that despite the additional training objective, the full PAD develops equally good or even better latent representations of unoccluded images (0% occlusion intensity) compared to this pathological condition without perturbed dreams.
Crucially, the perturbed dreams in NREM are generated by replaying single episodic memories.If the latent activity fed to the generator during NREM was of similar origin as during REM, i.e. obtained from a convex combination of multiple episodic memories coupled with cortical spontaneous activity, the quality of the latent representations significantly decreases (see also Supplements Fig. 15).This suggests that only replaying single memories, as hypothesized to occur during NREM sleep (O'Neill et al., 2010), rather than their noisy combination, is beneficial to robustify latent representations against input perturbations.
This robustification originates from the training objective defined in the NREM phase, forcing feedforward pathways to map perturbed inputs to the latent representation corresponding to their clean, non-occluded version.This procedure is reminiscent of a regularization technique from machine learning called 'data augmentation' (Shorten and Khoshgoftaar, 2019), which increases the amount of training data by adding stochastic perturbations to each input sample.However, in contrast to data augmentation methods which directly operate on samples, here the system autonomously generates augmented data in offline states, preventing interference with online cognition and avoiding storage of the original samples.Our 'dream augmentation' suggests that NREM hippocampal replay not only maintains or strengthens cortical memories, as traditionally suggested (Klinzing et al., 2019), but also improves latent representations when only partial information is available.For example, our model predicts that animals lacking such dream augmentation, potentially due to impaired NREM sleep, fail to react reliably to partially occluded stimuli even though their responses to clean stimuli are accurate.

Latent organization in healthy and pathological models
The results so far demonstrate that perturbed and adversarial dreaming (PAD), during REM and NREM sleep states, contribute to cortical representation learning by increasing the linear separability of latent representations into object classes.We next investigate how the learned latent space is organized, i.e., whether representations of sensory inputs with similar semantic content are grouped together even if their low-level structure may be quite different, for example due to different viewing angles, variations among an object category, or (partial) occlusions.
We illustrate the latent organization by projecting the latent variable z using Principal Component Analysis (PCA, Fig. 6a, Jolliffe and Cadima, 2016).This method is well-suited for visualizing highdimensional data in a low-dimensional space while preserving as much of the data's variation as possible.
For PAD, the obtained PCA projection shows relatively distinct clusters of latent representations according to the semantic category ("class identity") of their corresponding images (Fig. 6b).The model thus tends to organize latent representations such that high-level, semantic clusters are discernable.Furthermore, partially occluded objects (Fig. 6b, empty circles) are represented closeby their corresponding un-occluded version (Fig. 6b, full circles).
As shown in the previous sections, removing either REM or NREM has a negative impact on the linear separability of sensory inputs.However, the reasons for these effects are different between REM and NREM.If REM sleep is removed from training (P d d AD), representations of unoccluded images are less organized according their semantic category, but still match their corresponding occluded versions (Fig. 6c).REM is thus necessary to organize latent representations into semantic clusters, providing an easily readable representation for downstream neurons.In contrast, removing NREM ( PAD) causes representations of occluded inputs to be remote from their un-occluded representations (Fig. 6d).
We quantify these observations by computing the average distances between latent representations from the same object category (intra-class distance) and between representations of different object category (inter-class distance).Since the absolute distances are difficult to interpret, we focus on their ratio (Fig. 6e).On both datasets, this ratio increases if the REM phase is removed from training (Fig. 6e, compare black and pink bars), reaching levels comparable to the one with the untrained network.Moreover, removing NREM from training also increases this ratio.These observations suggest that both perturbed and adversarial dreaming jointly reorganize the latent space such that stimuli with similar semantic structure are mapped to similar latent representations.In addition, we compute the distance between the latent representations inferred from clean images and their corresponding occluded versions, also divided by the inter-class distance (Fig. 6f).By removing NREM from training, this ratio increases significantly, highlighting the importance of NREM in making latent representations invariant to input perturbations.

Cortical implementation of PAD
We have shown that perturbed and adversarial dreaming (PAD) can learn semantic cortical representations useful for downstream tasks.Here we hypothesize how the associated mechanisms may be implemented in cortex.
First, PAD implies the existence of discriminator neurons that would learn to be differentially active during wakefulness and REM sleep.It also postulates a conductor that orchestrates learning by providing a teaching ('nudging') signal to the discriminator neurons during Wake and REM.Experimental evidence suggests that discriminator neurons, differentiating between internally generated end externally driven sensory activity, may reside in the anterior cingulate cortex (ACC) or the medial prefrontal cortex (mPFC), but functionally similar neurons may be located across cortex to deliver local learning signals (Subramaniam et al., 2012;Simons et al., 2017;Gershman, 2019;Benjamin and Kording, 2021).
Second, learning in PAD is orchestrated across three different phases: (i) learning stimulus reconstruction during Wake, (ii) learning latent variable reconstruction during NREM sleep ('perturbed dreaming'), and (iii) learning to generate realistic sensory activity during REM sleep ('adversarial dreaming').Our model suggests that objective functions and synaptic plasticity are affected by these phases (Fig. 7).Wakefulness is associated with increased activity of modulatory brainstem neurons releasing neuromodulators such as acetylcholine (ACh) and noradrenaline (NA), hypothesized to prioritize the amplification of information from external stimuli (Adamantidis et al., 2019;Aru et al., 2020).In contrast, neuromodulator concentrations during NREM are reduced compared to Wake, while REM is characterized by high ACh and low NA levels (Hobson, 2009).We postulate that the state-specific modulation provides a high activity target for the discriminator during Wake which is decreased during REM and entirely gated off during NREM.Furthermore, we suggest that adversarial learning is implemented by a sign-switched plasticity in the generative network during REM sleep,

High
Low High

Low-level activity
Externally driven

Internally generated
Internally generated with respect to Wake.During wakefulness, plasticity in these apical synapses may be enhanced by noradrenaline (NA) as opposed to NREM (Adamantidis et al., 2019;Aru et al., 2020).The presence of acetylcholine (ACh) alone during REM (Hobson et al., 2000) may switch the sign of plasticity in apical synapses of (hippocampal) pyramidal neurons (McKay et al., 2007).Furthermore, it is known that somato-dendritic synchrony is reduced in REM versus NREM sleep (Seibt et al., 2017); this suggests a reduced somato-dendritic backpropagation of action potentials, which, in turn, is known to switch the sign of apical plasticity (Sjöström and Häusser, 2006).

Discriminator
Third, learning in our model requires the computation of reconstruction errors, i.e., mismatches between top-down and bottom-up activity.So far, two non-exclusive candidates for computing mismatch signals have been proposed.One suggests a dendritic error representation in layer 5 pyramidal neurons that compare bottom-up with top-down inputs from our encoding (E) and generative (G) pathways (Guerguiev et al., 2017;Sacramento et al., 2018).The other suggests an explicit mismatch representation by subclasses of layer 2/3 pyramidal neurons (Keller and Mrsic-Flogel, 2018).
Fourth, our computational framework assumes effectively separate feedforward and feedback streams.A functional separation of these streams does not necessarily imply a structural separation at the network level.Indeed, such cross-projections are observed in experimental data (Gilbert and Li, 2013) and also used in, e.g., the predictive processing framework (Rao and Ballard, 1999).In our model, an effective separation of the information flows is required to prevent "information shortcuts" across early sensory cortices which would prevent learning of good representations in higher sensory areas.This suggests that for significant periods of time, intra-areal lateral interactions between cortical feedforward and feedback pathways are effectively gated off in most of the areas.
Fifth, similar to previous work (Káli and Dayan, 2004), the hippocampus is not explicitly modeled but rather mimicked by a buffer allowing simple store and retrieve operations.An extension of our model could replace this simple mechanism with attractor networks which have been previously employed to model hippocampal function (Tang et al., 2010).The combination of episodic memories underlying REM dreams in our model could either occur in hippocampus or in cortex.In either case, we would predict a nearly simultaneous activation of different episodic memories in hippocampus that results in the generation of creative virtual early cortical activity.
Finally, beyond the mechanisms discussed above, our model assumes that cortical circuits can efficiently perform credit assignment, similar to the classical error backpropagation algorithm.Most biologically plausible implementations for error-backpropagation involve feedback connections to deliver error signals (Whittington and Bogacz, 2019;Richards et al., 2019;Lillicrap et al., 2020), for example to the apical dendrites of pyramidal neurons (Sacramento et al., 2018;Guerguiev et al., 2017;Haider et al., 2021).An implementation of our model in such a framework would hence require addi-tional feedforward and feedback connections for each neuron.For example, neurons in the feedforward pathway would not only project to higher cortical areas to transmit signals, but additionally project back to earlier areas to allow these to compute the local errors required for effective learning.Overall, our proposed model could be mechanistically implemented in cortical networks through different classes of pyramidal neurons with a biological version of supervised learning based on a dendritic prediction of somatic activity (Urbanczik and Senn, 2014), and a corresponding global modulation of synaptic plasticity by state-specific neuromodulators.

Discussion
Semantic representations in cortical networks emerge in early life despite most observations lacking an explicit class label, and sleep has been hypothesized to facilitate this process (Klinzing et al., 2019).However, the role of dreams in cortical representation learning remains unclear.Here we proposed that creating virtual sensory experiences by randomly combining episodic memories during REM sleep lies at the heart of cortical representation learning.Based on a functional cortical architecture, we introduced the perturbed and adversarial dreaming model (PAD) and demonstrated that REM sleep can implement an adversarial learning process which, constrained by the network architecture and the choice of latent prior distributions, builds semantically organized latent representations.Additionally, perturbed dreaming based on the episodic memory replay during NREM stabilizes the cortical representations against sensory perturbations.Our computational framework allowed us to investigate the effects of specific sleep-related pathologies on cortical representations.Together, our results demonstrate complementary effects of perturbed dreaming from individual episodes during NREM and adversarial dreaming from mixed episodes during REM.PAD suggests that the generalization abilities exhibited by humans and other animals arise from distinct processes during the two sleep phases: REM dreams organize representations semantically and NREM dreams stabilize these representations against perturbations.Finally, the model suggests how adversarial learning inspired by GANs can potentially be implemented by cortical circuits and associated plasticity mechanisms.

Relation to cognitive theories of sleep
PAD focuses on the functional role of sleep, and in particular dreams.Many dynamical features of brain states during NREM and REM sleep, such as cortical oscillations (Léger et al., 2018) are hence ignored here but will potentially become relevant when constructing detailed circuit models of the suggested architectures, for example for switching between memories (Korcsak-Gorzo et al., 2021).Our proposed model of sleep is complementary to theories suggesting that sleep is important for physiological and cognitive maintenance (McClelland et al., 1995;Káli and Dayan, 2004;Rennó-Costa et al., 2019;van de Ven et al., 2020).In particular, Norman et al. (2005) proposed a model where autonomous reactivation of memories (from cortex and hippocampus) coupled with oscillating inhibition during REM sleep helps detect weak parts of memories and selectively strengthen them, to overcome catastrophic forgetting.While our REM phase serves different purposes, an interesting commonality is the view of REM as a period where the cortex "thinks about what it already knows" from past and recent memories and reorganizes its representations by replaying them together, as opposed to NREM where only recent memories are replayed and consolidated.Recent work has also suggested that the brain learns using adversarial principles, either as a reality monitoring mechanism potentially explaining delusions in some mental disorders (Gershman, 2019), in the context of dreams to overcome overfitting and promote generalization (Hoel, 2021), and for learning inference in recurrent biological networks (Benjamin and Kording, 2021).
Cognitive theories propose that sleep promotes the abstraction of semantic concepts from episodic memories through a hippocampo-cortical replay of waking experiences, referred to as "memory semantization" (Nadel and Moscovitch, 1997;Lewis and Durrant, 2011).The learning of organized representations is an important basis for semantization.An extension of our model would consider the influence of different sensory modalities on representation learning (Guo et al., 2019), which is known to significantly influence cortical schemas (Lewis et al., 2018) and can encourage the formation of computationally powerful representations (Radford et al., 2021).
Finally, sleep has previously been considered as a state where 'noisy' connections acquired during wakefulness are selectively forgotten (Crick and Mitchison, 1983;Poe, 2017), or similarly, as a homeostatic process to desaturate learning and renormalize synaptic strength (synaptic homeostasis hypothesis; Tononi andCirelli, 2014, 2020).In contrast, our model offers an additional interpretation of plasticity during sleep, where synapses are globally readapted to satisfy different but complementary learning objectives than Wake, either by improving feedforward recognition of perturbed inputs (NREM) or by adversarially tuning top-down generation (REM).

Relation to representation learning models
Recent advances in machine learning, such as self-supervised learning approaches, have provided powerful techniques to extract semantic information from complex datasets (Liu et al., 2021).Here, we mainly took inspiration from self-supervised generative models combining autoencoder and adversarial learning approaches (Radford et al., 2015;Donahue et al., 2016;Dumoulin et al., 2017;Berthelot et al., 2018;Liu et al., 2021).It is theoretically not yet fully understood how linearly separable representations are learned from objectives which do not explicitly encourage them, i.e., reconstruction and adversarial losses.We hypothesize that the presence of architectural constraints and latent priors, in combination with our objectives, enable their emergence (see also Alemi et al., 2018;Tschannen et al., 2020).Note that similar generative machine learning models often report a higher linear separability of network representations, but use all convolutional layers as a basis for the readout (Radford et al., 2015;Dumoulin et al., 2017), while we only used low-dimensional features z.Approaches similar to ours, i.e., those which perform classification only on the latent features, report comparable performance to ours (Berthelot et al., 2018;Hjelm et al., 2019;Beckham et al., 2019).
Furthermore, in contrast to previous GAN variants, our model removes many optimization tricks such as batch-normalization layers (Ioffe and Szegedy, 2015), spectral normalization layers (Miyato et al., 2018) or optimizing the min-max GAN objective in three steps with different objectives, which are challenging to implement in biological substrates.Despite their absence, our model maintains a high quality of latent representations.As our model is relatively simple, it is amenable to implementations within frameworks approximating backpropagation in the brain (Whittington and Bogacz, 2019;Richards et al., 2019;Lillicrap et al., 2020).However, some components remain challenging for implementations in biological substrates, for example convolutional layers (but see Pogodin et al., 2021) and batched training (but see Marblestone et al., 2016).

Dream augmentations, mixing strategies and fine-tuning
To make representations robust, a computational strategy consists of learning to map different sensory inputs containing the same object to the same latent representation, a procedure reminiscent of data augmentation (Shorten and Khoshgoftaar, 2019).As mentioned above, unlike standard data augmentation methods, our NREM phase does not require the storage of raw sensory inputs to create altered inputs necessary for such data augmentation and instead relies on (hippocampal) replay being able to regenerate similar inputs from high-level representations stored during wakefulness.Our results obtained through perturbed dreaming during NREM provide initial evidence that this dream augmentation may robustify cortical representations.
Furthermore, as discussed above, introducing more specific modifications of the replayed activity, for example mimicking translations or rotations of objects, coupled with a negative phase where latent representations from different images are pushed apart, may further contribute to the formation of invariant representations.Along this line, recent self-supervised contrastive learning methods (Gidaris et al., 2018;Chen et al., 2020;Zbontar et al., 2021) have been shown to enhance the semantic structure of latent representations by using a similarity objective where representations of stimuli under different views are pulled together in a first phase, while, crucially, embedding distances between unrelated images are increased in a second phase.
In our REM phase, different mixing strategies in the latent layer could be considered.For instance, latent activities could be mixed up by retaining some vector components of a representation and using the rest from a second one (Beckham et al., 2019).Moreover, more than two memory representations could have been used.Alternatively, our model could be trained with spontaneous cortical activity only.In our experimental setting we do not observe significant differences between using a combination of episodic memories with spontaneous activity or only using spontaneous activity (Supplements Fig. 13).However, we hypothesize that for models which learn continuously, a preferential replay of combinations of recent episodic memories encourages the formation of cortical representations that are useful in the present.
Here, we used a simple linear classifier to measure the quality of latent representations, which is an obvious simplification with regard to cortical processing.Note however that also for more complex 'readouts', organized latent representations enable more efficient and faster learning (Silver et al., 2017;Ha and Schmidhuber, 2018;Schrittwieser et al., 2020).In its current form, PAD assumes that training the linear readout does not lead to weight changes in the encoder network.However, in cortical networks, cognitive or motor tasks leveraging latent representations likely shape the encoder network, which could in our model be reflected in 'fine-tuning' the encoder for specific tasks (compare Liu et al., 2021).
Finally, our model does not show significant differences in performance when the order of sleep phases is switched (Supplements Fig. 14).However, NREM and REM are observed to occur in a specific order throughout the night (Diekelmann and Born, 2010) and this order has been hypothesized to be important for memory consolidation ("sequential hypothesis", Giuditta et al., 1995).The independence of phases in our model may be due to the relatively small synaptic changes occurring in each phase.We expect the order of sleep phases to influence model performance if these changes become larger, either due to longer phases or increased learning rates.The latter may become particularly relevant in continual learning settings where it becomes important to control the emphasis put on recent observations.

Signatures of generative learning
PAD makes several experimentally testable predictions at the neuronal and systems level.We first address generally whether the brain learns via generative models during sleep before discussing specific signatures of adversarial learning.
First, our NREM phase assumes that hippocampal replay generates perturbed wake-like early sensory activity (see also Ji and Wilson, 2007) which is subsequently processed by feedforward pathways.Moreover, our model predicts that over the course of learning, sensory-evoked neuronal activity and internally-generated activity during sleep become more similar.In particular, we predict that (spatial) activity in both NREM and REM become more similar to Wake, however, patterns observed during REM remain distinctly different due to the creative combination of episodic memories.Future experimental studies could confirm these hypotheses by recording early sensory activity during wakefulness, NREM and REM sleep at different developmental stages and evaluating commonalities and differences between activity patterns.Previous work has already demonstrated increasing similarity between stimulus-evoked and spontaneous (generated) activity patterns during wakefulness in ferret visual cortex (Berkes et al., 2011; but see Avitan et al., 2021).
On a behavioral level, the improvement of internally-generated activity patterns correlates with the development of dreams in children, that are initially unstructured, simple and plain, and gradually become full-fledged, meaningful, narrative, implicating known characters and reflecting life episodes (Nir and Tononi, 2010).In spite of their increase in realism, REM dreams in adulthood are still reported as bizarre (Williams et al., 1992).Bizarre dreams, such as a "flying dogs", are typically defined as discontinuities or incongruities of the sensory experience (Mamelak and Hobson, 1989) rather than completely structureless experiences.This definition hence focuses on high-level logical structure, not on the low-level sensory content.In contrast, the low FID score, i.e., high realism, of REM dreams in our experiments reflects that the low-level structure on which this evaluation metric mainly focuses (e.g., Brendel and Bethge, 2019) is similar to actual sensory input.Capturing the "logical realism" of our generated neuronal activities most likely requires a more sophisticated evaluation metric and an extension of the model capable of generating temporal sequences of sensory stimulation.We note, however, that even such surreal dreams as "flying dogs" can be interpreted as altered combinations of episodic memories and thus, in principle, can arise from our model.Second, our model suggests that the development of semantic representations is mainly driven by REM sleep.This allows us to make predictions which connect the network with the systems level, in the specific case of acquiring skills from complex and unfamiliar sensory input.For humans, this could be learning a foreign language with unfamiliar phonetics.Initially, cortical representations cannot reflect relevant nuances in these sounds.Phonetic representations develop gradually over experience and are reflected in changes of the sensory evoked latent activity, specifically in the reallocation of neuronal resources to represent the relevant latent dimensions.We hypothesize that in case of impaired REM sleep, this change of latent representations is significantly reduced, which goes hand in hand with decreased learning speed.Future experimental studies could investigate these effects for instance by trying to decode sound identity from high-level cortical areas in patients where REM sleep is impaired over long periods through pharmacological agents such as anti-depressants (Boyce et al., 2017).An equivalent task in the non-human animal domain would be song acquisition in songbirds (Fiete et al., 2007).On a neuronal level, one could selectively silence feedback pathways during REM sleep in animal models over many nights, for example via optogenetic tools.Our model predicts that this silencing would significantly impact the animal's learning speed, as reported from animals with reduced theta rhythm during REM sleep (Boyce et al., 2017).

Signatures of adversarial learning
The experimental predictions discussed above mainly address whether the brain learns via generative models during sleep.Here we make experimental predictions which would support our hypotheses and contrast it to alternative theories of learning during offline states.

Existence of an external/internal discriminator
The discriminator provides our model with the ability to distinguish externally driven from internally generated low-level cortical activity.Due to this unique property, the discriminator may be leveraged to distinguish actual from imagined sensations.According to our model, reduced REM sleep would lead to an impaired discriminator, and could thus result in an inability of subjects to realize that self-generated imagery is not part of the external sensorium.This may result in the formation of delusions, as previously suggested (Gershman, 2019).For instance, hallucinations in schizophrenic patients, often mistaken for veridical perceptions (Waters et al., 2016), could be partially caused by abnormal REM sleep patterns, related to observed reduced REM latency and density (Cohrs, 2008).Based on these observations, we predict in the context of our model a negative correlation between REM sleep quality and delusional perceptions of hallucinations.Systematic differences in REM sleep quality may hence explain why some patients are able to recognize that their hallucinations are self-generated while some others mistake them to be real.Moreoever, although locating discriminator neurons may prove non-trivial (but see "Cortical implementation" for specific suggestions), we predict that once the relevant cells have been identified, perturbing them may lead to detrimental effects on differentiating between external sensory inputs and internally generated percepts.
The state-specific activity of the discriminator population makes predictions about plasticity on synapses in the feedforward stream during wakefulness and sleep.In our model, the discriminator is trained to distinguish externally from internally generated patterns by opposed targets imposed during Wake and REM.After many wake-sleep cycles, the KL loss as well as the reconstruction loss (see Methods) in our model become small compared to the adversarial loss (Fig. 10, 11), which remains non-zero due to a balance between discriminator and generator.The same low-level activity pattern would hence cause opposite weight changes during wakefulness and sleep on feedforward synapses.This could be tested experimentally by actively instantiating similar spatial activity patterns in lowlevel sensory cortex during wakefulness and REM and compare the statistics of observed changes in (feedforward) downstream synapses.

Adversarial training of a generator during sleep
To drive adversarial learning and maintain a balance between the generator and discriminator, the generative network must be trained in parallel to the discriminative (encoder) network during REM.In contrast, in alternative representation learning models which involve offline states such as the Wake-Sleep algorithm (Hinton et al., 1995), generative pathways are not trained to produce realistic dreams during the sleep phase.Rather, they are trained by reconstruction on real input data during the wake phase.This allows an experimental distinction between our model and Wake-Sleep-like models: while our model predicts plasticity in both bottomup and top-down pathways both during wake and during REM sleep, Wake-Sleep models alternate between training feedback and feedforward connections during online and offline states, respectively.
Previous work has developed methods to infer plasticity rules from neuronal activity (Lim et al., 2015;Senn and Sacramento, 2015) or weight changes (Nayebi et al., 2020).In the spirit of existing in vivo experiments, we suggest to optogenetically monitor and potentially modulate apical dendritic activities in cortical pyramidal neurons of mice during wakefulness and REM sleep (Li et al., 2017;Voigts and Harnett, 2020;Schoenfeld et al., 2022).From the statistics of the recorded dendritic and neuronal activity, the plasticity rules could be inferred and compared to the state-dependent rules suggested by our model, in particular to the predicted sign-switch of plasticity between wakefulness and REM sleep.
Adversarial learning and creativity Adversarial learning, for example in GANs, enables a form of creativity, reflected in their ability to generate realistic new data or to create semantically meaningful interpolations (Radford et al., 2015;Berthelot et al., 2018;Karras et al., 2018).This creativity might be partly caused by the freedom in generating sensory activity that is not restricted by requiring good reconstructions, but is only guided by the internal/external judgment (Goodfellow, 2016).This is less constraining on the generator than direct reconstruction losses used in alternative models such as variational auto-encoders (Kingma and Welling, 2013) or the Wake-Sleep algorithm (Hinton et al., 1995).We thus predict that REM sleep, here implementing adversarial learning, should boost creativity, as previously reported (Cai et al., 2009;Llewellyn, 2016a;Lewis et al., 2018).Furthermore, we predict that REM sleep influences a subject's ability to visualize creative mental images, for instance associating non-obvious visual patterns from distinct memories.For example, we predict that participants chronically lacking REM sleep would perform worse than control participants at a creative synthesis task (Palmiero et al., 2015), consisting of combining different visual components into a new, potentially useful object.
Adversarial learning and lucid dreaming Finally, adversarial dreaming offers a theoretical framework to investigate neuronal correlates of normal versus lucid dreaming (Dresler et al., 2012;Baird et al., 2019).While in normal dreaming the internally generated activity is perceived as externally caused, in lucid dreaming it is perceived as what it is, i.e., internally generated.We hypothesize that the "neuronal conductor" that orchestrates adversarial dreaming is also involved in lucid dreaming, by providing to the dreamer conscious access to the target "internal" that the conductor imposes during REM sleep.Our cortical implementation suggests that the neuronal conductor could gate the discriminator teaching via apical activity of cortical pyramidal neurons.The same apical dendrites were also speculated to be involved in conscious perception (Takahashi et al., 2020), dreaming (Aru et al., 2020), and in representing the state and content of consciousness (Aru et al., 2019).
Our model demonstrates that adversarial learning during wakefulness and sleep can provide significant benefits to extract semantic concepts from sensory experience.By bringing insights from modern artificial intelligence to cognitive theories of sleep function, we suggest that cortical representation learning during dreaming is a creative process, orchestrated by brain-state-regulated adversarial games between separated feedforward and feedback streams.Adversarial dreaming may further be helpful to understand learning beyond the standard student-teacher paradigm.By 'seeing' the world from new perspectives every night, dreaming represents an active learning phenomenon, constantly improving our understanding, our creativity and our awareness.

Network architecture
The network consists of two separate pathways, mapping from the pixel to the latent space ('encoder'/'discriminator') and from the latent to pixel space ('generator').Encoder/Discriminator and Generator architectures follow a similar structure as the DCGANs model (Radford et al., 2015).The encoder E z has four convolutional layers (LeCun et al., 2015) containing 64, 128, 256 and 256 channels respectively (Fig. 8).Each layer uses a 4 × 4 kernel, a padding of 1 (0 for last layer), and a stride of 2, i.e., feature size is halved in each layer.All convolutional layers except the last one are followed by a LeakyReLU non-linearity (Maas et al., 2013).We denote the activity in the last convolutional layer as z.An additional convolutional layer followed by a sigmoid non-linearity is added on top of the second-to-last layer of the encoder and maps to a single scalar value d, the internal/external discrimination (with putative teaching signal 0 or 1).We denote the mapping from x to d by E d .E z and E d thus share the first three convolutional layers.We jointly denote them by E, where Mirroring the structure of E z , the generator G has four deconvolutional layers containing 256, 128, 64, and 3 channels.They all use a 4 × 4 kernel, a padding of 1 (0 for first deconvolutional layer) and a stride of 2, i.e, the feature-size is doubled in each layer.The first three deconvolutional layers are followed by a LeakyReLU non-linearity, and the last one by a tanh non-linearity.
As a detailed hippocampus model is outside the scope of this study, we mimic hippocampal storage and retrieval by storing and reading latent representations to and from memory.

Datasets
We use the CIFAR-10 ( Krizhevsky et al., 2013) and SVHN (Netzer et al., 2011) datasets to evaluate our model.They consist of 32 × 32 pixel images with three color channels.We consider their usual split into a training set and a smaller test set.

Training procedure
We train our model by performing stochastic gradient-descent with mini-batches on condition-specific objective functions, in the following also referred to as loss functions, using the ADAM-optimizer (β 1 = 0.5, β 2 = 0.999; Kingma and Ba, 2017) with learning rate of 0.0002 and mini-batch size of 64.We rely on our model being fully differentiable.The following section describes the loss functions for the respective conditions.
// convex combination of current and old latent vectors with noise // gradient ascent on discriminator loss Z old ← Z ; // keep current vectors for next iteration end 4.3.1 Loss functions Wake In the Wake condition, we minimize the following objective function, composed of a loss for image encoding, a regularization, and a real/fake (external/internal) discriminator, E z and G learn to reconstruct the mini-batch of images X = {x (1) , x (2) , ..., x (b) } similarly to autoencoders (Bengio et al., 2013) by minimizing the image reconstruction loss L img defined by where b denotes the size of the mini-batch.We store the latent vectors Z = E z (X) corresponding to the current mini-batch for usage during the NREM and REM phases.
We additionally impose a Kullback-Leibler divergence loss on the encoder E z .This acts as a regularizer and encourages latent activities to be Gaussian with zero mean and unit variance: where q(Z|X) ∼ N (µ, σ 2 ) is a distribution over the latent variables Z, parametrized by mean µ and standard deviation σ, and p(Z) ∼ N (0, 1) is the prior distribution over latent variables.E z is trained to minimize the following loss: where n z denotes the dimension of the latent space and where µ (Z) j and σ (Z) j represent the j th elements of respectively the empirical mean µ (Z) and empirical standard deviation σ (Z) of the set of latent vectors E z (X) = Z.
As part of the adversarial game, E d is trained to classify the mini-batch of images as real.This corresponds to minimizing the loss defined as sum across the mini-batch size b, Note that, in principle, L GAN can be any GAN-specific loss function (Gui et al., 2020).Here we choose the binary cross-entropy loss.
NREM sleep Each Wake phase is followed by a NREM phase.During this phase we make use of the mini-batch of latent vectors z stored during the Wake phase.Starting from a mini-batch of latent vectors, we generate images G(z).Each obtained image of G(z) is multiplied by a binary occlusion mask ω of the same dimension.This mask is generated by randomly picking two occlusion parameters, occlusion intensity and square size (for details see Sec. 4.3.2).The encoder E z learns to reconstruct the latent vectors z by minimizing the following reconstruction loss: where denotes the element-wise product.

REM sleep
In REM, each latent vector from the mini-batch considered during Wake is combined with the latent vector from the previous mini-batch, the whole being convex combined with a minibatch of noise vectors ∼ N (0, I), where I is the identity matrix, leading to a mini-batch of latent vectors Here, λ = 0.5 and λ = 0.5, where Z old is the previous mini-batch of latent activities.This batch of latent vectors is passed through G to generate the associated images G(Z mix ).In this phase, the loss function encourages E d to classify G(Z mix ) as fake, while adversarially pushing G to generate images which are less likely to be classified as fake by the minimax objective where In our model, the adversarial process is simply described by a full backpropagation of error through E d and G with a sign switch of weight changes in G.
In summary, each Wake-NREM-REM cycle consists of: 1) reconstructing a mini-batch x of images during Wake, 2) reconstructing a mini-batch of latent activities Z = E z (X) during NREM with perturbation of G(z), and 3) replaying Z convex combined with Z old and noise from the (n − 1)th cycle.In PAD training, all losses are weighted equally and we did not use a schedule for L KL , as opposed to standard Variational Autoencoder (VAE) training (Kingma and Welling, 2013).One training epoch is defined by the number of mini-batches necessary to cover the whole dataset.The evolution of losses with training epochs is shown in Fig. 10 and Fig. 11.The whole training procedure is summarized in the pseudo-code implemented in Algorithm 1.Following previous work (Zeiler and Fergus, 2013), grey squares of various sizes are applied along the image with a certain probability (Fig. 9).For each mini-batch, a probability and square size were randomly picked between 0 and 1, and 1 − 8 respectively.We divide the image into patches of the given size and we replace each patch with a constant value (here, 0) according to the defined probability.

Training of linear read-out
A linear classifier is trained on top of latent features Z = E z (X), with Z ∈ R N ×256 , where N is the number of training dataset images.A latent feature z ∈ R 256 is projected via a weight matrix W ∈ R 10×256 to the label neurons to obtain the vector y = W z.
This weight matrix is trained in a supervised fashion by using a multi-class cross-entropy loss.For a feature z labelled with a target class t ∈ {0, 1, .., 9}, the per-sample classification loss is given by Here, p W is the conditional probability of the classifier defined by the linear projection and the softmax function The classifier is trained by mini-batch (b = 64) stochastic gradient descent on the loss L C with a learning rate η = 0.2 for 20 epochs, using the whole training dataset.

Linear separability
Following previous work (Hjelm et al., 2019), we define linear separability as the classification accuracy of the trained classifier on inferred latent activities E z (X test ) from a separate test dataset X test .Given a latent feature z, class prediction is made by picking the index of the maximal activity in the vector y.We ran several simulations for 4 different initial parameters of E and G and report the average test accuracy and standard error of the mean over trials.To evaluate performance on occluded data, we applied random square occlusion masks on each sample from X test for a fixed probability of occlusion and square size.We report only results for occulusions of size 4, after observing similar results with other square sizes.

PCA visualization
To visualize the 256-dimensional latent representation E z (x) of the trained model we used the Principal Component Analysis reduction algorithm (Jolliffe and Cadima, 2016).We project the latent representations to the first two principle components.

Latent-space organization metrics
Intra-class distance is computed by randomly picking 1, 000 pairs of images of the same class, projecting them to the encoder latent space z and computing their Euclidian distance.This process is repeated over the 10 classes in order to obtain the average over 10 classes.Similarly, inter-class distance is computed by randomly picking 10, 000 pairs of images of different classes, projecting them to the encoder latent space z and computing their Euclidian distance.The ratio of intra-and inter-class distance is obtained by dividing the mean intra-class distance by the mean inter-class distance.Cleanoccluded distance is computed by randomly picking 10, 000 pairs of non-occluded/occluded images, projecting them to the encoder latent space and computing their Euclidian distance.The ratio of clean-occluded and inter-class distance is obtained by dividing the clean-occluded distance by the mean inter-class distance.We performed this analysis for several different trained networks with different initial conditions and report the mean ratios and standard error of the mean over trials.

Modifications specific to pathological models
To evaluate the differential effects of each phase, we removed NREM and/or REM phases from training (Fig. 4,5,6).For instance, for the condition w/o NREM, the network is never trained with NREM.A few adjustments were empirically observed to be necessary in order to obtain a fair comparison between each condition.When removing the REM phase during training, we observed a decrease of linear separaribility after some (> 25) epochs.We suspect that this decrease is a result of overfitting due to unconstrained autoencoding objective of E and G. Models trained without REM hence would not provide a good baseline to reveal the effect of adversarial dreaming on linear separability.For models without the REM phase, we hence added a vector of Gaussian noise ∼ N (0, 0.5 • I) to the encoded activities E z (X) of dimension n z before feeding them to the generator.Thus, Eq. 2 becomes: which stabilizes linear separability of latent activities around its maximal value for both CIFAR-10 and SVHN datasets until the end of training.Furthermore, we observed that the NREM phase alters linear performance in the absence of REM (w/o REM condition).To overcome this issue, we reduced the effect of NREM by scaling down its loss with a factor of 0.5.This enabled to benefit from NREM (recognition under image occlusion) without altering linear separability on full images.orange and gray curves), linear separability tends to decrease after many training epochs, suggesting that NREM helps to stabilize performance with training by preventing overfitting.

Comparison of performance with REM driven by convex combination or noise
We report the linear classifier performance for PAD using different latent inputs to the generator.In the main text, we use a convex combination of mixed memories (being a convex combination of two different replayed latent vectors) and noise sampled from a Gaussian unit distribution (Fig. 13, black).We here show the results when only random Gaussian noise is used (Fig. 13, green) and when only a convex combination of memories is used (Fig. 13, red).These different mixing strategies do not show a big difference in linear separability over training epochs.

The order of sleep phases has no influence on the performance of the linear classifier
To investigate the role of the order of NREM and REM sleep phases, we consider a variation in which their order is reversed with respect to the model described in the main manuscript.The performance of the linear classifier is not influenced by this change (Fig. 14).

Replaying multiple episodic memories during NREM sleep
While in the main text we considered NREM to use only a single episodic memory, here we report results for a model in which also NREM uses multiple (here: two) episodic memories.(Fig. 15, black curves, same data as in Fig. 5c,d), NREM uses a single stored latent representation.Here we additionally consider an additional model in which these representations are obtained from a convex combination of mixed memories and spontaneous cortical activity.The better performance of a single replay suggests that replay from single episodic memories as postulated to occur during NREM sleep is more efficient to robustify latent representations against input perturbations.

Figure 1 :
Figure 1: Cortical representation learning through perturbed and adversarial dreaming (PAD).(a) During wakefulness (Wake), cortical feedforward pathways learn to recognize that low-level activity is externally-driven and feedback pathways learn to reconstruct it from high-level neuronal representations.These high-level representations are stored in the hippocampus.(b) During NREM sleep (NREM), feedforward pathways learn to reconstruct high-level activity patterns replayed from the hippocampus affected by low-level perturbations, referred to as perturbed dreaming.(c) During REM sleep (REM), feedforward and feedback pathways operate in an adversarial fashion, referred to as adversarial dreaming.Feedback pathways generate virtual low-level activity from combinations of multiple hippocampal memories and spontaneous cortical activity.While feedforward pathways learn to recognize low-level activity patterns as internally generated, feedback pathways learn to fool feedforward pathways.

Figure 2 :
Figure 2: Different objectives during wakefulness, NREM, and REM sleep govern the organization of feedforward and feedback pathways in PAD The variable x corresponds to 32x32 image, z is a 256-dimensional vector representing the latent layer (higher sensory cortex).Encoder (E, green) and generator (G, blue) networks project bottom-up and top-down signals between lower and higher sensory areas.An oblique arrow ( ) indicates that learning occurs in a given pathway.(a) During Wake, low-level activities x are reconstructed.At the same time, E learns to classify lowlevel activity as external (red target 'external!')with its output discriminator d.The obtained latent representations z are stored in the hippocampus.(b) During NREM, the activity z stored during wakefulness is replayed from the hippocampal memory and regenerates visual input from the previous day perturbed by occlusions, modelled by squares of various sizes applied along the generated low-level activity with a certain probability (see Methods).In this phase, E adapts to reproduce the replayed latent activity.(c) During REM, convex combinations of multiple random hippocampal memories (z and z old ) and spontaneous cortical activity ( ), here with specific prefactors, generate a virtual activity in lower areas.While the encoder learns to classify this activity as internal (red target 'internal!'),the generator adversarially learns to generate visual inputs that would be classified as external.The red minus on G indicates the inverted plasticity implementing this adversarial training.

Figure 3 :
Figure 3: Both NREM and REM dreams become more realistic over the course of learning.(a) Examples of sensory inputs observed during wakefulness.Their corresponding latent representations are stored in the hippocampus.(b, c) Single episodic memories (latent representations of stimuli) during NREM from the previous day and combinations of episodic memories from the two previous days during REM are recalled from hippocampus and generate early sensory activity via feedback pathways.This activity is shown for early (epoch 1) and late (epoch 50) training stages of the model.(d) Discrepancy between externally-driven and internally-generated early sensory activity as measured by the Fréchet inception distance (FID) (Heusel et al., 2018) during NREM and REM for networks trained on CIFAR-10 (top) and SVHN (bottom).Lower distance reflects higher similarity between sensory-evoked and generated activity.Error bars indicate ±1 SEM over 4 different initial conditions.

Figure 5 :Figure 6 :
Figure 5: Perturbed dreaming during NREM improves robustness of latent representations.(a) A trained linear classifier (cf.Fig. 4) infers class labels from latent representations.The classifier was trained on latent representations of original images, but evaluated on representations of images with varying levels of occlusion.(b) Training phases and pathological conditions: full model (PAD, black), without NREM phase ( PAD, orange).(c, d) Classification accuracy obtained on test dataset (C: CIFAR-10; D: SVHN) after 50 epochs for different levels of occlusion (0 to 100%).Full model (PAD): black line; w/o NREM ( PAD): orange line.SEM over 4 different initial conditions overlap with data points.Note that due to an unbalanced distribution of samples the highest performance of a naive classifier is 18.9% for the SVHN dataset.

Figure 7 :
Figure 7: Model features and physiological counterparts during Wake, NREM and REM phases.ACh: acetylcholine; NA: noradrenaline."Sign switch" indicates that identical local errors lead to opposing weight changes between Wake and REM sleep.

Figure 8 :
Figure 8: Convolutional neural network (CNN) architecture of encoder/discriminator and generator used in PAD.

Figure 9 :
Figure 9: Varying size and intensity of occlusions on example images from CIFAR-10.Image occlusions vary along 2 parameters: occlusion intensity, defined by the probability to apply a grey square at a given position, and square size (s).

Following
Heusel et al. (2018), Fréchet inception distance (FID) is computed by comparing the statistics of generated (NREM or REM) samples to real images from the training dataset projected through an Inception-v3 network pre-trained on ImageNetFID = µ real − µ gen 2 + Tr(Σ real + Σ gen − 2(Σ real Σ gen ) 1/2 ) (11)where µ and Σ represent the empirical mean and covariance of the 2048-dimensional activations of the Inception v3 pool3 layer for 10, 000 pairs of data samples and generated images.Results represent mean FID and standard error of the mean FID over 4 different trained networks with different initializations.

Figure 11 :
Figure 11: Training losses for full and pathological models with SVHN dataset.

Figure 12 :
Figure 12: Linear classification performance for full model and all pathological conditions.For details see Fig. 4.

Figure 13 :Figure 14 :Figure 15 :
Figure 13: Linear classification performance for different mixing strategies during REM.Linear separability of latent representations with training epochs for PAD trained with different REM phases: one driven by a convex combination of mixed memories and noise (black), one by pure noise (green), and one by mixed memories only (red).For details see Fig. 4.

linear classifier supervised evaluation latent features lower Training conditions a b d higher CIFAR-10 SVHN PAD c
(Grill-Spector et al., 2001;Hung et al., 2005;Majaj et al.,rom higher visual areas that contain linearly separable information about object category, invariant to other factors of variation, such as background, orientation or pose(Grill-Spector et al., 2001;Hung et al., 2005;Majaj et al.,