CerCo Anaïs Servais
email: anais.servais@cnrs.fr

Christophe Hurter
email: christophe.hurter@enac.fr

Emmanuel J Barbeau
email: emmanuel.barbeau@cnrs.fr

Attentional Switch to Memory: An early and critical phase of the cognitive cascade allowing autobiographical memory retrieval

Keywords: autobiographical memory, episodic memory retrieval, mental time travel, attention, attentional switch, default mode network, perceptual decoupling, gaze aversion

Remembering and mentally reliving yesterday's lunch is a typical example of episodic autobiographical memory retrieval. In the present review, we reappraised the complex cascade of cognitive processes involved in memory retrieval, by highlighting one particular phase that has received little interest so far: attentional switch to memory (ASM). As attention cannot be simultaneously directed toward external stimuli and internal memories, there has to be an attentional switch from the external to the internal world in order to initiate memory retrieval. We formulated hypotheses and developed hypothetical models of both the cognitive and brain processes that accompany ASM. We suggest that gaze aversion could serve as an objective temporal marker of the point at which people switch their attention to memory, and highlight several fields (neuropsychology, neuroscience, social cognition, comparative psychology) in which ASM markers could be essential.

Our review thus provides a new framework for understanding the early stages of autobiographical memory retrieval.

Introduction

Autobiographical memory retrieval allows humans to remember the personal events they have experienced in their lives [START_REF] Conway | Sensory-perceptual episodic memory and its context: Autobiographical memory[END_REF]. Retrieval from memory requires a complex cascade of cognitive operations. Although the cognitive processes involved in autobiographical memory have been extensively studied, the earliest phase has been largely overlooked, leading to incomplete models of autobiographical memory. We, therefore, focused the present review on the switch of attention from the external to the internal world that takes place at the onset of strategic autobiographical retrieval.

Without this early attentional switch, strategic autobiographical memory cannot occur. The three main goals of the present theoretical review were to turn the spotlight on this critical phase of autobiographical retrieval, clarify its neural correlates, and formulate hypotheses about objective behavioral markers that could bring about new advances in the field.

We cross-referenced knowledge about two different domains: episodic autobiographical memory retrieval (reminiscing about personal past events), and attention (ability to focus on objects or thoughts). More specifically, we looked at how the dichotomy between internal and external attention (Chun et al., 2011) can explain how the retrieval of information from autobiographical memory is initiated. As attentional resources are limited, internal attention and external attention compete for the same resources [START_REF] Smallwood | The restless mind[END_REF]. To enable retrieval from autobiographical memory, attention has to be disengaged from the external world and redirected toward an internal mental world containing thoughts and memories (Chun et al., 2011). Attention, therefore, needs to be switched from the external to the internal mental world. We call this moment the attentional switch to memory (ASM).

Because external and internal attention depend on anticorrelated and mutually exclusive brain networks [START_REF] Fox | The human brain is intrinsically organized into dynamic, anticorrelated functional networks[END_REF], ASM causes a transition between these two brain states. We can assume that a major change in brain activity takes place at the same time. We explore this major functional reorganization of the brain, with a special focus on the regions thought to act as switchboards between the two attentional networks. Last, we suggest that ASM is accompanied by objective measurable temporal markers. These behavioral (oculomotor) markers could be critical for different fields of research (Box 1).

Autobiographical memory retrieval

Autobiographical memory concerns personal memories and subtends the sense of identity and continuity [START_REF] Conway | Sensory-perceptual episodic memory and its context: Autobiographical memory[END_REF]. It is an essential cognitive ability for humans who spend a great deal of their time mentally reliving personal events they experienced in the past. For example, autobiographical memory retrieval is a prerequisite for resolving memory issues (e.g., "Where did I put my keys?") and joint reminiscing (e.g., "Do you remember that restaurant we went to in Paris some years ago?").

Historically, Tulving's proposal has distinguished two components within personal memory: an episodic component, concerning specific, contextualized memories about personal past events, and a semantic one, taking the form of general knowledge about the self [START_REF] Tulving | Priming of semantic autobiographical knowledge: A case study of retrograde amnesia[END_REF]. Although this episodic-semantic distinction has recently been thought of as less strict than it was initially proposed [START_REF] Renoult | From knowing to remembering: The semantic-episodic distinction[END_REF], it remains an influential view. Episodic memory is about relatively brief events that have occurred only once, in a given place and at a defining moment. To retrieve such information, mental time travel [START_REF] Tulving | Episodic and semantic memory[END_REF][START_REF] Tulving | Episodic memory: From mind to brain[END_REF] is required, that is an ability to mentally relive one's own past experiences [START_REF] Perrin | Memory as mental time travel[END_REF][START_REF] Suddendorf | The evolution of foresight : What is mental time travel, and is it unique to humans?[END_REF]. This is accompanied by a specific type of autonoetic consciousness that involves a strong subjective sense of self [START_REF] Tulving | Episodic memory: From mind to brain[END_REF] and which can be viewed as an epistemic feeling of pastness (Moulin & Souchay, 2013;[START_REF] Perrin | The phenomenology of remembering is an epistemic feeling[END_REF]. Episodic autobiographical memory retrieval is thus not only characterized by the content of the retrieved memories, but also by this unique subjective experience of reliving past events [START_REF] Tulving | Episodic memory: From mind to brain[END_REF]. Strategic (indirect) retrieval is an intentional and active search of memory for elements that will allow the target event to be reconstructed. It is therefore voluntary, sometimes effortful, and involves top-down attention. This contrasts with associative (direct) retrieval, which refers to events that spontaneously come to mind when a cue (i.e., internal thought or element of the environment such as the smell or sight of an object, e.g., Proust's madeleine) automatically reactivates a memory trace [START_REF] Moscovitch | The frontal cortex and working with memory[END_REF].

Strategic autobiographical memory retrieval is a dynamic process that goes through distinct phases.

It is essential to distinguish between two temporal phases of episodic recollection: an early access phase and a later elaboration phase [START_REF] Conway | The neuroanatomy of autobiographical memory: A slow cortical potential study of autobiographical memory retrieval[END_REF][START_REF] Conway | Neurophysiological correlates of memory for experienced and imagined events[END_REF]. The early access phase is dedicated to searching for and selecting the target event (i.e., memories about the recalled episode). To illustrate what goes on during the access phase and why it is important, observe what happens in your mind when you sincerely answer the following question: "How did you celebrate New Year's Eve last year?" Looking for a memory requires an active, controlled search, and an iterative process of reconstruction [START_REF] Conway | The construction of autobiographical memories in the self-memory system[END_REF]. It involves cue specification, a pre-retrieval process where humans think about what they are trying to remember [START_REF] Henson | Right prefrontal cortex and episodic memory retrieval: A functional MRI test of the monitoring hypothesis[END_REF]. This allows choosing specific memory cues to guide and refine their search for the correct episode [START_REF] Bastin | An integrative memory model of recollection and familiarity to understand memory deficits[END_REF].

According to the constructivist model [START_REF] Conway | The construction of autobiographical memories in the self-memory system[END_REF], strategic retrieval from autobiographical memory is a reconstruction process following a funnel strategy through three nested types of representations from the most general to the most specific representation [START_REF] Conway | Sensory-perceptual episodic memory and its context: Autobiographical memory[END_REF]. At the general level, lifetime periods represent periods of several years and are usually defined by a theme such as work, relationships, school, and so on. General events include repeated (e.g., weekly yoga sessions) and time-spanning (e.g., my holiday in Thailand) events. Finally, the most specific level is event-specific knowledge, which corresponds to the phenomenological register of memories: unique episodes with sensory-perceptual features, often visual images [START_REF] Conway | Sensory-perceptual episodic memory and its context: Autobiographical memory[END_REF]. The access phase ends with the selection of the relevant specific event and the simultaneous inhibition of other, similar memories (e.g., New Year's Eve parties from other years) [START_REF] Cabeza | Functional neuroimaging of autobiographical memory[END_REF]. This selection emerges from the interaction between the memory cue and information stored in autobiographical memory [START_REF] Cabeza | Memory systems, processing modes, and components: Functional neuroimaging evidence[END_REF]Moscovitch, 1995). A successful interaction is associated with ecphory, defined as the awakening of a memory trace from a latent state [START_REF] Frankland | The neurobiological foundation of memory retrieval[END_REF]Semon, 1921). Ecphory modifies the consciousness that humans have of their state, as it makes them highly conscious of the fact that they are currently remembering [START_REF] Tulving | Ecphoric processes in recall and recognition[END_REF]. If the retrieved memory corresponds to the searched one, it generates an intuitive feeling of rightness [START_REF] Moscovitch | The frontal cortex and working with memory[END_REF]. Post-retrieval monitoring processes then assess whether the retrieved event is correct and accurate, and verify its veracity further [START_REF] Gilboa | Autobiographical and episodic memory -one and the same ? Evidence from prefrontal activation in neuroimaging studies[END_REF]. If the event is incomplete or incorrect, additional cues are required and the search processes are repeated [START_REF] Henson | Right prefrontal cortex and episodic memory retrieval: A functional MRI test of the monitoring hypothesis[END_REF]. Finally, the internal representation of the memory is explored through mental imagery processes [START_REF] Rubin | The basic-systems model of episodic memory[END_REF][START_REF] Sheldon | The processes involved in mentally constructing event-and scene-based autobiographical representations[END_REF]. The event can be mentally re-experienced or relived with various perceptual, emotional, and contextual details [START_REF] Conway | Episodic memories[END_REF]. [START_REF] Breeden | The mental time travel continuum: On the architecture, capacity, versatility and extension of the mental bridge into the past and future[END_REF] proposed the existence of a component called the mental time travel platform, defined as the temporary internal mental world in which episodic memories can be mentally relived.

The present review aims to focus on the early access phase of strategic autobiographical memory retrieval. As already mentioned, episodic memory retrieval begins with an interaction between a memory cue and an autobiographical past event stored in memory. In daily life, almost all the stimuli that humans encounter can potentially trigger memories. Nevertheless, despite this incredible number of memory cues, humans do not spend their entire time reminiscing. According to [START_REF] Tulving | Priming of semantic autobiographical knowledge: A case study of retrograde amnesia[END_REF], episodic memory retrieval therefore also requires a specific mental state called episodic retrieval mode, namely a tonically maintained mental state oriented toward retrieval [START_REF] Rugg | Retrieval processing and episodic memory[END_REF]. Stimuli are therefore only regarded as memory cues when people are in this retrieval mode [START_REF] Herron | Preparation breeds success: Brain activity predicts remembering[END_REF] allowing them to access internal mental representations during memory retrieval [START_REF] Küper | On the functional significance of retrieval mode: Task switching disrupts the recollection of conceptual stimulus information from episodic memory[END_REF][START_REF] Tarder-Stoll | Dynamic internal states shape memory retrieval[END_REF][START_REF] Xia | Neural evidence that disengaging memory retrieval is modulated by stimulus valence and rumination[END_REF]. [START_REF] Tarder-Stoll | Dynamic internal states shape memory retrieval[END_REF] suggest that the retrieval mode reflects an intention to remember. It maintains the goal of memory retrieval in mind, which requires attention to be focused on the internal representation of the memory. Once activated, the retrieval mode is thought to last until the end of the memory retrieval period [START_REF] Rugg | Retrieval processing and episodic memory[END_REF].

From this brief overview, we can see that autobiographical memory retrieval involves a complex and highly dynamic cascade of cognitive processes. We now turn to the role of attention in this cascade.

Attention to Memory

Role of attention in memory retrieval

Autobiographical memory retrieval requires the selection of the relevant event in memory. Selective attention is therefore needed [START_REF] Long | Situating the default-mode network along a principal gradient of macroscale cortical organization[END_REF]. The internal attention devoted to episodic memory retrieval is widely referred to as reflective attention [START_REF] Chun | Memory: Enduring traces of perceptual and reflective attention[END_REF]. The attention to memory model (AtoM; [START_REF] Cabeza | The parietal cortex and episodic memory: An attentional account[END_REF][START_REF] Ciaramelli | Top-down and bottom-up attention to memory: A hypothesis (AtoM) on the role of the posterior parietal cortex in memory retrieval[END_REF] has already established that attention plays a crucial role in memory retrieval. According to the AtoM theory, both top-down and bottom-up attentional processes can contribute to episodic memory retrieval. Top-down attention is directed by cognitive processes (e.g., expectations or goals) and is largely involved in strategic retrieval while bottom-up attention is directed by sensory stimulations (e.g., environmental memory cues) [START_REF] Cabeza | The parietal cortex and episodic memory: An attentional account[END_REF][START_REF] Ciaramelli | Top-down and bottom-up attention to memory: A hypothesis (AtoM) on the role of the posterior parietal cortex in memory retrieval[END_REF][START_REF] Corbetta | Control of goal-directed and stimulus-driven attention in the brain[END_REF] and is involved in associative retrieval [START_REF] Moscovitch | The frontal cortex and working with memory[END_REF]. The major contribution of the AtoM model is the demonstration of the involvement of the posterior parietal cortex, a region well-known for its role in attentional processes, in memory retrieval [START_REF] Ciaramelli | Top-down and bottom-up attention to memory: A hypothesis (AtoM) on the role of the posterior parietal cortex in memory retrieval[END_REF]. More specifically, strategic retrieval is associated with activation in the dorsal parietal cortex [START_REF] Ciaramelli | Top-down and bottom-up attention to memory: A hypothesis (AtoM) on the role of the posterior parietal cortex in memory retrieval[END_REF], and the model suggests that this activity is similar during memory and perception [START_REF] Cabeza | Overlapping parietal activity in memory and perception: evidence for the attention to memory model[END_REF]. It is therefore assumed that perception and memory require similar attentional control processes [START_REF] Cabeza | Overlapping parietal activity in memory and perception: evidence for the attention to memory model[END_REF]. Nevertheless, the connectivity of the posterior parietal cortex with other brain regions differs between memory and perception -while it is highly connected with visual regions during perception, it is connected to the medial temporal lobe during memory. Our main goal here is to highlight the transition which is necessary to redirect attention from perception to memory. Fig. 2. illustrates how this attentional switch can be integrated into the cognitive cascade taking place during memory retrieval.

Dichotomy between internal and external attention

The famous definition of attention coined by 19 th -century thinker William James emphasized the ability to focus on either external objects or internal thoughts: "Everyone knows what attention is. It is the taking possession by the mind, in clear and vivid form, of one out of what seem several simultaneously possible objects or trains of thought." Similarly, the current taxonomy of attention (Chun et al., 2011) makes a fundamental distinction between external and internal attentional orientation. External attention is directed toward information that comes through the senses [START_REF] Dixon | A framework for understanding the relationship between externally and internally directed cognition[END_REF]. It refers to the selection of perceptual information from the environment. By contrast, internal attention refers to the selection and modulation of internally generated information (e.g., working memory, episodic and semantic long-term memory) (Chun et al., 2011). On the one side, some tasks require attention to be directed toward the environment (perceptually generated thought), as actions must respect environmental constraints [START_REF] Glenberg | Averting the gaze disengages the environment and facilitates remembering[END_REF]. On the other side, many meaningful cognitive activities, such as memory retrieval, require individuals to disengage from the environment to optimize ongoing internal cognitive functions [START_REF] Handy | Mind Wandering and Selective Attention to the External World[END_REF]. Attending to autobiographical memories during retrieval is such a form of internal attention. Internal attention should not be neglected since human beings spend about 50% of their time immersed in their thoughts [START_REF] Killingsworth | A wandering mind is an unhappy mind[END_REF].

Given the limited nature of attentional resources -and of working memory capacity-, it is largely assumed that when internal attention is engaged, external attention is suppressed, and vice versa [START_REF] Handy | Mind Wandering and Selective Attention to the External World[END_REF]; see Fig. 1 for an illustration). This is explained because internal and external attentional processes compete for the same resources [START_REF] Dixon | A framework for understanding the relationship between externally and internally directed cognition[END_REF]. Consequently, internal and external attention can coexist only when both are spontaneous and do not require voluntary processes. As soon as one of them is voluntary and effortful, it cancels the other one [START_REF] Dixon | A framework for understanding the relationship between externally and internally directed cognition[END_REF]. Given that strategic retrieval is voluntary and often effortful, it thus involves internal attention, hence a switch of attention.

Working memory temporarily maintains a limited amount of information in mind to guide ongoing behavior. The perceptual or memory content that enters working memory is controlled by a gating mechanism [START_REF] Verschooren | Early reduction of sensory processing within the visual cortex when switching from internal to external attention[END_REF]. Once the relevant information is activated in working memory, the system is closed and shielded from other distractions. As a result, when humans attend to the internal world (e.g., during autobiographical memory retrieval), they may be attentionally blind to the external world [START_REF] Fernandes | Factors modulating the effect of divided attention during retrieval of words[END_REF]. In the domain of memory, this has been exemplified by the competition between encoding (external attention) and retrieving (internal attention), which cannot occur simultaneously, leading, when necessary, to rapid switches between encoding new information and retrieving information from memory [START_REF] Kim | Encoding and retrieval along the long axis of the hippocampus and their relationships with dorsal attention and default mode networks: The HERNET model[END_REF]. Although attentional resources may not be the only cause of this competition as suggested by alternative interpretations [START_REF] Huijbers | When learning and remembering compete: A functional MRI study[END_REF], this decreased perceptual information processing during internal cognition, is widely referred to as perceptual decoupling [START_REF] Smallwood | The restless mind[END_REF].

Fig. 1. Illustration of the competition between internal and external attention. Attentional focus cannot be simultaneously directed to internal and external information, resulting in perceptual decoupling when attention is focused on the internal world.

There have been numerous studies of task switching (also called mental flexibility), a term commonly used to refer to attentional and executive control when switching between two different external tasks [START_REF] Gilbert | Task switching: A PDP model[END_REF][START_REF] Monsell | Task switching[END_REF], but much less is known about transitions from the external to the internal world [START_REF] Verschooren | Switching attention from internal to external information processing: A review of the literature and empirical support of the resource sharing account[END_REF]. The next section uncovers why attentional switches between the external and internal world cannot simply be considered under the general term of mental flexibility. [START_REF] Weber | Attention switching between perception and memory[END_REF] were the first authors to look at the daily activities that require an attentional switch between perception (external world) and memory (internal world). They were especially interested in the switch between perception and the maintenance of information in working memory (e.g., following a grocery list at the supermarket) [START_REF] Weber | Attention switching between perception and memory[END_REF]. The attentional cost of switching between external and internal tasks is asymmetrical, and depends on the direction of the switch: the transition from an external task to an internal one is slower and more expensive than the other way round [START_REF] Dark | Switching between memory and perception: Moving attention or memory retrieval?[END_REF][START_REF] Verschooren | Attentional flexibility is imbalanced: Asymmetric cost for switches between external and internal attention[END_REF][START_REF] Hautekiet | Attentional switching between perception and memory: Examining asymmetrical switch costs[END_REF]. This can be explained by the fact that residual attention remains directed toward the environment during internal attention, as action must respect environmental constraints to avoid dangerous situations. Consequently, switching attention away from the environment to optimize ongoing internal cognitive functions has a high cost.

Attentional switch (ASM) between external and internal attention

Conversely, when attention is focused on the internal world, it must switch back quickly to the external environment, in case of danger or unexpected stimulation. Moreover, task-switching tasks have shown that not all internal cognition modes incur the same attentional cost. For example, it appears to be harder to disengage from an episodic task than from a semantic one [START_REF] Mayr | Task-set switching and long-term memory retrieval[END_REF]. Of note, we did not find any study characterizing ASM in the specific case of strategic autobiographical retrieval. Fig. 2 presents a schematic representation of the cognitive processes involved in strategic autobiographical memory retrieval and how ASM relate to them.

Fig. 2. Schematic representation of the cascade of cognitive operations during autobiographical memory retrieval, incorporating ASM. The yellow circles represent the different phases in a putative

chronological order, although there may be considerable overlap between them. The phase shown in red is the hypothesized ASM phase. (1) Some tasks require the attention to be directed toward external stimuli in the environment. In this example, the person is driving and pays attention to the traffic. ( 2) An element of the environment triggers a memory need (e.g., the passenger asks the driver "How did you celebrate New Year's Eve last year?"). The mental state of the person is oriented toward retrieval, i.e. episodic retrieval mode. (3) Given the competition between external and internal attention, attention needs to be disengaged from the external environment and switched to an internal mental space. The external world vanishes through perceptual decoupling. This is the phase we have called attentional switch to memory (ASM). ( 4) Attention is oriented to an internal mental world. ( 5) Selective attention is then directed toward memories. The selection process requires a controlled active search of the memories stored in autobiographical memory and the inhibition of other, similar, memories. This whole process relies on cue specification and memory search processes. ( 6) The successful search in memory triggers ecphory (here, awareness of the success of the selection process). ( 7) During the subsequent elaboration phase, the event can be mentally re-experienced with various perceptual, emotional, and contextual details.

Functional brain activity reorganization during ASM

ASM is a critical phase that can change humans' perception of the world in a fraction of a second, by redirecting their attention from the external environment toward memories. We, therefore, hypothesized that the brain undergoes a rapid and major functional reorganization during ASM [START_REF] Zhou | Wandering minds with wandering brain networks[END_REF]. We reviewed different proposals that have been made regarding this switch, noting that many of these are still hypothetical or not necessarily specific to memory retrieval.

Because the ASM has been seldom studied. The hypotheses formulated below are to some extent inspired by the vast and trendy literature about mind-wandering -where the neural correlates and physiological signatures of internal attention have received a lot of interest. Mind-wandering shares similarities with autobiographical memory retrieval: they arise from similar neural substrates (Christoff, Ream, & Gabrieli, 2004), they are both dynamic, associative, and state-dependent (Mildner & Talmir, 2019), they both require mental time travel [START_REF] Karapanagiotidis | Tracking thoughts: Exploring the neural architecture of mental time travel during mind-wandering[END_REF] and interestingly, they both require an attentional switch toward the internal world since mind-wandering is defined as an attentional shift away from events in the external environment toward internal thoughts [START_REF] Smallwood | The restless mind[END_REF]. Therefore, some authors consider that there is an overlap between mind-wandering and autobiographical memory retrieval (Mildner & Talmir, 2019). Smallwood et al. (2015) pushed the interpretation further by considering mental travel as a characteristic specific to episodic memoryviewing mind-wandering as a by-product of episodic memory. Given those similarities, we can formulate relevant hypotheses and build a new framework for further investigation of the functioning of the attentional switch from the world to autobiographical memory.

Two anticorrelated networks involved in internal or external cognition

Many studies have supported the idea that the brain is intrinsically organized in two anticorrelated functional networks: one network exhibiting coherent activation during tasks that require attention to external stimuli, and the other showing coherent activation during internally oriented cognition [START_REF] Fornito | Competitive and cooperative dynamics of large-scale brain functional networks supporting recollection[END_REF][START_REF] Fox | The human brain is intrinsically organized into dynamic, anticorrelated functional networks[END_REF][START_REF] Vanhaudenhuyse | Two distinct neuronal networks mediate the awareness of environment and of self[END_REF][START_REF] Zabelina | Dynamic network interactions supporting internally-oriented cognition[END_REF]. Internal cognition, including successful episodic retrieval from autobiographical memory [START_REF] Bastin | Le réseau cérébral par défaut : un repos qui n'en est pas un[END_REF], is generally associated with activation of the default mode network (DMN) [START_REF] Fox | The wandering brain: Meta-analysis of functional neuroimaging studies of mind-wandering and related spontaneous thought processes[END_REF][START_REF] Mason | Wandering minds: The default network and stimulus-independent thought[END_REF][START_REF] Smallwood | Escaping the here and now: Evidence for a role of the default mode network in perceptually decoupled thought[END_REF]. The DMN comprises a distributed set of associative cortices, including the medial prefrontal cortex (MPFC), posterior cingulate cortex (PCC), retrosplenial cortex, inferior parietal lobule, temporoparietal junction, and hippocampal formation [START_REF] Buckner | The brain's default network: Anatomy, function, and relevance to disease[END_REF][START_REF] Dixon | A framework for understanding the relationship between externally and internally directed cognition[END_REF]. By contrast, it does not involve the sensory and motor cortices [START_REF] Long | Situating the default-mode network along a principal gradient of macroscale cortical organization[END_REF][START_REF] Murphy | Distant from input: Evidence of regions within the default mode network supporting perceptually-decoupled and conceptually-guided cognition[END_REF]. Distinct components of the DMN contribute differently to internal cognition, depending on its content. As a result, the DMN is viewed not as a single functional network, but rather as a set of subnetworks [START_REF] Buckner | The brain's default network: Updated anatomy, physiology and evolving insights[END_REF]. More specifically, the DMN can be divided into two main subsystems that are distinct from the core system (DMNCORE) composed of the By contrast, external cognition is supported by the dorsal attention network (DAN) including the frontal eye fields, superior parietal lobule, and inferior parietal sulcus [START_REF] Corbetta | Control of goal-directed and stimulus-driven attention in the brain[END_REF].

The DAN is closely related to visual and somatomotor networks respectively subtending perception and action [START_REF] Dixon | A framework for understanding the relationship between externally and internally directed cognition[END_REF][START_REF] Zabelina | Dynamic network interactions supporting internally-oriented cognition[END_REF]. As the DMN and the DAN are mutually exclusive [START_REF] Fox | The human brain is intrinsically organized into dynamic, anticorrelated functional networks[END_REF], they cannot be activated simultaneously, thereby favoring perceptual decoupling [START_REF] Sestieri | Attention to memory and the environment: Functional specialization and dynamic competition in human posterior parietal cortex[END_REF][START_REF] Smallwood | Escaping the here and now: Evidence for a role of the default mode network in perceptually decoupled thought[END_REF].

How does the brain switch between external and internal attention?

For an effective alternation between introspection and behavior directed toward the environment, the brain must frequently switch between these two states, which correspond to different information processing modes [START_REF] Tang | Neural correlates of establishing, maintaining, and switching brain states[END_REF]. However, the mechanisms by which these networks interact and are ordered to switch from one to another remain largely unknown [START_REF] Buckner | The brain's default network: Updated anatomy, physiology and evolving insights[END_REF]. Hypothesizing that the brain undergoes a rapid, major, functional reorganization during ASM [START_REF] Zhou | Wandering minds with wandering brain networks[END_REF], we review three proposals concerning the regions that might be involved in this reorganization. As these proposals were not mutually exclusive, we combined them to afford a more complete understanding of the dynamics taking place (see Fig. 3 for one such proposal). The first proposal involves the hippocampus in the switch between external and internal worlds [START_REF] Barbeau | Hippocampus duality: Memory and novelty detection are subserved by distinct mechanisms[END_REF][START_REF] Karapanagiotidis | Tracking thoughts: Exploring the neural architecture of mental time travel during mind-wandering[END_REF][START_REF] Mccormick | Functional and effective hippocampal-neocortical connectivity during construction and elaboration of autobiographical memory retrieval[END_REF][START_REF] Treder | The hippocampus as the switchboard between perception and memory[END_REF] and more precisely the anterior hippocampus [START_REF] Zeidman | Anterior hippocampus: The anatomy of perception, imagination and episodic memory[END_REF], which is connected to the lateral rostral PFC, a structure involved in the early construction stage of autobiographical memory retrieval [START_REF] Inman | Dynamic changes in large-scale functional network organization during autobiographical memory retrieval[END_REF][START_REF] Mccormick | Functional and effective hippocampal-neocortical connectivity during construction and elaboration of autobiographical memory retrieval[END_REF]. The hippocampus is activated early on, during the generation of spontaneous thought [START_REF] Ellamil | Dynamics of neural recruitment surrounding the spontaneous arising of thoughts in experienced mindfulness practitioners[END_REF], and intracranial electroencephalographic (EEG) data have shown a neural response in the MTL several seconds before spontaneous episodic memory retrieval [START_REF] Burke | Theta and high-frequency activity mark spontaneous recall of episodic memories[END_REF]. Recent intracerebral recordings in humans have revealed that the hippocampus participates in the transitions between memory (i.e., internal attention) and attentional processes directed toward external stimuli (i.e., external attention) [START_REF] Barbeau | Hippocampus duality: Memory and novelty detection are subserved by distinct mechanisms[END_REF]). That's what the HERNET model [START_REF] Kim | Encoding and retrieval along the long axis of the hippocampus and their relationships with dorsal attention and default mode networks: The HERNET model[END_REF] postulates: switches between encoding (external attention) and retrieval (internal attention) are underlined by the anterior-posterior gradient of the hippocampus -the anterior hippocampus is linked to the DAN while the posterior hippocampus is linked to the DMN [START_REF] Kim | Encoding and retrieval along the long axis of the hippocampus and their relationships with dorsal attention and default mode networks: The HERNET model[END_REF]. Internal and external attention activate different hippocampal subfields: CA1 receives external sensory information through the monosynaptic pathway, while CA3 and the trisynaptic pathway are involved in memory retrieval [START_REF] Tarder-Stoll | Dynamic internal states shape memory retrieval[END_REF].

According to the second proposal, a supervisory attentional gateway manages the coordination between external and internal attention [START_REF] Burgess | The gateway hypothesis of rostral prefrontal cortex (area 10) function[END_REF], namely, the switch of attentional focus from environmental stimuli to internal mental life, or vice versa. The lateral rostral PFC, part of the frontoparietal network (FPN) [START_REF] Kim | Parietal control network activation during memory tasks may be associated with the co-occurrence of externally and internally directed cognition: A cross-function metaanalysis[END_REF], plays a crucial role in the supervisory attentional gateway [START_REF] Burgess | The gateway hypothesis of rostral prefrontal cortex (area 10) function[END_REF][START_REF] Gilbert | Involvement of rostral prefrontal cortex in selection between stimulus-oriented and stimulus-independent thought[END_REF]. Although the internal and external cognition modes activate distinct neural networks (i.e., DMN and DAN), the lateral rostral PFC is part of both [START_REF] Christoff | Mindwandering as spontaneous thought: A dynamic framework[END_REF][START_REF] Dixon | A framework for understanding the relationship between externally and internally directed cognition[END_REF][START_REF] Fox | The wandering brain: Meta-analysis of functional neuroimaging studies of mind-wandering and related spontaneous thought processes[END_REF][START_REF] Kam | Lateral prefrontal cortex lesion impairs regulation of internally and externally directed attention[END_REF]. This structure is also involved in both external and internal attention, including episodic autobiographical memory retrieval [START_REF] Cabeza | Functional neuroimaging of autobiographical memory[END_REF][START_REF] Shapira-Lichter | Portraying the unique contribution of the default mode network to internally driven mnemonic processes[END_REF][START_REF] Svoboda | The functional neuroanatomy of autobiographical memory: A meta-analysis[END_REF]. The FPN is functionally connected to both the DAN and the DMN. It is assumed to allow for a flexible and rapid switch between the two anticorrelated networks [START_REF] Greenwood | Hypothesis for cognitive effects of transcranial direct current stimulation: Externally-and internally-directed cognition[END_REF]. The lateral rostral PFC is largely involved in executive control, which is available in a limited capacity. Hence, internal cognition competes with external cognition because they both recruit the capacity-limited processes of the lateral rostral PFC [START_REF] Brincat | Prefrontal cortex networks shift from external to internal modes during learning[END_REF][START_REF] Dixon | A framework for understanding the relationship between externally and internally directed cognition[END_REF].

According to the third proposal, the right fronto-insular cortex also plays a critical role in switching between distinct brain states [START_REF] Tang | Neural correlates of establishing, maintaining, and switching brain states[END_REF], particularly between the DAN and the DMN [START_REF] Goulden | The salience network is responsible for switching between the default mode network and the central executive network: Replication from DCM[END_REF][START_REF] Sridharan | A critical role for the right fronto-insular cortex in switching between central-executive and default-mode networks[END_REF]. This structure belongs to the salience network (SN), an essential interface for proper switching to take place between external and internal worlds [START_REF] Shaw | Dynamic task-linked switching between brain networks -A tri-network perspective[END_REF][START_REF] Zabelina | Dynamic network interactions supporting internally-oriented cognition[END_REF]. The SN is composed of the anterior insula and anterior cingulate cortex [START_REF] Menon | Saliency, switching, attention and control: A network model of insula function[END_REF]. Like the FPN, it is regarded as an important brain hub, enabling transitions between external and internal attentional networks [START_REF] Zabelina | Dynamic network interactions supporting internally-oriented cognition[END_REF]. According to [START_REF] Christoff | Mindwandering as spontaneous thought: A dynamic framework[END_REF], the transitions between these brain states depend on different constraints. First, the SN exerts continuous automatic control over the FPN, DAN (which influences activity in sensorimotor areas), and DMNCORE (which influences activity in DMNMTL). Second, the FPN can in turn exert constraints on the DAN, SN, and DMNCORE, depending on the current cognitive task.

Finally, sensorimotor areas and the DMNMTL can modulate activity in the SN, depending on the relevance of the information (i.e., external or internal). It is therefore essential to understand the functional dynamics between these different networks (DMN, FPN, and SN), in order to understand the brain dynamics that take place during ASM. Functional connectivity analyses have revealed that different brain states occur during different tasks. During periods of rest, which are conducive to the emergence of spontaneous thoughts, there is negative connectivity between the SN and FPN, as well as between the DMN and SN, whereas the connectivity between the DMN (especially in the PCC) and FPN is positive [START_REF] Denkova | Dynamic brain network configurations during rest and an attention task with frequent occurrence of mind wandering[END_REF]. By contrast, during an external attentional task, the DMN (especially the medial PFC) shows negative connectivity with the SN and FPN, whereas there is positive connectivity between the SN and FPN [START_REF] Denkova | Dynamic brain network configurations during rest and an attention task with frequent occurrence of mind wandering[END_REF]. There is also negative connectivity between the FPN and DMN [START_REF] Denkova | Dynamic brain network configurations during rest and an attention task with frequent occurrence of mind wandering[END_REF]. In summary, the SN seems to interact with the FPN and DMN, allowing switches to take place.

Albeit tentative, we can see from this short review that several large-scale networks and brain areas are probably involved in ASM, although it is as yet unclear which aspects are specific to autobiographical memory. The brain dynamics that take place during ASM therefore need to be clarified. As an attempt to provide a framework specific to autobiographical memory, we propose the hypothetical model depicted in Fig. 3. Because the hippocampus seems activated early even before the emergence of internal thoughts [START_REF] Burke | Theta and high-frequency activity mark spontaneous recall of episodic memories[END_REF][START_REF] Ellamil | Dynamics of neural recruitment surrounding the spontaneous arising of thoughts in experienced mindfulness practitioners[END_REF][START_REF] Rubin | The basic-systems model of episodic memory[END_REF], we believe that it plays a role in the initiation of the switch. Then, since the hippocampus is strongly connected to the aLPFC during the early access memory phase [START_REF] Mccormick | Functional and effective hippocampal-neocortical connectivity during construction and elaboration of autobiographical memory retrieval[END_REF][START_REF] Inman | Dynamic changes in large-scale functional network organization during autobiographical memory retrieval[END_REF], if the hippocampus activity signals a retrieval attempt (activation in CA3, [START_REF] Tarder-Stoll | Dynamic internal states shape memory retrieval[END_REF], the aLPFC could act as a "supervisory attentional gateway" [START_REF] Burgess | The gateway hypothesis of rostral prefrontal cortex (area 10) function[END_REF] to deactivate the DAN and activate the DMN [START_REF] Dixon | A framework for understanding the relationship between externally and internally directed cognition[END_REF] through modulation by the SN (Chirstoff et al., 2016;[START_REF] Tang | Neural correlates of establishing, maintaining, and switching brain states[END_REF].

Impact of perceptual decoupling on visual cortex

Patients with lesions in visual regions experience autobiographical memory impairments (e.g., patients with visual memory-deficit amnesia) [START_REF] Rubin | Visual memory-deficit amnesia: a distinct amnesic presentation and etiology[END_REF]. At the other extreme, a case study of highly superior autobiographical memory reported very high levels of activation in posterior visual areas such as the precuneus during autobiographical memory retrieval [START_REF] Mazzoni | Brain activation in highly superior autobiographical memory: The role of the praecuneus in the autobiographical memory retrieval network[END_REF].

Such activations in high-level visual areas demonstrate the fundamental role of visual imagery in autobiographical memory retrieval [START_REF] Cabeza | Functional neuroimaging of autobiographical memory[END_REF].

However, although the secondary visual and somatosensory cortices are activated during internal thoughts, the primary sensory cortices are not activated (Chun et al., 2011;[START_REF] Fox | The wandering brain: Meta-analysis of functional neuroimaging studies of mind-wandering and related spontaneous thought processes[END_REF][START_REF] Wheeler | Memory's echo: Vivid remembering reactivates sensory-specific cortex[END_REF]. More specifically, reduced visual processing has been observed in low-level visual areas during internal cognition (Chun et al., 2011;[START_REF] Gorgolewski | A correspondence between individual differences in the brain's intrinsic functional architecture and the content and form of selfgenerated thoughts[END_REF][START_REF] Smallwood | Going AWOL in the brain: Mind wandering reduces cortical analysis of external events[END_REF]. ASM may be accompanied by an early deactivation of primary visual areas supporting visual decoupling. The early access phase is associated with deactivation of visual areas, while the elaboration phase is associated with activation of associative visual areas [START_REF] Inman | Dynamic changes in large-scale functional network organization during autobiographical memory retrieval[END_REF]. Associative visual areas such as the precuneus, retrosplenial cortex, and lateral occipital regions exhibit increased activity during autobiographical memory retrieval [START_REF] Bréchet | Capturing the spatiotemporal dynamics of self-generated, task-initiated thoughts with EEG and fMRI[END_REF]Chun et al., 2011;[START_REF] Conway | The neuroanatomy of autobiographical memory: A slow cortical potential study of autobiographical memory retrieval[END_REF][START_REF] Fox | The wandering brain: Meta-analysis of functional neuroimaging studies of mind-wandering and related spontaneous thought processes[END_REF][START_REF] Inman | Dynamic changes in large-scale functional network organization during autobiographical memory retrieval[END_REF][START_REF] Wheeler | Memory's echo: Vivid remembering reactivates sensory-specific cortex[END_REF], and may be involved in the mental imagery needed to facilitate retrieval [START_REF] Cabeza | Functional neuroimaging of autobiographical memory[END_REF]. Consequently, if secondary visual areas are involved in visual mental imagery during memory retrieval, they, like the primary visual cortices, may not be able to simultaneously process external visual stimuli from the environment [START_REF] Johnson | Decoding individual natural scene representations during perception and imagery[END_REF], thus reinforcing the perceptual decoupling.

Gaze aversion as an objective behavioral signature of ASM

In this section we suggest that eye movements are potential objective signatures of ASM and we highlight in Box 1 why such an objective marker is important for different fields of research.

Eye movements seem crucial for good autobiographical memory retrieval, as preventing people from moving their gaze (by asking them to fixate a dot) reduces the quality of their mental imagery and the number of details it contains, compared with a free viewing condition [START_REF] Lenoble | Don't stare, unless you don't want to remember: Maintaining fixation compromises autobiographical memory retrieval[END_REF]. The most well-known theory demonstrating the intimate relation between autobiographical memory retrieval and eye movements is gaze reinstatement or the scan path theory -during memory retrieval, the gaze reenacts the visual pattern observed during the encoding of the event (for recent studies, see [START_REF] Johansson | Eye-movement replay supports episodic remembering[END_REF]Wynn et al., 2019). Other eye behaviors are however observed during autobiographical memory retrieval. One of those is looking at nothing -staring at a neutral part of the environment with little visual distractors [START_REF] Salvi | Looking for creativity: Where do we look when we look for new ideas[END_REF]. Visual distractors in the environment can disturb episodic memory retrieval and lead to less precise episodic recollection [START_REF] Sheldon | The processes involved in mentally constructing event-and scene-based autobiographical representations[END_REF][START_REF] Wais | Neural mechanisms underlying the impact of visual distraction on retrieval of long-term memory[END_REF]. By the same token, a reduction in external visual information substantially improves retrieval from memory [START_REF] Einstein | Gaze aversion: Spared inhibition for visual distraction in older adults[END_REF], even for weakly accessible knowledge [START_REF] Radel | The influence of external stimulation in missing knowledge retrieval[END_REF]. Consequently, some studies have identified oculomotor behavior that appears to be aimed at reducing visual input during autobiographical memory retrieval. For example, witnesses usually recall more details when their eyes are closed [START_REF] Perfect | How can we help witnesses to remember more? It's an (eyes) open and shut case[END_REF][START_REF] Vredeveldt | A field evaluation of the Eye-Closure Interview with witnesses of serious crimes[END_REF], probably owing to enhanced mental visualization [START_REF] Vredeveldt | Eyeclosure helps memory by reducing cognitive load and enhancing visualisation[END_REF].

Nevertheless, in daily life, it is quite rare to see people closing their eyes while remembering.

Instead, gaze aversion is frequently encountered in everyday situations. It may even have happened to you when you were trying to answer the earlier question about your New Year's Eve party. [START_REF] Glenberg | Averting the gaze disengages the environment and facilitates remembering[END_REF] showed that people trying to answer difficult memory questions tend to shift their gaze away from their interlocutor and naturally avert their gaze. They give the impression of searching for the answer on the ceiling or in the sky [START_REF] Doherty-Sneddon | Gaze aversion: A response to cognitive or social difficulty?[END_REF][START_REF] Glenberg | Averting the gaze disengages the environment and facilitates remembering[END_REF], which is compatible with the "looking at nothing" phenomenon where people prefer looking at neutral parts of the space such as blank walls while retrieving [START_REF] Salvi | Looking for creativity: Where do we look when we look for new ideas[END_REF]. Gaze aversion may play a functional role in memory retrieval, as performance is better when people avert their gaze [START_REF] Glenberg | Averting the gaze disengages the environment and facilitates remembering[END_REF]. The cognitive load hypothesis of gaze aversion [START_REF] Abeles | Just look away : Gaze aversions as an overt attentional disengagement mechanism[END_REF] suggests that averting the gaze from external distractors in the surrounding environment optimizes performance on tasks requiring internal attention (e.g., autobiographical memory retrieval). Therefore, gaze aversion can be regarded as a strategy that supports perceptual decoupling. It may allow individuals to disengage from the current spatial and temporal context, in order to concentrate on past mental images.

Interestingly, when the gaze is averted to reduce the influence of external distractors and facilitate ongoing internal thoughts, it is preferentially directed upward [START_REF] Andrist | Conversational gaze aversion for humanlike robots[END_REF]. However, we do not currently have a proper scientific explanation as to why the upward direction is preferred during internal attention other than a ceiling or the sky is a relatively neutral visual stimulus, with few distracting details.

Gaze aversion can last for several seconds, on average 3.54 ± 1.26 seconds [START_REF] Andrist | Conversational gaze aversion for humanlike robots[END_REF] during conversations for example. It should be noted that such behavior may be correctly interpreted by a viewer. When a person is looking upwards and sideways at a location with no meaningful object, for example, children can infer that the person is thinking (i.e., internal attention) [START_REF] Baron-Cohen | Reading the eyes: Evidence for the role of perception in the development of a theory of mind[END_REF]. Gaze aversion may therefore also allow other people's mental states to be inferred. If this is the case, it confirms that gaze aversion occurs regularly enough to have become a social marker of a specific cognitive state. As gaze aversion is related to cognitive effort [START_REF] Glenberg | Averting the gaze disengages the environment and facilitates remembering[END_REF] and starts early during the early access phase, the moment at which gaze aversion begins presumably signals the attentional switch toward memories, which initiates strategic autobiographical retrieval. Directing the gaze toward a neutral part of the space may allow attentional resources to be focused on the mental time travel platform (i.e., temporary internal mental space), in order to search for information in memory and maintain this information in a representational space (internal attention). Keeping the gaze away from distractions could indicate that the person is mentally exploring the representation, visualizing the scene, and reliving the event. Gaze reinstatement in contrast is closely linked to mental imagery and is supposed to occur during the elaboration phase to allow the mental exploration of the scene (Bone et al., 2019;Daselaar et al., 2008). How both gaze aversion and gaze reinstatement relate is an interesting topic for future studies.

Given that gaze aversion during autobiographical memory retrieval seems such an ecological, easy-to-study, and common behavior, we were surprised to find such a dearth of relevant scientific literature. It is worth studying gaze aversion as a marker of internal cognition, as the other eye behaviors that have been reported during internal cognition cannot be detected at a single-trial level in real time.

For example, higher eye blink frequency during internal versus external cognition is an indicator based on an a posteriori mean [START_REF] Benedek | Eye behavior associated with internally versus externally directed cognition[END_REF]. Blinking per se does not indicate a switch toward the internal world. By contrast, gaze aversion could be an objective and temporally accurate marker of engagement in autobiographical retrieval, potentially allowing researchers to detect in real-time attentional switch between internal and external worlds.

Cognitively, gaze aversion is hypothesized to favor perceptual decoupling. This could occur at two different levels. The first mechanism, which has already been proposed by [START_REF] Glenberg | Averting the gaze disengages the environment and facilitates remembering[END_REF] and the looking at nothing hypothesis [START_REF] Salvi | Looking for creativity: Where do we look when we look for new ideas[END_REF], consists in directing the gaze toward the floor, ceiling, or sky -i.e., neutral and uniform surface containing far fewer visual distractors than the rest of the surrounding environment. The second possible mechanism is based on the characteristics of the oculomotor system. The eyes have a limited range of movement, of around 50° from the central primary position (i.e., looking straight ahead), and at far eccentricities (greater than approximately 20°), the eye position becomes less stable, leading to less precise vision [START_REF] Nakashima | Why do we move our head to look at an object in our peripheral region? Lateral viewing interferes with attentive search[END_REF].

Consequently, to visually explore the environment -a situation requiring optimal visual processingthe head rotates for gaze changes greater than 20° [START_REF] Land | Looking and acting: Vision and eye movements in natural behaviour[END_REF]) -allowing to compensate for this anatomical limitation. By contrast, we hypothesize that the head does not follow the direction of the eyes during gaze aversion. Although gaze aversion brings the gaze at far eccentricity, the head would not follow the eyes to favor perceptual decoupling. In this situation where attention must be directed toward internal memories, taking advantage of this anatomical limitation is beneficial to reducing the visual processing of potential external distractors. Internal and external attentional states could therefore be differentiated according to the match or mismatch between the direction of the eyes and the direction of the head (see Fig. 4 for an illustration).

Note that we exclusively focus on eye movements in this section and decide to not tackle other potential markers of ASM. Nevertheless, as explained earlier, ASM is presumably accompanied by a massive modification in brain activity, raising the possibility that ASM has also an EEG signature. This, along with eye movement monitoring, could also be a powerful and measurable temporal marker of autobiographical memory retrieval. Fig. 4. A) An illustration of a gaze that we assume to be related to external attention (selective): the head congruently rotates in the same direction as the eyes. B) An illustration of an averted gaze that is assumed to be related to a cognitive state requiring internal attention (e.g., autobiographical memory retrieval): during the eye movement, the head remains still or moves in a different direction. (Images created with the open-source software DAZ Studio 4.12,www.daz3d.com)

Box 1. Applications of ASM

We hypothesized that ASM has observable and measurable oculomotor signatures. This is critical since detectable markers of ASM could be extremely valuable in various fields, as we briefly set out below.

Neuropsychology: investigating amnesia

One application of ASM markers would, of course, be to assess whether failure to perform ASM can contribute to amnesia or other cognitive dysfunctions (e.g., if part of the network needed for ASM is damaged). Patients with memory impairment stemming from frontal lesions have difficulty accessing memories (Wheeler et al., 1995). They also have difficulty disengaging their attention from the external environment, and exhibit dependence on the latter [START_REF] O'callaghan | Hippocampal atrophy and intrinsic brain network dysfunction relate to alterations in mind wandering in neurodegeneration[END_REF]. We can hypothesize that the attention they direct toward their internal world is not sufficient to retrieve memories, owing to a disturbance of ASM. By contrast, after a traumatic event, patients with posttraumatic stress disorder experience intrusive memories [START_REF] Berntsen | The unbidden past: Involuntary autobiographical memories as a basic mode of remembering[END_REF]) that could also be due to a dysfunction of the system supporting ASM. Other patients present spontaneous confabulations in the form of stories dominated by autobiographical experiences and contaminated by imaginary elements [START_REF] Schnider | Spontaneous confabulation and the adaptation of thought to ongoing reality[END_REF].

Spontaneous confabulations reflect deep confusion between ongoing reality (external world) and past memories (internal world), owing to a failure to suppress the activation of past episodic memories. A disturbance of ASM, which is also a gating mechanism to avoid confusion between the external and internal worlds, could generate inappropriate switches. These hypotheses require confirmation, but open up a new avenue of research in neuropsychology.

2. Research in neurosciences: an objective, temporal marker of autobiographical memory retrieval If researchers found a specific temporal oculomotor marker of autobiographical memory retrieval, it could be highly useful in EEG and functional brain imaging studies investigating the neural correlates of autobiographical memory. This marker would provide an objective measure of whether the participant was actually engaging in remembering [START_REF] Conti | Harnessing visual imagery and oculomotor behaviour to understand prospection[END_REF]. Experimenters generally use lengthy subjective self-report to ensure that participants engaged in autobiographical memory retrieval.

An objective temporal marker would allow skipping this fastidious step. In addition, the oculomotor activity could be used as a temporal marker to precisely track brain activity-something that is currently impossible with oral interviews. Retrieval trials could thus be temporally aligned before averaging, thus increasing the power of the analyses.

Social cognition: gaze aversion as a social cue

ASM is accompanied by gaze aversion [START_REF] Glenberg | Averting the gaze disengages the environment and facilitates remembering[END_REF]. The latter may play a role in social interactions, as the gaze is a powerful social cue that allows us to decode others' mental states [START_REF] Baron-Cohen | The "Reading the Mind in the Eyes" Test revised version: A study with normal adults, and adults with Asperger syndrome or high-functioning autism[END_REF]. During social interactions, there is generally eye or eye-to-face contact [START_REF] Pasupathi | The social construction of the personal past and its implications for adult development[END_REF][START_REF] Turkstra | Looking while listening and speaking: Eye-to-face gaze in adolescents with and without traumatic brain injury[END_REF], and a listener's gaze tends to follow the gaze direction of the speaker so that their attention is directed toward the same external information [START_REF] Droulers | Perceived gaze direction modulates ad memorization[END_REF][START_REF] Koike | Neural substrates of shared attention as social memory: A hyperscanning functional magnetic resonance imaging study[END_REF][START_REF] Nummenmaa | Neural mechanisms of social attention[END_REF], in a form of joint attention [START_REF] Emery | The eyes have it: The neuroethology, function and evolution of social gaze[END_REF][START_REF] Frischen | Gaze cueing of attention: visual attention, social cognition, and individual differences[END_REF].

One question that remains to be investigated is whether gaze aversion and which of its characteristics, can be interpreted by a viewer as a sign that the speaker is focusing on personal memories, rather than on an external stimulus.

Comparative psychology

The existence of episodic memory and mental time travel in nonhuman species is still a subject of hot debate [START_REF] Crystal | Episodic memory in nonhuman animals?[END_REF]. In humans, language allows for easy communication about past events, but it is of course difficult to investigate this ability in other species. An objective marker that would be specific to ASM, but common across species, even in a prototypical form, could be highly useful for assessing whether nonhumans can switch to an internal world.

Limitations

In this review, we focused on ASM, an early component of the cascade of processes involved in memory retrieval that has been largely ignored, despite its presumably critical role. Most of what we were able to infer about ASM was derived from studies that were not specific to autobiographical memories, but more generally related to the switch from external to internal cognition or from related fields such as mind wandering. This was notably the case for the brain reorganization that is hypothesized to take place during ASM. It therefore still has to be clarified whether there is anything specific to autobiographical memory in ASM.

We focused mainly on strategic, rather than associative, retrieval from autobiographical memory as ASM is then most conspicuous. Strategic retrieval can last for several seconds and can easily be induced in the lab, making it a good candidate for investigation. In this regard, the type of ASM that takes place during associative retrieval has yet to be investigated.

Last, some forms of ASM may take place during retrieval from semantic memory, particularly for difficult questions (e.g., trying to retrieve the name of the capital of Mongolia or the names of British Prime Ministers since World War II), or even during other tasks requiring internal attention, such as future thinking and imagination. There are well-known debates about the specificity of human episodic memory or mental time travel with regard to either other types of memory or nonhuman species. We cannot discuss them here, but it should be noted that studying ASM may be helpful to clarify some aspects of these debates.

Conclusion

Our review suggests that ASM is an early and necessary phase of autobiographical memory retrieval. It is fascinating to realize just how critical a moment ASM is in humans' cognitive lives, changing their perception of the world in a fraction of a second. It allows them to divert their attention from the external world to focus on the internal world containing memories and thoughts. Despite its importance in everyday life, our review also highlights how little we know about ASM and calls for future research on this promising topic.

Declarations

• Funding

AS is supported by a grant from the Aeronautics-Astronautics doctoral school of Toulouse and Paul Sabatier University.

Open Practices Statement

This paper is a theoretical review. Preregistration, as well as data and code sharing, are therefore not applicable.

  anterior medial prefrontal cortex (aMPFC) and PCC[START_REF] Andrews-Hanna | Functional-anatomic fractionation of the brain's default network[END_REF]: (1) the dorsal medial prefrontal cortex subsystem (DMNPFC) including the dorsal medial prefrontal cortex (dMPFC), temporoparietal junction, lateral temporal cortex, and temporal pole; and (2) the medial temporal lobe (MTL) subsystem (DMNMTL) including the ventral medial prefrontal cortex (vMPFC), posterior inferior parietal lobule, retrosplenial cortex, parahippocampal cortex and hippocampal formation. Whereas the DMNPFC is mainly involved in theory of mind and mental simulations, autobiographical memory retrieval relies on the activity of the DMNMTL.

Fig. 3 .

 3 Fig. 3. Hypothetical illustration of the functional brain reorganization that takes place during ASM.

•

  Conflict of interest/Competing interestsThe authors do not have any competing interests to declare.• Ethics approvalThis is a theoretical paper. No ethical approval is required.

	• Consent to participate
	Not applicable
	• Consent for publication
	Not applicable
	• Availability of data and materials
	Not applicable
	• Code availability
	Not applicable

Acknowledgments

The authors would like to thank Christine Bastin for her comments on an earlier version of this manuscript.


domain: info math

text:
Adam Desormiere
email: adam.desormiere@intel.com.

Lilia Gzara

Jean Bigeon

Luc Nguyen-Thê

Comparing Power Models for circuits design with Mathematical Language Processing

Keywords: Power Modeling, Models Management, Machine Learning, Clustering

The work presented in this paper is part of a project that focuses on sorting simulation models used at Intel to calculate power consumption of electronic devices. Hundreds of thousands of analytical power models have already been accumulated in a directory of files and folders, for the simulation of the consumption of thousands of products. As a first step, this work focuses on comparing and grouping together models of smaller granularity -the formulas -which consist of power equations, the definition of the parameters involved in these equations, and a description.

To manage this large data problem, we follow the principles of Model Management and Analytics, to decompose the problem into the analysis of constituent fields. We believe that the equations describing power consumption are the most highly information-rich field of our models. The aim of this work is to group together the formulas models, using Mathematical Language Processing (MLP), to take advantage of the business information contained in electrical equations. We calculate the embeddings of our formulas, to enable comparisons between them, to cluster together similar equations (and therefore models).

Introduction

We work with analytical power models that are built hierarchically from simple electrical equation models to complex models in order to simulate the power consumption of products, such as CPUs. Hundreds of thousands of power models have already been accumulated in our databases, for thousands of simulations, and we want to take advantage of this knowledge.

We have two goals: to sort the existing models in our databases, and to help future users in their reuse of existing models [START_REF] Desormiere | Hierarchical Clustering of Power Models for circuits design[END_REF]. We focus on models of smaller granularity, the formulas models, which can be of three types (static, dynamic, supply) dedicated to different simulations. This allows us to pre-treat the models by separating them into three subsets. Each resulting formula model contains equations for calculating electrical power, the definition of parameters involved in these equations and a description field.

Model Management and Analysis (MMA) [START_REF] Tekinerdogan | Introduction to model management and analytics[END_REF]- [START_REF] Babur | Models, More Models, and Then a Lot More[END_REF] proposes to tackle this big data problem by analyzing all the fields available in the models and processing them with machine learning [START_REF] Heaton | Deep learning[END_REF], [START_REF] Haque | Semantic Similarity Metrics for Evaluating Source Code Summarization[END_REF]. Among these fields, we believe that the richest information is the equation that expresses the power. So, we use Mathematical Language Processing (MLP) [START_REF] Cobbe | Training Verifiers to Solve Math Word Problems[END_REF]- [START_REF] Meadows | A Survey in Mathematical Language Processing[END_REF], which is based on architectures close to Natural Language Processing (NLP) [START_REF] Mikolov | Efficient estimation of word representations in vector space[END_REF]- [START_REF] Dadure | BERT-based embedding model for formula retrieval[END_REF] to encode the semantics of the equation contained in each power model. Once this information is contained in a vector, we can compare the equations with each other by comparing the vectors [START_REF] Krstovski | Equation Embeddings[END_REF] (Figure 1), to obtain similarity scores. This paper is organized as follows. Section 2 presents the tools and protocol used for mathematical data extraction and encoding, as well as model clustering based on similarity scores. Section 3 evaluates performance of the clustering algorithm applied to the similarity scores obtained between equations. Section 4 enumerates the conclusions from our work and introduces future perspectives.

Equations Embedding and Clustering

a. Need for Mathematical Language Processing (MLP)

As time goes by, advances in natural language processing continue to improve information retrieval capabilities. Today's machine translators are no longer just word-by-word processors, but are capable of capturing context. Search engines no longer simply offer a list of results, but also the ability to understand users' questions and propose answers. The progress of OpenAI with successive versions of GPT is revolutionizing the scientific community [START_REF] Openai | [END_REF], [START_REF] Brown | Language models are few-shot learners[END_REF]. However, it is precisely scientific content that is the most complex to reference. NLP algorithms are designed to process words in natural language, but do not allow encoding the mathematical portions of scientific content. Whether in scientific papers, training courses, tutorials, or encyclopedias, scientific content often includes mathematical equations. As a result, an immense amount of scientific content contains equations that current algorithms do not utilize for analysis and classification [START_REF] Hendrycks | Measuring Mathematical Problem Solving With the MATH Dataset[END_REF]. Also, the use of mathematical notation is dialectical. Different communities use different conventions for naming variables and defining operators (for example, using a horizontal line above an "x" to represent Boolean negation, versus the average of a set of values). Each author redefines and adapts the notation to his or her immediate needs. This flexibility benefits authors and readers alike, but makes automatic interpretation extremely difficult. Mathematical Language Processing is concerned with capturing mathematical language, and including it in the content to be encoded, in order to convey the meaning of a document. We want to use an algorithm based on this approach to compare our models. We only consider, for each of our models, an equation describing the amount of power consumed, as input material for an MLP algorithm.

b. Algorithm choice

The key to MLP is to choose the right way to analyze and decompose the formula, to capture its semantics. Two types of representations can be found in the literature: Operator Trees (OPTs) and Symbol Layout Trees (SLTs). OPTs contain the mathematical meaning, and SLTs the layout of the formula (the positions of the symbols with respect to each other). OPTs capture formula semantics while SLTs capture visual structure, as illustrated in figure 1.

In order to evaluate algorithms, NTCIR-12 MathIR [START_REF] Zanibbi | NTCIR-12 MathIR Task Overview[END_REF], [START_REF] Joho | Overview of NTCIR-11[END_REF] is an open task for retrieving mathematical information in documents from queries. The candidate algorithms enable users to search for a particular math concept using math formulae. Queries can be keywords, formulae, or a combination. Candidate algorithms need to return a ranked list of retrieval documents (document excerpts) matching the input query. This task enables Mathematical Language Processing algorithms to be evaluated with a single, clear evaluation procedure. Algorithms proposed in literature can be compared with the formula retrieval task, on the NTCIR-12 dataset (cf. Table 1). and SLT (c) representations Table 1: Bpref [START_REF]Bag Semantics[END_REF] scores comparison between literature algorithms When reviewing the different approaches made by the scientific community for the NTCIR task, we observe that algorithms using combined representations (OPT + SLT) tend to have better results [START_REF] Mansouri | Tangent-CFT: An embedding model for mathematical formulas[END_REF]- [START_REF] Davila | Layout and semantics: Combining representations for mathematical formula search[END_REF]. Mathematical formulas are often unique: It is rare for the same equation to be found identically in another theorem or another field of science. Hence, FastText embedding model will learn more abstract formula representations when compared with classic treebased approaches, especially thanks to the n-gram embedding which allows to capture local semantic of the formula.

We've chosen Tangent-CFT [START_REF] Mansouri | Tangent-CFT: An embedding model for mathematical formulas[END_REF] for its high performance on this task, which demonstrates that the features included in the embeddings produced contain significant information about the formulas. Then, unlike the original algorithm which operates as a search engine, we compare all pairs of formula embeddings with a cosine similarity, to obtain a distance matrix ready to be used by a clustering algorithm.

c. Data pre-processing

We extract the equations describing the power for each model. We first sort the formulas into their 3 different types: static, dynamic and supply. These 3 types of equations cover different use cases and will be treated separately. These equations are written in a computational language from Intel, used to compute the power value. We convert these equations into LaTeX, then into MathML (content + presentation), which is suitable for Tangent-CFT. Figure 3 illustrates this process with an example. The algorithm uses these two MathML forms respectively to obtain the OPT and SLT expressions of the formula. We also perform a preprocessing step by eliminating strictly identical models, to save computation time by eliminating all duplicates. Finally, we store all those cosine distance scores in a matrix, for all pairs of equations of the database. This format is ready to be used as input by the clustering algorithm.

e. Clustering from scores

We wanted to avoid classical methods such as K-means, which require knowing the number of clusters in advance, as we don't have this information. We tried to cluster with DBSCAN, but the optimal value for the neighborhood was not always the same, depending on formula type and length.

(a) OPTICS reachability plot. (b) OPTICS clustering proposal. (c) Zoom on (b) on a random area. (d), (e), (f), (g), DBSCAN clustering proposal with different neighborhood settings. (h), (i), (j), (k), same as (d), (e), (f), (g) but zoomed on the same area as (c).

Where DBSCAN (Figure 4) fails to capture clusters in areas of varying density, OPTICS succeeds: -On figure (d), DBSCAN is set with a very high epsilon value, and clusters all the dataset in the same cluster. Figure (h), zoomed in on a high-density area, shows that no discrimination is performed.

-As we reduce the epsilon value, we see in figures (i), (j) and (k) that clusters in high-density areas are better and better captured. However, the number of outliers increases disproportionately (>60% of the dataset for (g)) and we can see from figures (e), (f) and (g) that low-density areas are no longer considered by DBSCAN.

-Fortunately, (b) and (c) show that OPTICS manages to capture clusters in areas of varying density: rather than a neighborhood value, it takes into account abrupt variations of reachability in successive points.

As a consequence, we choose to cluster with OPTICS, which allows variable neighborhood densities [START_REF] Dubey | -Dbscan and Optics[END_REF]. OPTICS [START_REF] Ankerst | OPTICS : Ordering Points To Identify the Clustering Structure[END_REF] is a density-based clustering algorithm similar to DBSCAN, but that can extract clusters of varying densities and shapes. It is useful for identifying clusters of different densities in large, high-dimensional datasets.

Taking a small set of four equations as an example, Figures 5 &6 respectively show the scores calculated between pairs of equations, and the Multidimensional Scaling representation of the samples. Indexes start at 0. Hence, we compared mathematical formulas with each other, and used the resulting similarity scores to cluster the corresponding models. In the following, we evaluate the quality of our algorithm's proposals.

Validation and results

a. Validation sets

Unfortunately, once a clustering proposal has been made by our algorithm, we can't evaluate it. We have no ground truth for the models in our database, so, even if we verified that the clustering proposals made by our algorithm are satisfactory and bring together similar patterns, we can't quantify this without a validation set. To overcome this problem, we asked three Intel engineers to cluster by hand all the models belonging to three different teams. We chose three teams working on different and diversified products to get a representative sample of all power engineers. There are three diverse types of equations, so each engineer will have to manually cluster nine subsets of equations, giving us 27 manual proposals on representative samples from our database. Each proposal made by the engineers is valid, their manual clustering is subjective and based on their business knowledge, so the proposals can vary.

On the other hand, we can evaluate (cf. Table 2) the similarity of different proposals made by each engineer on each cluster using the Rand Index [START_REF] Zhang | Generalized adjusted rand indices for cluster ensembles[END_REF], which represents the frequency of occurrence of agreements over the total pairs. Given two partitions A and B of a set Ω, we call:

• u the number of pairs of elements of Ω that are in the same subset in A and in the same subset in B

b. Algorithm evaluation

It's important to remember that clustering proposals are subjective, and result from the engineer's interpretation. There is no one proposition that can prevail over another, and we keep all these propositions as valid ground truths for evaluating our algorithms. Nevertheless, we note that these propositions are often extremely close. Thanks to these validation sets, we can now evaluate our algorithm's clustering proposals. We use the 9 validation subsets described above, and the 3 ground truths from the engineers who manually labelled the models.

We use the classic evaluation measures [START_REF] Amigó | A comparison of extrinsic clustering evaluation metrics based on formal constraints[END_REF], we recall that a clustering result satisfies:

• Homogeneity -if all of its clusters contain only data points that are members of a single class.

• Completeness -if all the data points that are members of a given class are elements of the same cluster.

Both scores (cf. Table 3) have positive values between 0.0 and 1.0; larger values being desirable. V-measure [START_REF] Rosenberg | V-Measure: A conditional entropy-based external cluster evaluation measure[END_REF] is the harmonic mean of the first two.

Table 3: Evaluation of our algorithm with classic measures, when compared to three different ground truths In most cases, the algorithm proposes the same thing as the engineers. In the few cases where it proposes a different clustering, the proposal is logical and makes sense, and we understand its purpose when examining it. As a result, we are satisfied with its ability to cluster similar power models.

Conclusion & Future research

In this paper, we have shown that we can take advantage of the semantic information contained in mathematical equations to compare models. Using MLP, we have encoded our formulas in a space that expresses their mathematical characteristics, and we can then compare the formulas with each other thanks to the cosine similarity between the vectors. We can use these similarity scores to sort our databases, by grouping the formulas into subsets using a clustering algorithm, whose proposals are quite close to those that an expert would have obtained manually. We can also use these comparison scores to suggest to the user, like a search algorithm (Tangent-CFT's initial use case), equations like the one they are currently typing. In this way, the tool is an excellent assistant to an application administrator for tidying and sorting equations.

Unfortunately, this clustering does not allow us to automatically label subsets once the models have been grouped. A manual interpretation from an expert is required to finish exploiting these results and arranging the models.

Our prospects for future work target the creation of a search engine, which redirects the user of our application to similar models (based on the MLP as described in this paper), in real time as he types in the mathematical formula for the power consumption of his model.

We're also considering changing the embedding algorithm, as some recent algorithms offer different embedding methods, potentially more efficient than FastText, which is an area worth exploring.

Fig. 1 :

 1 Fig. 1: Formula (a) with its OPT (b) and SLT (c) representations

Fig. 2 :

 2 Fig.2: Overview of the workflow applied to Intel's simulation models in this article.

Figure 2

 2 Figure2summarizes our complete workflow. We use Tangent-CFT to produce the embeddings of our formulas. Then, unlike the original algorithm which operates as a search engine, we compare all pairs of formula embeddings with a cosine similarity, to obtain a distance matrix ready to be used by a clustering algorithm.

Fig. 3 :

 3 Fig. 3: Pre-processing

Fig. 4 :

 4 Fig. 4: Comparison between DBSCAN (with different neighborhood settings) and OPTICS.

Fig. 5 :Fig. 6 :

 56 Fig. 5: Distance matrix between pairs of samples

3 •

 3 u' the number of pairs of elements of Ω that are in different subsets in A and in different subsets in B• v the number of pairs of elements of Ω that are in the same subset in A and in different subsets in B• v' the number of pairs of elements of Ω that are in different subsets in A and in the same subset in B Then the Rand Index is defined by 𝑅𝐼 = 𝑢 + 𝑢′ 𝑢 + 𝑢′ + 𝑣 + 𝑣′

Table 2 :

 2 Comparison (Rand Index) of clustering proposals from three engineers for two subsets of models.

Acknowledgments

The authors would like to thank the Association Nationale Recherche et Technologie (ANRT) for its financial contribution. We also thank the members of the Intel® Docea™ team.