Sharad Goulam
email: sharad.goulam@gmail.com

Luba Tchertanov

Alain Trouvé

Novel insight on molecular dynamics trajectories : local equilibrium viewed by kappa-segmentation

Keywords: Molecular dynamics simulation, kinetic-based clustering, local equilibrium, segmentation, macromolecules

Molecular dynamics (MD) simulations can produce nowadays huge amount of data using high-throughput CPU/GPU clusters. However, the systematic and routine use of MD simulations for a study of the large molecules of real biological systems is still considerably impeded by a lack of adequate modelling. This leads to a limited understanding of the produced highly complex signals that emerge at the level of the relevant subsystems for various time scales. We will present here an ongoing work towards the dynamics modelling and detection of local equilibrium for relevant subsystems compatible with the usual practice of MD and aiming at avoiding the detection of spurious artefactual local equilibrated states. Such well characterized local equilibrium would be basic descriptive atoms extracted from various MD trajectories.

Introduction

Due to scientific and technological advancement of the past decades, the bioinformatics community is now able to generate a huge amount of data encoding molecular dynamics (MD), i.e. MD trajectories of large molecular systems on a long time scale (∼ µs level). However, if we often analyse the generated conformational space in terms of meta-stable states, or at least, as conformational wells that correspond to local minima of the energy of a biomolecule, the existing methods and tools employed by researchers remain deficient [START_REF] Peng | Clustering algorithms to analyze molecular dynamics simulation trajectories for complex chemical and biological systems[END_REF]. Indeed, classical clustering approaches ignore the dynamics of the problem, and do not allow to quantify, and thusly to compare the depth of the identified wells and their content. On the other hand, the widely used RMSD and RMSF methods are likely enable to consider the stable or equilibrated states, which are in reality transient segments of MD trajectory. Finally, as we do not have access to the energy of the biological macromolecule itself, but only of the global system including its environment, any method requiring a minimization of the energy of the system is not appropriate.

Here we present a new method, the κ-segmentation, conceived for clustering of MD-trajectory on the segments to fill the drawbacks of the previously quoted approaches. The algorithm of the κ-segmentation method is based on the original criteria (metrics) providing a quantification of wells depth, allowing the user to compare a well content and sort them, but also to reject any false artefacts.

The lap number κ: a new tool to investigate well depth

To start with, we consider the projected trajectory on the d first PCA coordinates so that we get a trajectory (X(t)) t∈[0,T ] in R d . Our core idea is to derive a kinetically based segmentation algorithm through the detection and analysis of regions of the configuration space into which the process spend an unexpected large time before exit.

We first the assume that trajectory as a continuous stochastic process solution of Stochastic Differential Equation (SDE) dX t = b(X i ) + σ(X i )dB t driven by a d-dimensional brownian motion. A natural idea is to compute for any time segment [s, T ] ⊂ [0, T ] the radius of the smallest ball centered at X s containing the path u → X u pour s ≤ u ≤ t:

R max (s, t) . = sup{ X u -X s : s ≤ u ≤ t }
The rational is that, in the case of a pure diffusion process, i.e b ≡ 0 and σ is constant) R 2 max (s, t) is expected to be of the order D(t -s) (where D is the D = dσ 2 is the diffusion factor. It is natural to introduce the dimensionless quantity κ, called hereafter the lap number:

κ(s, t) . = D(t -s) R 2 max (s, t) . (1)
We can expect that under the null hypothesis H 0 (b ≡ 0, pure diffusion), t → κ(s, t) stay of the order 1 (in fact, this quantity may converge to zero very slowly as 1/ log(log(t)) for large t due to the law of iterated logarithm). On the opposite, a large lap number may lead to the rejection of H 0 and trigger the detection of potential local equilibrium for the dynamic.

We illustrate this phenomenon in Fig. 2, comparing the evolution of R max computed for two trajectories: the first one corresponding to the solution of a Langevin SDE where the drift term is the gradient of a three wells energy landscape (see [START_REF] Nadler | Diffusion maps, spectral clustering and reaction coordinates of dynamical systems[END_REF]). Both trajectories are calibrated to have a diffusion coefficient compatible with observed ones on real MD trajectories (see the VKOR case below) and sample every 4 ps on a T = 100 ns simulation time. Despite having the same diffusion coefficient, the radius R max (0, t) is increasing faster in the brownian case. However the differences As predicted the t → κ(0, t) value stays small (below 2) along the full trajectory in the brownian case whereas it displays clear sharp drops from after reaching linearly local extremum well above 10 in the three well case.

κ-segmentation algorithm

Following upon this, we built an algorithm providing an automatic segmentation of any MD trajectory, based on the lap number. First, we sum up every possible lap number in a matrix κ(s, t) s≤t , within which the algorithm will travel by vertical stripes (see Fig. 3). For a given vertical strip, the width corresponds to a subset of possible candidate conformations at the center of a cluster. Inside a given strip, the analysis is done in a window W traveling along the vertical strip with a fixed stride. Within a given window, the maximum value κ * = κ(s * , t * ), where [s * , t * ] defined a possible segment corresponding to a portion of the trajectory starting near the center of a cluster at time s * called hereafter acces time to the center -indeed centering that point induces a lower R max and a greater κ value -and exiting the cluster at time t * (exit time). Then a decision is taken to accept or reject the segment [s * t * ] as a real cluster according the several acceptance test. Briefly we consider two main tests. The first one is to check for κ * ≥ κ 0 where the threshold κ 0 is chosen to prevent against false alarm and spurious detections. The second one is to test if inf t∈[t * ,t * +∆ 0 ] R max (s * , t)/R max (s * , t * ) ≥ ρ 0 (ρ 0 = 3/4 in our experiments), to check that the trajectory is not returning too close to the center after exit. The main hyperparameters on the algorithm are then the sliding window size (w 0 , h 0 ), the threshold κ 0 and the test time after exit ∆ 0 that have to be chosen of the order of R 2 0 /D 0 where R 0 is the expected size of the clusters and D 0 the measured or expected diffusion constant.

Applications

Brownian motion

Here we present the results obtained for the Brownian motion. The lap number matrix shows that κ cannot increase because of a constantly growing R max . As a result, and thanks to the incorporation of wells rejection criteria, the algorithm only detects transient segments, and do not pronounce any decision concerning the last segment, as it considers its investigation as ongoing.

Three wells trajectory

Here we present the results obtained for the three-wells case. The lap number matrix clearly reveals local maximas of κ. The algorithm performed on this trajectory recognize the relevant wells centered in (-1,0) and (1,0), but also points out the third one centered in (0,5/3) as irrelevant, identifying it as a transient segment.

VKORC1

This algorithm has been successfully applied to real MD simulation data generated with GRO-MACS (AMBER force-field). These MD trajectories were generated for VKORC1 [START_REF] Chatron | Identification of the functional states of human vitamin k epoxide reductase from molecular dynamics simulations[END_REF], the membrane protein involved in vitamin K recycling that is mandatory for essential physiological processes, such as coagulation, calcium homeostasis, energy metabolism, signal transduction and cell development. Two 5 ps-sampled of 1 µs MD trajectories were produced starting from a structural model of VKORC1 in which all cysteine residues were assigned to be protonated (Fig. 5.). We suggested that MD simulation of such highly flexible model will generate a large conformational space that can be used to predict different enzymatic states of VKORC1 observing upon its enzymatic cycle. In the following, we demonstrate the κ-segmentation of the one of these 5 ps-sampled 1 µs VKORC1 trajectories. The segmentation was performed after a 2D-projection of the trajectory with a PCA, and after the removal of both lower extremities of the protein located outside the membrane and inducing noise. According to this plot, we can already assume a final well being far deeper than the previous ones, which present cold exit times in terms of lap number, due to the normalization of the plot.

The κ-segmentation of this trajectory is presented in Fig. 7. First we observe the very high value of the lap number for the last well (∼ 17000), meaning that the well is very deep. Furthermore, the comparison of wells no. 2 and no. 5 is a good example of a well being deeper than another one, while presenting a lower exit time. In order to obtain reasonably good center points, we had to fix a very large strip width to explore the lap number matrix, ∼ 200 × δt, where δt represents the time needed by the process to travel a radius distance by diffusion only. If we look closely to the identified wells, we note that the process seems to be trapped in a subset of the well for a short time corresponding to the strip width (∼ 10 ns) before visiting the entire well. This symptom reveals that each well potentially presents several sub-wells, meaning that the algorithm could perform a multi-scale analysis. In the case where wells are overlapping each other, one may use a 3D-PCA of the trajectory, and visualize these wells based on the relevant frames identified with the 2D κ-segmentation. For VKORC1, the comparison of wells no. 2 and no. 3 shows an absence of intersection in 3D (Fig. 8). This is remarkable as the algorithm demonstrates the ability to highlight, from 2D dynamics information only, a disjoint phenomenon in higher dimension. Comparing VKORC1 conformations localized within the same well, one -in the center of each well and the other at exit time from the well, we observed that the flexible region demonstrates a notable difference in the well no. 2 while in the well no. 6 this difference is significantly reduced (Fig. 9). The conformations localized in the center of two different wells (e.g., no. 1 and no. 6) display the most significant divergence appears not only in flexible region, but also across the helices and C-terminal coil.

Conclusion and perspectives

The algorithm described here allows the user to perform a dynamic based segmentation of MDtrajectories driven by the analysis of the lap number κ to quantify the depth of a well (metastable state). The method is robust to false alarm and produces a sequence of wells coming with descriptive metrics (entrance and exit time, center of the well, lap number) allowing comparison between wells. Using the metrics, we can for instance characterize the metastable states, decide if the simulation is long enough to reach a relevant equilibrated state of protein or is worth being extended. Moreover, the κsegmentation could provide a hierarchical cluster representation containing information on metastables states at different levels, which can further help the user to characterize the architecture of the free energy landscapes. However, we note that the κ-segmentation method needs additional development such as graphic interface that can help identify a structural content of the wells. Also, consideration of multi-component systems, such as the protein complexes is required.

Fig. 1 .Fig. 2 .

 12 Fig. 1. Left: Three wells trajectory and standard Brownian motion (starting points in red). Right: Evolution od of R max for both three wells and Brownian case.

Fig. 3 .

 3 Fig. 3. κ-segmentation analysis of the κ matrix. The horizontal axis corresponds to arbitrary starting time s and the vertical axis to arbitrary exit time t with increasing values from top to bottom ((0, 0) is at the top left corner)

Fig. 4 .

 4 Fig. 4. (Left) lap number matrix. This matrix is read from left to right (shifting the starting point), and from top to bottom (reading the whole trajectory from the starting point). The lap number level is described by the heat intensity. (Right) κ-segmentation with transient segments shown in magenta.

Fig. 5 .

 5 Fig. 5. (Left) lap number matrix. (Right) κ-segmentation with transient segments shown in magenta, segments in well are shown in red, sets of initial conformations before and after center are in magenta and in yellow respectively, segment before and after exit are in green and black respectively.

Fig. 6 .

 6 Fig. 6. (Left) VKORC1 protein inserted into membrane (grey, rose) and surrounded by water molecules (blue light). (Right) Viewing of the highly flexible region (contoured) of VKORC1. Protein is shown as cartoon with cysteine residues as balls or as sticks.

Fig. 7 .

 7 Fig. 7. (Left) 2D-PCA of VKORC1 trajectory. (Right) Lap number matrix.

Fig. 8 .

 8 Fig.8. κ-segmentation of the 1 µs MD trajectories of VKORC1 with κ-segmentation. Segments in well are shown in red, sets of initial conformations before and after center are in magenta and in yellow respectively, segment before and after exit are in green and black respectively. Each well is associated with its lap number κ, maximum radius r (nm) and exit time T i (ns).

Fig. 9 .

 9 Fig. 9. 3D representation of wells no. 2 and 3 identified with the 2D-κ-segmentation of VKORC1 trajectory. Each well is associated with its lap number κ, maximum radius r (nm) and exit time T i (ns)

Fig. 10 .

 10 Fig. 10. Left and Middle: Superimposition of VKORC1 conformations corresponding to the well's center (blue light) and at exit time (red) illustrated for the wells no. 2 and no. 6. Right: Superimposition of VKORC1 conformations observed in the center of two wells -no. 1 (blue dark) and no. 6 (blue light) . Protein is represented by C α atoms showed as spheres.


Amit Regev Krugwasser

Yonatan Stern

Nathan Faivre

Eiran Vadim Harel

Roy Salomon

Amit Regev Krugwasser

Susan Gonda

Impaired Sense of Agency and Associated Confidence in Psychosis Running title: Aberrant Agency and Metacognition in Psychosis

Keywords: Sense of Agency, Metacognition, Psychosis, Virtual Reality, Clinical Classification

The Sense of Agency (SoA), our sensation of control over our actions, is a fundamental mechanism for delineating the Self from the environment and others. SoA arises from implicit processing of sensorimotor signals as well as explicit higher-level judgments.

Psychosis patients suffer from difficulties in the sense of control over their actions and accurate demarcation of the Self. Moreover, it is unclear if they have metacognitive insight into their aberrant abilities. In this pre-registered study, we examined SoA and its associated confidence judgments using an embodied virtual reality paradigm in psychosis patients and controls. Our results show that psychosis patients not only have a severely reduced ability for discriminating their actions but they also do not show proper metacognitive insight into this deficit. Furthermore, an exploratory analysis revealed that the SoA capacities allow for high levels of accuracy in clinical classification of psychosis. These results indicate that SoA and its metacognition are core aspects of the psychotic state and provide possible venues for understanding the underlying mechanisms of psychosis, that may be leveraged for novel clinical purposes.

Introduction

Psychosis is a severe psychiatric condition which includes numerous symptoms in which the delineation of the Self is compromised. Psychosis patients often report sensations of loss of control over their thoughts or actions, which has led to the suggestion that deficits in the demarcation of the Self constitute a core aspect of psychosis and schizophrenia spectrum disorders [START_REF] Hur | The crisis of minimal selfawareness in schizophrenia: A meta-analytic review[END_REF][START_REF] Raballo | Looking at the Schizophrenia Spectrum Through the Prism of Self-disorders: An Empirical Study[END_REF][START_REF] Sass | Schizophrenia, Consciousness, and the Self[END_REF][START_REF] Schneider | Clinical psychopathology[END_REF]. A central process giving rise to the sense of Self is the Sense of Agency (SoA), the feeling of control over one's actions. Research has highlighted the role of SoA in delineating one's bodily and mental functions from the environment and conspecifics, allowing one's experience as a distinct embodied agent in the world [START_REF] Gallagher | Multiple aspects in the sense of agency[END_REF][START_REF] Gallagher | Philosophical conceptions of the self: Implications for cognitive science[END_REF][START_REF] Haggard | Sense of agency in the human brain[END_REF][START_REF] Krugwasser | The boundaries of the self: The sense of agency across different sensorimotor aspects[END_REF].

Contemporary theories suggest that SoA is based on pre-reflexive predictive sensorimotor processes [START_REF] Bays | Attenuation of self-generated tactile sensations is predictive, not postdictive[END_REF][START_REF] David | The "sense of agency" and its underlying cognitive and neural mechanisms[END_REF][START_REF] Haggard | Sense of agency in the human brain[END_REF][START_REF] Wolpert | An internal model for sensorimotor integration[END_REF], as well as explicit processes that take into account contextual and conceptual factors [START_REF] Moore | Modulating the sense of agency with external cues[END_REF][START_REF] Synofzik | Beyond the comparator model: A multifactorial two-step account of agency[END_REF]. Within this theoretical framework, actions are accompanied by efferent copies that generate predictions regarding the expected sensory outcomes of these actions. Incoming afferent sensory information is then compared to the predictions. If the two match, the action is ascribed to the Self and accompanied by a SoA. These predictive mechanisms allow one to suppress the consequences of one's actions both at the perceptual [START_REF] Bays | Attenuation of self-generated tactile sensations is predictive, not postdictive[END_REF][START_REF] Blakemore | Central cancellation of selfproduced tickle sensation[END_REF][START_REF] Kilteni | Body ownership determines the attenuation of selfgenerated tactile sensations[END_REF]) and the neural level [START_REF] Hughes | ERP correlates of action effect prediction and visual sensory attenuation in voluntary action[END_REF][START_REF] Palmer | Physiological and Perceptual Sensory Attenuation Have Different Underlying Neurophysiological Correlates[END_REF][START_REF] Shergill | Modulation of somatosensory processing by action[END_REF][START_REF] Stripeikyte | Increased functional connectivity of the intraparietal sulcus underlies the attenuation of numerosity estimations for self-generated words[END_REF][START_REF] Van Elk | Suppression of the N1 auditory evoked potential for sounds generated by the upper and lower limbs[END_REF]. However, if a mismatch occurs the sensory outcomes are ascribed to an external origin and are passed up the hierarchy to explicit processes that explain them in light of beliefs, knowledge and other contextual factors. Thus the integration of efferent predictive models and afferent sensory signals shape SoA and play a key role in delineating the Self [START_REF] Hughes | Mechanisms of intentional binding and sensory attenuation: The role of temporal prediction, temporal control, identity prediction, and motor prediction[END_REF][START_REF] Synofzik | Me or not me-An optimal integration of agency cues?[END_REF].

Disturbances of SoA are a striking aspect of psychosis, common across schizophrenia spectrum disorders [START_REF] Franck | Defective recognition of one's own actions in patients with schizophrenia[END_REF][START_REF] Frith | Experiences of alien control in schizophrenia reflect a disorder in the central monitoring of action[END_REF][START_REF] Haggard | Awareness of action in schizophrenia[END_REF][START_REF] Hauser | Altered sense of agency in schizophrenia and the putative psychotic prodrome[END_REF][START_REF] Maeda | Aberrant sense of agency in patients with schizophrenia: Forward and backward over-attribution of temporal causality during intentional action[END_REF][START_REF] Voss | Altered awareness of action in schizophrenia: A specific deficit in predicting action consequences[END_REF]. It has been suggested that aberrant hierarchical prediction mechanisms underlie psychosis symptoms [START_REF] Corlett | Hallucinations and Strong Priors[END_REF][START_REF] Fletcher | Perceiving is believing: A Bayesian approach to explaining the positive symptoms of schizophrenia[END_REF][START_REF] Sterzer | The Predictive Coding Account of Psychosis[END_REF] and specifically abnormal SoA [START_REF] Frith | Experiences of alien control in schizophrenia reflect a disorder in the central monitoring of action[END_REF][START_REF] Leptourgos | Embodied predictions, agency, and psychosis[END_REF]. Accordingly, psychosis patients exhibit reduced sensory and neural attenuation for actions [START_REF] Ford | Did I do that? Abnormal predictive processes in schizophrenia when button pressing to deliver a tone[END_REF][START_REF] Shergill | Evidence for Sensory Prediction Deficits in Schizophrenia[END_REF][START_REF] Shergill | Evidence for sensory prediction deficits in schizophrenia[END_REF], impaired ability to predict the outcomes of their actions [START_REF] Lindner | Disorders of Agency in Schizophrenia Correlate with an Inability to Compensate for the Sensory Consequences of Actions[END_REF][START_REF] Synofzik | Misattributions of agency in schizophrenia are based on imprecise predictions about the sensory consequences of one's actions[END_REF][START_REF] Voss | Altered awareness of action in schizophrenia: A specific deficit in predicting action consequences[END_REF] and erroneous explicit judgments of agency [START_REF] Fourneret | Lack of conscious recognition of one's own actions in a haptically deafferented patient[END_REF][START_REF] Franck | Defective recognition of one's own actions in patients with schizophrenia[END_REF]. Thus, abnormal sensorimotor predictive mechanisms may induce inaccurate experiences of agency, causing confusion between self and externally induced sensations. Indeed, recent research has demonstrated a causal relationship between predictive processes and demarcation of the Self. For example, inducing tactile sensorimotor conflicts caused auditory selfdiscrimination deficits in first episode psychosis patients [START_REF] Salomon | Sensorimotor Induction of Auditory Misattribution in Early Psychosis[END_REF], and psychosis-like symptoms in healthy participants [START_REF] Bernasconi | Robot-induced hallucinations in Parkinson's disease depend on altered sensorimotor processing in fronto-temporal network[END_REF][START_REF] Blanke | Neurological and robot-controlled induction of an apparition[END_REF][START_REF] Faivre | Sensorimotor conflicts alter metacognitive and action monitoring[END_REF][START_REF] Serino | Thought consciousness and source monitoring depend on robotically-controlled sensorimotor conflicts and illusory states[END_REF].

However, most studies of SoA have employed non embodied paradigms in which action-outcomes contingencies are acquired during the experiment (e.g., press a button hear a tone). While these paradigms have enriched our understanding of learned action outcome mechanisms, they do not tap into the strong predictive capacities afforded by a lifelong experience of controlling our bodies [START_REF] Stern | Assessing the Relationship between Sense of Agency, the Bodily-Self and Stress: Four Virtual-Reality Experiments in Healthy Individuals[END_REF]. Thus, embodied SoA may differ in regards to the strength of the priors of the predictive processes [START_REF] Allen | The body as first prior: Interoceptive predictive processing and the primacy[END_REF][START_REF] Leptourgos | Embodied predictions, agency, and psychosis[END_REF], and better capture psychotic patients' anomalous self-experiences [START_REF] Sass | Schizophrenia, Consciousness, and the Self[END_REF].

While deficits in SoA have been found across the schizophrenia spectrum, it is yet unclear whether patients are aware of this impairment. Metacognitive deficits, involving lack of insight into their condition, are commonly found in psychosis and are associated with poorer prognosis [START_REF] Koren | Real-World Cognitive-and Metacognitive-Dysfunction in Schizophrenia: A New Approach for Measuring (and Remediating) More "Right Stuff[END_REF][START_REF] Lysaker | Metacognition amidst narratives of self and illness in schizophrenia: Associations with neurocognition, symptoms, insight and quality of life[END_REF][START_REF] Lysaker | Metacognitive Capacities for Reflection in Schizophrenia: Implications for Developing Treatments[END_REF]. However, recent research has shown that metacognitive capacities for some simple perceptual tasks do not seem to be deficient in schizophrenia patients [START_REF] Faivre | Confidence in visual motion discrimination is preserved in individuals with schizophrenia[END_REF][START_REF] Rouy | Systematic review and meta-analysis of metacognitive abilities in individuals with schizophrenia spectrum disorders[END_REF]. Awareness of control over our actions, is critical for meaningful interactions with the world. While there have been some suggestions that SoA itself is a metacognitive mechanism [START_REF] Chambon | What is the Human Sense of Agency, and is it Metacognitive[END_REF], but see Constant et al., 2021), to date there has been no study of metacognitive abilities of embodied SoA in psychosis.

The current pre-registered study examined embodied SoA and metacognition in psychosis patients and healthy participants. We employed a virtual hand (VH) paradigm previously used in healthy participants [START_REF] Krugwasser | The boundaries of the self: The sense of agency across different sensorimotor aspects[END_REF][START_REF] Stern | Assessing the Relationship between Sense of Agency, the Bodily-Self and Stress: Four Virtual-Reality Experiments in Healthy Individuals[END_REF] in which we manipulate the sensorimotor correspondence between the participants' real hand movement and the displayed VH's movement by inserting a temporal or spatial alteration. First, we hypothesized that patients' embodied SoA, operationalized as their ability to detect sensorimotor conflicts, would be impaired for both temporal and spatial alterations. Second, we hypothesized that their metacognition of SoA, operationalized as the correspondence between accurate sensorimotor conflict detection and associated confidence ratings, would be diminished compared to healthy participants.

Finally, in an exploratory analysis we examined whether we could accurately classify psychosis and control participants based on task performance using an automated Experimental procedure. Participants' right hand was occluded from their view and placed below a Leap Motion controller (Leap Motion Inc., San Francisco, CA) that tracked their hand's movement. A realistic 3D VH that mimicked the real hand's movement was displayed on a monitor (see supplementary material section A and [START_REF] Krugwasser | The boundaries of the self: The sense of agency across different sensorimotor aspects[END_REF] for further details). Each trial began with a fixation cross, followed by presentation of the VH during which participants performed a single bending movement with their index finger. In 25% of the trials, the VH's movement was identical to the real hand's movement, while in 75% of the trials a sensorimotor alteration was introduced. Three magnitudes of sensorimotor alterations were presented in temporal or spatial aspects. In the temporal aspect, the VH's movement was delayed (100/200/300 ms; [START_REF] Krugwasser | The boundaries of the self: The sense of agency across different sensorimotor aspects[END_REF][START_REF] Salomon | Full body illusion is associated with widespread skin temperature reduction[END_REF][START_REF] Shimada | Rubber Hand Illusion under Delayed Visual Feedback[END_REF][START_REF] Wen | The influence of action-outcome delay and arousal on sense of agency and the intentional binding effect[END_REF], and in the spatial aspect an angular deviation of the VH's index finger's was inserted (i.e., its lateral trajectory was diverged towards the thumb by 6/10/14°; [START_REF] Franck | Defective recognition of one's own actions in patients with schizophrenia[END_REF][START_REF] Kannape | The limits of agency in walking humans[END_REF][START_REF] Krugwasser | The boundaries of the self: The sense of agency across different sensorimotor aspects[END_REF]. Importantly, only a single alteration (or none) was presented in each trial. Each magnitude of alteration per aspect was presented 30 times, in a random order across five blocks, resulting in a total of 240 trials. Following the VH presentation, participants responded to a Yes/No question "Was the movement of the VH identical to my movement?", measuring SoA via the perceived congruence between the action and its outcome [START_REF] Franck | Defective recognition of one's own actions in patients with schizophrenia[END_REF][START_REF] Krugwasser | The boundaries of the self: The sense of agency across different sensorimotor aspects[END_REF][START_REF] Stern | Assessing the Relationship between Sense of Agency, the Bodily-Self and Stress: Four Virtual-Reality Experiments in Healthy Individuals[END_REF]. Participants then rated their confidence in the agency judgment on a continuous slider ranging from 'Not confident' (i.e., -3) to 'Very confident' (i.e., 3; see Fig. 1 for paradigm flow chart). Finally, the clinical symptoms of the psychosis patients were assessed using the Positive and Negative Syndrome Scale (PANSS, see [START_REF] Kay | The positive and negative syndrome scale (PANSS) for schizophrenia[END_REF], and HC participants completed the Schizotypal Personality Questionnaire-Brief Version (SPQ-B, see [START_REF] Raine | The SPQ-B: A Brief Screening Instrument for Schizotypal Personality Disorder[END_REF]. Data analysis. Data was pre-processed using in-house Matlab scripts (MATLAB, 2019). Following the pre-registration, trials in which no movement was made, camera malfunctioned, or participants failed to respond were removed from subsequent analyses (1.9% and 8.4% of the trials for HC and psychosis patients respectively).

Statistical analyses and visualization were performed in R (R Core Team, 2019).

SoA. SoA (i.e., self-attributing the VH's movement) was analyzed by comparing a series of logistic mixed-effects regressions implemented in the 'lme4' package [START_REF] Bates | Fitting Linear Mixed-Effects Models using lme4[END_REF]. Following [START_REF] Barr | Random effects structure for confirmatory hypothesis testing: Keep it maximal[END_REF], we attempted to include maximal random effects that also allow for model convergence. Models were compared using the differences of their Bayesian Information Criteria (i.e., Δ BIC, see [START_REF] Schwarz | Estimating the dimension of a model[END_REF], with values between 2 and 6, between 6 and 10 and > 10 considered as positive, strong and very strong evidence respectively for the model with the lower value [START_REF] Kass | Bayes Factors[END_REF][START_REF] Wagenmakers | A practical solution to the pervasive problems ofp values[END_REF]. The winning model's fixed parameters' significance were derived using the Satterthwaite's degrees of freedom approximation and type III error implemented in the 'lmerTest' package [START_REF] Kuznetsova | lmerTest Package: Tests in Linear Mixed Effects Models[END_REF]. Signal detection measures of sensitivity and bias (d' and c, respectively; See [START_REF] Macmillan | Signal detection theory[END_REF] of SoA were also calculated, across magnitudes of alteration.

Confidence ratings. Similar to SoA, confidence was analyzed by comparing a series of linear mixed-effects regression models. Following an observed hyperbolic effect of Alteration Magnitude on Confidence (see Fig. 2B and supplemental Fig. 2S), a quadratic expansion of Alteration Magnitude was used as a fixed parameter.

Metacognitive performance was also assessed using the gamma (γ) ranked correlations [START_REF] Goodman | Measures of Association for Cross Classifications[END_REF] between confidence ratings and accuracy. Gamma correlations range from minus one to one, with a value of zero indicating that there is no association between accuracy and confidence. Gamma was calculated across the magnitudes of alteration for each participant.

Correlations with clinical measures. In line with our pre-registration, Pearson correlations were used to examine the relation between sensitivity and clinical ratings (i.e., PANSS scores for psychosis patients, and SPQ-B scores for HC). To further inspect the relation between performance and clinical measures, this analysis was supplemented with an exploratory analysis of the correlations between criterion, metacognitive performance and clinical ratings, as well as metacognitive performance and clinical ratings.

Clinical classification based on SoA performance.

In an exploratory analysis we examined the potential clinical utility of our SoA paradigm for classification of participants to psychosis or control groups based on their SoA performance. We developed an algorithm that classifies a given participant based on the comparison of his/her SoA judgments' linear fit's slope, to the mean slopes of both groups. Participants were classified to the group with the smaller Euclidean distance (from each group linear fit's slope) combined across aspects of alteration (see Fig. 3A). The algorithm repeats this process 10,000 times, randomly leaving out the same proportion of participants from each group. Furthermore, we used the classifier with different proportions of leftout-participants as well as smaller subsets of trials for each participant (see Fig. 3C, left panel).

Results

Impaired SoA in psychosis patients.

In line with our pre-registered hypothesis, the best model included the main effects of Alteration Magnitude, Group and their interaction. This model was better (Δ BIC = 3.9) than the next model that included the same terms in addition to Aspect and its interactions. The intercept and slope of Alteration Magnitude were included as random effects (see supplementary material section C for full details of models). There was a significant main effect of Alteration Magnitude (β = -1.18, p < 0.0001, Z = 18.2, 95% CI [-1.31, -1.05]), such that as magnitude increased SoA ratings decreased across groups. There was a significant main effect of Group (β = -0.61, p < 0.0001, Z = 5.9, 95% CI [-0.82, -0.41]), with the psychosis group showing an increased tendency to self-attribute the observed movements across the magnitudes of alteration. Notably, as predicted, there was a significant interaction between Alteration Magnitude and Group (β = -0.52, p < 0.0001, Z = 8.1, 95% CI [-0.65, -0.4]), resulting from the psychosis group's moderate decrease in SoA ratings as alteration magnitude increased in comparison to HC's steep decrease in SoA as magnitude increased. Importantly, similar results were obtained for different random effects structure (see supplementary material section C). Complementing our finding of impaired SoA using mixed models, an independent samples t-test of sensitivity and bias revealed that participants in the control group had higher sensitivity and lower bias than the psychosis patients (d' Control = 1.8, d' Psychosis = 0.76, t 56 = 7.39, Cohen's d = 1.9, p < 0.0001; C Control = -0.43, C Psychosis = -0.73, t 52 = 2.88, Cohen's d = 0.74, p < 0.01, see supplemental Fig. S1). Thus, in line with our pre-registration, the psychosis group exhibited impaired SoA.

Impaired metacognition in psychosis patients.

In line with our preregistered hypothesis, the best model included all main effects and interactions of Alteration Magnitude, Group and SoA Accuracy (i.e., was the SoA judgment correct), with very strong evidence (Δ BIC = 70) over a model that did not include Group and its interactions. The intercept and slope of Alteration Magnitude were included as random effects. Examining the winning model's parameters, we found a significant three-way interaction between Alteration Magnitude, Group and Accuracy (β = 0.18, p < .001, t = 6.1, 95% CI [0.12, 0.24]). This interaction was driven by the psychosis group's consistently higher confidence ratings despite their low levels of accuracy especially in trials with large alteration magnitudes (see Fig. 2B and supplemental Fig. 2S). Thus, the psychosis group exhibited impaired metacognitive capacities as their confidence ratings did not track their accuracy in comparison to the HCs. In addition, there was a main effect of Alteration Magnitude (β = -0.18, p < .001, t = 7.47, 95% CI [-0.13, -0.23]), reflecting the increased confidence when there was either an extreme alteration or none. Likewise, a main effect of Accuracy was found (β = -0.47, p < .001, t = 11.44, 95% CI [-0.55, -0.39]), reflecting that across groups, confidence was increased when SoA judgments were correct. In contrast, Group was not significant (β = -0.18, p = 0.07, t = 1.78, 95% CI [-0.39, 0.02]), thus overall confidence ratings between groups were not significantly different. Importantly, similar results were obtained for different random effects structure (see supplementary material section C).

Further comparing the groups' metacognitive performance using gamma ranked correlation between confidence and accuracy, we found that the HC group exhibited a higher correlation (γ = 0.26, 59% CI [0.17, 0.35]) in comparison to the psychosis group (γ = -0.02, 59% CI [-0.12, 0.08]; see Fig. 2C), and this difference was significant (t 57 = 4.27, p < 0.0001, Cohen's d = 1.1). Examining whether each group's gamma significantly differed from zero (i.e., no correlation between accuracy and confidence) via a one-sample t-test, HC's gamma distribution was significantly higher than zero (t 29 = 5.8, p < 0.001, Cohen's d = 1.07), whereas the psychosis group's was not significantly different from zero (t 29 = 0.49, p = 0.63, Cohen's d = 0.09). These findings complement the three-way interaction found in the mixed-models, demonstrating that psychosis patients exhibit impaired metacognition and their confidence ratings do not track their accuracy. Correlation between task performance and clinical measures. In psychosis patients, contrary to our hypothesis, we did not find a significant correlation between sensitivity and the total PANSS score (r = -0.03, p = 0.86) nor its subscales (see Table 2). Likewise, bias was not significantly correlated with the total PANSS score (r = 0.04, p = 0.84) nor its subscales (see Table 2). In an exploratory analysis, we found that metacognitive performance was significantly negatively correlated with the PANSS Positive subscale score (r = -0.47, p < 0.01, uncorrected for multiple comparisons), such that metacognitive performance was higher in patients with fewer positive symptoms.

In HC, contrary to our hypothesis, we did not find a significant correlation between sensitivity and schizotypy (i.e., total SPQ-B score) (r = -0.12 p = 0.53) nor its subscales (see Table 2). Likewise, bias was not significantly correlated with the total SPQ-B score (r = 0.32, p = 0.08), yet it was significantly correlated with SPQ-B Disorganization subscale (r = 0.84, p < 0.010, uncorrected for multiple comparisons). Group classifier. Overall, the classifier was able to accurately classify participants in 89% of the cases (see Fig. 3B). Using a two-sample Kolmogorov-Smirnov test for a difference between distributions, we found this accuracy rate to be significantly higher than chance level (D = 0.95, p < 0.001, tested by randomly labeling participants as control or patients, and comparing the accuracy rate of the classifier to the actual accuracy rate; See supplemental Fig. S3). This finding was robust across different proportions of trials and participants left out, such that using only half the trials (i.e., 120 trials) and leaving out 80% of the participants (i.e., 24 out of 30 per group), only decreased the classifier performance to 85% accuracy. To further examine the realworld applicability of our task, we also examined classification by sampling trials from the first block of the experiment only. This excludes the possibility that the high classification accuracy rates are dependent on the participants' learning along the task.

Using only the first 48 trials and leaving out 20% of the participants, we obtained 81% accuracy, that was reduced to 73% when using only 24 trials and leaving out 80% of the participants (see Fig. 3C, right panel).

Discussion

Employing an ecological VR paradigm, we examined embodied SoA and associated confidence ratings in healthy and psychosis patient populations. Our results revealed several important findings. First, psychosis participants showed an extensive deficit in SoA, and were impaired in discriminating self from externally altered actions for both temporal and spatial alterations. Second, psychosis patients' metacognition of SoA was impaired, and their confidence ratings did not track the accuracy of their SoA judgments. Finally, using a data driven approach to classify psychosis patients based on their embodied SoA task performance yielded high classification rates, suggesting that our task may be clinically useful in the detection and monitoring of psychotic states.

Psychosis patients showed a considerable deficit in their ability to judge whether the movement of the VH was identical to their actual movement or altered. For both temporal and spatial alternations their sensitivity to sensorimotor conflicts was significantly reduced compared to the control group, and they tended to erroneously attribute actions to themselves (i.e., an over-attribution of SoA). This impairment is in line with previous reports of reduced abilities to predict the outcomes of one's actions in schizophrenia [START_REF] Lindner | Disorders of Agency in Schizophrenia Correlate with an Inability to Compensate for the Sensory Consequences of Actions[END_REF][START_REF] Synofzik | Misattributions of agency in schizophrenia are based on imprecise predictions about the sensory consequences of one's actions[END_REF][START_REF] Voss | Altered awareness of action in schizophrenia: A specific deficit in predicting action consequences[END_REF]. It has been previously suggested that abnormal temporal predictions and processing may underlie these SoA deficits [START_REF] Graham-Schmidt | When one's sense of agency goes wrong: Absent modulation of time perception by voluntary actions and reduction of perceived length of intervals in passivity symptoms in schizophrenia[END_REF][START_REF] Koreki | Behavioral evidence of delayed prediction signals during agency attribution in patients with schizophrenia[END_REF][START_REF] Waters | Time discrimination deficits in schizophrenia patients with first-rank (passivity) symptoms[END_REF][START_REF] Whitford | Schizophrenia, myelination, and delayed corollary discharges: A hypothesis[END_REF]. However the current findings indicate that embodied sensorimotor predictions in the spatial domain are also compromised [START_REF] Franck | Defective recognition of one's own actions in patients with schizophrenia[END_REF][START_REF] Synofzik | Misattributions of agency in schizophrenia are based on imprecise predictions about the sensory consequences of one's actions[END_REF]. In line with accounts highlighting disturbances of embodiment and the Self in psychosis [START_REF] Hur | The crisis of minimal selfawareness in schizophrenia: A meta-analytic review[END_REF][START_REF] Sass | Schizophrenia, Consciousness, and the Self[END_REF], our findings provide support for an impairment in the processing of the Self that extends across different perceptual dimensions.

In addition to SoA performance, we also investigated participants' metacognition of SoA. While psychosis patients had comparable overall levels of confidence in their SoA judgments, this contrasted strongly with their low level of accuracy. Converging evidence from the mixed model analysis and gamma-ranked correlations indicate that while the control participants' confidence tracked their SoA accuracy, this metacognition of SoA was absent in psychosis patients. Deficits of metacognitive capacities are well documented across the schizophrenia spectrum and has been related to poorer outcomes [START_REF] Dietrichkeit | Using virtual reality to explore differences in memory biases and cognitive insight in people with psychosis and healthy controls[END_REF][START_REF] Hasson-Ohayon | The centrality of cognitive symptoms and metacognition within the interacting network of symptoms, neurocognition, social cognition and metacognition in schizophrenia[END_REF][START_REF] Koren | Real-World Cognitive-and Metacognitive-Dysfunction in Schizophrenia: A New Approach for Measuring (and Remediating) More "Right Stuff[END_REF][START_REF] Lysaker | Metacognition in schizophrenia: Correlates and stability of deficits in theory of mind and self-reflectivity[END_REF]. However, recent work on perceptual metacognition indicates that when task difficulty is stringently controlled, metacognitive deficits in schizophrenia are small or even absent [START_REF] Faivre | Confidence in visual motion discrimination is preserved in individuals with schizophrenia[END_REF][START_REF] Powers | Pavlovian conditioning-induced hallucinations result from overweighting of perceptual priors[END_REF][START_REF] Rouy | Systematic review and meta-analysis of metacognitive abilities in individuals with schizophrenia spectrum disorders[END_REF]. The current study examining embodied SoA in patients, found an extensive deficit in SoA discrimination, combined with high confidence in their judgments pointing to a considerable deficit in metacognition for SoA (although, one must take into account that first order performance was not equated here, which may account for some of the differences between the groups, see [START_REF] Rouy | Systematic review and meta-analysis of metacognitive abilities in individuals with schizophrenia spectrum disorders[END_REF]. This suggests that in contrast to low-level perceptual metacognitive capacities which may be preserved, metacognition of SoA involving the integration of sensorimotor signals and higher-order constructs such as beliefs and intentions is severely impaired. This deficit is of clinical interest as the lack of SoA abilities compounded by their unawareness of this deficit, may relate to patients' lack of insight into clinical symptoms such as hallucinations and delusions (American Psychiatric Association, 2013; [START_REF] Koren | Real-World Cognitive-and Metacognitive-Dysfunction in Schizophrenia: A New Approach for Measuring (and Remediating) More "Right Stuff[END_REF]. Interestingly, an exploratory analysis revealed a strong and significant correlation between GK metacognitive measure and positive symptoms in the psychosis patient group (r = -0.47, p < 0.01, see Table 2). Thus, of all experimental measures, metacognitive ability was most strongly related to psychosis symptoms, yet further research is needed to robustly examine this relation between metacognition of SoA and psychosis symptoms.

Psychosis patients showed a higher tendency to erroneously attribute actions to themselves, and while this self-attribution bias has been shown in previous studies with psychosis patients (e.g., [START_REF] Daprati | Looking for the agent: An investigation into consciousness of action and self-consciousness in schizophrenic patients[END_REF][START_REF] Franck | Defective recognition of one's own actions in patients with schizophrenia[END_REF][START_REF] Hauser | Altered sense of agency in schizophrenia and the putative psychotic prodrome[END_REF], it stands in stark contrast to clinical symptoms of psychosis such as passivity symptoms in which reduced agency is experienced [START_REF] Synofzik | Misattributions of agency in schizophrenia are based on imprecise predictions about the sensory consequences of one's actions[END_REF]. It has been suggested

that the over-attribution bias may originate from more explicit top-down processes that take into account intentions, beliefs and contextual information in forming judgments of agency that compensate for the lack of sensorimotor signals that typically form the basis for SoA [START_REF] Synofzik | Beyond the comparator model: A multifactorial two-step account of agency[END_REF][START_REF] Synofzik | Me or not me-An optimal integration of agency cues?[END_REF]. Indeed, reduced precision of sensorimotor predictive models may lead to overweighting top-down priors, causing an overattribution of SoA to the Self [START_REF] Corlett | Hallucinations and Strong Priors[END_REF][START_REF] Leptourgos | Embodied predictions, agency, and psychosis[END_REF]. Our current finding of high subjective ratings of confidence despite low accuracy of SoA performance (i.e., impaired metacognition), support this hypothesis that top-down explicit processes (i.e., 'I moved and saw a movement so it is likely me') may receive higher weightings despite impairments in sensorimotor prediction function in psychosis.

The relation between clinical symptoms and SoA metrics revealed several interesting findings. Contrary to our pre-registered hypothesis, positive symptoms were not significantly correlated with SoA sensitivity (r = -0.16, p = 0.41, see Table 2) nor were SPQ-B perceptual deficits (r = -0.32, p = 0.08, see Table 2). An exploratory analysis revealed a correlation between the SPQ-B disorganization scale and bias (r = 0.48, p < 0.01, see Table 2). Indeed, previous studies have shown inconsistent correlations between prodromal symptoms [START_REF] Asai | Schizotypal personality traits and prediction of one's own movements in motor control: What causes an abnormal sense of agency?[END_REF][START_REF] Krugwasser | The boundaries of the self: The sense of agency across different sensorimotor aspects[END_REF][START_REF] Stern | Assessing the Relationship between Sense of Agency, the Bodily-Self and Stress: Four Virtual-Reality Experiments in Healthy Individuals[END_REF], psychosis symptoms [START_REF] Graham-Schmidt | Self-and other-agency in people with passivity (first rank) symptoms in schizophrenia[END_REF][START_REF] Hauser | Altered sense of agency in schizophrenia and the putative psychotic prodrome[END_REF][START_REF] Hur | The crisis of minimal selfawareness in schizophrenia: A meta-analytic review[END_REF] and SoA measures. It should be noted that the current study's sample size had low statistical power to detect such correlations.

Finally, we tested whether our embodied SoA paradigm might have clinical utility for identification and monitoring of psychosis. Using a classifier based on individual SoA performance, we were able to classify psychosis patients and controls with high levels of accuracy (~90%). Critically, this finding was robust when using only a small subset of trials or participants. This indicates that the differences in the tuning curve for the Self (i.e., the shape of the SoA slopes) is a strong predictor of psychosis across subjects. This is in line with accounts of an expanded sensorimotor temporal or spatial integration windows in psychosis, which may induce a wider "tuning curve" for the Self [START_REF] Haggard | Awareness of action in schizophrenia[END_REF][START_REF] Synofzik | Me or not me-An optimal integration of agency cues?[END_REF][START_REF] Voss | Altered awareness of action in schizophrenia: A specific deficit in predicting action consequences[END_REF]. At the practical level, such The current study suffers from several limitations. First, the psychosis cohort was not very large and was diverse in their psychiatric diagnosis (see Table 1). However, we suggest that the robustness of our SoA findings, despite this heterogeneity in the patients group indicates that SoA and metacognitive deficits are a major feature of the psychotic state. Second, as we aimed to test SoA across different levels of sensorimotor ambiguity, our data was not aimed to stringently control for task difficulty and this limited our ability to employ novel metacognitive measures [START_REF] Faivre | Sensorimotor conflicts alter metacognitive and action monitoring[END_REF][START_REF] Fleming | How to measure metacognition[END_REF]. Future work on metacognition of SoA should control first order performance more stringently. Finally, the control and psychosis groups were not matched for age, however no relations between age and any of the SoA or confidence measures were found (see supplemental Table S2).

In summary, employing an embodied virtual reality paradigm, we showed that psychosis patients are not only significantly impaired in their ability to discriminate their actions, but also show a substantial lack of awareness of this impairment. These results suggest deficits across multiple systems underlying SoA, including both low precision sensorimotor prediction mechanisms causing reduced sensitivity to deviations, as well as overreliance on top-down priors causing high confidence in erroneous judgments of agency. Importantly, patients' insight to their difficulties in the demarcation of the Self may provide a foothold for understanding and treating Self disorders in psychosis.

Figure 1 .

 1 Figure 1. Trial flow. Each trial began with a fixation cross (i), followed by the VH

Figure 2 .

 2 Figure 2. Group mean and individual ratings of SoA, confidence and metacognitive

Figure 3 .

 3 Figure 3. Group classifier performance. (A) Classification of two sample subjects

  computerized measurements could augment current in-person diagnosis of psychotic states by providing a telehealth option for online diagnosis and monitoring. Future studies employing multiple measurements could assess the relation of SoA to patients' clinical states over the course of hospitalization and recovery.

PANSS Total PANSS Negative PANSS Positive Age Diagnosis (N) Group

	of the experiment were hospitalized and under pharmacological treatment (see
	supplemental Table S1 for medication details).
	All participants gave written informed consent, were right-handed, with normal or
	corrected-to-normal vision and naïve to the purpose of the experiment. The experiment
	was performed in accordance with the ethical standards of the Declaration of Helsinki
	and the experimental protocols were approved by the Gonda Multidisciplinary Brain
	classifier, thereby probing the task's clinical utility. Pre-registration is available at
	Research Center ethics committee (for HC) and by the Beer Yaakov-Ness Ziona Mental
	https://bit.ly/2US57bX,	code	and	data	are	available	at
	Health Center ethics committee (for psychosis participants).
	github.com/amitrekru/SoA_Metacognition_Psychosis.
	Methods	Schizophrenia (17)		30.6 (7.2)	14.6 (3.1)	16.6 (4.7)	64.3 (12.4)
		Schizoaffective disorder (5)	35 (13.5)	15.2 (2.6)	9.4 (2.4)	52.8 (7.5)
	Participants Psychosis	Active psychosis (4) Paranoid schizophrenia (2)	29.3 (8.8) 28.5 (2.1)	17.3 (4.3) 12 (1.4)	16.5 (6.8) 16 (4.2)	67.5 (13.4) 59 (9.9)
	Healthy controls (HC). Thirty-four control participants that self-reported no psychiatric 69.5 (19) 13.5 (6.3) 18 (0) 28 (8.5) Bipolar Disorder (2)
	or neurological history from Bar-Ilan University participated in the experiment. Four 62.8 (12.4) 15.2 (5.2) 15.1 (3.2) 30.9 (8.3) Mean
	Control	None (30)		24.4 (3)			-
	participants were excluded from the analysis (see pre-registration and supplementary
	material section A for criteria and details) leaving a total of 30 healthy participants
	(mean age: 24.4 years, STD: 3 years, 15 females).
	Psychosis patients. Thirty-one participants with psychosis from Beer Yaakov-Ness
	Ziona Mental Health Center participated in the experiment. One participant was
	excluded from the analysis (see pre-registration and supplementary material section A
	for criteria and details) leaving a total of 30 psychosis participants (mean age: 32 years,
	STD: 9.2 years, all males. See Table 1 for clinical characteristics). Patients at the time

Table 1 . Participants' demographic and clinical characteristics. PANSS

 1 = Positive and Negative Syndrome Scale. Numbers represent the mean, numbers within the parenthesis represent the standard deviation.

Table 2 . Correlation between SoA performance and clinical measures.

 2

	Group	Scale	d'	c	Goodman-Kruskal γ
		SPQ-B Cognitive-perceptual deficits -0.32	0.24	0.21
	Control	SPQ-B Interpersonal deficits	0.23	0.02	0.2
		SPQ-B Disorganization	-0.25	0.48** 0.11
		SPQ-B Total	-0.12	0.32	0.26
		PANSS Positive	-0.16	0.01	-0.47**
	Psychosis	PANSS Negative	0.11	0.04	-0.17
		PANSS General	-0.08	0.05	-0.08
		PANSS Total	-0.03	0.04	-0.23

Correlations between clinical measures and sensitivity, bias & metacognition. **p < 0.01 (uncorrected for multiple comparisons).

Acknowledgments

We would like to thank Viktoria Vul for her help in collecting the data and Yair Zvilichovsky for developing the software used to run the experiment. We would also like to thank the patients for taking part in the experiment.

Funding

This study was supported by Israeli Science Foundation Grant (#1169/17) and a National Institute for Psychobiology in Israel grant to R.S.

Conflicts of Interest

The authors declare no conflict of interest.


Georgios Zervakis
email: georgios.zervakis@inria.fr

Emmanuel Vincent
email: emmanuel.vincent@inria.fr

Miguel Couceiro
email: miguel.couceiro@inria.fr

Marc Schoenauer
email: marc.schoenauer@inria.fr

On Refining BERT Contextualized Embeddings using Semantic Lexicons

Keywords: Contextualized embeddings, BERT, Knowledge integration, Retrofitting, Qualitative analysis

Word vector representations play a fundamental role in many NLP applications. Exploiting human-curated knowledge was proven to improve the quality of word embeddings and their performance on many downstream tasks. Retrofitting is a simple and popular technique for refining distributional word embeddings based on relations coming from a semantic lexicon. Inspired by this technique, we present two methods for incorporating knowledge into contextualized embeddings. We evaluate these methods with BERT embeddings on three biomedical datasets for relation extraction and one movie review dataset for sentiment analysis. We demonstrate that the retrofitted vectors do not substantially impact the performance for these tasks, and conduct a qualitative analysis to provide further insights on this negative result.

Introduction

The introduction of word embeddings was a breakthrough in NLP. Early approaches based on the distributional hypothesis -words that appear in the same context tend to be semantically similar -such as word2vec [START_REF] Mikolov | Distributed representations of words and phrases and their compositionality[END_REF] provided a fixed embedding for each word. Recently, contextualized embedding systems like BERT [START_REF] Devlin | BERT: Pre-training of deep bidirectional transformers for language understanding[END_REF] allow the generation of context-dependent word representations, which substantially improve the performance on many downstream NLP tasks.

Although such systems can be trained on data specific to the domain of interest, it is not yet clear how we can encode factual knowledge or impose constraints in the embeddings. Knowledge bases typically provide this type of information, hence it is reasonable to exploit them in order to obtain more accurate and explainable embeddings.

Retrofitting [START_REF] Faruqui | Retrofitting word vectors to semantic lexicons[END_REF] is a popular technique that modifies any set of pretrained distributional word embeddings to account for relational information encoded by a semantic lexicon. This is done as a post-processing step using an iterative update method called belief propagation [START_REF] Bengio | Label propagation and quadratic criterion[END_REF] on a graph of relations obtained from the lexicon to update the word vectors. This method was proven to improve performance on various intrinsic and extrinsic evaluation tasks [START_REF] Chiu | Enhancing biomedical word embeddings by retrofitting to verb clusters[END_REF][START_REF] Ferret | Turning distributional thesauri into word vectors for synonym extraction and expansion[END_REF][START_REF] Lengerich | Retrofitting distributional embeddings to knowledge graphs with functional relations[END_REF][START_REF] Mrkšić | Counter-fitting word vectors to linguistic constraints[END_REF][START_REF] Mrkšić | Semantic specialization of distributional word vector spaces using monolingual and cross-lingual constraints[END_REF].

In this paper, we aim to extend retrofitting to operate with contextualized word embeddings. More specifically, we propose two different methods that, as in the original retrofitting approach, make use of similarity relations between words in order to move the respective embeddings closer to each other in the latent space. The first method combines the embedding of a given test sentence with the embeddings of sentences involving similar words in the training set, while the second method replaces a word in the test sentence by all possible similar words and combines the resulting embeddings. We evaluate the proposed methods with BERT embeddings on three biomedical datasets for a relation extraction task and one movie review dataset for sentiment analysis, and compare them with an oracle topline and two baselines (weighted majority vote and class posterior averaging). We show that both methods do not substantially impact the performance for this task, and conduct a qualitative analysis to provide further insights on this negative result.

The paper is organised as follows. We discuss related work in Section 2, and present the proposed methods in Section 3. We describe the experimental evaluation setup in Section 4, and we analyze the obtained results in Section 5. We provide conclusions and discuss future work in Section 6.

Related Work

There have been several attempts to improve the quality of word embeddings by incorporating knowledge into the process. Two main categories of methods can be distinguished, which we refer to as joint or post-hoc.

Joint methods integrate knowledge by retraining the embedding model from scratch using a modified training objective. For example, [START_REF] Levy | Dependency-based word embeddings[END_REF] proposed to replace the classical bag-of-words contexts in the word2vec Skip Gram model by dependency-based contexts, and showed that the resulting embeddings better reflect the syntactic similarities between words. In another approach, [START_REF] Yang | Leveraging knowledge bases in LSTMs for improving machine reading[END_REF] modified a BiLSTM recurrent neural network to take into account information coming from the WordNet and NELL knowledge bases. To this end, they employed an attention mechanism that computes the relevance of candidate concepts from the knowledge base to the current input, and a second component that decides whether to exploit this information or not, and they reported improvements on both entity and event extraction tasks. In the same fashion, KnowBERT [START_REF] Peters | Knowledge enhanced contextual word representations[END_REF] incorporates WordNet and part of Wikipedia into BERT, showing the ability of the model to recall facts from the databases, improving downstream relation extraction, entity typing and word sense disambiguation tasks at the same time. Nonetheless, joint methods come with the downside that they are model-specific, and often time-consuming since they require retraining the system afresh.

Post-hoc methods surpass these limitations, since knowledge is inserted in the word embeddings after training, regardless of the model used to obtain them. The most popular technique among these is retrofitting [START_REF] Faruqui | Retrofitting word vectors to semantic lexicons[END_REF]. This is a graph-based approach that, given a semantic lexicon, i.e., a knowledge graph whose nodes represent words and edges represent relations between them, tries to reposition the word embeddings in such a way that they become closer (under some distance metric) to neighborhood embeddings in the graph. Initially, [START_REF] Faruqui | Retrofitting word vectors to semantic lexicons[END_REF] considered a single type of relation between words, namely 'similarity'. Later approaches have extended retrofitting to account for 'dissimilarity' relations [START_REF] Lengerich | Retrofitting distributional embeddings to knowledge graphs with functional relations[END_REF][START_REF] Mrkšić | Counter-fitting word vectors to linguistic constraints[END_REF][START_REF] Mrkšić | Semantic specialization of distributional word vector spaces using monolingual and cross-lingual constraints[END_REF] and ordering (ranking) between the relations [START_REF] Ferret | Turning distributional thesauri into word vectors for synonym extraction and expansion[END_REF].

By default, all of the above retrofitting methods can only be applied to distributional word embeddings, i.e., a single representation vector per word. When we shift to contextualized embeddings, each word in the vocabulary can have a different representation in each sentence. An attempt to retrofit contextualized embeddings coming from ELMo is presented in the Paraphrase-aware Retrofitting (PAR) [START_REF] Shi | contextualized word embeddings with paraphrases[END_REF] method. More specifically, PAR learns an orthogonal transformation matrix that pulls closer the embeddings of words in paraphrased contexts, and separates those in unrelated contexts. However, this approach is limited to pairs of paraphrased contexts and cannot benefit from different sources of linguistic information. To our knowledge, there is no existing method for contextualized embeddings that takes full advantage of the benefits of retrofitting.

Proposed Contextualized Embedding Refinement Methods

As in the conventional retrofitting approaches discussed in Section 2, we assume a vocabulary of words V = {w 1 , . . . , w n } and an ontology Ω of semantic relations between words in V. We can then represent Ω in the form of an undirected graph (V, E), where nodes correspond to words in V and edges (w i , w j ) ∈ E ⊆ V × V to semantic relations between nodes. Now, suppose that we have a contextualized word representation model M, along with a training corpus D train on which it is fine-tuned and a test corpus D test on which it is evaluated for a particular task.

Method A

The first proposed embedding refinement method, which we refer to as Method A, combines the contextualized embedding of a given word in the test set with the contextualized embeddings of all occurrences of all similar words in the training set. Let qi ∈ R d be the contextualized embedding of word w i ∈ V coming from M for a given test instance 3 . Let us further denote by J i the set of words w j which are adjacent to w i according to Ω, and by K j the set of training instances where w j occurs. Then we define qjk ∈ R d to be the contextualized embedding computed for all occurrences of w j in D train , as index by k ∈ K j . The index sets J i and K j vary dynamically for every word.

The goal is to learn a new embedding q i that it is close to qi and to adjacent nodes in Ω under the L 2 norm by minimizing

L(q i ) = q i -qi 2 + j∈Ji k∈Kj b ijk q i -qjk 2 (1)
The weights b ijk must naturally depend on the number of neighbours |J i | of w i , and on the number of occurrences |K j | of each neighbor w j in D train . In the following we define them as

b ijk = c ij ×d jk = 1 |Ji| α • 1 |Kj | β , α, β ∈ [0, ∞)
where c ij controls the contribution of each neighbour and d jk controls the contribution of each of its occurrences. For example, α = β = 0 results in equal weights b ijk = 1 for all occurrences, while α = β = 1 results in weights b ijk that sum up to 1.

Equating to zero the derivative of L with respect to q i and expressing the k b ijk qjk in terms of the mean µ qj of all qjk results in the following update rule:

q i = qi + j k b ijk qjk 1 + j k b ijk = qi + |J i | -α j |K j | 1-β µ qj 1 + |J i | -α j K 1-β j . (2)
The retrofitting operation therefore takes the form of a weighted average of the original embedding and the embeddings of all occurrences of all similar words in the training set.

Method B

The second proposed method, which we refer to as Method B, does not involve D train at all. Instead, everything happens at test time. Again, we utilise M to obtain the embedding qi of word w i for a specific sentence in D test . In addition, we derive one embedding qj for every word w j which is adjacent to w i according to Ω. To do so, we create a new sentence by replacing w i with w j in the test sentence, and repeat for every adjacent node of w i in Ω. The objective is once more to learn a new vector q i that is close to both qi and all qj under the L 2 norm by minimizing

L(q i ) = q i -qi 2 + j∈Ji b ij q i -qj 2 (3)
Similarly to the above, we define the weights as

b ij = 1 |Ji| α , α ∈ [0, ∞).
Equating to zero the derivative of L with respect to q i and expressing the j b ij qj in terms of the mean µ qj of all qj results in the following update rule:

q i = qi + j b ij qj 1 + j b ij = qi + |J i | 1-α µ qj 1 + |J i | 1-α . (4)
Again, the retrofitting operation takes the form of a weighted average of the original embedding and the embeddings of all neighbouring words.

The main difference between the two methods lies in the way we exploit the information coming from the knowledge graph. Method A typically results in a large number of neighbouring vectors qik that contain noise, since the context around the corresponding words differs from that of the test sentence in general. In contrast, Method B generates fewer neighbouring vectors qj that share exactly the same context as the test sentence being processed.

Experimental Setup

In this section, we first provide information with respect to the data, the semantic lexicons and the contextual word embedding model we used to evaluate the proposed retrofitting methods. Then, we describe the experimental evaluation and we suggest three alternative strategies for comparison.

Data

We consider two tasks: relation extraction from biomedical data 4 and sentiment analysis of movie reviews. Two semantic verb lexicons are introduced in [START_REF] Chiu | Enhancing biomedical word embeddings by retrofitting to verb clusters[END_REF], referred to as annotated and expanded clusters. The former contains 192 verbs that appear frequently in a corpus of 2,230 biomedical journal articles, while the latter is an extended version of 1,149 verbs. Both lexicon come with three levels of granularity, i.e., verbs are grouped into 16, 34 and 50 classes 5 , and are used for relation extraction.

ChemProt is a manually annotated corpus of relations between drugs/ chemical compounds and genes/proteins mentions found in PubMed abstracts. The relations are categorized into ten classes from which only five are used during evaluation. The task is to predict whether a pair of such entities is related or not, and if so, output the type of relation.

The DDI corpus aims in the development of systems that can automatically detect drug entities and drug-to-drug interactions in biomedical text. The corpus itself consists of texts from the DrugBank database and abstracts from the MedLine database. Annotations were provided by domain experts that classified drug-drug interactions into four DDI types.

i2b2 2010 corpus promotes the study of extraction/classification/relations of medical problems, tests, and treatments. The data consist of discharge summaries collected from Partners Healthcare, Beth Israel Deaconess Medical Center, and the University of Pittsburgh Medical Center, where relations of medical problems-treatments were grouped into eight classes.

For the sentiment analysis task, we use the exact same semantic lexicons as in [START_REF] Faruqui | Retrofitting word vectors to semantic lexicons[END_REF], namely, FrameNet, PPDB and two variants of WordNet which we refer to as WordNet syn and WordNet all (see more details in [START_REF] Faruqui | Retrofitting word vectors to semantic lexicons[END_REF]). The size of these lexicons is relatively large, since they are general and contain knowledge about words which do not convey any sentiment, e.g., pronouns, prepositions, etc.. In order to focus on relevant words for the task, in conjunction with the semantic lexicons we utilize the Bing Liu Sentiment Lexicon [START_REF] Hu | Mining and summarizing customer reviews[END_REF], a domainindependent list of 6,786 adjectives that is manually created and that categorizes words as either positive or negative according to their sentiment.

SST-2 (Stanford Sentiment Treebank) [START_REF] Socher | compositionality over a sentiment treebank[END_REF] is a collection of 11,855 sentences from movie reviews including human annotations of their sentiment. The goal is to classify a given sentence as either positive or negative. Since the test labels are not publicly available, we split the training set such that 13% of the sentences are used for testing and the remaining are used for training. The resulting test set has 462 positive and 438 negative reviews, while the training set has 3,148 positive and 2,872 negative reviews. Finally, we use the development set provided by the authors.

BERT Architecture and Retrofitting

There are different locations within the architecture of BERT, where retrofitting transformations can be applied. In general, the model consists of 12 Transformer blocks [START_REF] Vaswani | Attention is all you need[END_REF] followed by a pooling layer, i.e., a fully connected layer with a dropout layer and a tanh activation. Each block contains a sequence of transformations that is divided into layers. The output layer of each block consists of a linear transformation, followed by dropout and layer normalisation. For both approaches we experimented with four retrofitting different settings: before or after layer normalisation at Transformer block 11 or 12.

The motivation behind these choices is related to the complex architecture of the model. We hypothesize that the impact of any change into the embeddings would be more noticeable as we get closer to the output space, rather than in earlier layers of the model. Thus, we started experimenting at the pooling layer, which is the closest to the output space, but the results were not promising. Consequently, we moved one step back at the output layer of the last Transformer block, and further back to the same place of the preceding Transformer block.

In the retrofitting equations ( 1) or (3), we initially considered as qi the embedding corresponding to the word token in the test sentence, but preliminary experiments showed that this did not have an impact on the final performance. To verify this, we replaced the embeddings of these individual words with random numbers, or even zeroes. Both cases did not affect the performance, indicating that the output classifier is not very much dependent on single word embeddings. Instead, we focus on the [CLS] token embedding which is a weighted linear average of all word embeddings in the test sentence, it is closer to the output space, and has a bigger impact on the final result. All qij in (1) correspond to the activations of the word token in training sentences, whereas all qj in (3) correspond to the activations of the [CLS] token in modified test sentences.

Technical Details

For the relation extraction task we chose BlueBERT [START_REF] Peng | biomedical natural language processing: An evaluation of BERT and ELMo on ten benchmarking datasets[END_REF] a specific variant of BERT that is further pre-trained on PubMed abstracts and clinical notes from MIMIC-III database, while for sentiment analysis we experimented with the classical BERT. In particular, for both tasks we selected the BERT-Base release of the model, which makes use of the exact same configurations, (e.g., vocabulary, length) as in the original BERT, and we further fine-tuned it on the downstream task for each dataset. We treat both tasks as a sentence classification problem. For relation extraction the named entities are anonymized with pre-defined tags (e.g., @GENE, @CHEMICAL for ChemProt) as in [START_REF] Lee | Biobert: a pre-trained biomedical language representation model for biomedical text mining[END_REF]. Then, we feed an input sentence into BERT which makes use of the [CLS] token of that sentence to perform the classification. In particular, the [CLS] representation is forwarded into the output layer of the last Transformer block, that produces an estimation for each class.

Grid Search Optimization

In order to find a good set of values for the retrofitting hyperparameters α, β, we performed a grid search using the development sets. For the first approach, we used both annotated and expanded clusters and we searched for α, β ∈ [0, 2] with a step of 0.2. We do not proceed on testing Method A for SST-2, as it turns out to be inferior to Method B. For the second approach, we use all four lexicons for sentiment analysis in conjunction with Bing Liu's sentiment lexicon (explained in Section in 4.1), while for relation extraction we only used the 34 and 50 classes of the annotated clusters 6 . Once again, we performed a grid search on the development sets where we searched for α ∈ [0, 2] with a step of 0.2.

Alternative Classification Strategies

In order to assess the ability of our method to leverage the information in the lexicons, we augmented all datasets by adding all modified sentences that occur by replacing the underlying word with a neighbouring one, and compared with the following alternative strategies:

Topline: Always selecting the true class of a test sentence as the final prediction, if it was predicted by at least one of the original or the modified sentences.

Weighted majority vote (WMJ): Picking the predicted class with the most occurrences as the final prediction out of the original and the modified test sentences. Here, we assigned a weight of 1 to the original and a weight of 1 |S| δ , δ ∈ [0, 1] to each modified sentence, where |S| is the total number of sentences for the current test input. We experimentally noticed that choices of δ outside [0, 1] did not affect the final prediction.

Average probabilities (AVGP): Averaging the probabilities of the predicted classes for both the original and the modified test sentences, and taking the class with the maximum probability as the final prediction.

Results and Qualitative Study

In this section we present the results obtained from the grid search, and conduct additional experiments that give more insight on the reasons why the proposed methods yield a similar performance to the baseline model.

Grid Search Experimental Results

After finding the best performing set of hyperparameters amongst all combinations of lexicons, Transformer blocks, and positions that were tested on the development set, we evaluated the corresponding model on the test set. We report the performance for each dataset in terms of micro F 1 -score for relation extraction, and accuracy for sentiment analysis 7 . The results for both retrofitting approaches are displayed in Table 1. At first sight, both approaches seem to have no significant impact compared to the baseline performance. More specifically, Method A results in a decrease of performance on all datasets, while Method B slightly improves it for ChemProt and SST-2. Furthermore, we notice that in many cases the alternative strategies we propose work better than our retrofitting approaches. This suggests that i) the use of the lexicons is meaningful, but ii) we have not yet found the correct way of exploiting this knowledge. It is also worth highlighting the abrupt decrease in test performance on the i2b2-2010 for the AVGP method. We assume this is due to the model outputting different probabilities for each of the modified sentences. To confirm this, we compared with the score obtained from WMV for every δ ∈ [0, 1] with a step of 0.1, and we observed that for low values of the weight the performance is significantly worse. This indicates that the original sentence is more important than the modified ones, implying in turn that we should assign a higher weight on it. However, in AVGP the averaging equally favours each class, and thus performs poorly.

Euclidean Distance Ranking of Retrofitted Vectors

In order to understand in greater depth how our proposed methods change the embeddings in space, let us focus on a single test case 8 where the proportion of disagreements between the baseline model and the test case model is statistically significant (based on McNemar's test). This points out that both models behave differently, but on average they result in similar performance. To further analyse how Method A affects the embeddings in the latent space, we randomly select 5, 000 (out of 18, 014) test sentences where we apply our method, and we compute the corresponding activation of the [CLS] token before and after retrofitting. Next, we compute the Euclidian distance between every retrofitted vector and every [CLS] vector before retrofitting. This results in a 5000×5000 matrix, where Table 1: Performance results across all datasets and proposed strategies as well as some retrofitting approaches for static word embeddings. Baseline corresponds to BERT base model finetuned on each dataset for the specific task. Method A, B denote the proposed retrofitting approaches. Topline, AVGP and WMV were discussed in Section 4.5, where for the last we select the weight (δ) based on the best performance on the validation set. each row contains the distances of one retrofitted vector to all original vectors (before retrofitting). We then rank from 0 -5000 each retrofitted embedding by sorting each row in the matrix in ascending order. By doing so, we can check how far our method is moving the embeddings in the latent space. The distribution of the resulting rankings across all vectors is summarized in the histogram in Figure 1. From this plot, we can observe that a large proportion of vectors has a relatively low ranking (around [0, 80]), but there is also a considerable amount of vectors with high ranking (around [950, 1000]), suggesting that potentially the vectors do not move as far as they should, or sometimes they move too far. This is an indication that there is a lot of variation in the neighbouring embeddings, and therefore not all words in the lexicons are relevant for the task at hand. The following experiment will check if restricting the lexicons to the domain has any impact when retrofitting.

Neighbouring Word Filtering

Bing Liu's list of adjectives allow us to focus on appropriate words in the semantic lexicons for the task of sentiment analysis. The next question we want to answer is which neighbouring words are relevant for the underlying word, and which are not. It is evident that not all neighbouring words for a given word in the lexicons are actual synonyms in the context of movie reviews. Replacing single words in the input sentence in Method B, forces the same context between the original and the modified sentence. Consequently, we restrict the lexicons to the domain by selecting neighbours that are "good" replacements instead of using the whole list. This is done by inspecting the predictions of BERT for every original and modified sentence on the augmented development set for a given lexicon (see Section 4.5). Then, we can distinguish between the following cases: (A) the original sentence was wrongly classified but the modified sentence was correctly classified (good case), (B) the original and the modified sentence were correctly/wrongly classified (neutral case), and (C) the original sentence was correctly classified but the modified sentence was wrongly classified (bad case). Next, we compute the counts that correspond to good, neutral and bad cases for every pair of original-neighbouring word. These will show on average if a neighbour is a good replacement or not for a given word. Then, using the Mc-Nemar's statistical test, we create three reduced versions, one for each semantic lexicon, by selecting a neighbour for a given word with a 10%, 50% and 90% confidence level 9 . The higher the confidence level the more certain we are about replacing a word by another one, but the smaller the lexicon becomes (and vice versa). Finally, we repeat the grid search optimisation (see Section 4.4) and present in Table 2 the results for the best settings. Overall, there is some gain in performance compared to the baseline on the development set which is expected. For example, Method B reaches Topline performance for FrameNet 10% , which suggests that retrofitting in the sense of averaging embeddings can be meaningful. Moreover, we can see that the Topline performance is almost identical to that of the baseline model on the test data. This is due to the limited size of the reduced lexicons 10 . Ideally, if the dataset were bigger, we would have selected lexicons with higher confidence level that would also be large enough to improve over the baseline, i.e., the Topline score would significantly outperform the baseline.

Conclusion and Future Work

In this paper, we proposed two approaches that extend the original retrofitting technique to operate with contextualized embedding systems. More precisely, we incorporated external knowledge coming from semantic lexicons into BERT contextualized representations. After conducting a large-scale series of experiments on three biomedical datasets for relation extraction, and one movie review dataset for sentiment analysis, we observe that both approaches do not substantially affect the performance on these downstream tasks. Our test results show that the lexicons can be a useful source of information to further improve the results. However, the current experimental setting did not make it viable. This is demonstrated in our qualitative study, where we show that when we improve the quality of the semantic lexicons by selecting only relevant neighbours for a given word, the resulting lexicons are not sufficiently large to be able to generalize at test time. In the future, we plan to experiment with more fine-grained tasks where we are certain about the knowledge source, and where we would not need to heavily depend on word statistics to apply the proposed method.

Fig. 1 :

 1 Fig. 1: Histogram of the ranking across [CLS] token retrofitted vectors for all 5000 ChemProt test sentences where Method A is applied.

Table 2 :

 2 Results for the best performing lexicons derived from our neighbouring word selection for Method B and the proposed alternative strategies. Baseline corresponds to BERT base model, fine-tuned on SST-2 for sentiment analysis.

	Lexicon	Model	Dev Acc Test Acc
	-	Baseline	91.86	92.00
		Method B	92.09	92.00
	FrameNet 10% Topline	92.09	92.11
		AVGP	92.09	92.00
		WMV (δ = 0)	92.09	92.00
		Method B	92.09	92.00
	WordNetsyn 10% Topline	92.66	92.00
		AVGP	92.09	91.89
		WMV (δ = 0)	92.09	92.00

For simplicity, qi does not have a superscript for the test sentence as we only process one test sentence at a time.

The biomedical datasets are included in the Biomedical Language Understanding Evaluation (BLUE) benchmark, as well as the preprocessing codes for creating the training, development and test sets.

We refer to each different version of the verb lexicons simply by adding the number of the verb classes next to its name, e.g., annotated-34.

This is due to the extensive amount of neighbouring verbs on the annotated-16 and the expanded clusters, which significantly increases the computational cost.

This is the standard choice of metrics for these tasks and datasets[START_REF] Peng | biomedical natural language processing: An evaluation of BERT and ELMo on ten benchmarking datasets[END_REF][START_REF] Socher | compositionality over a sentiment treebank[END_REF].

This corresponds to Method A on ChemProt, using the expanded-16 clusters, and retrofitting after layer normalisation at Transformer block 12, with α = 0.4 and β = 1.4 (second row of Table1).

We use the confidence level percentage as a subscript to denote the reduced lexicon, e.g., FrameNet 90% .

For example FrameNet originally consists of 1700 words and 90140 relations, while its largest reduced version, FrameNet 10% , has only 1 word and 5 relations.

Acknowledgements

This research was partially supported by the European Union's Horizon 2020 Research and Innovation Program under Grant Agreement No. 952215 TAILOR and by the Inria Project Lab "Hybrid Approaches for Interpretable AI" (HyA-IAI). Experiments presented in this paper were carried out using the Grid'5000 testbed, supported by a scientific interest group hosted by Inria and including CNRS, RENATER and several Universities as well as other organizations (see https://www.grid5000.fr).