Dissociative and prioritized modeling of behaviorally relevant neural dynamics using recurrent neural networks.

Understanding the dynamical transformation of neural activity to behavior requires new capabilities to nonlinearly model, dissociate and prioritize behaviorally relevant neural dynamics and test hypotheses about the origin of nonlinearity. We present dissociative prioritized analysis of dynamics (DPAD), a nonlinear dynamical modeling approach that enables these capabilities with a multisection neural network architecture and training approach. Analyzing cortical spiking and local field potential activity across four movement tasks, we demonstrate five use-cases. DPAD enabled more accurate neural-behavioral prediction. It identified nonlinear dynamical transformations of local field potentials that were more behavior predictive than traditional power features. Further, DPAD achieved behavior-predictive nonlinear neural dimensionality reduction. It enabled hypothesis testing regarding nonlinearities in neural-behavioral transformation, revealing that, in our datasets, nonlinearities could largely be isolated to the mapping from latent cortical dynamics to behavior. Finally, DPAD extended across continuous, intermittently sampled and categorical behaviors. DPAD provides a powerful tool for nonlinear dynamical modeling and investigation of neural-behavioral data.

Return of intracranial beta oscillations and traveling waves with recovery from traumatic brain injury.

Traumatic brain injury (TBI) remains a pervasive clinical problem associated with significant morbidity and mortality. However, TBI remains clinically and biophysically ill-defined, and prognosis remains difficult even with the standardization of clinical guidelines and advent of multimodality monitoring. Here we leverage a unique data set from TBI patients implanted with either intracranial strip electrodes during craniotomy or quad-lumen intracranial bolts with depth electrodes as part of routine clinical practice. By extracting spectral profiles of this data, we found that the presence of narrow-band oscillatory activity in the beta band (12-30 Hz) closely corresponds with the neurological exam as quantified with the standard Glasgow Coma Scale (GCS). Further, beta oscillations were distributed over the cortical surface as traveling waves, and the evolution of these waves corresponded to recovery from coma, consistent with the putative role of waves in perception and cognitive activity. We consequently propose that beta oscillations and traveling waves are potential biomarkers of recovery from TBI. In a broader sense, our findings suggest that emergence from coma results from recovery of thalamo-cortical interactions that coordinate cortical beta rhythms.

Stable, chronic in-vivo recordings from a fully wireless subdural-contained 65,536-electrode brain-computer interface device.

Minimally invasive, high-bandwidth brain-computer-interface (BCI) devices can revolutionize human applications. With orders-of-magnitude improvements in volumetric efficiency over other BCI technologies, we developed a 50-µm-thick, mechanically flexible micro-electrocorticography (µECoG) BCI, integrating 256×256 electrodes, signal processing, data telemetry, and wireless powering on a single complementary metal-oxide-semiconductor (CMOS) substrate containing 65,536 recording and 16,384 stimulation channels, from which we can simultaneously record up to 1024 channels at a given time. Fully implanted below the dura, our chip is wirelessly powered, communicating bi-directionally with an external relay station outside the body. We demonstrated chronic, reliable recordings for up to two weeks in pigs and up to two months in behaving non-human primates from somatosensory, motor, and visual cortices, decoding brain signals at high spatiotemporal resolution.

Event detection and classification from multimodal time series with application to neural data.

The detection of events in time-series data is a common signal-processing problem. When the data can be modeled as a known template signal with an unknown delay in Gaussian noise, detection of the template signal can be done with a traditional matched filter. However, in many applications, the event of interest is represented in multimodal data consisting of both Gaussian and point-process time series. Neuroscience experiments, for example, can simultaneously record multimodal neural signals such as local field potentials (LFPs), which can be modeled as Gaussian, and neuronal spikes, which can be modeled as point processes. Currently, no method exists for event detection from such multimodal data, and as such our objective in this work is to develop a method to meet this need. Here we address this challenge by developing the multimodal event detector (MED) algorithm which simultaneously estimates event times and classes. To do this, we write a multimodal likelihood function for Gaussian and point-process observations and derive the associated maximum likelihood estimator of simultaneous event times and classes. We additionally introduce a cross-modal scaling parameter to account for model mismatch in real datasets. We validate this method in extensive simulations as well as in a neural spike-LFP dataset recorded during an eye-movement task, where the events of interest are eye movements with unknown times and directions. We show that the MED can successfully detect eye movement onset and classify eye movement direction. Further, the MED successfully combines information across data modalities, with multimodal performance exceeding unimodal performance. This method can facilitate applications such as the discovery of latent events in multimodal neural population activity and the development of brain-computer interfaces for naturalistic settings without constrained tasks or prior knowledge of event times.

Dynamical flexible inference of nonlinear latent factors and structures in neural population activity.

Modelling the spatiotemporal dynamics in the activity of neural populations while also enabling their flexible inference is hindered by the complexity and noisiness of neural observations. Here we show that the lower-dimensional nonlinear latent factors and latent structures can be computationally modelled in a manner that allows for flexible inference causally, non-causally and in the presence of missing neural observations. To enable flexible inference, we developed a neural network that separates the model into jointly trained manifold and dynamic latent factors such that nonlinearity is captured through the manifold factors and the dynamics can be modelled in tractable linear form on this nonlinear manifold. We show that the model, which we named 'DFINE' (for 'dynamical flexible inference for nonlinear embeddings') achieves flexible inference in simulations of nonlinear dynamics and across neural datasets representing a diversity of brain regions and behaviours. Compared with earlier neural-network models, DFINE enables flexible inference, better predicts neural activity and behaviour, and better captures the latent neural manifold structure. DFINE may advance the development of neurotechnology and investigations in neuroscience.

Responsive deep brain stimulation guided by ventral striatal electrophysiology of obsession durably ameliorates compulsion.

Treatment-resistant obsessive-compulsive disorder (OCD) occurs in approximately one-third of OCD patients. Obsessions may fluctuate over time but often occur or worsen in the presence of internal (emotional state and thoughts) and external (visual and tactile) triggering stimuli. Obsessive thoughts and related compulsive urges fluctuate (are episodic) and so may respond well to a time-locked brain stimulation strategy sensitive and responsive to these symptom fluctuations. Early evidence suggests that neural activity can be captured from ventral striatal regions implicated in OCD to guide such a closed-loop approach. Here, we report on a first-in-human application of responsive deep brain stimulation (rDBS) of the ventral striatum for a treatment-refractory OCD individual who also had comorbid epilepsy. Self-reported obsessive symptoms and provoked OCD-related distress correlated with ventral striatal electrophysiology. rDBS detected the time-domain area-based feature from invasive electroencephalography low-frequency oscillatory power fluctuations that triggered bursts of stimulation to ameliorate OCD symptoms in a closed-loop fashion. rDBS provided rapid, robust, and durable improvement in obsessions and compulsions. These results provide proof of concept for a personalized, physiologically guided DBS strategy for OCD.

Multimodal subspace identification for modeling discrete-continuous spiking and field potential population activity.

Objective.Learning dynamical latent state models for multimodal spiking and field potential activity can reveal their collective low-dimensional dynamics and enable better decoding of behavior through multimodal fusion. Toward this goal, developing unsupervised learning methods that are computationally efficient is important, especially for real-time learning applications such as brain-machine interfaces (BMIs). However, efficient learning remains elusive for multimodal spike-field data due to their heterogeneous discrete-continuous distributions and different timescales.Approach.Here, we develop a multiscale subspace identification (multiscale SID) algorithm that enables computationally efficient learning for modeling and dimensionality reduction for multimodal discrete-continuous spike-field data. We describe the spike-field activity as combined Poisson and Gaussian observations, for which we derive a new analytical SID method. Importantly, we also introduce a novel constrained optimization approach to learn valid noise statistics, which is critical for multimodal statistical inference of the latent state, neural activity, and behavior. We validate the method using numerical simulations and with spiking and local field potential population activity recorded during a naturalistic reach and grasp behavior.Main results.We find that multiscale SID accurately learned dynamical models of spike-field signals and extracted low-dimensional dynamics from these multimodal signals. Further, it fused multimodal information, thus better identifying the dynamical modes and predicting behavior compared to using a single modality. Finally, compared to existing multiscale expectation-maximization learning for Poisson-Gaussian observations, multiscale SID had a much lower training time while being better in identifying the dynamical modes and having a better or similar accuracy in predicting neural activity and behavior.Significance.Overall, multiscale SID is an accurate learning method that is particularly beneficial when efficient learning is of interest, such as for online adaptive BMIs to track non-stationary dynamics or for reducing offline training time in neuroscience investigations.

Top-down control of exogenous attentional selection is mediated by beta coherence in prefrontal cortex.

Salience-driven exogenous and goal-driven endogenous attentional selection are two distinct forms of attention that guide selection of task-irrelevant and task-relevant targets in primates. Top-down attentional control mechanisms enable selection of the task-relevant target by limiting the influence of sensory information. Although the lateral prefrontal cortex (LPFC) is known to mediate top-down control, the neuronal mechanisms of top-down control of attentional selection are poorly understood. Here, we trained two rhesus monkeys on a two-target, free-choice luminance-reward selection task. We demonstrate that visual-movement (VM) neurons and nonvisual neurons or movement neurons encode exogenous and endogenous selection. We then show that coherent beta activity selectively modulates mechanisms of exogenous selection specifically during conflict and consequently may support top-down control. These results reveal the VM-neuron-specific network mechanisms of attentional selection and suggest a functional role for beta-frequency coherent neural dynamics in the modulation of sensory communication channels for the top-down control of attentional selection.

Multimodal subspace identification for modeling discrete-continuous spiking and field potential population activity.

Learning dynamical latent state models for multimodal spiking and field potential activity can reveal their collective low-dimensional dynamics and enable better decoding of behavior through multimodal fusion. Toward this goal, developing unsupervised learning methods that are computationally efficient is important, especially for real-time learning applications such as brain-machine interfaces (BMIs). However, efficient learning remains elusive for multimodal spike-field data due to their heterogeneous discrete-continuous distributions and different timescales. Here, we develop a multiscale subspace identification (multiscale SID) algorithm that enables computationally efficient modeling and dimensionality reduction for multimodal discrete-continuous spike-field data. We describe the spike-field activity as combined Poisson and Gaussian observations, for which we derive a new analytical subspace identification method. Importantly, we also introduce a novel constrained optimization approach to learn valid noise statistics, which is critical for multimodal statistical inference of the latent state, neural activity, and behavior. We validate the method using numerical simulations and spike-LFP population activity recorded during a naturalistic reach and grasp behavior. We find that multiscale SID accurately learned dynamical models of spike-field signals and extracted low-dimensional dynamics from these multimodal signals. Further, it fused multimodal information, thus better identifying the dynamical modes and predicting behavior compared to using a single modality. Finally, compared to existing multiscale expectation-maximization learning for Poisson-Gaussian observations, multiscale SID had a much lower computational cost while being better in identifying the dynamical modes and having a better or similar accuracy in predicting neural activity. Overall, multiscale SID is an accurate learning method that is particularly beneficial when efficient learning is of interest.

Flexible, high-resolution cortical arrays with large coverage capture microscale high-frequency oscillations in patients with epilepsy.

OBJECTIVE: Effective surgical treatment of drug-resistant epilepsy depends on accurate localization of the epileptogenic zone (EZ). High-frequency oscillations (HFOs) are potential biomarkers of the EZ. Previous research has shown that HFOs often occur within submillimeter areas of brain tissue and that the coarse spatial sampling of clinical intracranial electrode arrays may limit the accurate capture of HFO activity. In this study, we sought to characterize microscale HFO activity captured on thin, flexible microelectrocorticographic (µECoG) arrays, which provide high spatial resolution over large cortical surface areas. METHODS: We used novel liquid crystal polymer thin-film µECoG arrays (.76-1.72-mm intercontact spacing) to capture HFOs in eight intraoperative recordings from seven patients with epilepsy. We identified ripple (80-250 Hz) and fast ripple (250-600 Hz) HFOs using a common energy thresholding detection algorithm along with two stages of artifact rejection. We visualized microscale subregions of HFO activity using spatial maps of HFO rate, signal-to-noise ratio, and mean peak frequency. We quantified the spatial extent of HFO events by measuring covariance between detected HFOs and surrounding activity. We also compared HFO detection rates on microcontacts to simulated macrocontacts by spatially averaging data. RESULTS: We found visually delineable subregions of elevated HFO activity within each µECoG recording. Forty-seven percent of HFOs occurred on single 200-µm-diameter recording contacts, with minimal high-frequency activity on surrounding contacts. Other HFO events occurred across multiple contacts simultaneously, with covarying activity most often limited to a .95-mm radius. Through spatial averaging, we estimated that macrocontacts with 2-3-mm diameter would only capture 44% of the HFOs detected in our µECoG recordings. SIGNIFICANCE: These results demonstrate that thin-film microcontact surface arrays with both highresolution and large coverage accurately capture microscale HFO activity and may improve the utility of HFOs to localize the EZ for treatment of drug-resistant epilepsy.

Putative cell-type-specific multiregional mode in posterior parietal cortex during coordinated visual behavior.

In the reach and saccade regions of the posterior parietal cortex (PPC), multiregional communication depends on the timing of neuronal activity with respect to beta-frequency (10-30 Hz) local field potential (LFP) activity, termed dual coherence. Neural coherence is believed to reflect neural excitability, whereby spiking tends to occur at a particular phase of LFP activity, but the mechanisms of multiregional dual coherence remain unknown. Here, we investigate dual coherence in the PPC of non-human primates performing eye-hand movements. We computationally model dual coherence in terms of multiregional neural excitability and show that one latent component, a multiregional mode, reflects shared excitability across distributed PPC populations. Analyzing the power in the multiregional mode with respect to different putative cell types reveals significant modulations with the spiking of putative pyramidal neurons and not inhibitory interneurons. These results suggest a specific role for pyramidal neurons in dual coherence supporting multiregional communication in PPC.

Dynamical flexible inference of nonlinear latent structures in neural population activity.

Inferring complex spatiotemporal dynamics in neural population activity is critical for investigating neural mechanisms and developing neurotechnology. These activity patterns are noisy observations of lower-dimensional latent factors and their nonlinear dynamical structure. A major unaddressed challenge is to model this nonlinear structure, but in a manner that allows for flexible inference, whether causally, non-causally, or in the presence of missing neural observations. We address this challenge by developing DFINE, a new neural network that separates the model into dynamic and manifold latent factors, such that the dynamics can be modeled in tractable form. We show that DFINE achieves flexible nonlinear inference across diverse behaviors and brain regions. Further, despite enabling flexible inference unlike prior neural network models of population activity, DFINE also better predicts the behavior and neural activity, and better captures the latent neural manifold structure. DFINE can both enhance future neurotechnology and facilitate investigations across diverse domains of neuroscience.

Subdural CMOS optical probe (SCOPe) for bidirectional neural interfacing.

Optical neurotechnologies use light to interface with neurons and can monitor and manipulate neural activity with high spatial-temporal precision over large cortical extents. While there has been significant progress in miniaturizing microscope for head-mounted configurations, these existing devices are still very bulky and could never be fully implanted. Any viable translation of these technologies to human use will require a much more noninvasive, fully implantable form factor. Here, we leverage advances in microelectronics and heterogeneous optoelectronic packaging to develop a transformative, ultrathin, miniaturized device for bidirectional optical stimulation and recording: the subdural CMOS Optical Probe (SCOPe). By being thin enough to lie entirely within the subdural space of the primate brain, SCOPe defines a path for the eventual human translation of a new generation of brain-machine interfaces based on light.

Top-down control of exogenous attentional selection is mediated by beta coherence in prefrontal cortex.

Salience-driven exogenous and goal-driven endogenous attentional selection are two distinct forms of attention that guide selection of task-irrelevant and task-relevant targets in primates. During conflict i.e, when salience and goal each favor the selection of different targets, endogenous selection of the task-relevant target relies on top-down control. Top-down attentional control mechanisms enable selection of the task-relevant target by limiting the influence of sensory information. Although the lateral prefrontal cortex (LPFC) is known to mediate top-down control, the neuronal mechanisms of top-down control of attentional selection are poorly understood. Here, using a two-target free-choice luminance-reward selection task, we demonstrate that visual-movement neurons and not visual neurons or movement neurons encode exogenous and endogenous selection. We then show that coherent-beta activity selectively modulates mechanisms of exogenous selection specifically during conflict and consequently may support top-down control. These results reveal the VM-neuron-specific network mechanisms of attentional selection and suggest a functional role for beta-frequency coherent neural dynamics in the modulation of sensory communication channels for the top-down control of attentional selection.

Modeling and inference methods for switching regime-dependent dynamical systems with multiscale neural observations.

Objective.Realizing neurotechnologies that enable long-term neural recordings across multiple spatial-temporal scales during naturalistic behaviors requires new modeling and inference methods that can simultaneously address two challenges. First, the methods should aggregate information across all activity scales from multiple recording sources such as spiking and field potentials. Second, the methods should detect changes in the regimes of behavior and/or neural dynamics during naturalistic scenarios and long-term recordings. Prior regime detection methods are developed for a single scale of activity rather than multiscale activity, and prior multiscale methods have not considered regime switching and are for stationary cases.Approach.Here, we address both challenges by developing a switching multiscale dynamical system model and the associated filtering and smoothing methods. This model describes the encoding of an unobserved brain state in multiscale spike-field activity. It also allows for regime-switching dynamics using an unobserved regime state that dictates the dynamical and encoding parameters at every time-step. We also design the associated switching multiscale inference methods that estimate both the unobserved regime and brain states from simultaneous spike-field activity.Main results.We validate the methods in both extensive numerical simulations and prefrontal spike-field data recorded in a monkey performing saccades for fluid rewards. We show that these methods can successfully combine the spiking and field potential observations to simultaneously track the regime and brain states accurately. Doing so, these methods lead to better state estimation compared with single-scale switching methods or stationary multiscale methods. Also, for single-scale linear Gaussian observations, the new switching smoother can better generalize to diverse system settings compared to prior switching smoothers.Significance.These modeling and inference methods effectively incorporate both regime-detection and multiscale observations. As such, they could facilitate investigation of latent switching neural population dynamics and improve future brain-machine interfaces by enabling inference in naturalistic scenarios where regime-dependent multiscale activity and behavior arise.

Flexural bending to approximate cortical forces exerted by electrocorticography (ECoG) arrays.

Objective.The force that an electrocorticography (ECoG) array exerts on the brain manifests when it bends to match the curvature of the skull and cerebral cortex. This force can negatively impact both short-term and long-term patient outcomes. Here we provide a mechanical characterization of a novel liquid crystal polymer (LCP) ECoG array prototype to demonstrate that its thinner geometry reduces the force potentially applied to the cortex of the brain.Approach.We built a low-force flexural testing machine to measure ECoG array bending forces, calculate their effective flexural moduli, and approximate the maximum force they could exerted on the human brain.Main results.The LCP ECoG prototype was found to have a maximal force less than 20% that of any commercially available ECoG arrays that were tested. However, as a material, LCP was measured to be as much as 24× more rigid than silicone, which is traditionally used in ECoG arrays. This suggests that the lower maximal force resulted from the prototype's thinner profile (2.9×-3.25×).Significance.While decreasing material stiffness can lower the force an ECoG array exhibits, our LCP ECoG array prototype demonstrated that flexible circuit manufacturing techniques can also lower these forces by decreasing ECoG array thickness. Flexural tests of ECoG arrays are necessary to accurately assess these forces, as material properties for polymers and laminates are often scale dependent. As the polymers used are anisotropic, elastic modulus cannot be used to predict ECoG flexural behavior. Accounting for these factors, we used our four-point flexure testing procedure to quantify the forces exerted on the brain by ECoG array bending. With this experimental method, ECoG arrays can be designed to minimize force exerted on the brain, potentially improving both acute and chronic clinical utility.

Intraoperative microseizure detection using a high-density micro-electrocorticography electrode array.

One-third of epilepsy patients suffer from medication-resistant seizures. While surgery to remove epileptogenic tissue helps some patients, 30-70% of patients continue to experience seizures following resection. Surgical outcomes may be improved with more accurate localization of epileptogenic tissue. We have previously developed novel thin-film, subdural electrode arrays with hundreds of microelectrodes over a 100-1000 mm2 area to enable high-resolution mapping of neural activity. Here, we used these high-density arrays to study microscale properties of human epileptiform activity. We performed intraoperative micro-electrocorticographic recordings in nine patients with epilepsy. In addition, we recorded from four patients with movement disorders undergoing deep brain stimulator implantation as non-epileptic controls. A board-certified epileptologist identified microseizures, which resembled electrographic seizures normally observed with clinical macroelectrodes. Recordings in epileptic patients had a significantly higher microseizure rate (2.01 events/min) than recordings in non-epileptic subjects (0.01 events/min; permutation test, P = 0.0068). Using spatial averaging to simulate recordings from larger electrode contacts, we found that the number of detected microseizures decreased rapidly with increasing contact diameter and decreasing contact density. In cases in which microseizures were spatially distributed across multiple channels, the approximate onset region was identified. Our results suggest that micro-electrocorticographic electrode arrays with a high density of contacts and large coverage are essential for capturing microseizures in epilepsy patients and may be beneficial for localizing epileptogenic tissue to plan surgery or target brain stimulation.

Modulation of inhibitory communication coordinates looking and reaching.

Looking and reaching are controlled by different brain regions and are coordinated during natural behaviour1. Understanding how flexible, natural behaviours such as coordinated looking and reaching are controlled depends on understanding how neurons in different regions of the brain communicate2. Neural coherence in a gamma-frequency (40-90 Hz) band has been implicated in excitatory multiregional communication3. Inhibitory control mechanisms are also required to flexibly control behaviour4, but little is known about how neurons in one region transiently suppress individual neurons in another to support behaviour. How neuronal firing in a sender region transiently suppresses firing in a receiver region remains poorly understood. Here we study inhibitory communication during a flexible, natural behaviour, termed gaze anchoring, in which saccades are transiently inhibited by coordinated reaches. During gaze anchoring, we found that neurons in the reach region of the posterior parietal cortex can inhibit neuronal firing in the parietal saccade region to suppress eye movements and improve reach accuracy. Suppression is transient, only present around the coordinated reach, and greatest when reach neurons fire spikes with respect to beta-frequency (15-25 Hz) activity, not gamma-frequency activity. Our work provides evidence in the activity of single neurons for a novel mechanism of inhibitory communication in which beta-frequency neural coherence transiently inhibits multiregional communication to flexibly coordinate natural behaviour.

Modeling multiscale causal interactions between spiking and field potential signals during behavior.

Objective.Brain recordings exhibit dynamics at multiple spatiotemporal scales, which are measured with spike trains and larger-scale field potential signals. To study neural processes, it is important to identify and model causal interactions not only at a single scale of activity, but also across multiple scales, i.e. between spike trains and field potential signals. Standard causality measures are not directly applicable here because spike trains are binary-valued but field potentials are continuous-valued. It is thus important to develop computational tools to recover multiscale neural causality during behavior, assess their performance on neural datasets, and study whether modeling multiscale causalities can improve the prediction of neural signals beyond what is possible with single-scale causality.Approach.We design a multiscale model-based Granger-like causality method based on directed information and evaluate its success both in realistic biophysical spike-field simulations and in motor cortical datasets from two non-human primates (NHP) performing a motor behavior. To compute multiscale causality, we learn point-process generalized linear models that predict the spike events at a given time based on the history of both spike trains and field potential signals. We also learn linear Gaussian models that predict the field potential signals at a given time based on their own history as well as either the history of binary spike events or that of latent firing rates.Main results.We find that our method reveals the true multiscale causality network structure in biophysical simulations despite the presence of model mismatch. Further, models with the identified multiscale causalities in the NHP neural datasets lead to better prediction of both spike trains and field potential signals compared to just modeling single-scale causalities. Finally, we find that latent firing rates are better predictors of field potential signals compared with the binary spike events in the NHP datasets.Significance.This multiscale causality method can reveal the directed functional interactions across spatiotemporal scales of brain activity to inform basic science investigations and neurotechnologies.

Deep Pinsker and James-Stein Neural Networks for Decoding Motor Intentions From Limited Data.

Non-parametric regression has been shown to be useful in extracting relevant features from Local Field Potential (LFP) signals for decoding motor intentions. Yet, in many instances, brain-computer interfaces (BCIs) rely on simple classification methods, circumventing deep neural networks (DNNs) due to limited training data. This paper leverages the robustness of several important results in non-parametric regression to harness the potentials of deep learning in limited data setups. We consider a solution that combines Pinsker's theorem as well as its adaptively optimal counterpart due to James-Stein for feature extraction from LFPs, followed by a DNN for classifying motor intentions. We apply our approach to the problem of decoding eye movement intentions from LFPs collected in macaque cortex while the animals perform memory-guided visual saccades to one of eight target locations. The results demonstrate that a DNN classifier trained over the Pinsker features outperforms the benchmark method based on linear discriminant analysis (LDA) trained over the same features.