The increase in spatiotemporal resolution of neuroimaging devices is accompanied by a trend towards more powerful multivariate analysis methods. Often it is desired to interpret the outcome of these methods with respect to the cognitive processes under study. Here we discuss which methods allow for such interpretations, and provide guidelines for choosing an appropriate analysis for a given experimental goal: For a surgeon who needs to decide where to remove brain tissue it is most important to determine the origin of cognitive functions and associated neural processes. In contrast, when communicating with paralyzed or comatose patients via brain-computer interfaces, it is most important to accurately extract the neural processes specific to a certain mental state. These equally important but complementary objectives require different analysis methods. Determining the origin of neural processes in time or space from the parameters of a data-driven model requires what we call a forward model of the data; such a model explains how the measured data was generated from the neural sources. Examples are general linear models (GLMs). Methods for the extraction of neural information from data can be considered as backward models, as they attempt to reverse the data generating process. Examples are multivariate classifiers. Here we demonstrate that the parameters of forward models are neurophysiologically interpretable in the sense that significant nonzero weights are only observed at channels the activity of which is related to the brain process under study. In contrast, the interpretation of backward model parameters can lead to wrong conclusions regarding the spatial or temporal origin of the neural signals of interest, since significant nonzero weights may also be observed at channels the activity of which is statistically independent of the brain process under study. As a remedy for the linear case, we propose a procedure for transforming backward models into forward models. This procedure enables the neurophysiological interpretation of the parameters of linear backward models. We hope that this work raises awareness for an often encountered problem and provides a theoretical basis for conducting better interpretable multivariate neuroimaging analyses.

Saliency methods aim to explain the predictions of deep neural networks. These methods lack reliability when the explanation is sensitive to factors that do not contribute to the model prediction. We use a simple and common pre-processing step -adding a constant shift to the input data-to show that a transformation with no effect on the model can cause numerous methods to incorrectly attribute. In order to guarantee reliability, we posit that methods should fulfill input invariance, the requirement that a saliency method mirror the sensitivity of the model with respect to transformations of the input. We show, through several examples, that saliency methods that do not satisfy input invariance result in misleading attribution.

In humans, spontaneous movements are often preceded by early brain signals. One such signal is the readiness potential (RP) that gradually arises within the last second preceding a movement. An important question is whether people are able to cancel movements after the elicitation of such RPs, and if so until which point in time. Here, subjects played a game where they tried to press a button to earn points in a challenge with a brain-computer interface (BCI) that had been trained to detect their RPs in real time and to emit stop signals. Our data suggest that subjects can still veto a movement even after the onset of the RP. Cancellation of movements was possible if stop signals occurred earlier than 200 ms before movement onset, thus constituting a point of no return.free choice | readiness potential | brain-computer interface | point of no return | veto I t has been repeatedly shown that spontaneous movements are preceded by early brain signals (1-8). As early as a second before a simple voluntary movement, a so-called readiness potential (RP) is observed over motor-related brain regions (1-3, 5). The RP was found to precede the self-reported time of the "'decision' to act" (ref. 3, p. 623). Similar preparatory signals have been observed using invasive electrophysiology (8, 9) and functional MRI (7, 10), and have been demonstrated also for choices between multiple-response options (6,7,10), for abstract decisions (10), for perceptual choices (11), and for value-based decisions (12). To date, the exact nature and causal role of such early signals in decision making is debated (12)(13)(14)(15)(16)(17)(18)(19)(20).One important question is whether a person can still exert a veto by inhibiting the movement after onset of the RP (13,18,21,22). One possibility is that the onset of the RP triggers a causal chain of events that unfolds in time and cannot be cancelled. The onset of the RP in this case would be akin to tipping the first stone in a row of dominoes. If there is no chance of intervening, the dominoes will gradually fall one-by-one until the last one is reached. This has been coined a ballistic stage of processing (23,24). A different possibility is that participants can still terminate the process, akin to taking out a domino at some later stage in the chain and thus preventing the process from completing. Here, we directly tested this in a real-time experiment that required subjects to terminate their decision to move once a RP had been detected by a brain-computer interface (BCI) (25-31). ResultsSubjects were confronted with a floor-mounted button and a light presented on a computer screen. Once the light turned green ("go signal"), subjects waited for a short, self-paced period of about 2 s after which they were allowed to press the button with their right foot at any time. They could earn points if they pressed while the light was green, but lose points if they pressed after the light had turned red ("stop signal"). The experiment had three consecutive stages (Fig. 1A). In stage I, stop signals were e...

Previously, modulations in power of neuronal oscillations have been functionally linked to sensory, motor and cognitive operations. Such links are commonly established by relating the power modulations to specific target variables such as reaction times or task ratings. Consequently, the resulting spatio-spectral representation is subjected to neurophysiological interpretation. As an alternative, independent component analysis (ICA) or alternative decomposition methods can be applied and the power of the components may be related to the target variable. In this paper we show that these standard approaches are suboptimal as the first does not take into account the superposition of many sources due to volume conduction, while the second is unable to exploit available information about the target variable. To improve upon these approaches we introduce a novel (supervised) source separation framework called Source Power Comodulation (SPoC). SPoC makes use of the target variable in the decomposition process in order to give preference to components whose power comodulates with the target variable. We present two algorithms that implement the SPoC approach. Using simulations with a realistic head model, we show that the SPoC algorithms are able extract neuronal components exhibiting high correlation of power with the target variable. In this task, the SPoC algorithms outperform other commonly used techniques that are based on the sensor data or ICA approaches. Furthermore, using real electroencephalography (EEG) recordings during an auditory steady state paradigm, we demonstrate the utility of the SPoC algorithms by extracting neuronal components exhibiting high correlation of power with the intensity of the auditory input. Taking into account the results of the simulations and real EEG recordings, we conclude that SPoC represents an adequate approach for the optimal extraction of neuronal components showing coupling of power with continuously changing behaviorally relevant parameters.