Category: deep neural networks

Can parameter-free associative lateral connectivity boost generalization performance of CNNs?

[I7R7]

Montobbio, Bonnasse-Gahot, Citti, & Sarti (pp2019) present an interesting model of lateral connectivity and its computational function in early visual areas. Lateral connections emanating from each unit drive other units to the degree that they are similar in their receptive profiles. Two units are symmetrically laterally connected if they respond to stimuli in the same region of the visual field with similar selectivity.

More precisely, lateral connectivity in this model implements a diffusion process in a space defined by the similarity of bottom-up filter templates. The similarity of the filters is measured by the inner product of the filter weights. Two filters that do not spatially overlap, thus, are not similar. Two filters are similar to the extent that their filters don’t merely overlap, but have correlated weight templates. Connecting units in proportion to their filter similarity results in a connectivity matrix that defines the paths of diffusion. The diffusion amounts to a multiplication with a convolution matrix. It is the activations (after the ReLU nonlinearity) that form the basis of the linear diffusion process.

The idea is that the lateral connections implement a diffusive spreading of activation among units with similar filters during perceptual inference. The intuitive motivation is that the spreading activation fills in missing information or regularizes the representation. This might make the representation of an image compromised by noise or distortion more like the representation of its uncompromised counterpart.

Instead of performing n iterations of the lateral diffusion at inference, we can equivalently take the convolutional matrix to the n-th power. The recurrent convolutional model is thus equivalent to a feedforward model with the diffusion matrix multiplication inserted after each layer.

Screen Shot 12-04-19 at 02.55 AM.PNG
Montobbio’s model for MNIST

 

In the context of Gabor-like orientation-selective filters, the proposed formula for connectivity results in an anisotropic kernel of lateral connectivity  that looks plausible in that it connects approximately collinear edge filters. This is broadly consistent with anatomical studies showing that V1 neurons selective for oriented edges form long-range (>0.5 mm in tree shrew cortex) horizontal connections that preferentially target neurons selective for collinear oriented edges.

 

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Figure from Bosking et al. (1997). Long-range lateral connections of oriented-edge-selective neurons in tree-shrew V1 preferentially project to other neurons selective for collinear oriented edges.

 

Since the similarity between filters is defined in terms of the bottom-up filter templates, it can be computed for arbitrary filters, e.g. filters learned through task training. The lateral connectivity kernel for each filter, thus, does not have to be learned through experience. Adding this type of recurrent lateral connectivity to a convolutional neural network (CNN), thus, does not increase the parameter count.

The authors argue that the proposed connectivity makes CNNs more robust to local perturbations of the image. They tested 2-layer CNNs on MNIST, Kuzushiji-MNIST, Fashion-MNIST, and CIFAR-10. They present evidence that the local anisotropic diffusion of activity improves robustness to noise, occlusions, and adversarial perturbations.

Overall, the authors took inspiration from visual psychophysics (Field et al. 1992; Geisler et al. 2001) and neurobiology (Bosking et al. 1997), abstracted a parsimonious mathematical model of lateral connectivity, and assessed the computational benefits of the model in the context of CNNs that perform visual recognition tasks. The proposed diffusive lateral activation might not be the whole story of lateral and recurrent connectivity in the brain, but it might be part of the story. The idea deserves careful consideration.

The paper is well written and engaging. I’m left with many questions as detailed below. In case the authors chose to revise the paper, it would be great to see some of the questions addressed, a deeper exploration of the functional mechanism underlying the benefits, and some more challenging tests of performance.

 

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Figure from Geisler et al. (2001). Edge elements tend to be locally approximately collinear in natural images. Given that there is an orientated edge segment (shown as horizontal) in a particular location (shown in the center), the arrangement shows in what direction each orientation (oriented line) is most probable for each distance to the reference location.

Questions and thoughts

1 Can the increase in robustness be attributed to trivial forms of contextual integration?

If the filters were isotropic Gaussian blobs, then the diffusion process would simply blur the image. Blurring can help reduce noise and might reduce susceptibility to adversarial perturbations (especially if the adversary is not enabled to take this into account). Image blurring could be considered the layer-0 version of the proposed model. What is its effect on performance?

Consider another simplified scenario: If the network were linear, then the lateral connectivity would modify the effective filters, but each filter would still be a linear combination of the input. The model with lateral connectivity could thus be replaced by an equivalent feedforward model with larger kernels. Larger kernels might yield responses that are more robust to noise. Here the activation function is nonlinear, but the benefits might work similarly. It would be good to assess whether larger kernels in a feedforward network bring similar benefits to generalization performance.

 

2 Were the adversarial perturbations targeted at the tested model?

Robustness to adversarial attack should be tested using adversarial examples targeting each particular model with a given combination of numbers of iterations of lateral diffusion in layers 1 and 2. Was this the case?

 

3 Is the lateral diffusion process invertible?

The lateral diffusion is a linear transform that maps to a space of equal dimension (like Gaussian blurring of an image).

If the transform were invertible, then it would constitute the simplest possible change (linear, information preserving) to the representational geometry (as characterized by the Euclidean representational distance matrix for a set of stimuli). To better understand why this transform helps, then, it would be interesting to investigate how it changes the representational geometry for a suitable set of stimuli.

If lateral diffusion were not invertible, then it is perhaps best thought of as an intelligent type of pooling (despite the output dimension being equal to the input dimension).

 

4 Do the lateral connections make representations of corrupted images more similar to representations of uncorrupted versions of the same images?

The authors offer an intuitive explanation of the benefits to performance: Lateral diffusion restores the missing parts or repairs what has been corrupted (presumably using accurate prior information about the distribution of natural images). One could directly assess whether this is the case by assessing whether lateral diffusion moves the representation of a corrupted image closer to the representation of its uncorrupted variant.

 

5 Do correlated filter templates imply correlated filter responses under natural stimulation?

Learned filters reflect features that occur in the training images. If each image is composed of a mosaic of overlapping features, it is intuitive that filters whose templates overlap and are correlated will tend to co-occur and hence yield correlated responses across natural images. The authors seem to assume that this is true. But is there a way to prove that the correlations between filter templates really imply correlation of the filter outputs under natural stimulation? For independent noise images, filters with correlated templates will surely produce correlated outputs. However, it’s easy to imagine stimuli for which filters with correlated templates yield uncorrelated or anticorrelated outputs.

 

6 Does lateral connectivity reflecting the correlational structure of filter responses under natural stimulation work even better than the proposed approach?

Would the performance gains be larger or smaller if lateral connectivity were determined by filter-output correlation under natural stimulation, rather than by filter-template similarity?

Is filter-template similarity just a useful approximation to filter-output correlation under natural stimulation, or is there a more fundamental computational motivation for using it?

 

7 How does the proposed lateral connectivity compare to learned lateral connectivity when the number of connections (instead of the number of parameters) is matched?

It would be good to compare CNNs with lateral diffusive connectivity to recurrent convolutional neural networks (RCNNs) for matched sizes of bottom-up and lateral filters (and matched numbers of connections, not parameters). In addition, it would then be interesting to initialize the RCNNs with diffusive lateral connectivity according to the proposed model (after initial training without lateral connections). Lateral connections could precede (as in typical RCNNs) or follow (as in KerCNNs) the nonlinear activation function.

 

8 Does the proposed mechanism have a motivation in terms of a normative model of visual inference?

Can the intuition that lateral connections implement shrinkage to a prior about natural image statistics be more explicitly justified?

If the filters serve to infer features of a linear generative model of the image, then features with correlated templates are anti-correlated given the image (competing to explain the same variance). This suggests that inhibitory connections are needed to implement the dynamics for inference. Cortex does rely on local inhibition. How does local inhibitory connectivity fit into the picture?

Can associative filling in and competitive explaining away be reconciled and combined?

 

Strengths

  • A mathematical model of lateral connectivity, motivated by human visual contour integration and studies on V1 long-range lateral connectivity, is tested in terms of the computational benefits it brings in the context of CNNs that recognize images.
  • The model is intuitive, elegant, and parsimonious in that it does not require learning of additional parameters.
  • The paper presents initial evidence for improved generalization performance in the context of deep convolutional neural networks.

 

Weaknesses

  • The computational benefits of the proposed lateral connectivity is tested only in the context of toy tasks and two-layer neural networks.
  • Some trivial explanations for the performance benefits have not been ruled out yet.
  • It’s unclear how to choose the number of iterations of lateral diffusion for each of the the two layers, and choosing the best combination might positively bias the estimate of the gain in accuracy.

 

Screen Shot 12-04-19 at 12.43 AM.PNG
Figure from Boutin et al. (pp2019) showing how feedback from layer 2 to layer 1 in a sparse deep predictive coding model trained on natural images can give rise to collinear “association fields” (a concept suggested by Field et al. (1993) on the basis of psychophysical experiments). Montobbio et al. plausibly suggest that direct lateral connections may contribute to this function.

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Figure from Montobbio et al. showing the kinds of perturbations that lateral connectivity rendered the networks more robust to.

 

Minor point

“associated to” -> “associated with” (in several places)

Embracing behavioral complexity to understand how brains implement cognition

[I8R8]

 

New behavioral monitoring and neural-net modeling techniques are revolutionizing animal neuroscience. How can we use the new tools to understand how brains implement cognitive processes? Musall, Urai, Sussillo and Churchland (pp2019) argue that these tools enable a less reductive approach to experimentation, where the tasks are more complex and natural, and brain and behavior are more comprehensively measured and modeled. (The picture above is Figure 1 of the paper.)

There have recently been amazing advances in measurement, modeling, and manipulation of complex brain and behavioral dynamics in rodents and other animals. These advances point toward the ultimate goal of total experimental control, where the environment as well as the animal’s brain and behavior are comprehensively measured and where both environment and brain activity can be arbitrarily manipulated. The review paper by Musall et al. focuses on the role that monitoring and modeling complex behaviors can play in the context of modern neuroscientific animal experimentation. In particular, the authors consider the following elements:

  • Rich task environments: Rodents and other animals can be placed in virtual-reality experiments where they experience complex visual and other sensory stimuli. Researchers can richly and flexibly control the virtual environment, combining naturalistic and unnaturalistic elements to optimize the experiment for the question of interest.
  • Comprehensive measurement of behavior: The animal’s complex behavior can be captured in detail (e.g. running on a track ball and being videoed to measure running velocity and turns as well as subtle task-unrelated limb movements). The combination of video and novel neural-net-model-based computer vision, enables researchers to track the trajectories of multiple limbs simultaneously with great precision. Instead of focusing on binary choices and reaction times, some researchers now use comprehensive and detailed quantitative measurements of behavioral dynamics.
  • Data-driven modeling of behavioral dynamics: The richer quantitative measurements of behavioral dynamics enable the data-driven discovery of the dynamical components of behavior. These components can be continuous or categorical. An example of categorical components are behavioral motifs (categories of similar behavioral patterns). Such motifs used to be inferred subjectively by researchers observing the animals. Today they can be inferred more objectively, using probabilistic models and machine learning. These methods can learn the repertoire of motifs, and, given new data, infer the motifs and the parameters of each instantiation of a motif.
  • Cognitive models of task performance: Cognitive models of task performance provide the latent variables that the animal’s brain must represent to be able to perform the task. The latent variables connect stimuli to behavioral responses and enable us to take a normative, top-down perspective: What information processing should the animal perform to succeed at the task?
  • Comprehensive measurement of neural activity: Techniques for measuring neural activity, including multi-electrode recording devices (e.g. Neuropixels) and optical imaging techniques (e.g. Calcium imaging) have advanced to enable the simultaneous measurement of many thousands of neurons with cellular precision.
  • Modeling of neural dynamics: Neural-network models provide task-performing models of brain-information processing. These models abstract sufficiently from neurobiology to be efficiently simulated and trained, but are neurobiologically plausible in that they could be implemented with biological components. (One might say that these models leave out biological complexity at the cellular scale so as to be able to better capture the dynamic complexity at a larger scale, which might help us understand how the brain implements control of behavior.)

The paper provides a great concise introduction to these exciting developments and describes how the new techniques can be used in concert to help us understand how brains implement cognition. The authors focus on the role of monitoring and modeling behavior. They stress the need to capture uninstructed movements, i.e. movements that are not required for task performance, but nevertheless occur and often explain large amounts of variance in neural activity. They also emphasize the importance of behavioral variation across trials, brain states, and individuals. Detailed quantitative descriptions of behavioral dynamics enable researchers to model nuisance variation and also to understand the variation of performance across trials, which can reflect variation related to the brain state (e.g. arousal, fear), cognitive strategy (different algorithms for performing the task), and the individual studied (after all, every mouse is unique –– see figure above, which is Figure 1 in the paper).

Improvements to consider in case the paper is revised

The paper is well-written and useful already. In case the authors were to prepare a revision, they could consider improving it further by addressing some of the following points.

(1) Add a figure illustrating the envisaged style of experimentation and modeling.

It might be helpful for the reader to have another figure, illustrating how the different innovations fit together. Such a figure could be based on an existing study, or it could illustrate an ideal for future experimentation, amalgamating elements from different studies.

(2) Clarify what is meant by “understanding circuits” and the role of NNs as “tools” and “model organisms”.

The paper uses the term “circuit” in the title and throughout as the explanandum. The term “circuit” evokes a particular level of description: above the single neuron and below “systems”. The term is associated with small subsets of interacting neurons (sometimes identified neurons), whose dynamics can be understood in detail.

This is somewhat at a tension with the approach of neural-network modeling, where there isn’t necessarily a one-to-one mapping between units in the model and neurons in the brain. The neural-network modeling would appear to settle for a somewhat looser relationship between the model and the brain. There is a case to be made that this is necessary to enable us to engage higher-level cognitive processes.

The authors hint at their view of this issue by referring to the neural-network models as “artificial model organisms”. This suggests a feeling that these models are more like other biological species (e.g. the mouse “model”) than like data-analytical models. However, models are never identical to the phenomena they capture and the relationship between model and empirical phenomenon (i.e. what aspects of the data the model is supposed to predict) must be separately defined anyway. So why not consider the neural-network models more simply as models of brain information processing?

(3) Explain how the insights apply across animal species.

The basic argument of the paper in favor of comprehensive monitoring and modeling of behavior appears to hold equally for C. elegans, zebrafish, flies, rodents, tree shrews, marmosets, macaques, and humans. However, the paper appears to focus on rodents. Does the rationale change across species? If so how and why? Should human researchers not consider the same comprehensive measurement of behavior for the very same reasons?

(4) Clarify the relation to similar recent arguments.

Several authors have recently argued that behavioral modeling must play a key role if we are to understand how the brain implements cognitive processes (Krakauer et al. 2017, Neuron [cited already]; Yamins & DiCarlo 2016, Nature Neuroscience; Kriegeskorte & Douglas 2018, Nature Neuroscience 2018). It would be interesting to hear how the authors see the relationship between these arguments and the one they are making.

From bidirectional brain-computer interfaces toward neural co-processors

[I7R8]

Rajesh Rao (pp2019) gives a concise review of the current state of the art in bidirectional brain-computer interfaces (BCIs) and offers an inspiring glimpse of a vision for future BCIs, conceptualized as neural co-processors.

A BCI, as the name suggests, connects a computer to a brain, either by reading out brain signals or by writing in brain signals. BCIs that both read from and write to the nervous system are called bidirectional BCIs. The reading may employ recordings from electrodes implanted in the brain or located on the scalp, and the writing must rely on some form of stimulation (e.g., again, through electrodes).

An organism in interaction with its environment forms a massively parallel perception-to-action cycle. The causal routes through the nervous system range in complexity from reflexes to higher cognition and memories at the temporal scale of the life span. The causal routes through the world, similarly, range from direct effects of our movements feeding back into our senses, to distal effects of our actions years down the line.

Any BCI must insert itself somewhere in this cycle – to supplement, or complement, some function. Typically a BCI, just like a brain, will take some input and produce some output. The input can come from the organism’s nervous system or body, or from the environment. The output, likewise, can go into the organism’s nervous system or body, or into the environment.

This immediately suggests a range of medical applications (Figs. 1, 2):

  • replacing lost perceptual function: The BCI’s input comes from the world (e.g. visual or auditory signals) and the output goes to the nervous system.
  • replacing lost motor function: The BCI’s input comes from the nervous system (e.g. recordings of motor cortical activity) and the output is a prosthetic device that can manipulate the world (Fig. 1).
  • bridging lost connectivity or replacing lost nervous processing: The BCI’s input comes from the nervous system and the output is fed back into the nervous system (Fig. 2).

 

uni- and bidirectional motor bciFig. 1 | Uni- and bidirectional prosthetic-control BCIs. (a) A unidirectional BCI (red) for control of a prosthetic hand that reads out neural signals from motor cortex. The patient controls the hand using visual feedback (blue arrow). (b) A bidirectional BCI (red) for control of a prosthetic hand that reads out neural signals from motor cortex and feeds back tactile sensory signals acquired through artificial sensors to somatosensory cortex.

Beyond restoring lost function, BCIs have inspired visions of brain augmentation that would enable us to transcend normal function. For example, BCI’s might enable us to perceive, communicate, or act at higher bandwidth. While interesting to consider, current BCIs are far from achieving the bandwidth (bits per second) of our evolved input and output interfaces, such as our eyes and ears, our arms and legs. It’s fun to think that we might write a text in an instant with a BCI. However, what limits me in writing this open review is not my hands or the keyboard (I could use dictation instead), but the speed of my thoughts. My typing may be slower than the flight of my thoughts, but my thoughts are too slow to generate an acceptable text at the pace I can comfortably type.

But what if we could augment thought itself with a BCI? This would require the BCI to listen in to our brain activity as well as help shape and direct our thoughts. In other words, the BCI would have to be bidirectional and act as a neural co-processor (Fig. 3). The idea of such a system helping me think is science fiction for the moment, but bidirectional BCIs are a reality.

I might consider my laptop a very functional co-processor for my brain. However, it doesn’t include a BCI, because it neither reads from nor writes to my nervous system directly. It instead senses my keystrokes and sends out patterns of light, co-opting my evolved biological mechanisms for interfacing with the world: my hands and eyes, which provide a bandwidth of communication that is out of reach of current BCIs.

bidirectional motor and sensory bcis

Fig. 2 | Bidirectional motor and sensory BCIs. (a) A bidirectional motor BCI (red) that bridges a spinal cord injury, reading signals from motor cortex and writing into efferent nerves beyond the point of injury or directly contacting the muscles. (b) A bidirectional sensory BCI that bridges a lesion along the sensory signalling pathway.

Rao reviews the exciting range of proof-of-principle demonstrations of bidirectional BCIs in the literature:

  • Closed-loop prosthetic control: A bidirectional BCI may read out motor cortex to control a prosthetic arm that has sensors whose signals are written back into somatosensory cortex, replacing proprioceptive signals. (Note that even a unidirectional BCI that only records activity to steer the prosthetic device will be operated in a closed loop when the patient controls it while visually observing its movement. However, a bidirectional BCI can simultaneously supplement both the output and the input, promising additional benefits.)
  • Reanimating paralyzed limbs: A bidirectional BCI may bridge a spinal cord injury, e.g. reading from motor cortex and writing to the efferent nerves beyond the point of injury in the spinal cord or directly to the muscles.
  • Restoring motor and cognitive functions: A bidirectional BCI might detect a particular brain state and then trigger stimulation is a particular region. For example, a BCI may detect the impending onset of an epileptic seizure in a human and then stimulate the focus region to prevent the seizure.
  • Augmenting normal brain function: A study in monkeys demonstrated that performance on a delayed-matching-to-sample task can be enhanced by reading out the CA3 representation and writing to the CA1 representation in the hippocampus (after training a machine learning model on the patterns during normal task performance). BCIs reading from and writing to brains have also been used as (currently still very inefficient) brain-to-brain communication devices among rats and humans.
  • Inducing plasticity and rewiring the brain: It has been demonstrated that sequential stimulation of two neural sites A and B can induce Hebbian plasticity such that the connections from A to B are strengthened. This might eventually be useful for restoration of lost connectivity.

Most BCIs use linear decoders to read out neural activity. The latent variables to be decoded might be the positions and velocities capturing the state of a prosthetic hand, for example. The neural measurements are noisy and incomplete, so it is desirable to combine the evidence over time. The system should use not only the current neural activity pattern to decode the latent variables, but also the recent history. Moreover, it should use any prior knowledge we might have about the dynamics of the latent variables. For example, the components of a prosthetic arm are inert masses. Forces upon them cause acceleration, i.e. a change of velocity, which in turn changes the positions. The physics, thus, entails smooth positional trajectories.

When the neuronal activity patterns linearly encode the latent variables, the dynamics of the latent variables is also linear, and the noise is Gaussian, then the optimal way of inferring the latent variables is called a Kalman filter. The state vector for the Kalman filter may contain the kinematic quantities whose brain representation is to be estimated (e.g. the position, velocity, and acceleration of a prosthetic hand). A dynamics model that respects the laws of physics can help constrain the inference so as to obtain more reliable estimates of the latent variables.

For a perceptual BCI, similarly, the signals from the artificial sensors might be noisy and we might have prior knowledge about the latent variables to be encoded. Encoders, as well as decoders, thus, can benefit from using models that capture relevant information about the recent input history in their internal state and use optimal inference algorithms that exploit prior knowledge about the latent dynamics. Bidirectional BCIs, as we have seen, combine neural decoders and encoders. They form the basis for a more general concept that Rao introduces: the concept of a neural co-processor.

laptop and neural co-processor

Fig. 3 | Devices augmenting our thoughts. (a) A laptop computer (black) that interfaces with our brains through our hands and eyes (not a BCI). (b) A neural co-processor that reads out neural signals from one region of the brain and writes in signals into another region of the brain (bidirectional BCI).

The term neural co-processor shifts the focus from the interface (where brain activity is read out and/or written in) to the augmentation of information processing that the device provides. The concept further emphasizes that the device processes information along with the brain, with the goal to supplement or complement what the brain does.

The framework for neural co-processors that Rao outlines generalizes bidirectional BCI technology in several respects:

  • The device and the user’s brain jointly optimize a behavioral cost function:
    BCIs from the earliest days have involved animals or humans learning to control some aspect of brain activity (e.g. the activity of a single neuron). Conversely, BCIs standardly employ machine learning to pick up on the patterns of brain activity that carry a particular meaning. The machine learning of patterns associated, say, with particular actions or movements is often followed by the patient learning to operate the BCI. In this sense mutual co-adaptation is already standard practice. However, the machine learning is usually limited to an initial phase. We might expect continual mutual co-adaptation (as observed in human interaction and other complex forms of communication between animals and even machines) to be ultimately required for optimal performance.
  • Decoding and encoding models are integrated: The decoder (which processes the neural data the device reads as its input) and encoder (which prepares the output for writing into the brain) are implemented in a single integrated model.
  • Recurrent neural network models replace Kalman filters: While a Kalman filter is optimal for linear systems with Gaussian noise, recurrent neural networks provide a general modeling framework for nonlinear decoding and encoding, and nonlinear dynamics.
  • Stochastic gradient descent is used to adjust the co-processor so as to optimize behavioral accuracy: In order to train a deep neural network model as a neural co-processor, we would like to be able to apply stochastic gradient descent. This poses two challenges: (1) We need a behavioral error signal that measures how far off the mark the combined brain-co-processor system is during behavior. (2) We need to be able to backpropagate the error derivatives. This requires that we have a mathematically specified model not only for the co-processor, but also for any further processing performed by the brain to produce the behavior whose error is to drive the learning. The brain-information processing from co-processor output to behavioral response is modeled by an emulator model. This enables us to backpropagate the error derivatives from the behavioral error measurements to the co-processor and through the co-processor. Although backpropagation proceeds through the emulator first, only the co-processor learns (as the emulator is not involved in the interaction and only serves to enable backpropagation). The emulator needs to be trained to emulate the part of the perception-to-action cycle it is meant to capture as well as possible.

The idea of neural co-processors provides an attractive unifying framework for developing devices that augment brain function in some way, based on artificial neural networks and deep learning.

Intriguingly, Rao argues that neural co-processors might also be able to restore or extend the brain’s own processing capabilities. As mentioned above, it has been demonstrated that Hebbian plasticity can be induced via stimulation. A neural co-processor might initially complement processing by performing some representational transformation for the brain. The brain might then gradually learn to predict the stimulation patterns contributed by the co-processor. The co-processor would scaffold the processing until the brain has acquired and can take over the representational transformation by itself. Whether this would actually work remains to be seen.

The framework of neural co-processors might also be relevant for basic science, where the goal is to build models of normal brain-information processing. In a basic-science context, the goal is to drive the model parameters to best predict brain activity and behavior. The error derivatives of the brain or behavioral predictions might be continuously backpropagated through a model during interactive behavior, so as to optimize the model.

Overall, this paper gives an exciting concise view of the state of the literature on bidirectional BCIs, and the concept of neural co-processors provides an inspiring way to think about the bigger picture and future directions for this technology.

Strengths

  • The paper is well-written and gives a brief, but precise overview of the current state of the art in bidirectional BCI technology.
  • The paper offers an inspiring unifying framework for understanding bidirectional BCIs as neural co-processors that suggests exciting future developments.

Weaknesses

  • The neural co-processor idea is not explained as intuitively and comprehensively as it could be.
  • The paper could give readers from other fields a better sense of quantitative benchmarks for BCIs.

Improvements to consider in revision

The text is already at a high level of quality. These are just ideas for further improvements or future extensions.

  • The figure about neural co-processors could be improved. In particular, the author could consider whether it might help to
    • clarify the direction of information flow in the brain and the two neural networks (clearly discernible arrows everywhere)
    • illustrate the parallelism between the preserved healthy output information flow (e.g. M1->spinal cord->muscle->hand movement) and the emulator network
    • illustrate the function intuitively using plausible choices of brain regions to read from (PFC? PPC?) and write to (M1? – flipping the brain?)
    • illustrate an intuitive example, e.g. a lesion in the brain, with function supplemented by the neural co-processor
    • add an external actuator to illustrate that the co-processor might directly interact with the world via motors as well as sensors
    • clarify the source of the error signal
  • The text on neural co-processors is very clear, but could be expanded by considering another example application in an additional paragraph to better illustrate the points made conceptually about the merits and generality of the approach.
  • The expected challenges on the path to making neural co-processors work could be discussed in more detail.
    • It would be good to clarify how the behavioral error signals to be backpropagated would be obtained in practice, for example, in the context of motor control.
    • Should we expect that it might be tractable to learn the emulator and co-processor models under realistic conditions? If so, what applied and basic science scenarios might be most promising to try first?
    • If the neural co-processor approach were applied to closed-loop prosthetic arm control, there would have to be two separate co-processors (motor cortex -> artificial actuators, artificial sensors -> sensory cortex) and so the emulator would need to model the brain dynamics intervening between perception and action.
  • It would be great to include some quantitative benchmarks (in case they exist) on the performance of current state-of-the-art BCIs (e.g. bit rate) and a bit of text that realistically assesses where we are on the continuum between proof of concept and widely useful application for some key applications. For example, I’m left wondering: What’s the current maximum bit rate of BCI motor control? How does this compare to natural motor control signals, such as eye blinks? Does a bidirectional BCI with sensory feedback improve the bit rate (despite the fact that there is already also visual feedback)?
  • It would be helpful to include a table of the most notable BCIs built so far, comparing them in terms of inputs, outputs, notable achievements and limitations, bit rate, and encoding and decoding models employed.
  • The current draft lacks a conclusion that draws the elements together into an overall view.

 

Is a cow-mug a cow to the ventral stream, and a mug to a deep neural network?

[I7R7]

An elegant new study by Bracci, Kalfas & Op de Beeck (pp2018) suggests that the prominent division between animate and inanimate things in the human ventral stream’s representational space is based on a superficial analysis of visual appearance, rather than on a deeper analysis of whether the thing before us is a living thing or a lifeless object.

Bracci et al. assembled a beautiful set of stimuli divided into 9 equivalent triads (Figure 1). Each triad consists of an animal, a manmade object, and a kind of hybrid of the two: an artefact of the same category and function as the object, designed to resemble the animal in the triad.

Screen Shot 08-16-18 at 05.52 PM 001
Figure 1: The entire set of 9 triads = 27 stimuli. Detail from Figure 1 of the paper.

 

Bracci et al. measured response patterns to each of the 27 stimuli (stimulus duration: 1.5 s) using functional magnetic resonance imaging (fMRI) with blood-oxygen-level-dependent (BOLD) contrast and voxels of 3-mm width in each dimension. Sixteen subjects viewed the images in the scanner while performing each of two tasks: categorizing the images as depicting something that looks like an animal or not (task 1) and categorizing the images as depicting a real living animal or a lifeless artefact (task 2).

The authors performed representational similarity analysis, computing representational dissimilarity matrices (RDMs) using the correlation distance (1 – Pearson correlation between spatial response patterns). They averaged representational dissimilarities of the same kind (e.g. between the animal and the corresponding hybrid) across the 9 triads. To compare different kinds of representational distance, they used ANOVAs and t tests to perform inference (treating the subject variable as a random effect). They also studied the representations of the stimuli in the last fully connected layers of two deep neural networks (DNNs; VGG-19, GoogLeNet) trained to classify objects, and in human similarity judgments. For the DNNs and human judgements, they used stimulus bootstrapping (treating the stimulus variable as a random effect) to perform inference.

Results of a series of well-motivated analyses are summarized in Figure 2 below (not in the paper). The most striking finding is that while human judgments and DNN last-layer representations are dominated by the living/nonliving distinction, human ventral temporal cortex (VTC) appears to care more about appearance: the hybrid animal-lookalike objects, despite being lifeless artefacts, fall closer to the animals than to the objects. In addition, the authors find:

  • Clusters of animals, hybrids, and objects: In VTC, animals, hybrids, and objects form significantly distinct clusters (average within-cluster dissimilarity < average between-cluster dissimilarity for all three pairs of categories). In DNNs and behavioral judgments, by contrast, the hybrids and the objects do not form significantly distinct clusters (but animals form a separate cluster from hybrids and from objects).
  • Matching of animals to corresponding hybrids: In VTC, the distance between a hybrid animal-lookalike and the corresponding animal is significantly smaller than that between a hydrid animal-lookalike and a non-matching animal. This indicates that VTC discriminates the animals and animal-lookalikes and (at least to some extent) matches the lookalikes to the correct animals. This effect was also present in the similarity judgments and DNNs. However, the latter two similarly matched the hybrids up with their corresponding objects, which was not a significant effect in VTC.

 

Screen Shot 08-16-18 at 05.52 PM
Figure 2: A qualitative visual summary of the results. Connection lines indicate different kinds of representational dissimilarity, illustrated for two triads although estimates and tests are based on averages across all 9 triads. Gray underlays indicate clusters (average within-cluster dissimilarity < average between-cluster dissimilarity, significant). Arcs indicate significantly different representational dissimilarities. It would be great if the authors added a figure like this in the revision of the paper. However, unlike the mock-up above, it should be a quantitatively accurate multidimensional scaling (MDS, metric stress) arrangement, ideally based on unbiased crossvalidated representational dissimilarity estimates.

 

The effect of the categorization task on the VTC representation was subtle or absent, consistent with other recent studies (cf. Nastase et al. 2017, open review). The representation appears to be mostly stimulus driven.

The results of Bracci et al. are consistent with the idea that the ventral stream transforms images into a semantic representation by computing features that are grounded in visual appearance, but correlated with categories (Jozwik et al. 2015). VTC might be 5-10 nonlinear transformations removed from the image. While it may emphasize visual features that help with categorization, it might not be the stage where all the evidence is put together for our final assessment of what we’re looking at. VTC, thus, is fooled by these fun artefacts, and that might be what makes them so charming.

Although this interpretation is plausible enough and straightforward, I am left with some lingering thoughts to the contrary.

What if things were the other way round? Instead of DNNs judging correctly where VTC is fooled, what if VTC had a special ability that the DNNs lack: to see the analogy between the cow and the cow-mug, to map the mug onto the cow? The “visual appearance” interpretation is based on the deceptively obvious assumption that the cow-mug (for example) “looks like” a cow. One might, equally compellingly, argue that it looks like a mug: it’s glossy, it’s conical, it has a handle. VTC, then, does not fail to see the difference between the fake animal and the real animal (in fact these categories do cluster in VTC). Rather it succeeds at making the analogy, at mapping that handle onto the tail of a cow, which is perhaps an example of a cognitive feat beyond current AI.

Bracci et al.’s results are thought-provoking and the study looks set to inspire computational and empirical follow-up research that links vision to cognition and brain representations to deep neural network models.

 

Strengths

  • addresses an important question
  • elegant design with beautiful stimulus set
  • well-motivated and comprehensive analyses
  • interesting and thought-provoking results
  • two categorization tasks, promoting either the living/nonliving or the animal-appearance/non-animal appearance division
  • behavioral similarity judgment data
  • information-based searchlight mapping, providing a broader view of the effects
  • new data set to be shared with the community

 

Weaknesses

  • representational geometry analyses, though reasonable, are suboptimal
  • no detailed analyses of DNN representations (only the last fully connected layers shown, which are not expected to best model the ventral stream) or the degree to which they can explain the VTC representation
  • only three ROIs (V1, posterior VTC, anterior VTC)
  • correlation distance used to measure representational distances (making it difficult to assess which individual representational distances are significantly different from zero, which appears important here)

 

Suggestions for improvement

The analyses are effective and support most of the claims made. However, to push this study from good to excellent, I suggest the following improvements.

 

Major points

Improved representational-geometry analysis

The key representational dissimilarities needed to address the questions of this study are labeled a-g in Figure 2. It would be great to see these seven quantities estimated, tested for deviation from 0, and all 7 choose 2 = 21 pairwise comparisons tested. This would address which distinctions are significant and enable addressing all the questions with a consistent approach, rather than combining many qualitatively different statistics (including clustering index, identity index, and model RDM correlation).

With the correlation distance, this would require a split-data RDM approach, consistent with the present approach, but using the repeated response measurements to the same stimulus to estimate and remove the positive bias of the correlation-distance estimates. However, a better approach would be to use a crossvalidated distance estimator (more details below).

 

Multidimensional scaling (MDS) to visualize representational geometries

This study has 27 unique stimuli, a number well suited for visualization of the representational geometries by MDS. To appreciate the differences between the triads (each of which has unique features), it would be great to see an MDS of all 27 objects and perhaps also MDS arrangements of subsets, e.g. each triad or pairs of triads (so as to reduce distortions due to dimensionality reduction).

Most importantly, the key representational dissimilarities a-g can be visualized in a single MDS as shown in Figure 2 above, using two triads to illustrate the triad-averaged representational geometry (showing average within- and between-triad distances among the three types of object). The MDS could use 2 or 3 dimensions, depending on which variant better visually conveys the actual dissimilarity estimates.

 

Crossvalidated distance estimators

The correlation distance is not an ideal dissimilarity measure because a large correlation distance does not indicate that two stimuli are distinctly represented. If a region does not respond to either stimulus, for example, the correlation of the two patterns (due to noise) will be close to 0 and the correlation distance will be close to 1, a high value that can be mistaken as indicating a decodable stimulus pair.

Crossvalidated distances such as the linear-discriminant t value (LD-t; Kriegeskorte et al. 2007, Nili et al. 2014) or the crossnobis distance (also known as the linear discriminant contrast, LDC; Walther et al. 2016) would be preferable. Like decoding accuracy, they use crossvalidation to remove bias (due to overfitting) and indicate that the two stimuli are distinctly encoded. Unlike decoding accuracy, they are continuous and nonsaturating, which makes them more sensitive and a better way to characterize representational geometries.

Since the LD-t and the crossnobis distance estimators are symmetrically distributed about 0 under the null hypothesis (H0: response patterns drawn from the same distribution), it would be straightforward to test these distances (and averages over sets of them) for deviation from 0, treating subjects and/or stimuli as random effects, and using t tests, ANOVAs, or nonparametric alternatives. Comparing different dissimilarities or set-average dissimilarities is similarly straightforward.

 

Linear crossdecoding with generalization across triads

An additional analysis that would give complementary information is linear decoding of categorical divisions with generalization across stimuli. A good approach would be leave-one-triad-out linear classification of:

  • living versus nonliving
  • things that look like animals versus other things
  • animal-lookalikes versus other things
  • animals versus animal-lookalikes
  • animals versus objects
  • animal-lookalikes versus objects

This might work for devisions that do not show clustering (within dissimilarity < between dissimilarity), which would indicate linear separability in the absence of compact clusters.

For the living/nonliving destinction, for example, the linear discriminant would select responses that are not confounded by animal-like appearance (as most VTC responses seem to be), responses that distinguish living things from animal-lookalike objects. This analysis would provide a good test of the existence of such responses in VTC.

 

More layers of the two DNNs

To assess the hypothesis that VTC computes features that are more visual than semantic with DNNs, it would be useful to include an analysis of all the layers of each of the two DNNs, and to test whether weighted combinations of layers can explain the VTC representational geometry (cf. Khaligh-Razavi & Kriegeskorte 2014).

 

More ROIs

How do these effects look in V2, V4, LOC, FFA, EBA, and PPA?

 

Minor points

The use of the term “bias” in the abstract and main text is nonstandard and didn’t make sense to me. Bias only makes sense when we have some definition of what the absence of bias would mean. Similarly the use of “veridical” in the abstract doesn’t make sense. There is no norm against which to judge veridicality.

 

The polar plots are entirely unmotivated. There is no cyclic structure or even meaningful order to the the 9 triads.

 

“DNNs are very good, and even better than than human visual cortex, at identifying a cow-mug as being a mug — not a cow.” This is not a defensible claim for several reasons, each of which by itself suffices to invalidate this.

  • fMRI does not reveal all the information in cortex.
  • VTC is not all of visual cortex.
  • VTC does cluster animals separately from animal-lookalikes and from objects.
  • Linear readout of animacy (cross-validated across triads) might further reveal that the distinction is present (even if it is not dominant in the representational geometry.

 

 

Grammar, typos

“how an object looks like” -> ‘how an object looks” or “what an object looks like”

“as oppose to” -> “as opposed to”

“where observed” -> “were observed”