Efficient analysis-by-synthesis in vision: A computational framework, behavioraltests, and comparison with neural representations

Ilker Yildirim (ilkery@mit.edu) Tejas D. Kulkarni (tejask@mit.edu)1BCS, MIT 2Lab of Neural Systems, RU BCS, MIT

Winrich A. Freiwald (wfreiwald@rockefeller.edu) Joshua B. Tenenbaum (jbt@mit.edu)Laboratory of Neural Systems, Rockefeller University BCS, MIT

AbstractA glance at an object is often sufficient to recognize it andrecover fine details of its shape and appearance, even underhighly variable viewpoint and lighting conditions. How canvision be so rich, but at the same time fast? The analysis-by-synthesis approach to vision offers an account of the rich-ness of our percepts, but it is typically considered too slowto explain perception in the brain. Here we propose a ver-sion of analysis-by-synthesis in the spirit of the Helmholtz ma-chine (Dayan, Hinton, Neal, & Zemel, 1995) that can be im-plemented efficiently, by combining a generative model basedon a realistic 3D computer graphics engine with a recognitionmodel based on a deep convolutional network. The recogni-tion model initializes inference in the generative model, whichis then refined by brief runs of MCMC. We test this approachin the domain of face recognition and show that it meets sev-eral challenging desiderata: it can reconstruct the approximateshape and texture of a novel face from a single view, at a levelindistinguishable to humans; it accounts quantitatively for hu-man behavior in “hard” recognition tasks that foil conventionalmachine systems; and it qualitatively matches neural responsesin a network of face-selective brain areas. Comparison to othermodels provides insights to the success of our model.Keywords: analysis-by-synthesis, 3d scene understanding,face processing, neural, behavioral.

IntroductionEveryday vision requires us to perceive and recognize objectsunder huge variability in viewing conditions. In a glance, youcan often (if not always) identify a friend whether you catcha good frontal view of their face, or see just a sliver of themfrom behind and on the side; whether most of their face isvisible, or occluded by a door or window blinds; or whetherthe room is dark, bright, or lit from an unusual angle. Youcan likewise recognize two images of an unfamiliar face asdepicting the same individual, even under similarly severevariations in viewing conditions (Figure 1), picking out finedetails of the face’s shape, color, and texture that are invariantacross views and diagnostic of the person’s underlying phys-iological and emotional state. Explaining how human visioncan be so rich and so fast at the same time is a central chal-lenge for any perceptual theory.

The analysis-by-synthesis or “vision as inverse graphics”approach presents one way to think about how vision can beso rich in its content. The perceptual system models the gen-erative processes by which natural scenes are constructed, aswell as the process by which images are formed from scenes;this is a mechanism for the hypothetical “synthesis” of nat-ural images, in the style of computer graphics. Perception(or “analysis”) is then the search for or inference to the bestexplanation of an observed image in terms of this synthesis

Figure 1: Same scene viewedat two different angles, illus-trating level of viewing vari-ability in everyday vision.

model: What would have been the most likely underlyingscene that could have produced this image?

While analysis-by-synthesis is intuitively appealing, itsrepresentational richness is often seen as making inferencehighly impractical. There are two factors at work: First, inrich generative models a large space of latent scene variablesleads to a hard search problem in finding a set of parame-ters that explains the image well. Second, the posterior land-scape over the latent variables may have multiple modes orextended ridges of probability, making standard local searchor stochastic inference methods such as Markov Chain MonteCarlo (MCMC) slow to burn in or mix, and potentially highlysensitive to the viewing conditions of scenes.

Here, we propose an efficient and neurally inspired im-plementation of the analysis-by-synthesis approach that canrecover rich scene representations surprisingly quickly. Weuse a generic and powerful visual feature extraction pipelineto learn a recognition model with the goal of approximately“recognizing” certain latent variables of the generative modelin a fast feed-forward manner, and then using those initialguesses to bootstrap a top-down search for the globally bestscene interpretation. The recognition model is learned in anentirely self-supervised fashion, from scenes and correspond-ing images that are hallucinations from the generative model.We apply our approach to the specific problem of face per-ception, and find that (1) our recognition model can identifyscene-generic latent variables such as object pose and lightingin a single feed-forward pass, and (2) brief runs of MCMC inthe generative model are sufficient to make highly accurateinferences about object-specific latents, such as the 3d shapeand texture of a face, when initialized by good guesses fromthe feed-forward recognition model.

Our approach is inspired by and builds upon earlier propos-als for efficient analysis-by-synthesis such as the Helmholtzmachine and breeder learning (Dayan et al., 1995; Nair,Susskind, & Hinton, 2008), but it goes beyond prior workin several ways:

• We apply this approach to much richer generative mod-els than previously considered, such as near-photorealisticgraphics models of faces based on high-dimensional 3dshape and texture maps, lighting and shading models, and

varying (affine) camera pose. This lets us perceive and rec-ognize objects under much greater variability in more nat-ural scenes than previous attempts.

• We directly compare human perceptual abilities with ourmodel, as well as other recently popular approaches to vi-sion such as convolutional neural networks (Krizhevsky,Sutskever, & Hinton, 2012).

• We explore this approach as an account of actual neuralrepresentations arising from single-unit cell recordings.

Face perception is an appealing domain in which to test ourapproach, for several reasons. First, faces are behaviorallysignificant for humans, hence an account of face perceptionis valuable in its own right, although we also expect the ap-proach to generalize to other vision problems. Second, virtu-ally all approaches to computational vision have been testedon faces (e.g., Taigman, Yang, Ranzato, & Wolf, 2014), of-fering ample opportunities for comparing different models.Third, the shape and the texture of faces are complex andcarry rich content. Therefore, it provides a good test bed formodels with rich representations. Finally, recent neurophys-iology research in macaques revealed a functionally specifichierarchy of patches of neurons selective for face process-ing (e.g., Freiwald & Tsao, 2010). As far as high-level vi-sion is concerned, this level of a detailed picture from a neuralperspective is so far unheard of. Therefore, faces provide anexcellent opportunity to relate models of high-level vision toneural activity.

The rest of this paper is organized as follows. We firstintroduce our efficient analysis-by-synthesis approach in thecontext of face perception. Next, we test our model in a com-putationally difficult task of 3D face reconstruction from asingle image. We then describe a behavioral experiment test-ing people’s face recognition abilities under “hard” viewingconditions, and show that our model best accounts for peo-ple’s behavior. Finally, we show that our model bears somequalitative similarity to neural responses in the Macaque faceprocessing system. We conclude with a discussion of quan-titative comparisons between our model and alternatives thatuse only variants of bottom-up, recognition networks.

ModelOur model takes an inverse graphics approach to face pro-cessing. Latent variables in the model represent facial shape,S, and texture, T , lighting direction, l, and head pose, r.Once these latent variables are assigned values, an approxi-mate rendering engine, g(·) generates a projection in the im-age space, IS = g({S,T, l,r}). See Figure 2a for a schematicof the model.

Following (Kulkarni, Kohli, Tenenbaum, & Mansinghka,2015), we use the Morphable Face Model (MFM; Blanz& Vetter, 1999) as a prior distribution over facial shapesand textures, S and T , respectively. This model, obtainedfrom a dataset of laser scanned heads of 200 people, pro-vides a mean face (both its shape and texture) in a part-based manner (four parts: nose, eyes, mouth, and outline)

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Figure 2: (a) Overview of the inverse graphics model. (b)Random draws from the model. (c) Training and the use ofthe recognition model.

and a covariance matrix to perturb the mean face to draw newfaces by eigendecomposition. Accordingly, both the shapeand texture take the form of multivariate Gaussian randomvariables: S ∼ N(µshape,Σshape) and T ∼ N(µtexture,Σtexture),where µshape and µtexture are the mean shape and texture vec-tors respectively, and Σshape and Σtexture are the covariancematrices, each of which is set to be a unit diagonal matrix.The dimensionality of S and T are 200 each. The prior dis-tributions over lighting direction and head pose are uniformover a discrete space (lighting direction could vary in eleva-tion or azimuth in range −80◦ to 80◦; the head pose couldvary along the z-axis in range−90◦ to 90◦, or on the x-axis inrange −36◦ to 36◦). Figure 2b shows several random drawsfrom this model.

Given a single image of a face as observation, ID, and anapproximate rendering engine, g(·), face processing can bedefined as inverse graphics in probability terms:

P(S,T, l,r|ID) ∝ P(ID|IS)P(IS|S,T, l,r)P(S,T, l,r)δg(·) (1)

The image likelihood is chosen to be noisy Gaussian,P(ID|IS) = N(ID; IS,Σ). We set Σ to 0.05 in our simulations.Note that the posterior space is of high-dimensionality con-sisting of more than 400 highly coupled shape, texture, light-ing direction, and head pose variables, rendering inference asignificant challenge.

Recognition modelThe idea of learning a recognition model to invert genera-tive models has been proposed in various forms before (e.g.,Dayan et al., 1995; Nair et al., 2008). We use a recognitionmodel consisting of a generically trained deep Convolutionalnetwork (ConvNet) and linear mappings from that network tothe latent variables in the generative model. To obtain thisrecognition model, we first used our generative model to hal-lucinate images from 300 different faces (each defined by a3d shape and texture vector), and rendered each distinct faceat 225 different viewing conditions (25 possible head poses×9 possible lighting directions). Second, we used a ConvNet

trained on ImageNet (a labeled dataset of more than millionimages collected from the internet, Deng et al., 2009) thatis very similar in architecture to that of (Krizhevsky et al.,2012) to obtain features for each of images in our dataset atall layers of the network.1 In doing so, we first selected the“face-selective” units in each layer of the network by runninga normal or a scrambled face test. The units that were acti-vated twice as much to normal faces than to scrambled faceson the average (out of responses to 75 normal + 75 scrambled= 150 faces) were designated as “face-selective.” Finally, welearn to construct bottom-up guesses for both scene-genericvariables (pose and lighting direction) and object-specific la-tents (3d face shape and texture) via linear mappings fromface-selective units in intermediate layers of the ConvNet. Wehave found that we can extract pose and lighting from the topconvolutional layer (TCL) of the ConvNet, with close to per-fect accuracy, using a linear support vector machine (SVM)for each combination of scene generic variables. We use a lin-ear model with inputs from both TCL and the first fully con-nected layer (FFL) of the ConvNet to predict the shape andtexture variables using Lasso regression (a schematic shownin Figure 2c).

InferenceGiven an image, ID, the recognition model described abovemakes fast bottom-up guesses about all latent variables inthe generative model. Inference proceeds by fixing the headpose and the lighting direction variables to their “recognized”values, and then performing multi-site elliptical slice sam-pling (Murray, Adams, & MacKay, 2009), a form of MCMC,on the shape and texture vectors. At each MCMC sweep,we iterate a proposal-and-acceptance loop over eight groupsof random variables: four shape vectors and four texture vec-tors, with one vector pair for each of four face parts (For moredetails see Kulkarni et al., 2015). In elliptical slice sampling,proposals are based on defining an ellipse using an auxiliaryvariable x ∼ N(0,Σ) and the current state of the latent vari-ables, and sampling from an adaptive bracket on this ellipsebased upon the log-likelihood function.

3d reconstruction from single imagesHumans are capable of grasping much of the 3d shape andsurface characteristics of faces or other objects from a sin-gle view, and can use that knowledge to recognize or imag-ine the object’s appearance from very different viewpoints.We tested our model’s capacity to perform this challengingtask using a held-out set of faces (not among those used tobuild the generative or recognition models) from (Blanz &Vetter, 1999). Figure 3a shows several of these test facesas inputs, reconstructions based on only the bottom-up passfrom the recognition model, and reconstructions from our fullmodel after initializing with the recognition model and run-ning MCMC to convergence. In addition to frontal faces, our

1We used the Caffe system to extract features, and also to trainalternative networks that we describe later (Jia et al., 2014).

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Figure 3: (a) Top: input images from a held-out laser scanneddataset (Blanz & Vetter, 1999). Middle: Reconstructions onthe basis of the initial bottom-up pass. We used our generativeprocess to visualize the shape and texture vectors obtainedonly from the recognition model. Bottom: Reconstructionsafter MCMC iterations. (b) The average and individual log-likelihood scores arising from randomly initialized 96 differ-ent chains vs. the recognition model initialized 96 chains.The recognition model initialized chains converge fast in lessthan 20 MCMC sweeps, and the variability across chains be-comes much smaller.model can reconstruct the shape and the texture of images offaces under non-frontal lighting and non-frontal pose, demon-strating robustness to non-standard viewing conditions andmotivating the behavioral studies we describe below.

Initializing inference for latent shape and texture variablesusing the recognition model dramatically improves both thequality and the speed of inference, as compared with thestandard MCMC practice of initializing with random val-ues (or samples from the prior). Figure 3b shows the log-likelihood traces of a number of chains for multiple input im-ages that were initialized either randomly, or from the recog-nition model. Recognition-initialized chains converge muchfaster: In just a few MCMC sweeps, every chain reaches alog-likelihood that is almost as good as the best randomlyinitialized inference chains reach after tens or hundreds ofsweeps. Furthermore, in comparison to the random initial-ization, recognition-model initialization leads to much lowervariance: Inferences become uniformly good, very quickly.

Behavioral experimentOn common benchmark tasks for machine face recognition,the best systems now regularly report near-perfect perfor-

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Figure 4: (a) Stimuli from the experiment illustrating the variability of lighting, pose, and identities. (b) Participants’ averageperformance across all possible test viewing conditions. (c) Participants’ and models’ accuracy. (d) Coefficients of mixedeffects logistic regression analyses. Error bars show standard deviations.

mance (e.g., Taigman et al., 2014). However, Leibo, Liao,and Poggio (2014) observed that most face databases are“easy”, in the sense that the faces in the images are oftenfrontal and fully visible. They found increasing viewing vari-ability severely hurt the performance of these systems. Build-ing upon this observation, we asked how well people can per-form face recognition under widely varying pose and lightingconditions. The task was a simple passport-photo verificationtask: participants saw images of two faces sequentially, andtheir task was to judge whether the images showed the sameperson or two different people. Explaining human behaviorin this task provides a challenging test for our model, as wellas alternatives from the literature.

Participants24 participants were recruited from Amazon’s crowdsourc-ing web-service Mechanical Turk. The experiment tookabout 10 minutes to complete. Participants were paid $1.50($9.00/hour).

Stimuli and ProcedureThe stimuli were generated using our generative model de-scribed above (Figure 2a). A stimulus face could be viewedat one of the five different poses (right profile to left profile)and under five different lighting directions (from top to frombottom), making a total of 25 possible viewing conditions.A subset of the facial identities and the 25 possible viewingconditions are shown in Figure 4a.

On a given trial, participants saw a study image for 750ms.After a brief period of blank interval (750ms), they sawthe test image, which remained visible until they responded.They were asked to fixate a cross in the center of the screen atthe beginning of each trial and between the study and the teststimuli presentations. The viewing condition for the studyimage was always frontal lighting at frontal pose (e.g., cen-ter image in Figure 4a). The viewing condition for the testimage could be any of the remaining 24 possible combina-tions of lighting and pose. Participants judged whether two

face images (study and test) belonged to the same person orto two different people, by pressing keys “s” for same or “k”for different on their keyboards.

There were a total of 96 trials, with 48 of the trials beingsame trials. Each test image viewing condition was repeatedfour times (4×24 = 96), split half between same and differ-ent trials. The presentation order of the 96 pairs of imageswas randomized across participants. None of the identitieswas repeated except in the same trials, where the same iden-tity was presented between the study image and correspond-ing test image. On different trials, faces were chosen to beas similar as possible while still remaining discriminable onclose scrutiny.

ResultsParticipants performed well despite the difficulty of the task:Performance was above chance for all possible test face view-ing conditions (Figure 4b), and ranged between 65% for lightat the bottom and right-profile pose to 92% for frontal lightand right-half profile pose. Overall, participants performed atan average accuracy of 78% (red dot and the associated er-ror bars in Figure 4c), a level of performance that challengeseven the most capable machine-vision systems.

Simulation detailsWe ran our model on the same 96 pairs of images that ex-perimental participants saw. We ran at least 18 and at most24 chains for each of the study and test images. Once ini-tialized with the recognition model, each chain was run for80 MCMC sweeps. Each chain simulated a participant inour study. For a given image, the values of the latent shapeand texture variables from the last sample were taken as themodel’s representation of identity. We denote the representa-tion of the study image i as studyi, and of the test image i astesti for i ∈ 1, . . . ,96.

We calculated the performance of our model (and the alter-native models that we introduce later) in the following man-

ner. We first scaled the study and the test image representa-tions independently to be centered at 0 and have a standarddeviation of 1.2 Then, for each pair i, we calculated the Pear-son correlation coefficient between the representations of thestudy and the test images, denoted as corri. Below, we usedthese pair-specific correlation values to model people’s binaryresponses (same vs. different) in regression analyses.

Finally, we need to obtain same vs. different judgmentsfrom the model, to compare its performance with groundtruth. Similar to an ROC analysis, we searched for a thresh-old correlation ∈ [−1,1] such that the model’s performancewill be highest with respect to ground truth. Pairs of corre-lation values lower than the threshold were called different,and the pairs of equal or higher correlation values than thethreshold were assigned same. We report results based uponthe threshold that gave the highest performance.

Simulation resultsOur inverse graphics model performs at 78% (see Figure 4c),matching the participants’ average performance. Matchingaverage level participant is an important criteria in eval-uating a model, but only a crude one. We also testedwhether the internal representations of our model (corri fori ∈ 1, . . . ,96) could predict participants’ same/different re-sponses on unique stimuli pairs. We performed mixed ef-fects logistic regression from our model’s internal represen-tations (corri for i ∈ 1, . . . ,96) to participants’ judgments,where we allowed a random slope for each participant us-ing the lme4 package and R statistics toolbox (R Core Team,2013). The coefficient and the standard deviation estimatedfor our model are shown in Figure 4d. The internal repre-sentations of our model can strongly predict participants re-sponses, providing evidence for an inverse graphics approachto vision (β̂ = 5.69,σ = 0.26, p < 0.01).

Macaque face patch system as inverse graphicsEncouraged by these behavioral findings, we next askedwhether our model could explain neural responses in the face-processing hierarchy in the brain. Face processing is perhapsthe best understood aspect of higher-level vision at the neu-ral level. The spiking patterns of neurons at different fMRI-identified face patches in macaque monkeys show a hierarchi-cal organization of selectivity: neurons in the most posteriorpatch (ML/MF) appear to be tuned to specific poses, neuronsin AL (a more anterior patch) exhibit specificity to mirror-symmetric poses, and those in the most anterior patch (AM)show specificity to individuals but appear largely viewpoint-invariant (Freiwald & Tsao, 2010).3

We ran our model on a dataset of faces generated usingour generative model, which mimicked the FV image datasetfrom Freiwald and Tsao (2010). Our dataset contained 7 head

2This scaling step was not crucial for our model, but it was re-quired to obtain the best out of other models that we will introducebelow.

3Recent studies suggest homologue architecture between humanand macaque face processing systems.

poses of 25 different identities under a fixed frontal lightingdirection. We compared the representational similarity ma-trices of the population responses from Freiwald and Tsao(2010) in patches ML/MF, AL, and AM, and the represen-tational similarity matrices arising from the representationsof the different components of our recognition model: face-selective TCL units, face-selective FFL units, and the fastbottom-up guesses for shape and texture vectors.

ML/MF representations were captured best by the TCLactivations (pearson correlation 0.67), suggesting that pose-specificity arises from a computational need to make inversegraphics tractable. Our results also suggest that this layermight carry information about the lighting of the scene, whichis experimentally not systematically tested yet. AL represen-tations were best accounted by the FFL activations (pearsoncorrelation 0.67). Our model also provides a reason why mir-ror symmetry should be found in the brain: Computationalexperiments showed that mirror symmetry arises only at fullyconnected layers (i.e., dense connectivity) and only when thetraining data contains images of the same face from view-points distributed across both left and right sides. Our modelcaptures AM patterns best via inferred latent shape and tex-ture representations. The shape and texture vectors obtainedjust using the recognition model (that is, without running anyMCMC iterations) captured AM responses best in compari-son to all other layers in the recognition model (pearson cor-relation 0.42), suggesting the possibility of a generative 3Drepresentation of shape and texture in the patch AM.

Discussion: Comparison to other modelsIn comparing our model against other approaches, we con-centrated on alternatives that are based upon ConvNets, dueto their success in many visual tasks including face recog-nition (DeepFace, Taigman et al., 2014), and the fact thatthey are architecturally similar (or even identical, in somecases) to our recognition model.4 We considered three al-ternative models: (1) a baseline model, which simply is aConvNet trained on ImageNet (CNN baseline), (2) a Con-vNet that is trained on a challenging real faces dataset calledSUFR-W introduced in Leibo et al. (2014) (CNN faces), and(3) a ConvNet that is selected from a number of networks thatwere all fine-tuned using samples from our generative model(CNN optimized).

We focused on these alternative models’ ability to explainour behavioral data. But we should note that ConvNets, ontheir own, cannot do 3D reconstruction. Also, even thougheach ConvNet can partially account for the neural data suchas the pose specificity at patch ML/MF, they are worse at ex-plaining the other two patches. The performance of all alter-native models on our behavioral task was assessed just as forour model, with the only difference being that internal repre-

4We attempted to evaluate the DeepFace on our behavioraldataset. However, email exchanges with its authors suggested that acomponent of the model (3d spatial alignment) would not work withimages of profile faces. Accordingly, we estimate the performanceof that model on our behavioral dataset to be around 65%.

sentations of images were obtained as the FFL layer activa-tions when that image is input to the model. For the mixedeffects logistic regressions, a given pair of study and test im-ages is represented by the correlation of the FFL activationsfor each of the two images.

The baseline model (CNN baseline) performed at 67%(Figure 4c). This is impressive given that the model wasnot trained to recognize faces explicitly, and arguably justi-fies our use of ConvNets as good feature representations. TheConvNet trained on SUFR-W dataset (CNN faces) performedat 72% (Figure 4c), closer to but significantly worse thanhuman-level performance. We should note that CNN facesis remarkable for its identification performance on a held-outportion of the SUFR-W dataset (67%; chance level = 0.25%).The last ConvNet, CNN optimized, performed better thanpeople did with 86% (Figure 4c).

We are not the first to show that a computer system cantop human performance in unfamiliar face recognition. How-ever, we argue that the discrepancy between people andCNN optimized points to the computational superiority ofhuman face processing system: our face processing machin-ery is not optimized for a single bit information (i.e., identity),but instead can capture much richer content from an image ofa face. This comes with a cost of accuracy in our same vs.different task. Our model accounts for the rich content vs.accuracy trade-off by acquiring much richer representationsfrom faces while performing only slightly worse on identitymatching than an optimized ConvNet. 5

But, do people actually undertake the difficult chal-lenge of 3d reconstruction when they look at unfamiliarfaces? Our data suggests so: internal representations of theCNN optimized, corri for i ∈ 1, . . . ,96, is a worse fit to peo-ple’s responses (also using a mixed effects logistic regressionmodel; β̂ = 3.97,σ = 0.22, p < 0.01; Figure 4d). Indeed,none of the alternative models could account for participants’precise patterns of same/different responses as well as ourmodel did(Figure 4d).

Do our computational and behavioral approaches extendto other object categories? A representational aspect of ourmodel that lets us account for behavioral and neural data atthe same time is that it represents 3D content in the formof a vector. Therefore, our approach should easily extend toother classes of 3D objects that can be represented similarlyby vectors. Immediate possibilities include bodies, classesof animals such as birds, generic 3D objects such as vases,bottles, and so on. These object classes, in particular bod-ies, are exciting future directions, where revealing neural re-sults have also been accumulating, our psychophysics meth-ods can be straightforwardly extended to, and a generalizationof our model already efficiently handles 3D reconstructiontasks (Kulkarni et al., 2015).

5We should also note that if we average the results across all thechains that we ran for each image, our model’s performance signifi-canly increases to 89% too.

ConclusionThis paper shows that an efficient implementation of theanalysis-by-synthesis approach can account for people’s be-havior on a “hard” visual recognition task. The same modelalso solves a computationally challening task of reconstruct-ing 3d shape and texture from a single image. Finally, it ac-counts qualitatively for the main response characteristics ofneurons in the face processing system in macaque monkeys.None of the alternative ConvNet models, lacking a generativemodel and the capacity for top-down model-based inference,can account for all three of this phenomena. These resultspoint to an account of vision with inverse graphics at its cen-ter, supported by bottom-up recognition models that can belearned from generative model fantasies in a self-supervisedfashion, that allow top-down processing to refine their ini-tial guesses but still do most of the work of inference in abottom-up fashion, and that thereby enable even very richmodel-based inferences to proceed almost as quickly as thefast feedforward processing of neural networks.

AcknowledgmentsWe thank the reviewers for their helpful comments. This re-search was supported by the Center for Brains Minds and Ma-chines (CBMM), funded by NSF STC award CCF-1231216and by ONR grant N00014-13-1-0333.

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