{"title": "Input Reconstruction Reliability Estimation", "book": "Advances in Neural Information Processing Systems", "page_first": 279, "page_last": 286, "abstract": null, "full_text": "Input Reconstruction Reliability Estimation \n\nDean A. Pomerleau \n\nSchool of Computer Science \nCarnegie Mellon University \n\nPittsburgh, PA 15213 \n\nAbstract \n\nThis paper describes a technique called Input Reconstruction Reliability Estimation \n(IRRE) for determining the response reliability of a restricted class of multi-layer \nperceptrons (MLPs). The technique uses a network's ability to accurately encode \nthe input pattern in its internal representation as a measure of its reliability. The \nmore accurately a network is able to reconstruct the input pattern from its internal \nrepresentation, the more reliable the network is considered to be. IRRE is provides \na good estimate of the reliability of MLPs trained for autonomous driving. Results \nare presented in which the reliability estimates provided by IRRE are used to select \nbetween networks trained for different driving situations. \n\n1 Introduction \n\nIn many real world domains it is important to know the reliability of a network's response \nsince a single network cannot be expected to accurately handle all the possible inputs. Ideally, \na network should not only provide a response to a given input pattern, but also an indication of \nthe likelihood that its response is \"correct\". This reliability measure could be used to weight \nthe outputs from multiple networks and to determine when a new network needs to be trained. \n\nThis paper describes a technique for estimating a network's reliability called Input Recon(cid:173)\nstruction Reliability Estimation (IRRE). IRRE relies on the fact that the hidden representation \ndeveloped by an artificial neural network can be considered to be a compressed representation \nof important input features. For example, when the network shown in Figure 1 is trained to \nproduce the correct steering direction from images of the road ahead, the hidden units learn to \nencode the position and orientation of important features like the road edges and lane markers \n(See [pomerleau, 1991] for more details). Because there are many fewer hidden units than \ninput units in the network, the hidden units cannot accurately represent all the details of an \n\n279 \n\n\f280 \n\nPomerleau \n\nSUp \nRi&hI \n\n30 Output \n\nUnits \n\n3Ox32 SelUlor \nInput Retina \n\nFigure 1: Original driving network architecture. \n\narbitrary input pattern. Instead, the hidden units learn to devote their limited representational \ncapabilities to encoding the position and orientation of consistent, frequently-occurring fea(cid:173)\ntures from the training set. When presented with an atypical input, such as a road with a \ndifferent number of lanes, the feature detectors developed by the hidden units will not be \ncapable of accurately encode all the actual input features. \nInput Reconstruction Reliability Estimation exploits this limitation in representational capacity \nto estimate a network's reliability. In IRRE, the network's internal representation is used to \nreconstruct in the input pattern being presented. The more closely the reconstructed input \nmatches the actual input, the more familiar the input and hence the more reliable the network's \nresponse. \n\n2 Reconstructing the Input \n\nIRRE utilized an additional set of output units to perform input reconstruction called the \nencoder output array, as depicted in Figure 2. This second set of output units has the same \ndimensionality as the input retina. In the experiments described in this paper, the input layer \nand encoder output array have 30 rows and 32 columns. The desired activation for each of \nthese additional output units is identical to the activation of the corresponding input unit. In \nessence, these additional output units turn the network into an autoencoder. \n\nThe network is trained using backpropagation both to produce the correct steering response \non the steering output units, and to reconstruct the input image as accurately as possible \non the encoder output array. During the training process, the network is presented with \nseveral hundred images taken with a camera onboard our test vehicle as a person drives \n(See [pomerleau, 1991] for more details). Training typically requires approximately 3 minutes \nduring which the person drives over a 1/4 to 1/2 mile stretch of road. \n\n\fInput Reconstruction Reliability Estimation \n\n281 \n\nFigure 2: Network architecture augmented to include an encoder output array. \n\nDuring testing on a new stretch of road, images are presented to the network and activation is \npropagated forward through the network to produce a steering response and a reconstructed \ninput image. The reliability of the steering response is estimated by computing the correlation \ncoefficient p(l , R) between the activation levels of units in the actual input image I and the \nreconstructed input image R using the following formula: \n\np(I ,R) = iR - I . II \n\n01 OR \n\nwhere I and R are the mean activation value of the actual and the reconstructed images, IR is \nthe mean of the set formed by the unit-wise product of the two images, and u/ and UR represent \nthe standard deviations of the activation values of each image. The higher the correlation \nbetween the two images, the more reliable the network's response is estimated to be. The \nreason correlation is used to measure the degrees of match between the two images is that, \nunlike Euclidean distance, the correlation measure is invariant to differences in the mean \nand variance between the two images. This is important since the mean and variance of the \ninput and the reconstructed images can sometimes vary, even when the input image depicts a \nfamiliar situation. \n\n3 Results and Applications \n\nThe degree of correlation between the actual and the reconstructed input images is an extremely \ngood indicator of network response accuracy in the domain of autonomous driving, as shown \nin Figure 3. It shows a trained network's steering error and reconstruction error as the vehicle \ndrives down a quarter mile stretch of road that starts out as a single lane path and eventually \nbecomes a two-lane street. The solid line indicates the network's steering error, as measured \nby the difference in turn curvature between the network's steering response and a person's \n\n\f282 \n\nPomerleau \n\n0.04 \n\n~ g -;;- 0.03 \n~~ ..... \nb.OV \n'S e 0.02 \n..... -en \nv ........ \nv(cid:173)\n\n0.01 \n\nCoJTelation Coeff\"u:ienl = 0.92 \n\nSteering Error \nii.PU;Reoo~n&ror \n\nIntersection \n\n\u00ae \n\n~l. \n\n1.25 \n~ \n1.00 ~ \nc::~ \no~ \n'a .. \n0.75 ~b: \njg~ \n0.50 8--\n~ \n\n\u2022 L-__________________________________ ~ \n000 \n\nO~ \n\nI ..... t__---- One Lane Road Im.gel----~ .. ~nll\"' .. ---.r--t .. ~1 \n\nFigure 3: Reconstruction error obtained using autoencoder reconstruction versus network \nsteering error over a stretch of one-lane and two-lane road. \n\nTwo Lane Road Images \n\nsteering response at that point along the road. The dashed line represents the network's \n\"reconstruction error\", which is defined to be the degree of statical independence between the \nactual and reconstructed images, or 1 - p(I , R}. \n\nThe two curves are nearly identical, having a correlation coefficient of 0.92. This close match \nbetween the curves demonstrates that when the network is unable to accurately reconstruct the \ninput image, it is also probably suggesting an incorrect steering direction. Visual inspection \nof the actual and reconstructed input images demonstrates that the degree of resemblance \nbetween them is a good indication of the actual input's familiarity, as shown in Figure 4. It \ndepicts the input image, network response, and reconstructed input at the three points along the \nroad,labeled A, Band C in Figure 3. When presented with the image at point A, which closely \nresembles patterns from training set, the network's reconstructed image closely resembles the \nactual input, as shown by the close correspondence between the images labeled \"Input Acts\" \nand \"Reconstructed Input\" in the left column of Figure 4. This close correspondence between \nthe input and reconstructed images suggests that the network can reliably steer in this situation. \nIt in fact it can steer accurately on this image, as demonstrated by the close match between the \nnetwork's steering response labeled \"Output Acts\" and the desired steering response labeled \n''Target Acts\" in the upper left corner of Figure 4. \n\nWhen presented with a situation the network did not encounter during training, such as the \nfork image and the two-lane road image shown in the other two columns of Figure 4, the \nreconstructed image bears much less resemblance to the original input. This suggests that the \nnetwork is confused. This confusion results in an incorrect steering response, illustrated in \nthe discrepancy between the network's steering response and the target steering response for \nthe two atypical images. \n\nThe reliability prediction provided by IRRE has been used to improve the performance of \nthe neural network based autonomous driving system in a number of ways. The simplest is \n\n\fInput Reconstruction Reliability Estimation \n\n283 \n\nFigure 4: The actual input. the reconstructed input and the point-wise absolute difference \nbetween them on a road image similar to those in the training set (labeled A), and on two \natypical images (labeled B and C). \n\n\f284 \n\nPomerleau \n\n1.00 \n\n0.80 \n\n0.60 \n\n0.40 \n\n0.20 \n\nI \na \n\n~ \nt-' \n!'i, \nI \n.. : v\u00b7, it \nf \\ \n: f ~ \"\\ \n\\ \ni . / \n\\ \n';. 1 'V: \n\\.J \n\n\\ . . \n\nII \n\nI \n\n1 .' \nL i\\ \n\u2022 \n!iJ \u2022\u2022 \n:!I\\ II I \n\\.:1 i != \n,,':: \n\u2022 II \u2022 II \n.\" \nI !i \n\\ ii \n1 II \ny \n\\\\! \n, \n~ \n\n\u2022 . : \n\na I \n\nOJ \n\nOne Lane Net Rcconstuction Error \nTW~ line-Net Rct;;n;tiiCtion Eir~; \n\n(\\ \n. \n: \\ \n,. , \n. . , : \n: \\.-: \n, \n~. J \n'\\i \n\n: \n\n= \n\n: \n\n, \n\n....: \n\\_ \u2022\u2022 .: \nO.OOL.-_______________ ___ _ \nOne Lane Images ---11-- Two Lane Images -..j \n\nI.. \n\n. \n\nFigure 5: Reconstruction error of networks trained for one-lane road driving (solid line) and \ntwo-lane road driving (dashed line), \n\nto use IRRE to control vehicle speed. The more accurate the input reconstruction, the more \nconfident the network, and hence the faster the system drives the vehicle. A second use the \nsystem makes of the reliability estimate provided by IRRE is to update the vehicle's position \non a rough map of the area being driven over. When the map indicates there should be an \nintersection or other confusing situation up ahead, a subsequent sharp rise in reconstruction \nerror is a good indication that the vehicle has actually reached that location, allowing the \nsystem to pinpoint the vehicle's position. Knowing the vehicle's location on a map is useful \nfor integrating symbolic processing, such as planning, into the neural network driving system \n(for more details, see [pomerleau et al., 1991]). \n\nFigure 5 illustrates how IRRE can be used to integrate the outputs from multiple expert \nnetworks. The two lines in this graph illustrate the reconstruction error of two networks, one \ntrained to steer on one-lane roads (solid line), and the other trained to steer on two-lane roads \n(dashed line). The reconstruction error for the one-lane network is low on the one-lane road \nimages, and high on the two-lane road images. The opposite is true for the network trained \nfor two-lane road driving. The reliability estimate provided by IRRE allows the system to \ndetermine which network is most reliable for driving in the current situation. By simulating \nmultiple networks in parallel, and then selecting the one with the highest reliability, the system \nhave been able to drive the Navlab test vehicle on one, two and four lane roads automatically \nat speeds of up to 30 miles per hour. \n\n4 Discussion \n\nThe effectiveness of input reconstruction reliable estimation stems from the fact that the net(cid:173)\nwork has a small number of hidden units and is only trained in a narrow range of situations. \nThese constraints prevent the network from faithfully encoding arbitrary input patterns. In(cid:173)\nstead, the hidden units learn to encode features in the training images that are most important \nfor the task. Baldi and Hornik [Baldi & Hornik, 1989] have shown that if an autoencoder \n\n\fInput Reconstruction Reliability Estimation \n\n285 \n\nnetwork with a single layer of N linear hidden units is trained with back-propagation, the acti(cid:173)\nvation levels of the hidden units will represent the first N principal components of the training \nset. Since the units in the driving network are non-linear, this assertion does not strictly hold in \nthis case. However, Cottrell and Munro [Cottrell & Munro, 1988] have found empirically that \nautoencoder networks with a sigmoidal activation function develop hidden units that span the \nprincipal subspace of the training images, with some noise on the first principal component \ndue to network non-linearity. Because the principal components represent the dimensions \nalong which the training examples varies most, it can be shown that using linear combinations \nof the principal components to represent the individual training patterns optimally preserves \nthe information contained in the training set [Linsker, 1989]. \n\nHowever the compressed representation developed by a linear autoencoder network is only \noptimal for encoding images from the same distribution as the training set. When presented \nwith images very different from those in the training set, the image reconstructed from the \ninternal representation is not as accurate. The results presented in this paper demonstrate that \nthis reconstruction error can be employed to estimate the likelihood and magnitude of error in \nMLPs trained for autonomous driving. \n\nHowever the input reconstruction technique presented here has a serious potential shortcom(cid:173)\ning, namely that it forces the network's hidden units to encode all input features, including \npotentially irrelevant ones. While this increased representation load on the hidden units has \nthe potential to degrade network performance, this effect has not been observed in the tests \nconducted so far. In support of this finding, Gluck [Gluck, personal communications] has \nfound that forcing a network to autoencode its input frequently improves its generalization. \nIn [Gluck & Myers, 1992], Gluck and Myers use the representation developed by an autoen(cid:173)\ncoder network as a model for simple types of learning in biological systems. The model \nsuggests that the hippocampus acts as an autoencoder, developing internal representations that \nare then used to perform other tasks. \n\nBut if interference from the autoencoder task proves to be a problem, one way to eliminate \nit would be to have separate groups of hidden units connected exclusively to one group of \noutputs or the other. Having a separate set of hidden units for the autoencoder task would \nensure that the representation developed for the input reconstruction does not interfere with \nrepresentation developed for the \"normal\" task. It remains to be seen if this decoupling of \ninternal representations will adversely affect IRRE's ability to predict network errors. \n\nAs a technique for multi-network integration, IRRE has several advantages over exist(cid:173)\ning connectionist arbitration methods, such as Hampshire and Waibel's Meta-Pi architec(cid:173)\nture [Hampshire & Waibel, 1992] and the Adaptive Mixture of Experts Model of Jacobs et \naI. [Jacobs et al., 1991]. It is a more modular approach, since each expert can be trained \nentirely in isolation and then later combined with other experts without any additional training \nby simply selecting the most reliable network for the current input. Since IRRE provides an \nabsolute measure of a single network's reliability, and not just a measure of how appropriate \na network is relative to others, IRRE can be also used to determine when none of the experts \nis capable of coping with the current situation. \n\nA potentially interesting extension to IRRE is the development of techniques for reasoning \nabout the difference between the actual input and the reconstructed input. For instance, it \nshould be possible to recognize when the vehicle has reached a fork in the road by the char(cid:173)\nacteristic mistakes the network makes in reconstructing the input image. Another important \ncomponent of future work in is to test the ability of IRRE to estimate network reliability in \ndomains other than autonomous driving. \n\n\f286 \n\nPomerleau \n\nAcknowledgements \n\nI thank Dave Touretzky, Chuck Thorpe and the entire Unmanned Ground Vehicle Group at \nCMU for their support and suggestions. Principle support for this research has come from \nDARPA, under contracts \"Perception for Outdoor Navigation\" (contract number DACA76-\n89-C-OOI4, monitored by the US Army Topographic Engineering Center) and ''Unmanned \nGround Vehicle System\" (contract number DAAE07-90-C-R059, monitored by TACOM). \n\nReferences \n\n[Baldi & Hornik,1989] Baldi, P. and Hornik, K. (1989) Neural networks and principal com(cid:173)\nponent analysis: Learning from examples without local minima. Neural Networks, Vol. \n2 pp. 53-58. \n\n[Cottrell & Munro, 1988] Cottrell, G.W. and Munro, P. (1988) Principal components analysis \nofimages via back-propagation. Proc. Soc. of Photo-Opticallnstr. Eng., Cambridge MA. \n[Gluck, personal communications] Gluck, M.A. (1992) Personal Communications. Rutgers \n\nUniv., Newark NJ. \n\n[Gluck & Myers, 1992] Gluck, M.A. and Myers, C.E. (1992) Hippocampal function in rep(cid:173)\n\nresentation and generalization: a computational theory. Proc.1992 Cogn. Sci. Soc. Con/. \nHillsdale, NJ: Erlbaum Assoc. \n\n[Hampshire & Waibel, 1992] Hampshire J.B. and Waibel, A.H. (1989) The Meta-Pi network: \nbuilding distributed knowledge representations for robust pattern recognition. IEEE \nTrans. on Pattern Analysis and Machine Intelligence. \n\n[Jacobs et al., 1991] Jacobs, R.A., Jordan, M.I. Nowlan, SJ. and Hinton, G.E. (1991) Adap(cid:173)\n\ntive mixtures of local experts. Neural Computation, 3 :1, Terrence Sejnowski (ed). \n\n[Linsker, 1989] Linsker, R. (1989) Designing a sensory processing system: What can be \nlearned from principal component analysis? IBM Technical Report RC 14983 (#66896). \n[pomerleau, 1991] Pomerleau, D.A. (1991) Efficient Training of Artificial Neural Networks \n\nfor Autonomous Navigation. Neural Computation 3:1, Terrence Sejnowski (ed). \n\n[pomerleau et al., 1991] Pomerleau, D.A., Gowdy, J., Thorpe, C.E. (1991) Combining arti(cid:173)\nficial neural networks and symbolic processing for autonomous robot guidance. Engi(cid:173)\nneering Applications of Artificial Intelligence, 4:4 pp. 279-285. \n\n\f", "award": [], "sourceid": 631, "authors": [{"given_name": "Dean", "family_name": "Pomerleau", "institution": null}]}