{"title": "Deep Generative Video Compression", "book": "Advances in Neural Information Processing Systems", "page_first": 9287, "page_last": 9298, "abstract": "The usage of deep generative models for image compression has led to impressive\nperformance gains over classical codecs while neural video compression is still in its infancy. Here, we propose an end-to-end, deep generative modeling approach to compress temporal sequences with a focus on video. Our approach builds upon variational autoencoder (VAE) models for sequential data and combines them with recent work on neural image compression. The approach jointly learns to transform the original sequence into a lower-dimensional representation as well as to discretize and entropy code this representation according to predictions of the sequential VAE. Rate-distortion evaluations on small videos from public data sets with varying complexity and diversity show that our model yields competitive results when trained on generic video content. Extreme compression performance is achieved when training the model on specialized content.", "full_text": "Deep Generative Video Compression\n\nJun Han\u2217\n\nDartmouth College\n\njunhan@cs.dartmouth.edu\n\nSalvator Lombardo\u2217\nDisney Research LA\n\nsalvator.d.lombardo@disney.com\n\nChristopher Schroers\nDisneyResearch|Studios\n\nchristopher.schroers@disney.com\n\nAbstract\n\nStephan Mandt\n\nUniversity of California, Irvine\n\nmandt@uci.edu\n\nThe usage of deep generative models for image compression has led to impressive\nperformance gains over classical codecs while neural video compression is still in\nits infancy. Here, we propose an end-to-end, deep generative modeling approach to\ncompress temporal sequences with a focus on video. Our approach builds upon\nvariational autoencoder (VAE) models for sequential data and combines them\nwith recent work on neural image compression. The approach jointly learns to\ntransform the original sequence into a lower-dimensional representation as well\nas to discretize and entropy code this representation according to predictions of\nthe sequential VAE. Rate-distortion evaluations on small videos from public data\nsets with varying complexity and diversity show that our model yields competitive\nresults when trained on generic video content. Extreme compression performance\nis achieved when training the model on specialized content.\n\n1\n\nIntroduction\n\nThe transmission of video content is responsible for up to 80% of the consumer internet traf\ufb01c, and\nboth the overall internet traf\ufb01c as well as the share of video data is expected to increase even further\nin the future (Cisco, 2017). Improving compression ef\ufb01ciency is more crucial than ever. The most\ncommonly used standard is H.264 (Wiegand et al., 2003); more recent codecs include H.265 (Sullivan\net al., 2012) and VP9 (Mukherjee et al., 2015). All of these existing codecs follow the same block\nbased hybrid structure (Musmann et al., 1985) which essentially emerged from engineering out and\nre\ufb01ning this concept over decades. From a high level perspective, they differ in a huge number of\nsmaller design choices and have grown to become more and more complex systems.\nWhile there is room for improving the block based hybrid approach even further (Fraunhofer,\n2018), the question remains as to how much longer signi\ufb01cant improvements can be obtained while\nfollowing the same paradigm. In the context of image compression, deep learning approaches that\nare fundamentally different to existing codecs have already shown promising results (Ball\u00e9 et al.,\n2018, 2016; Theis et al., 2017; Agustsson et al., 2017; Minnen et al., 2018). Motivated by these\nsuccesses for images, we propose a \ufb01rst step towards innovating beyond block-based hybrid codecs\nby framing video compression in a deep generative modeling context. To this end, we propose an\nunsupervised deep learning approach to encoding video. The approach simultaneously learns the\noptimal transformation of the video to a lower-dimensional representation and a powerful predictive\nmodel that assigns probabilities to video segments, allowing us to ef\ufb01ciently entropy-code the\ndiscretized latent representation into a short code length.\n\n\u2217 Shared \ufb01rst authorship.\n\n33rd Conference on Neural Information Processing Systems (NeurIPS 2019), Vancouver, Canada.\n\n\fH.265 (21.1 dB @ 0.86 bpp)\n\nVP9 (26.0 dB @ 0.57 bpp)\n\nOurs (44.6 dB @ 0.06 bpp)\n\nFigure 1: Reconstructed video frames using the established codecs H.265 (left), VP9 (middle),\nand ours (right), with videos taken from the Sprites data set (Section 4). On specialized content as\nshown here, higher PSNR values in dB (corresponding to lower distortion) can be achieved at almost\nan order of magnitude smaller bits per pixel (bpp) rates. Compared to the classical codecs, fewer\ngeometrical artifacts are apparent in our approach.\n\nOur end-to-end neural video compression scheme is based on sequential variational autoen-\ncoders (Bayer & Osendorfer, 2014; Chung et al., 2015; Li & Mandt, 2018). The transformations to\nand from the latent representation (the encoder and decoder) are parametrized by deep neural networks\nand are learned by unsupervised training on videos. These latent states have to be discretized before\nthey can be compressed into binary. Ball\u00e9 et al. (2016) address this problem by using a box-shaped\nvariational distribution with a \ufb01xed width, forcing the VAE to \u2018forget\u2019 all information stored on\nsmaller length scales due to the insertion of noise during training. This paper follows the same\nparadigm for temporally-conditioned distributions. A sequence of quantized latent representations\nstill contains redundant information as the latents are highly correlated. (Lossless) entropy encoding\nexploits this fact to further reduce the expected \ufb01le size by expressing likely data in fewer bits and\nunlikely data in more bits. This requires knowledge of the probability distribution over the discretized\ndata that is to be compressed, which our approach obtains from the sequential prior.\nAmong the many architectural choices that our approach enables, we empirically investigate a model\nthat is well suited for the regime of extreme compression. This model uses a combination of both\nlocal latent variables, which are inferred from a single frame, and a global state, inferred from a multi-\nframe segment, to ef\ufb01ciently store a video sequence. The dynamics of the local latent variables are\nmodeled stochastically by a deep generative model. After training, the context-dependent predictive\nmodel is used to entropy code the latent variables into binary with an arithmetic coder.\nIn this paper, we focus on low-resolution video (64 \u00d7 64) as the \ufb01rst step towards deep generative\nvideo compression. Figure 1 shows a test example of the possible performance improvements using\nour approach if the model is trained on restricted content (video game characters). The plots show\ntwo frames of a video, compressed and reconstructed by our approach and by classical video codecs.\nOne sees that \ufb01ne granular details, such as the hands of the cartoon character, are lost in the classical\napproach due to artifacts from block motion estimation (low bitrate regime), whereas our deep\nlearning approach successfully captures these details with less than 10% of the \ufb01le length.\nOur contributions are as follows:\n1) A general paradigm for generative compression of sequential data. We propose a general\nframework for compressing sequential data by employing a sequential variational autoencoder (VAE)\nin conjuction with discretization and entropy coding to build an end-to-end trainable codec.\n2) A new neural codec for video compression. We employ the above paradigm towards building\nan end-to-end trainable codec. To the best of our knowledge, this is the \ufb01rst work to utilize a deep\ngenerative video model together with discretization and entropy coding to perform video compression.\n3) High compression ratios. We perform experiments on three public data sets of varying complexity\nand diversity. Performance is evaluated in terms of rate-distortion curves. For the low-resolution\nvideos considered in this paper, our method is competitive with traditional codecs after training and\ntesting on a diverse set of videos. Extreme compression performance can be achieved on a restricted\nset of videos containing specialized content if the model is trained on similar videos.\n4) Ef\ufb01cient compression from a global state. While a deep latent time series model takes temporal\nredundancies in the video into account, one optional variation of our model architecture tries to\ncompress static information into a separate global variable (Li & Mandt, 2018) which acts similarly\nas a key frame in traditional methods. We show that this decomposition can be bene\ufb01cial.\n\n2\n\n\fOur paper is organized as follows. In Section 2, we summarize related works before describing\nour method in Section 3. Section 4 discusses our experimental results. We give our conclusions in\nSection 5.\n\n2 Related Work\n\nThe approaches related to our method fall into three categories: deep generative video models, neural\nimage compression, and neural video compression.\n\nDeep generative video models. Several works have applied the variational autoencoder\n(VAE) (Kingma & Welling, 2014; Rezende et al., 2014) to stochastically model sequences (Bayer &\nOsendorfer, 2014; Chung et al., 2015). Babaeizadeh et al. (2018); Xu et al. (2020) use a VAE for\nstochastic video generation. He et al. (2018) and Denton & Fergus (2018) apply a long short term\nmemory (LSTM) in conjunction with a sequential VAE to model the evolution of the latent space\nacross many video frames. Li & Mandt (2018) separate latent variables of a sequential VAE into local\nand global variables in order to learn a disentangled representation for video generation. Vondrick\net al. (2016) generate realistic videos by using a generative adversarial network (Goodfellow et al.,\n2014) to learn to separate foreground and background, and Lee et al. (2018) combine variational and\nadversarial methods to generate realistic videos. This paper also employs a deep generative model to\nmodel the sequential probability distribution of frames from a video source. In contrast to other work,\nour method learns a continuous latent representation that can be discretized with minimal information\nloss, required for further compression into binary. Furthermore, our objective is to convert the original\nvideo into a short binary description rather than to generate new videos.\n\nNeural image compression. There has been signi\ufb01cant work on applying deep learning to image\ncompression. In Toderici et al. (2016, 2017); Johnston et al. (2018), an LSTM based codec is used\nto model spatial correlations of pixel values and can achieve different bit-rates without having to\nretrain the model. Ball\u00e9 et al. (2016) perform image compression with a VAE and demonstrate how\nto approximately discretize the VAE latent space by introducing noise during training. This work\nis re\ufb01ned by (Ball\u00e9 et al., 2018) which improves the prior model (used for entropy coding) beyond\nthe mean-\ufb01eld approximation by transmitting side information in the form of a hierarchical model.\nMinnen et al. (2018) consider an autoregressive model to achieve a similar effect. Santurkar et al.\n(2018) studies the performance of generative compression on images and suggests it may be more\nresilient to bit error rates. These image codecs encode each image independently and therefore\ntheir probabilistic models are stationary with respect to time. In contrast, our method performs\ncompression according to a non-stationary, time-dependent probability model which typically has\nlower entropy per pixel.\n\nNeural video compression. The use of deep neural networks for video compression is relatively\nnew. Wu et al. (2018) perform video compression through image interpolation between reference\nframes using a predictive model based on a deep neural network. Chen et al. (2017) and Chen et al.\n(2019) use a deep neural architecture to predict the most likely frame with a modi\ufb01ed form of block\nmotion prediction and store residuals in a lossy representation. Since these works are based on motion\nestimation and residuals, they are somewhat similar in function and performance to existing codecs.\nLu et al. (2019) and Djelouah et al. (2019) also follow a pipeline based on motion estimation and\nresidual computation as in existing codecs. In contrast, our method is not based on motion estimation,\nand the full inferred probability distribution over the space of plausible subsequent frames is used\nfor entropy coding the frame sequence (rather than residuals). In a concurrent publication, Habibian\net al. (2019) perform video compression by utilizing a 3D variational autoencoder. In this case, the\n3D encoder removes temporal redundancy by decorrelating latents, wheras our method uses entropy\ncoding (with time-dependent probabilities) to remove temporal redundancy.\n\n3 Deep Generative Video Compression\n\nOur end-to-end approach simultaneously learns to transform a video into a lower-dimensional latent\nrepresentation and to remove the remaining redundancy in the latents through model-based entropy\ncoding. Section 3.1 gives an overview of the deep generative video coding approach as a whole\n\n3\n\n\fFigure 2: High-level operational diagram of our compression codec (see Section 3). A video segment\nis encoded into per-frame latent variables zt and (optionally) also into a per-segment global state f\nusing a VAE architecture. Both latent variables are then quantized and arithmetically encoded into\nbinary according to the respective prior models. To recover an approximation to the original video,\nthe latent variables are arithmetically decoded from the binary and passed through the neural decoder.\n\nbefore Sections 3.2 and 3.3 detail on the model-based entropy coding and the lower-dimensional\nrepresentation, respectively.\n\n3.1 Overview\n\nLossy video compression is a constrained optimization problem that can be approached from two\ndifferent angles: 1) either as \ufb01nding the shortest description of a video without exceeding a certain\nlevel of information loss or 2) as \ufb01nding the minimal level of information loss without exceeding\na certain description length. Both optimization problems are equivalent with either a focus on\ndescription length (rate) or information loss (distortion) constraints. The distortion is a measure of\nhow much error encoding and subsequent decoding incurs while the rate quanti\ufb01es the amount of bits\nthe encoded representation occupies. When denoting distortion by D, rate by R, and the maximal\nrate constraint by Rc, the compression problem can be expressed as\n\nminD subject to R \u2264 Rc.\n\nSuch a constrained formulation is often cumbersome but can be solved in a Lagrange multiplier\nformulation, where the rate and distortion terms are weighted against each other by a Lagrange\nmultiplier \u03b2:\n\nminD + \u03b2R.\n\n(1)\n\nIn existing video codecs, encoders and decoders have been meticulously engineered to improve\ncoding ef\ufb01ciency.\nInstead of engineering encoding and decoding functions, in our end-to-end\nmachine learning approach we aim to learn these mappings by parametrizing them by deep neural\nnetworks and then optimizing Eq. 1 accordingly.\nThere is a well-known equivalence (Ball\u00e9 et al., 2018; Alemi et al., 2018) between the evidence lower\nbound in amortized variational inference (Gershman & Goodman, 2014; Zhang et al., 2018), and the\nLagrangian formulation of lossy coding of Eq. 1. Variational inference involves a probabilistic model\np(x, z) = p(x|z)p(z) over data x and latent variables z. The goal is to lower-bound the marginal\nlikelihood p(x) using a variational distribution q(z|x). When the variational distribution q has a\n\ufb01xed entropy (e.g., by \ufb01xing its variance), this bound is, up to a constant,\n(2)\nwhere H is the cross entropy between the approximate posterior and the prior. When allowing\nfor arbitrary \u03b2, Ball\u00e9 et al. (2016) showed in the context of image compression with variational\nautoencoders that the negative of Eq. 2 becomes a manifestation of Eq. 1. While the \ufb01rst term\nmeasures the expected reconstruction error of the encoded images, the cross entropy term becomes\nthe expected code length as the (learned) prior p(z) is used to inform a lossless entropy coder about\nthe probabilities of the discretized encoded images. In this paper we generalize this approach to\nvideos by employing probabilistic deep sequential latent state models.\nFig. 2 summarizes our overall design. Given a sequence of frames x1:T = (x1, . . . , xT ), we\ntransform them into a sequence of latent states z1:T and optionally also a global state f. Although\nthis transformation into a latent representation is lossy, the video is not yet optimally compressed\nas there are still correlations in the latent space variables. To remove this redundancy, the latent\n\nEq[log p(x|z)] \u2212 \u03b2 H[q(z|x), p(z)],\n\n4\n\nx1:TAAAB/XicbVDNS8MwHE39nPOrfty8BIfgabQiKJ6GXjxO2BdspaRpuoWlSUlScZbiv+LFgyJe/T+8+d+Ybj3o5oOQx3u/H3l5QcKo0o7zbS0tr6yurVc2qptb2zu79t5+R4lUYtLGggnZC5AijHLS1lQz0kskQXHASDcY3xR+955IRQVv6UlCvBgNOY0oRtpIvn04CAQL1SQ2V/aQ+5l71cp9u+bUnSngInFLUgMlmr79NQgFTmPCNWZIqb7rJNrLkNQUM5JXB6kiCcJjNCR9QzmKifKyafocnhglhJGQ5nANp+rvjQzFqghoJmOkR2reK8T/vH6qo0svozxJNeF49lCUMqgFLKqAIZUEazYxBGFJTVaIR0girE1hVVOCO//lRdI5q7tO3b07rzWuyzoq4Agcg1PgggvQALegCdoAg0fwDF7Bm/VkvVjv1sdsdMkqdw7AH1ifP/x2lYw=AAAB/XicbVDNS8MwHE39nPOrfty8BIfgabQiKJ6GXjxO2BdspaRpuoWlSUlScZbiv+LFgyJe/T+8+d+Ybj3o5oOQx3u/H3l5QcKo0o7zbS0tr6yurVc2qptb2zu79t5+R4lUYtLGggnZC5AijHLS1lQz0kskQXHASDcY3xR+955IRQVv6UlCvBgNOY0oRtpIvn04CAQL1SQ2V/aQ+5l71cp9u+bUnSngInFLUgMlmr79NQgFTmPCNWZIqb7rJNrLkNQUM5JXB6kiCcJjNCR9QzmKifKyafocnhglhJGQ5nANp+rvjQzFqghoJmOkR2reK8T/vH6qo0svozxJNeF49lCUMqgFLKqAIZUEazYxBGFJTVaIR0girE1hVVOCO//lRdI5q7tO3b07rzWuyzoq4Agcg1PgggvQALegCdoAg0fwDF7Bm/VkvVjv1sdsdMkqdw7AH1ifP/x2lYw=AAAB/XicbVDNS8MwHE39nPOrfty8BIfgabQiKJ6GXjxO2BdspaRpuoWlSUlScZbiv+LFgyJe/T+8+d+Ybj3o5oOQx3u/H3l5QcKo0o7zbS0tr6yurVc2qptb2zu79t5+R4lUYtLGggnZC5AijHLS1lQz0kskQXHASDcY3xR+955IRQVv6UlCvBgNOY0oRtpIvn04CAQL1SQ2V/aQ+5l71cp9u+bUnSngInFLUgMlmr79NQgFTmPCNWZIqb7rJNrLkNQUM5JXB6kiCcJjNCR9QzmKifKyafocnhglhJGQ5nANp+rvjQzFqghoJmOkR2reK8T/vH6qo0svozxJNeF49lCUMqgFLKqAIZUEazYxBGFJTVaIR0girE1hVVOCO//lRdI5q7tO3b07rzWuyzoq4Agcg1PgggvQALegCdoAg0fwDF7Bm/VkvVjv1sdsdMkqdw7AH1ifP/x2lYw=AAAB/XicbVDNS8MwHE39nPOrfty8BIfgabQiKJ6GXjxO2BdspaRpuoWlSUlScZbiv+LFgyJe/T+8+d+Ybj3o5oOQx3u/H3l5QcKo0o7zbS0tr6yurVc2qptb2zu79t5+R4lUYtLGggnZC5AijHLS1lQz0kskQXHASDcY3xR+955IRQVv6UlCvBgNOY0oRtpIvn04CAQL1SQ2V/aQ+5l71cp9u+bUnSngInFLUgMlmr79NQgFTmPCNWZIqb7rJNrLkNQUM5JXB6kiCcJjNCR9QzmKifKyafocnhglhJGQ5nANp+rvjQzFqghoJmOkR2reK8T/vH6qo0svozxJNeF49lCUMqgFLKqAIZUEazYxBGFJTVaIR0girE1hVVOCO//lRdI5q7tO3b07rzWuyzoq4Agcg1PgggvQALegCdoAg0fwDF7Bm/VkvVjv1sdsdMkqdw7AH1ifP/x2lYw=xtAAAB+XicbVDLSgMxFL3js9bXqEs3wSK4KjMi6LLoxmUF+4B2GDKZtA3NJEOSKZahf+LGhSJu/RN3/o2ZdhbaeiDkcM695OREKWfaeN63s7a+sbm1Xdmp7u7tHxy6R8dtLTNFaItILlU3wppyJmjLMMNpN1UUJxGnnWh8V/idCVWaSfFopikNEjwUbMAINlYKXbcfSR7raWKv/GkWmtCteXVvDrRK/JLUoEQzdL/6sSRZQoUhHGvd873UBDlWhhFOZ9V+pmmKyRgPac9SgROqg3yefIbOrRKjgVT2CIPm6u+NHCe6CGcnE2xGetkrxP+8XmYGN0HORJoZKsjioUHGkZGoqAHFTFFi+NQSTBSzWREZYYWJsWVVbQn+8pdXSfuy7nt1/+Gq1rgt66jAKZzBBfhwDQ24hya0gMAEnuEV3pzceXHenY/F6JpT7pzAHzifP2FtlCE=AAAB+XicbVDLSgMxFL3js9bXqEs3wSK4KjMi6LLoxmUF+4B2GDKZtA3NJEOSKZahf+LGhSJu/RN3/o2ZdhbaeiDkcM695OREKWfaeN63s7a+sbm1Xdmp7u7tHxy6R8dtLTNFaItILlU3wppyJmjLMMNpN1UUJxGnnWh8V/idCVWaSfFopikNEjwUbMAINlYKXbcfSR7raWKv/GkWmtCteXVvDrRK/JLUoEQzdL/6sSRZQoUhHGvd873UBDlWhhFOZ9V+pmmKyRgPac9SgROqg3yefIbOrRKjgVT2CIPm6u+NHCe6CGcnE2xGetkrxP+8XmYGN0HORJoZKsjioUHGkZGoqAHFTFFi+NQSTBSzWREZYYWJsWVVbQn+8pdXSfuy7nt1/+Gq1rgt66jAKZzBBfhwDQ24hya0gMAEnuEV3pzceXHenY/F6JpT7pzAHzifP2FtlCE=AAAB+XicbVDLSgMxFL3js9bXqEs3wSK4KjMi6LLoxmUF+4B2GDKZtA3NJEOSKZahf+LGhSJu/RN3/o2ZdhbaeiDkcM695OREKWfaeN63s7a+sbm1Xdmp7u7tHxy6R8dtLTNFaItILlU3wppyJmjLMMNpN1UUJxGnnWh8V/idCVWaSfFopikNEjwUbMAINlYKXbcfSR7raWKv/GkWmtCteXVvDrRK/JLUoEQzdL/6sSRZQoUhHGvd873UBDlWhhFOZ9V+pmmKyRgPac9SgROqg3yefIbOrRKjgVT2CIPm6u+NHCe6CGcnE2xGetkrxP+8XmYGN0HORJoZKsjioUHGkZGoqAHFTFFi+NQSTBSzWREZYYWJsWVVbQn+8pdXSfuy7nt1/+Gq1rgt66jAKZzBBfhwDQ24hya0gMAEnuEV3pzceXHenY/F6JpT7pzAHzifP2FtlCE=AAAB+XicbVDLSgMxFL3js9bXqEs3wSK4KjMi6LLoxmUF+4B2GDKZtA3NJEOSKZahf+LGhSJu/RN3/o2ZdhbaeiDkcM695OREKWfaeN63s7a+sbm1Xdmp7u7tHxy6R8dtLTNFaItILlU3wppyJmjLMMNpN1UUJxGnnWh8V/idCVWaSfFopikNEjwUbMAINlYKXbcfSR7raWKv/GkWmtCteXVvDrRK/JLUoEQzdL/6sSRZQoUhHGvd873UBDlWhhFOZ9V+pmmKyRgPac9SgROqg3yefIbOrRKjgVT2CIPm6u+NHCe6CGcnE2xGetkrxP+8XmYGN0HORJoZKsjioUHGkZGoqAHFTFFi+NQSTBSzWREZYYWJsWVVbQn+8pdXSfuy7nt1/+Gq1rgt66jAKZzBBfhwDQ24hya0gMAEnuEV3pzceXHenY/F6JpT7pzAHzifP2FtlCE=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state neural encoderDecoderArithmetic encoderArithmetic encoderArithmetic decoderArithmetic decoderGlobal state neural encoder\fspace must be entropy coded into binary. This is the distinguishing element between variational\nautoencoders and full compression algorithms. The bit stream can then be sent to a receiver where it\nis decoded into video frames. Our end-to-end machine learning approach simultaneously learns the\npredictive model required for entropy coding and the optimal lossy transformation into the latent\nspace. Both components are described in detail in the next sections, respectively.\n\n3.2 Entropy Coding via a Deep Sequential Model\n\nPredictive modeling is crucial at the entropy coding stage. A better model which more accurately\ncaptures the true certainty about the next symbol has a smaller cross entropy with the data distribution\nand thus produces a bit rate that is closer to the theoretical lower bound for long sequences (Shannon,\n2001). For videos, temporal modeling is most important, making a learned temporal model an integral\npart of our model design. We now discuss a preliminary version of our model which does not yet\ninclude the global state, saving the speci\ufb01c details and encoder of our proposed model for Section 3.3.\n\nGeneral model design. When it comes to designing a generative model, the challenge over image\ncompression is that videos exhibit strong temporal correlations in addition to the spatial correlations\npresent in images. Treating a video segment as an independent data point in the latent representation\n(as would a 3D autoencoder) leads to data sparseness and poor generalization performance. Therefore,\nwe propose to learn a temporally-conditioned prior distribution parametrized by a deep generative\nmodel to ef\ufb01ciently code the latent variables associated with each frame. Let x1:T = (x1,\u00b7\u00b7\u00b7 , xT )\nbe the video sequence and z1:T be the associated latent variables. A generic generative model of this\ntype takes the form:\n\nT(cid:89)\n\nt=1\n\np\u03b8(x1:T , z1:T ) =\n\np\u03b8(zt|z