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Our experiments on three multi-modal structured sequence prediction", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 141, + 315, + 469, + 327 + ], + "spans": [ + { + "bbox": [ + 141, + 315, + 469, + 327 + ], + "score": 1.0, + "content": "datasets – MNIST Sequences, Stanford Drone and HighD – show that the proposed", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 141, + 326, + 421, + 338 + ], + "spans": [ + { + "bbox": [ + 141, + 326, + 421, + 338 + ], + "score": 1.0, + "content": "method obtains state of art results across different evaluation metrics.", + "type": "text" + } + ], + "index": 18 + } + ], + "index": 11.5, + "bbox_fs": [ + 141, + 182, + 470, + 338 + ] + }, + { + "type": "title", + "bbox": [ + 108, + 356, + 206, + 368 + ], + "lines": [ + { + "bbox": [ + 105, + 354, + 208, + 371 + ], + "spans": [ + { + "bbox": [ + 105, + 354, + 208, + 371 + ], + "score": 1.0, + "content": "1 INTRODUCTION", + "type": "text" + } + ], + "index": 19 + } + ], + "index": 19 + }, + { + "type": "text", + "bbox": [ + 107, + 380, + 505, + 522 + ], + "lines": [ + { + "bbox": [ + 106, + 381, + 505, + 392 + ], + "spans": [ + { + "bbox": [ + 106, + 381, + 505, + 392 + ], + "score": 1.0, + "content": "Anticipating future states of the environment is a key competence necessary for the success of", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 106, + 390, + 506, + 403 + ], + "spans": [ + { + "bbox": [ + 106, + 390, + 506, + 403 + ], + "score": 1.0, + "content": "autonomous agents. In complex real world environments, the future is highly uncertain. Therefore,", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 104, + 401, + 507, + 415 + ], + "spans": [ + { + "bbox": [ + 104, + 401, + 507, + 415 + ], + "score": 1.0, + "content": "structured predictions, one to many mappings of the likely future states of the world, are important.", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 105, + 412, + 506, + 425 + ], + "spans": [ + { + "bbox": [ + 105, + 412, + 506, + 425 + ], + "score": 1.0, + "content": "In many scenarios, these tasks can be cast as sequence prediction problems. Particularly, Conditional", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 106, + 423, + 506, + 436 + ], + "spans": [ + { + "bbox": [ + 106, + 423, + 506, + 436 + ], + "score": 1.0, + "content": "Variational Autoencoders (CVAE) (Sohn et al., 2015; Bayer & Osendorfer, 2014; Chung et al., 2015)", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 105, + 433, + 506, + 448 + ], + "spans": [ + { + "bbox": [ + 105, + 433, + 506, + 448 + ], + "score": 1.0, + "content": "have been very successful – from prediction of pedestrians trajectories (Lee et al., 2017; Bhattacharyya", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 105, + 446, + 506, + 459 + ], + "spans": [ + { + "bbox": [ + 105, + 446, + 506, + 459 + ], + "score": 1.0, + "content": "et al., 2018; Pajouheshgar & Lampert, 2018) to outcomes of robotic actions (Babaeizadeh et al.,", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 105, + 455, + 505, + 469 + ], + "spans": [ + { + "bbox": [ + 105, + 455, + 505, + 469 + ], + "score": 1.0, + "content": "2018). The distribution of future sequences is diverse and highly multi-modal. CVAEs model diverse", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 106, + 468, + 505, + 479 + ], + "spans": [ + { + "bbox": [ + 106, + 468, + 505, + 479 + ], + "score": 1.0, + "content": "futures by factorizing the distribution of future states using a set of latent variables which are mapped", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 106, + 478, + 505, + 491 + ], + "spans": [ + { + "bbox": [ + 106, + 478, + 505, + 491 + ], + "score": 1.0, + "content": "to likely future states. However, CVAEs assume a standard Gaussian prior on the latent variables", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 105, + 489, + 505, + 501 + ], + "spans": [ + { + "bbox": [ + 105, + 489, + 505, + 501 + ], + "score": 1.0, + "content": "which induces a strong model bias (Hoffman & Johnson, 2016; Tomczak & Welling, 2018) which", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 106, + 500, + 505, + 513 + ], + "spans": [ + { + "bbox": [ + 106, + 500, + 505, + 513 + ], + "score": 1.0, + "content": "makes it challenging to capture multi-modal distributions. This also leads to missing modes due to", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 105, + 511, + 353, + 524 + ], + "spans": [ + { + "bbox": [ + 105, + 511, + 353, + 524 + ], + "score": 1.0, + "content": "posterior collapse (Bowman et al., 2016; Razavi et al., 2019).", + "type": "text" + } + ], + "index": 32 + } + ], + "index": 26, + "bbox_fs": [ + 104, + 381, + 507, + 524 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 528, + 505, + 605 + ], + "lines": [ + { + "bbox": [ + 105, + 528, + 504, + 541 + ], + "spans": [ + { + "bbox": [ + 105, + 528, + 504, + 541 + ], + "score": 1.0, + "content": "Recent work (Tomczak & Welling, 2018; Wang et al., 2017; Gu et al., 2018) has therefore focused on", + "type": "text" + } + ], + "index": 33 + }, + { + "bbox": [ + 105, + 539, + 505, + 552 + ], + "spans": [ + { + "bbox": [ + 105, + 539, + 505, + 552 + ], + "score": 1.0, + "content": "more complex Gaussian mixture based priors. Gaussian mixtures still have limited expressiveness", + "type": "text" + } + ], + "index": 34 + }, + { + "bbox": [ + 105, + 550, + 506, + 563 + ], + "spans": [ + { + "bbox": [ + 105, + 550, + 506, + 563 + ], + "score": 1.0, + "content": "and optimization suffers from complications e.g. determining the number of mixture components.", + "type": "text" + } + ], + "index": 35 + }, + { + "bbox": [ + 105, + 561, + 506, + 574 + ], + "spans": [ + { + "bbox": [ + 105, + 561, + 506, + 574 + ], + "score": 1.0, + "content": "Normalizing flows are more expressive and enable the modelling of complex multi-modal priors.", + "type": "text" + } + ], + "index": 36 + }, + { + "bbox": [ + 105, + 572, + 505, + 585 + ], + "spans": [ + { + "bbox": [ + 105, + 572, + 505, + 585 + ], + "score": 1.0, + "content": "Recent work on flow based priors (Chen et al., 2017; Ziegler & Rush, 2019), have focused only on the", + "type": "text" + } + ], + "index": 37 + }, + { + "bbox": [ + 105, + 583, + 505, + 595 + ], + "spans": [ + { + "bbox": [ + 105, + 583, + 505, + 595 + ], + "score": 1.0, + "content": "unconditional (plain VAE) case. However, this not sufficient for CVAEs because in the conditional", + "type": "text" + } + ], + "index": 38 + }, + { + "bbox": [ + 105, + 595, + 421, + 606 + ], + "spans": [ + { + "bbox": [ + 105, + 595, + 421, + 606 + ], + "score": 1.0, + "content": "case the complexity of the distributions are highly dependent on the condition.", + "type": "text" + } + ], + "index": 39 + } + ], + "index": 36, + "bbox_fs": [ + 105, + 528, + 506, + 606 + ] + }, + { + "type": "text", + "bbox": [ + 106, + 611, + 506, + 732 + ], + "lines": [ + { + "bbox": [ + 106, + 611, + 506, + 623 + ], + "spans": [ + { + "bbox": [ + 106, + 611, + 506, + 623 + ], + "score": 1.0, + "content": "In this work, 1. We propose Conditional Flow Variational Autoencoders (CF-VAE) based on novel", + "type": "text" + } + ], + "index": 40 + }, + { + "bbox": [ + 105, + 622, + 505, + 634 + ], + "spans": [ + { + "bbox": [ + 105, + 622, + 505, + 634 + ], + "score": 1.0, + "content": "conditional normalizing flow based priors In order to model complex multi-modal conditional", + "type": "text" + } + ], + "index": 41 + }, + { + "bbox": [ + 106, + 633, + 505, + 645 + ], + "spans": [ + { + "bbox": [ + 106, + 633, + 505, + 645 + ], + "score": 1.0, + "content": "distributions over sequences. In Figure 1, we show example predictions of MNIST handwriting stroke", + "type": "text" + } + ], + "index": 42 + }, + { + "bbox": [ + 105, + 643, + 506, + 657 + ], + "spans": [ + { + "bbox": [ + 105, + 643, + 506, + 657 + ], + "score": 1.0, + "content": "of our CF-VAE. We observe that, given a starting stroke, our CF-VAE model with data dependent", + "type": "text" + } + ], + "index": 43 + }, + { + "bbox": [ + 106, + 656, + 506, + 667 + ], + "spans": [ + { + "bbox": [ + 106, + 656, + 506, + 667 + ], + "score": 1.0, + "content": "normalizing flow based latent prior captures the two main modes of the conditional distribution –", + "type": "text" + } + ], + "index": 44 + }, + { + "bbox": [ + 105, + 666, + 506, + 678 + ], + "spans": [ + { + "bbox": [ + 105, + 666, + 506, + 678 + ], + "score": 1.0, + "content": "i.e. 1 and 8 – while CVAEs with fixed uni-modal Gaussian prior predictions have limited diversity.", + "type": "text" + } + ], + "index": 45 + }, + { + "bbox": [ + 105, + 676, + 506, + 690 + ], + "spans": [ + { + "bbox": [ + 105, + 676, + 506, + 690 + ], + "score": 1.0, + "content": "2. We propose a regularization scheme that stabilizes the optimization of the evidence lower bound", + "type": "text" + } + ], + "index": 46 + }, + { + "bbox": [ + 105, + 688, + 506, + 700 + ], + "spans": [ + { + "bbox": [ + 105, + 688, + 506, + 700 + ], + "score": 1.0, + "content": "and leads to better fit to the target data distribution. 3. We leverage our conditional flow prior to deal", + "type": "text" + } + ], + "index": 47 + }, + { + "bbox": [ + 105, + 699, + 506, + 711 + ], + "spans": [ + { + "bbox": [ + 105, + 699, + 506, + 711 + ], + "score": 1.0, + "content": "with posterior collapse which causes standard CVAEs to ignore modes in sequence prediction tasks.", + "type": "text" + } + ], + "index": 48 + }, + { + "bbox": [ + 104, + 709, + 507, + 722 + ], + "spans": [ + { + "bbox": [ + 104, + 709, + 507, + 722 + ], + "score": 1.0, + "content": "4. Finally, our method outperforms the state of the art on three structured sequence prediction tasks –", + "type": "text" + } + ], + "index": 49 + }, + { + "bbox": [ + 105, + 720, + 483, + 733 + ], + "spans": [ + { + "bbox": [ + 105, + 720, + 483, + 733 + ], + "score": 1.0, + "content": "handwriting stroke prediction on MNIST, trajectory prediction on Stanford Drone and HighD.", + "type": "text" + } + ], + "index": 50 + } + ], + "index": 45, + "bbox_fs": [ + 104, + 611, + 507, + 733 + ] + } + ] + }, + { + "preproc_blocks": [ + { + "type": "image", + "bbox": [ + 138, + 79, + 471, + 168 + ], + "blocks": [ + { + "type": "image_body", + "bbox": [ + 138, + 79, + 471, + 168 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 138, + 79, + 471, + 168 + ], + "spans": [ + { + "bbox": [ + 138, + 79, + 471, + 168 + ], + "score": 0.968, + "type": "image", + "image_path": "2dd848aa9b523138419d8ded367d1d10054388c6945d9c0432ce1d1d2c0baa35.jpg" + } + ] + } + ], + "index": 1, + "virtual_lines": [ + { + "bbox": [ + 138, + 79, + 471, + 108.66666666666667 + ], + "spans": [], + "index": 0 + }, + { + "bbox": [ + 138, + 108.66666666666667, + 471, + 138.33333333333334 + ], + "spans": [], + "index": 1 + }, + { + "bbox": [ + 138, + 138.33333333333334, + 471, + 168.0 + ], + "spans": [], + "index": 2 + } + ] + }, + { + "type": "image_caption", + "bbox": [ + 106, + 177, + 506, + 222 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 105, + 177, + 507, + 190 + ], + "spans": [ + { + "bbox": [ + 105, + 177, + 507, + 190 + ], + "score": 1.0, + "content": "Figure 1: Clustered stroke predictions on MNIST sequences. Our multi-modal Conditional Nor-", + "type": "text" + } + ], + "index": 3 + }, + { + "bbox": [ + 105, + 188, + 506, + 200 + ], + "spans": [ + { + "bbox": [ + 105, + 188, + 506, + 200 + ], + "score": 1.0, + "content": "malizing Flow based prior (right) enables our regularized CF-VAE to capture the two modes of the", + "type": "text" + } + ], + "index": 4 + }, + { + "bbox": [ + 105, + 200, + 506, + 211 + ], + "spans": [ + { + "bbox": [ + 105, + 200, + 506, + 211 + ], + "score": 1.0, + "content": "conditional distribution, while predictions with uni-modal Gaussian prior (left) have limited diversity.", + "type": "text" + } + ], + "index": 5 + }, + { + "bbox": [ + 105, + 209, + 505, + 223 + ], + "spans": [ + { + "bbox": [ + 105, + 209, + 505, + 223 + ], + "score": 1.0, + "content": "Note, our 64D CF-VAE latent distribution is (approximately) projected to 2D using tSNE and KDE.", + "type": "text" + } + ], + "index": 6 + } + ], + "index": 4.5 + } + ], + "index": 2.75 + }, + { + "type": "title", + "bbox": [ + 108, + 243, + 210, + 255 + ], + "lines": [ + { + "bbox": [ + 104, + 241, + 213, + 258 + ], + "spans": [ + { + "bbox": [ + 104, + 241, + 213, + 258 + ], + "score": 1.0, + "content": "2 RELATED WORK", + "type": "text" + } + ], + "index": 7 + } + ], + "index": 7 + }, + { + "type": "text", + "bbox": [ + 106, + 269, + 505, + 357 + ], + "lines": [ + { + "bbox": [ + 106, + 270, + 506, + 281 + ], + "spans": [ + { + "bbox": [ + 106, + 270, + 506, + 281 + ], + "score": 1.0, + "content": "Normalizing Flows. Normalizing flows are a powerful class of density estimation methods with exact", + "type": "text" + } + ], + "index": 8 + }, + { + "bbox": [ + 105, + 280, + 505, + 292 + ], + "spans": [ + { + "bbox": [ + 105, + 280, + 505, + 292 + ], + "score": 1.0, + "content": "inference. (Dinh et al., 2015) introduced affine normalizing flows with triangular Jacobians. (Dinh", + "type": "text" + } + ], + "index": 9 + }, + { + "bbox": [ + 105, + 291, + 506, + 304 + ], + "spans": [ + { + "bbox": [ + 105, + 291, + 506, + 304 + ], + "score": 1.0, + "content": "et al., 2017) extend flows with masked convolutions which allow for complex (non-autoregessive)", + "type": "text" + } + ], + "index": 10 + }, + { + "bbox": [ + 106, + 302, + 506, + 315 + ], + "spans": [ + { + "bbox": [ + 106, + 302, + 401, + 315 + ], + "score": 1.0, + "content": "dependence between the dimensions. In (Kingma & Dhariwal, 2018),", + "type": "text" + }, + { + "bbox": [ + 401, + 303, + 426, + 313 + ], + "score": 0.88, + "content": "1 \\times 1", + "type": "inline_equation" + }, + { + "bbox": [ + 426, + 302, + 506, + 315 + ], + "score": 1.0, + "content": "convolutions were", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 105, + 313, + 506, + 326 + ], + "spans": [ + { + "bbox": [ + 105, + 313, + 506, + 326 + ], + "score": 1.0, + "content": "proposed for improved image generation compared to (Dinh et al., 2017). In (Huang et al., 2018)", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 104, + 322, + 507, + 339 + ], + "spans": [ + { + "bbox": [ + 104, + 322, + 507, + 339 + ], + "score": 1.0, + "content": "normalizing flows are auto-regressive and (Behrmann et al., 2019) extend it to ResNet. (Lu & Huang,", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 106, + 335, + 506, + 347 + ], + "spans": [ + { + "bbox": [ + 106, + 335, + 506, + 347 + ], + "score": 1.0, + "content": "2019) extended normalizing flows to model conditional distributions. Here, we propose conditional", + "type": "text" + } + ], + "index": 14 + }, + { + "bbox": [ + 106, + 347, + 405, + 358 + ], + "spans": [ + { + "bbox": [ + 106, + 347, + 405, + 358 + ], + "score": 1.0, + "content": "normalizing flows to learn conditional priors for variational latent models.", + "type": "text" + } + ], + "index": 15 + } + ], + "index": 11.5 + }, + { + "type": "text", + "bbox": [ + 107, + 362, + 505, + 440 + ], + "lines": [ + { + "bbox": [ + 106, + 363, + 505, + 375 + ], + "spans": [ + { + "bbox": [ + 106, + 363, + 505, + 375 + ], + "score": 1.0, + "content": "Variational Autoencoders. The original variational autoencoder (Kingma & Welling, 2014) used", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 105, + 374, + 506, + 386 + ], + "spans": [ + { + "bbox": [ + 105, + 374, + 506, + 386 + ], + "score": 1.0, + "content": "uni-modal Gaussian prior and posterior distributions. Thereafter, two lines of work have focused", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 105, + 385, + 506, + 397 + ], + "spans": [ + { + "bbox": [ + 105, + 385, + 506, + 397 + ], + "score": 1.0, + "content": "on developing either more expressive prior or posterior distributions. Rezende & Mohamed (2015)", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 104, + 396, + 506, + 409 + ], + "spans": [ + { + "bbox": [ + 104, + 396, + 506, + 409 + ], + "score": 1.0, + "content": "propose normalizing flows to model complex posterior distributions. Kingma et al. (2016); Tomczak", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 105, + 407, + 505, + 420 + ], + "spans": [ + { + "bbox": [ + 105, + 407, + 505, + 420 + ], + "score": 1.0, + "content": "& Welling (2016); Berg et al. (2018) present more complex inverse autoregessive flows, householder", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 105, + 417, + 505, + 430 + ], + "spans": [ + { + "bbox": [ + 105, + 417, + 505, + 430 + ], + "score": 1.0, + "content": "and Sylvester normalizing flow based posteriors. Here, we focus on the orthogonal direction of more", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 105, + 429, + 420, + 442 + ], + "spans": [ + { + "bbox": [ + 105, + 429, + 420, + 442 + ], + "score": 1.0, + "content": "expressive priors and the above approaches are compatible with our approach.", + "type": "text" + } + ], + "index": 22 + } + ], + "index": 19 + }, + { + "type": "text", + "bbox": [ + 107, + 445, + 505, + 545 + ], + "lines": [ + { + "bbox": [ + 105, + 446, + 506, + 459 + ], + "spans": [ + { + "bbox": [ + 105, + 446, + 506, + 459 + ], + "score": 1.0, + "content": "Recent work which focus more expressive priors include (Nalisnick & Smyth, 2017) which proposes", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 105, + 456, + 506, + 470 + ], + "spans": [ + { + "bbox": [ + 105, + 456, + 506, + 470 + ], + "score": 1.0, + "content": "a Dirichlet process prior and (Goyal et al., 2017) which proposes a nested Chinese restaurant process", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 105, + 467, + 506, + 480 + ], + "spans": [ + { + "bbox": [ + 105, + 467, + 506, + 480 + ], + "score": 1.0, + "content": "prior. However, these methods require sophisticated learning methods. In contrast, (Tomczak &", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 105, + 478, + 506, + 492 + ], + "spans": [ + { + "bbox": [ + 105, + 478, + 506, + 492 + ], + "score": 1.0, + "content": "Welling, 2018) proposes a mixture of Gaussians based prior (with fixed number of components)", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 105, + 489, + 507, + 504 + ], + "spans": [ + { + "bbox": [ + 105, + 489, + 507, + 504 + ], + "score": 1.0, + "content": "which is easier to train and shows promising results on some image generation tasks. 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While", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 106, + 533, + 496, + 547 + ], + "spans": [ + { + "bbox": [ + 106, + 533, + 496, + 547 + ], + "score": 1.0, + "content": "these works focus on unconditional priors, we aim to develop more expressive conditional priors.", + "type": "text" + } + ], + "index": 31 + } + ], + "index": 27 + }, + { + "type": "text", + "bbox": [ + 106, + 550, + 505, + 671 + ], + "lines": [ + { + "bbox": [ + 105, + 549, + 505, + 563 + ], + "spans": [ + { + "bbox": [ + 105, + 549, + 505, + 563 + ], + "score": 1.0, + "content": "Posterior Collapse. Posterior collapse arises when the latent posterior does not encode useful", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 106, + 561, + 505, + 574 + ], + "spans": [ + { + "bbox": [ + 106, + 561, + 505, + 574 + ], + "score": 1.0, + "content": "information. 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Normalizing flows are a powerful class of density estimation methods with exact", + "type": "text" + } + ], + "index": 8 + }, + { + "bbox": [ + 105, + 280, + 505, + 292 + ], + "spans": [ + { + "bbox": [ + 105, + 280, + 505, + 292 + ], + "score": 1.0, + "content": "inference. (Dinh et al., 2015) introduced affine normalizing flows with triangular Jacobians. (Dinh", + "type": "text" + } + ], + "index": 9 + }, + { + "bbox": [ + 105, + 291, + 506, + 304 + ], + "spans": [ + { + "bbox": [ + 105, + 291, + 506, + 304 + ], + "score": 1.0, + "content": "et al., 2017) extend flows with masked convolutions which allow for complex (non-autoregessive)", + "type": "text" + } + ], + "index": 10 + }, + { + "bbox": [ + 106, + 302, + 506, + 315 + ], + "spans": [ + { + "bbox": [ + 106, + 302, + 401, + 315 + ], + "score": 1.0, + "content": "dependence between the dimensions. In (Kingma & Dhariwal, 2018),", + "type": "text" + }, + { + "bbox": [ + 401, + 303, + 426, + 313 + ], + "score": 0.88, + "content": "1 \\times 1", + "type": "inline_equation" + }, + { + "bbox": [ + 426, + 302, + 506, + 315 + ], + "score": 1.0, + "content": "convolutions were", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 105, + 313, + 506, + 326 + ], + "spans": [ + { + "bbox": [ + 105, + 313, + 506, + 326 + ], + "score": 1.0, + "content": "proposed for improved image generation compared to (Dinh et al., 2017). In (Huang et al., 2018)", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 104, + 322, + 507, + 339 + ], + "spans": [ + { + "bbox": [ + 104, + 322, + 507, + 339 + ], + "score": 1.0, + "content": "normalizing flows are auto-regressive and (Behrmann et al., 2019) extend it to ResNet. (Lu & Huang,", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 106, + 335, + 506, + 347 + ], + "spans": [ + { + "bbox": [ + 106, + 335, + 506, + 347 + ], + "score": 1.0, + "content": "2019) extended normalizing flows to model conditional distributions. Here, we propose conditional", + "type": "text" + } + ], + "index": 14 + }, + { + "bbox": [ + 106, + 347, + 405, + 358 + ], + "spans": [ + { + "bbox": [ + 106, + 347, + 405, + 358 + ], + "score": 1.0, + "content": "normalizing flows to learn conditional priors for variational latent models.", + "type": "text" + } + ], + "index": 15 + } + ], + "index": 11.5, + "bbox_fs": [ + 104, + 270, + 507, + 358 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 362, + 505, + 440 + ], + "lines": [ + { + "bbox": [ + 106, + 363, + 505, + 375 + ], + "spans": [ + { + "bbox": [ + 106, + 363, + 505, + 375 + ], + "score": 1.0, + "content": "Variational Autoencoders. The original variational autoencoder (Kingma & Welling, 2014) used", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 105, + 374, + 506, + 386 + ], + "spans": [ + { + "bbox": [ + 105, + 374, + 506, + 386 + ], + "score": 1.0, + "content": "uni-modal Gaussian prior and posterior distributions. Thereafter, two lines of work have focused", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 105, + 385, + 506, + 397 + ], + "spans": [ + { + "bbox": [ + 105, + 385, + 506, + 397 + ], + "score": 1.0, + "content": "on developing either more expressive prior or posterior distributions. Rezende & Mohamed (2015)", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 104, + 396, + 506, + 409 + ], + "spans": [ + { + "bbox": [ + 104, + 396, + 506, + 409 + ], + "score": 1.0, + "content": "propose normalizing flows to model complex posterior distributions. Kingma et al. (2016); Tomczak", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 105, + 407, + 505, + 420 + ], + "spans": [ + { + "bbox": [ + 105, + 407, + 505, + 420 + ], + "score": 1.0, + "content": "& Welling (2016); Berg et al. (2018) present more complex inverse autoregessive flows, householder", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 105, + 417, + 505, + 430 + ], + "spans": [ + { + "bbox": [ + 105, + 417, + 505, + 430 + ], + "score": 1.0, + "content": "and Sylvester normalizing flow based posteriors. Here, we focus on the orthogonal direction of more", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 105, + 429, + 420, + 442 + ], + "spans": [ + { + "bbox": [ + 105, + 429, + 420, + 442 + ], + "score": 1.0, + "content": "expressive priors and the above approaches are compatible with our approach.", + "type": "text" + } + ], + "index": 22 + } + ], + "index": 19, + "bbox_fs": [ + 104, + 363, + 506, + 442 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 445, + 505, + 545 + ], + "lines": [ + { + "bbox": [ + 105, + 446, + 506, + 459 + ], + "spans": [ + { + "bbox": [ + 105, + 446, + 506, + 459 + ], + "score": 1.0, + "content": "Recent work which focus more expressive priors include (Nalisnick & Smyth, 2017) which proposes", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 105, + 456, + 506, + 470 + ], + "spans": [ + { + "bbox": [ + 105, + 456, + 506, + 470 + ], + "score": 1.0, + "content": "a Dirichlet process prior and (Goyal et al., 2017) which proposes a nested Chinese restaurant process", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 105, + 467, + 506, + 480 + ], + "spans": [ + { + "bbox": [ + 105, + 467, + 506, + 480 + ], + "score": 1.0, + "content": "prior. However, these methods require sophisticated learning methods. In contrast, (Tomczak &", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 105, + 478, + 506, + 492 + ], + "spans": [ + { + "bbox": [ + 105, + 478, + 506, + 492 + ], + "score": 1.0, + "content": "Welling, 2018) proposes a mixture of Gaussians based prior (with fixed number of components)", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 105, + 489, + 507, + 504 + ], + "spans": [ + { + "bbox": [ + 105, + 489, + 507, + 504 + ], + "score": 1.0, + "content": "which is easier to train and shows promising results on some image generation tasks. 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While", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 106, + 533, + 496, + 547 + ], + "spans": [ + { + "bbox": [ + 106, + 533, + 496, + 547 + ], + "score": 1.0, + "content": "these works focus on unconditional priors, we aim to develop more expressive conditional priors.", + "type": "text" + } + ], + "index": 31 + } + ], + "index": 27, + "bbox_fs": [ + 105, + 446, + 507, + 547 + ] + }, + { + "type": "text", + "bbox": [ + 106, + 550, + 505, + 671 + ], + "lines": [ + { + "bbox": [ + 105, + 549, + 505, + 563 + ], + "spans": [ + { + "bbox": [ + 105, + 549, + 505, + 563 + ], + "score": 1.0, + "content": "Posterior Collapse. Posterior collapse arises when the latent posterior does not encode useful", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 106, + 561, + 505, + 574 + ], + "spans": [ + { + "bbox": [ + 106, + 561, + 505, + 574 + ], + "score": 1.0, + "content": "information. 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(2018); Deo", + "type": "text" + } + ], + "index": 0 + }, + { + "bbox": [ + 105, + 93, + 505, + 106 + ], + "spans": [ + { + "bbox": [ + 105, + 93, + 505, + 106 + ], + "score": 1.0, + "content": "& Trivedi (2019); Pajouheshgar & Lampert (2018) considers structured (one to many) predictions", + "type": "text" + } + ], + "index": 1 + }, + { + "bbox": [ + 105, + 104, + 506, + 118 + ], + "spans": [ + { + "bbox": [ + 105, + 104, + 506, + 118 + ], + "score": 1.0, + "content": "using – a CVAE, improved CVAE training, pushforward policies for vehicle ego-motion prediction,", + "type": "text" + } + ], + "index": 2 + }, + { + "bbox": [ + 105, + 115, + 506, + 129 + ], + "spans": [ + { + "bbox": [ + 105, + 115, + 506, + 129 + ], + "score": 1.0, + "content": "motion planning, spatio-temporal convolutional network respectively. Kumar et al. (2019) proposes a", + "type": "text" + } + ], + "index": 3 + }, + { + "bbox": [ + 105, + 126, + 506, + 140 + ], + "spans": [ + { + "bbox": [ + 105, + 126, + 506, + 140 + ], + "score": 1.0, + "content": "normalizing flow based model for video sequence prediction, however the sequences considered have", + "type": "text" + } + ], + "index": 4 + }, + { + "bbox": [ + 106, + 137, + 506, + 150 + ], + "spans": [ + { + "bbox": [ + 106, + 137, + 506, + 150 + ], + "score": 1.0, + "content": "very limited diversity compared to the trajectory prediction tasks considered here. Here, we focus on", + "type": "text" + } + ], + "index": 5 + }, + { + "bbox": [ + 106, + 149, + 439, + 161 + ], + "spans": [ + { + "bbox": [ + 106, + 149, + 439, + 161 + ], + "score": 1.0, + "content": "improving structured predictions using conditional normalizing flows based priors.", + "type": "text" + } + ], + "index": 6 + } + ], + "index": 3 + }, + { + "type": "title", + "bbox": [ + 107, + 175, + 447, + 189 + ], + "lines": [ + { + "bbox": [ + 104, + 173, + 448, + 191 + ], + "spans": [ + { + "bbox": [ + 104, + 173, + 448, + 191 + ], + "score": 1.0, + "content": "3 CONDITIONAL FLOW VARIATIONAL AUTOENCODER (CF-VAE)", + "type": "text" + } + ], + "index": 7 + } + ], + "index": 7 + }, + { + "type": "text", + "bbox": [ + 106, + 199, + 505, + 281 + ], + "lines": [ + { + "bbox": [ + 106, + 200, + 505, + 212 + ], + "spans": [ + { + "bbox": [ + 106, + 200, + 505, + 212 + ], + "score": 1.0, + "content": "Our Conditional Flow Variational Autoencoder is based on the conditional variational autoencoder", + "type": "text" + } + ], + "index": 8 + }, + { + "bbox": [ + 106, + 212, + 505, + 223 + ], + "spans": [ + { + "bbox": [ + 106, + 212, + 505, + 223 + ], + "score": 1.0, + "content": "(Sohn et al., 2015) which is a deep directed graphical model for modeling conditional data distributions", + "type": "text" + } + ], + "index": 9 + }, + { + "bbox": [ + 107, + 222, + 506, + 236 + ], + "spans": [ + { + "bbox": [ + 107, + 223, + 137, + 234 + ], + "score": 0.9, + "content": "p _ { \\theta } ( \\mathbf { y } | \\mathbf { x } )", + "type": "inline_equation" + }, + { + "bbox": [ + 138, + 222, + 166, + 235 + ], + "score": 1.0, + "content": ". Here,", + "type": "text" + }, + { + "bbox": [ + 166, + 224, + 172, + 232 + ], + "score": 0.71, + "content": "\\mathbf { X }", + "type": "inline_equation" + }, + { + "bbox": [ + 173, + 222, + 277, + 235 + ], + "score": 1.0, + "content": "is the sequence up to time", + "type": "text" + }, + { + "bbox": [ + 278, + 225, + 282, + 232 + ], + "score": 0.7, + "content": "t", + "type": "inline_equation" + }, + { + "bbox": [ + 282, + 222, + 286, + 235 + ], + "score": 1.0, + "content": ",", + "type": "text" + }, + { + "bbox": [ + 286, + 223, + 357, + 236 + ], + "score": 0.92, + "content": "\\boldsymbol { x } = \\left[ x ^ { 1 } , \\cdots , x ^ { t } \\right]", + "type": "inline_equation" + }, + { + "bbox": [ + 357, + 222, + 375, + 235 + ], + "score": 1.0, + "content": "and", + "type": "text" + }, + { + "bbox": [ + 375, + 223, + 382, + 234 + ], + "score": 0.29, + "content": "_ \\textrm { y }", + "type": "inline_equation" + }, + { + "bbox": [ + 382, + 222, + 506, + 235 + ], + "score": 1.0, + "content": "is the sequence to be predicted", + "type": "text" + } + ], + "index": 10 + }, + { + "bbox": [ + 105, + 233, + 506, + 248 + ], + "spans": [ + { + "bbox": [ + 105, + 233, + 147, + 248 + ], + "score": 1.0, + "content": "up to time", + "type": "text" + }, + { + "bbox": [ + 148, + 236, + 156, + 245 + ], + "score": 0.62, + "content": "T", + "type": "inline_equation" + }, + { + "bbox": [ + 156, + 233, + 160, + 248 + ], + "score": 1.0, + "content": ",", + "type": "text" + }, + { + "bbox": [ + 160, + 234, + 241, + 248 + ], + "score": 0.88, + "content": "y = \\left[ y ^ { t + 1 } , \\cdot \\cdot \\cdot , y ^ { T } \\right]", + "type": "inline_equation" + }, + { + "bbox": [ + 241, + 233, + 506, + 248 + ], + "score": 1.0, + "content": ". CVAEs factorize the conditional distribution using latent variables", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 105, + 246, + 506, + 261 + ], + "spans": [ + { + "bbox": [ + 105, + 246, + 154, + 261 + ], + "score": 1.0, + "content": "z. In detail,", + "type": "text" + }, + { + "bbox": [ + 154, + 248, + 280, + 261 + ], + "score": 0.89, + "content": "\\begin{array} { r } { p _ { \\theta } ( \\mathbf { y } \\vert \\mathbf { x } ) = \\int p _ { \\theta } ( \\mathbf { y } \\vert \\mathbf { z } , \\mathbf { x } ) p ( \\mathbf { z } \\vert \\mathbf { x } ) d \\mathbf { z } } \\end{array}", + "type": "inline_equation" + }, + { + "bbox": [ + 281, + 246, + 310, + 261 + ], + "score": 1.0, + "content": ", where", + "type": "text" + }, + { + "bbox": [ + 311, + 248, + 336, + 260 + ], + "score": 0.92, + "content": "p ( \\mathbf { z } | \\mathbf { x } )", + "type": "inline_equation" + }, + { + "bbox": [ + 336, + 246, + 506, + 261 + ], + "score": 1.0, + "content": "is the prior on the latent variables. During", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 106, + 258, + 506, + 271 + ], + "spans": [ + { + "bbox": [ + 106, + 258, + 428, + 271 + ], + "score": 1.0, + "content": "training, amortized variational inference is used and the posterior distribution", + "type": "text" + }, + { + "bbox": [ + 428, + 258, + 468, + 271 + ], + "score": 0.93, + "content": "q _ { \\phi } ( \\mathbf { z } | \\mathbf { x } , \\mathbf { y } )", + "type": "inline_equation" + }, + { + "bbox": [ + 468, + 258, + 506, + 271 + ], + "score": 1.0, + "content": "is learnt", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 105, + 269, + 367, + 283 + ], + "spans": [ + { + "bbox": [ + 105, + 269, + 367, + 283 + ], + "score": 1.0, + "content": "using a recognition network. The ELBO is maximized, given by,", + "type": "text" + } + ], + "index": 14 + } + ], + "index": 11 + }, + { + "type": "interline_equation", + "bbox": [ + 168, + 285, + 442, + 300 + ], + "lines": [ + { + "bbox": [ + 168, + 285, + 442, + 300 + ], + "spans": [ + { + "bbox": [ + 168, + 285, + 442, + 300 + ], + "score": 0.89, + "content": "\\begin{array} { r } { \\log ( p _ { \\theta } ( \\mathbf { y } \\vert \\mathbf { x } ) ) \\geq \\mathbb { E } _ { q _ { \\phi } ( \\mathbf { z } \\vert \\mathbf { x } , \\mathbf { y } ) } \\log ( p _ { \\theta } ( \\mathbf { y } \\vert \\mathbf { z } , \\mathbf { x } ) ) - D _ { \\mathrm { K L } } ( q _ { \\phi } ( \\mathbf { z } \\vert \\mathbf { x } , \\mathbf { y } ) \\vert \\vert p ( \\mathbf { z } \\vert \\mathbf { x } ) ) . } \\end{array}", + "type": "interline_equation", + "image_path": "44800c1abef6a668cfb40295e7af53a020e4a7120101a54da6ba95142366fff6.jpg" + } + ] + } + ], + "index": 15, + "virtual_lines": [ + { + "bbox": [ + 168, + 285, + 442, + 300 + ], + "spans": [], + "index": 15 + } + ] + }, + { + "type": "text", + "bbox": [ + 107, + 302, + 505, + 369 + ], + "lines": [ + { + "bbox": [ + 106, + 303, + 506, + 314 + ], + "spans": [ + { + "bbox": [ + 106, + 303, + 506, + 314 + ], + "score": 1.0, + "content": "In practice, to simplify learning, simple unconditional standard Gaussian priors are used (Sohn et al.,", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 105, + 313, + 506, + 327 + ], + "spans": [ + { + "bbox": [ + 105, + 313, + 460, + 327 + ], + "score": 1.0, + "content": "2015). However, the complexity e.g. the number of modes of the target distributions", + "type": "text" + }, + { + "bbox": [ + 460, + 314, + 491, + 325 + ], + "score": 0.91, + "content": "p _ { \\theta } ( \\mathbf { y } | \\mathbf { x } )", + "type": "inline_equation" + }, + { + "bbox": [ + 491, + 313, + 506, + 327 + ], + "score": 1.0, + "content": ", is", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 105, + 323, + 505, + 338 + ], + "spans": [ + { + "bbox": [ + 105, + 323, + 252, + 338 + ], + "score": 1.0, + "content": "highly dependent upon the condition", + "type": "text" + }, + { + "bbox": [ + 253, + 327, + 259, + 334 + ], + "score": 0.7, + "content": "x", + "type": "inline_equation" + }, + { + "bbox": [ + 260, + 323, + 505, + 338 + ], + "score": 1.0, + "content": ". An unconditional prior demands identical latent distributions", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 105, + 335, + 505, + 348 + ], + "spans": [ + { + "bbox": [ + 105, + 335, + 505, + 348 + ], + "score": 1.0, + "content": "irrespective complexity of the target conditional distribution – a very strong constraint on the", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 105, + 347, + 506, + 359 + ], + "spans": [ + { + "bbox": [ + 105, + 347, + 506, + 359 + ], + "score": 1.0, + "content": "recognition network. Moreover, the latent variables cannot encode any conditioning information and", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 105, + 357, + 482, + 370 + ], + "spans": [ + { + "bbox": [ + 105, + 357, + 482, + 370 + ], + "score": 1.0, + "content": "this leaves the burden of learning the dependence on the condition completely on the decoder.", + "type": "text" + } + ], + "index": 21 + } + ], + "index": 18.5 + }, + { + "type": "text", + "bbox": [ + 106, + 373, + 505, + 462 + ], + "lines": [ + { + "bbox": [ + 106, + 374, + 505, + 387 + ], + "spans": [ + { + "bbox": [ + 106, + 374, + 505, + 387 + ], + "score": 1.0, + "content": "Furthermore, on complex conditional multi-modal data, Gaussian priors have been shown to induce", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 105, + 385, + 505, + 398 + ], + "spans": [ + { + "bbox": [ + 105, + 385, + 505, + 398 + ], + "score": 1.0, + "content": "a strong model bias (Tomczak & Welling, 2016; Ziegler & Rush, 2019). It becomes increasingly", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 105, + 396, + 506, + 408 + ], + "spans": [ + { + "bbox": [ + 105, + 396, + 506, + 408 + ], + "score": 1.0, + "content": "difficult to map complex multi-modal distributions to uni-modal Gaussian distributions, further", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 106, + 407, + 506, + 420 + ], + "spans": [ + { + "bbox": [ + 106, + 407, + 506, + 420 + ], + "score": 1.0, + "content": "complicated by the sensitivity of the RNNs encoder/decoders to subtle variations in the hidden states", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 105, + 418, + 505, + 430 + ], + "spans": [ + { + "bbox": [ + 105, + 418, + 505, + 430 + ], + "score": 1.0, + "content": "(Bowman et al., 2016). Moreover, the standard closed form estimate of the KL-divergence pushes the", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 104, + 428, + 505, + 443 + ], + "spans": [ + { + "bbox": [ + 104, + 428, + 505, + 443 + ], + "score": 1.0, + "content": "encoded latent distributions to the mean of the Gaussian leading to latent variable collapse (Wang", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 105, + 439, + 506, + 453 + ], + "spans": [ + { + "bbox": [ + 105, + 439, + 506, + 453 + ], + "score": 1.0, + "content": "et al., 2017; Gu et al., 2018) while discriminator based approaches (Tolstikhin et al., 2017) lead to", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 105, + 451, + 340, + 464 + ], + "spans": [ + { + "bbox": [ + 105, + 451, + 340, + 464 + ], + "score": 1.0, + "content": "underestimates of the KL-divergence (Rosca et al., 2017).", + "type": "text" + } + ], + "index": 29 + } + ], + "index": 25.5 + }, + { + "type": "text", + "bbox": [ + 107, + 468, + 505, + 512 + ], + "lines": [ + { + "bbox": [ + 105, + 468, + 506, + 480 + ], + "spans": [ + { + "bbox": [ + 105, + 468, + 506, + 480 + ], + "score": 1.0, + "content": "Therefore, we propose conditional priors based on conditional normalizing flows to enable the latent", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 105, + 478, + 507, + 492 + ], + "spans": [ + { + "bbox": [ + 105, + 478, + 507, + 492 + ], + "score": 1.0, + "content": "variables to encode conditional information and allow for complex multi-modal latent representations.", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 105, + 489, + 506, + 503 + ], + "spans": [ + { + "bbox": [ + 105, + 489, + 506, + 503 + ], + "score": 1.0, + "content": "Next, we introduce our new conditional non-linear normalizing flows followed by our regularized", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 106, + 500, + 374, + 513 + ], + "spans": [ + { + "bbox": [ + 106, + 500, + 374, + 513 + ], + "score": 1.0, + "content": "Conditional Flow Variational Autoencoder (CF-VAE) formulation.", + "type": "text" + } + ], + "index": 33 + } + ], + "index": 31.5 + }, + { + "type": "title", + "bbox": [ + 109, + 525, + 292, + 537 + ], + "lines": [ + { + "bbox": [ + 106, + 525, + 293, + 538 + ], + "spans": [ + { + "bbox": [ + 106, + 525, + 293, + 538 + ], + "score": 1.0, + "content": "3.1 CONDITIONAL NORMALIZING FLOWS", + "type": "text" + } + ], + "index": 34 + } + ], + "index": 34 + }, + { + "type": "text", + "bbox": [ + 107, + 545, + 505, + 590 + ], + "lines": [ + { + "bbox": [ + 106, + 546, + 505, + 558 + ], + "spans": [ + { + "bbox": [ + 106, + 546, + 505, + 558 + ], + "score": 1.0, + "content": "Recently, normalizing flow (Tabak et al., 2010; Dinh et al., 2015) based priors for VAEs have been", + "type": "text" + } + ], + "index": 35 + }, + { + "bbox": [ + 105, + 557, + 505, + 569 + ], + "spans": [ + { + "bbox": [ + 105, + 557, + 505, + 569 + ], + "score": 1.0, + "content": "proposed (Chen et al., 2017; Ziegler & Rush, 2019). 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During", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 106, + 258, + 506, + 271 + ], + "spans": [ + { + "bbox": [ + 106, + 258, + 428, + 271 + ], + "score": 1.0, + "content": "training, amortized variational inference is used and the posterior distribution", + "type": "text" + }, + { + "bbox": [ + 428, + 258, + 468, + 271 + ], + "score": 0.93, + "content": "q _ { \\phi } ( \\mathbf { z } | \\mathbf { x } , \\mathbf { y } )", + "type": "inline_equation" + }, + { + "bbox": [ + 468, + 258, + 506, + 271 + ], + "score": 1.0, + "content": "is learnt", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 105, + 269, + 367, + 283 + ], + "spans": [ + { + "bbox": [ + 105, + 269, + 367, + 283 + ], + "score": 1.0, + "content": "using a recognition network. 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An unconditional prior demands identical latent distributions", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 105, + 335, + 505, + 348 + ], + "spans": [ + { + "bbox": [ + 105, + 335, + 505, + 348 + ], + "score": 1.0, + "content": "irrespective complexity of the target conditional distribution – a very strong constraint on the", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 105, + 347, + 506, + 359 + ], + "spans": [ + { + "bbox": [ + 105, + 347, + 506, + 359 + ], + "score": 1.0, + "content": "recognition network. Moreover, the latent variables cannot encode any conditioning information and", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 105, + 357, + 482, + 370 + ], + "spans": [ + { + "bbox": [ + 105, + 357, + 482, + 370 + ], + "score": 1.0, + "content": "this leaves the burden of learning the dependence on the condition completely on the decoder.", + "type": "text" + } + ], + "index": 21 + } + ], + "index": 18.5, + "bbox_fs": [ + 105, + 303, + 506, + 370 + ] + }, + { + "type": "text", + "bbox": [ + 106, + 373, + 505, + 462 + ], + "lines": [ + { + "bbox": [ + 106, + 374, + 505, + 387 + ], + "spans": [ + { + "bbox": [ + 106, + 374, + 505, + 387 + ], + "score": 1.0, + "content": "Furthermore, on complex conditional multi-modal data, Gaussian priors have been shown to induce", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 105, + 385, + 505, + 398 + ], + "spans": [ + { + "bbox": [ + 105, + 385, + 505, + 398 + ], + "score": 1.0, + "content": "a strong model bias (Tomczak & Welling, 2016; Ziegler & Rush, 2019). It becomes increasingly", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 105, + 396, + 506, + 408 + ], + "spans": [ + { + "bbox": [ + 105, + 396, + 506, + 408 + ], + "score": 1.0, + "content": "difficult to map complex multi-modal distributions to uni-modal Gaussian distributions, further", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 106, + 407, + 506, + 420 + ], + "spans": [ + { + "bbox": [ + 106, + 407, + 506, + 420 + ], + "score": 1.0, + "content": "complicated by the sensitivity of the RNNs encoder/decoders to subtle variations in the hidden states", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 105, + 418, + 505, + 430 + ], + "spans": [ + { + "bbox": [ + 105, + 418, + 505, + 430 + ], + "score": 1.0, + "content": "(Bowman et al., 2016). Moreover, the standard closed form estimate of the KL-divergence pushes the", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 104, + 428, + 505, + 443 + ], + "spans": [ + { + "bbox": [ + 104, + 428, + 505, + 443 + ], + "score": 1.0, + "content": "encoded latent distributions to the mean of the Gaussian leading to latent variable collapse (Wang", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 105, + 439, + 506, + 453 + ], + "spans": [ + { + "bbox": [ + 105, + 439, + 506, + 453 + ], + "score": 1.0, + "content": "et al., 2017; Gu et al., 2018) while discriminator based approaches (Tolstikhin et al., 2017) lead to", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 105, + 451, + 340, + 464 + ], + "spans": [ + { + "bbox": [ + 105, + 451, + 340, + 464 + ], + "score": 1.0, + "content": "underestimates of the KL-divergence (Rosca et al., 2017).", + "type": "text" + } + ], + "index": 29 + } + ], + "index": 25.5, + "bbox_fs": [ + 104, + 374, + 506, + 464 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 468, + 505, + 512 + ], + "lines": [ + { + "bbox": [ + 105, + 468, + 506, + 480 + ], + "spans": [ + { + "bbox": [ + 105, + 468, + 506, + 480 + ], + "score": 1.0, + "content": "Therefore, we propose conditional priors based on conditional normalizing flows to enable the latent", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 105, + 478, + 507, + 492 + ], + "spans": [ + { + "bbox": [ + 105, + 478, + 507, + 492 + ], + "score": 1.0, + "content": "variables to encode conditional information and allow for complex multi-modal latent representations.", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 105, + 489, + 506, + 503 + ], + "spans": [ + { + "bbox": [ + 105, + 489, + 506, + 503 + ], + "score": 1.0, + "content": "Next, we introduce our new conditional non-linear normalizing flows followed by our regularized", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 106, + 500, + 374, + 513 + ], + "spans": [ + { + "bbox": [ + 106, + 500, + 374, + 513 + ], + "score": 1.0, + "content": "Conditional Flow Variational Autoencoder (CF-VAE) formulation.", + "type": "text" + } + ], + "index": 33 + } + ], + "index": 31.5, + "bbox_fs": [ + 105, + 468, + 507, + 513 + ] + }, + { + "type": "title", + "bbox": [ + 109, + 525, + 292, + 537 + ], + "lines": [ + { + "bbox": [ + 106, + 525, + 293, + 538 + ], + "spans": [ + { + "bbox": [ + 106, + 525, + 293, + 538 + ], + "score": 1.0, + "content": "3.1 CONDITIONAL NORMALIZING FLOWS", + "type": "text" + } + ], + "index": 34 + } + ], + "index": 34 + }, + { + "type": "text", + "bbox": [ + 107, + 545, + 505, + 590 + ], + "lines": [ + { + "bbox": [ + 106, + 546, + 505, + 558 + ], + "spans": [ + { + "bbox": [ + 106, + 546, + 505, + 558 + ], + "score": 1.0, + "content": "Recently, normalizing flow (Tabak et al., 2010; Dinh et al., 2015) based priors for VAEs have been", + "type": "text" + } + ], + "index": 35 + }, + { + "bbox": [ + 105, + 557, + 505, + 569 + ], + "spans": [ + { + "bbox": [ + 105, + 557, + 505, + 569 + ], + "score": 1.0, + "content": "proposed (Chen et al., 2017; Ziegler & Rush, 2019). Normalizing flows allows for complex priors by", + "type": "text" + } + ], + "index": 36 + }, + { + "bbox": [ + 105, + 568, + 505, + 580 + ], + "spans": [ + { + "bbox": [ + 105, + 568, + 505, + 580 + ], + "score": 1.0, + "content": "transforming a simple base density e.g. standard Gaussian to a complex multi-modal density through", + "type": "text" + } + ], + "index": 37 + }, + { + "bbox": [ + 105, + 579, + 314, + 592 + ], + "spans": [ + { + "bbox": [ + 105, + 579, + 149, + 592 + ], + "score": 1.0, + "content": "a series of", + "type": "text" + }, + { + "bbox": [ + 150, + 581, + 156, + 589 + ], + "score": 0.75, + "content": "n", + "type": "inline_equation" + }, + { + "bbox": [ + 157, + 579, + 300, + 592 + ], + "score": 1.0, + "content": "layers of invertible transformations", + "type": "text" + }, + { + "bbox": [ + 300, + 579, + 309, + 591 + ], + "score": 0.87, + "content": "f _ { i }", + "type": "inline_equation" + }, + { + "bbox": [ + 309, + 579, + 314, + 592 + ], + "score": 1.0, + "content": ",", + "type": "text" + } + ], + "index": 38 + } + ], + "index": 36.5, + "bbox_fs": [ + 105, + 546, + 505, + 592 + ] + }, + { + "type": "interline_equation", + "bbox": [ + 246, + 595, + 364, + 611 + ], + "lines": [ + { + "bbox": [ + 246, + 595, + 364, + 611 + ], + "spans": [ + { + "bbox": [ + 246, + 595, + 364, + 611 + ], + "score": 0.92, + "content": "\\epsilon \\longleftrightarrow { \\mathrm { h _ { 1 } } } \\longleftrightarrow { \\mathrm { h _ { 2 } } } \\to { \\mathrm { h _ { 2 } } } \\cdots \\langle ^ { f _ { n } } \\rangle { \\mathrm { z } } .", + "type": "interline_equation", + "image_path": "98b531b76ee0d49fa16e3f63535cfc22dbf3f519eb789eb612f4293862933e15.jpg" + } + ] + } + ], + "index": 39, + "virtual_lines": [ + { + "bbox": [ + 246, + 595, + 364, + 611 + ], + "spans": [], + "index": 39 + } + ] + }, + { + "type": "text", + "bbox": [ + 107, + 621, + 505, + 666 + ], + "lines": [ + { + "bbox": [ + 106, + 622, + 505, + 633 + ], + "spans": [ + { + "bbox": [ + 106, + 622, + 505, + 633 + ], + "score": 1.0, + "content": "However, such flows cannot model conditional priors. In contrast to prior work, we utilize conditional", + "type": "text" + } + ], + "index": 40 + }, + { + "bbox": [ + 105, + 633, + 505, + 645 + ], + "spans": [ + { + "bbox": [ + 105, + 633, + 505, + 645 + ], + "score": 1.0, + "content": "normalizing flows to model complex conditional priors. Conditional normalizing flows also consists", + "type": "text" + } + ], + "index": 41 + }, + { + "bbox": [ + 105, + 644, + 505, + 657 + ], + "spans": [ + { + "bbox": [ + 105, + 644, + 160, + 657 + ], + "score": 1.0, + "content": "of a series of", + "type": "text" + }, + { + "bbox": [ + 161, + 646, + 168, + 654 + ], + "score": 0.77, + "content": "n", + "type": "inline_equation" + }, + { + "bbox": [ + 168, + 644, + 312, + 657 + ], + "score": 1.0, + "content": "layers of invertible transformations", + "type": "text" + }, + { + "bbox": [ + 312, + 644, + 321, + 655 + ], + "score": 0.88, + "content": "f _ { i }", + "type": "inline_equation" + }, + { + "bbox": [ + 322, + 644, + 393, + 657 + ], + "score": 1.0, + "content": "(with parameters", + "type": "text" + }, + { + "bbox": [ + 393, + 644, + 401, + 655 + ], + "score": 0.79, + "content": "\\psi", + "type": "inline_equation" + }, + { + "bbox": [ + 402, + 644, + 505, + 657 + ], + "score": 1.0, + "content": "), however we modify the", + "type": "text" + } + ], + "index": 42 + }, + { + "bbox": [ + 105, + 655, + 376, + 667 + ], + "spans": [ + { + "bbox": [ + 105, + 655, + 171, + 667 + ], + "score": 1.0, + "content": "transformations", + "type": "text" + }, + { + "bbox": [ + 172, + 655, + 181, + 667 + ], + "score": 0.88, + "content": "f _ { i }", + "type": "inline_equation" + }, + { + "bbox": [ + 181, + 655, + 365, + 667 + ], + "score": 1.0, + "content": "such that they are dependent on the condition", + "type": "text" + }, + { + "bbox": [ + 365, + 657, + 371, + 665 + ], + "score": 0.68, + "content": "\\mathbf { X }", + "type": "inline_equation" + }, + { + "bbox": [ + 372, + 655, + 376, + 667 + ], + "score": 1.0, + "content": ",", + "type": "text" + } + ], + "index": 43 + } + ], + "index": 41.5, + "bbox_fs": [ + 105, + 622, + 505, + 667 + ] + }, + { + "type": "interline_equation", + "bbox": [ + 231, + 671, + 379, + 689 + ], + "lines": [ + { + "bbox": [ + 231, + 671, + 379, + 689 + ], + "spans": [ + { + "bbox": [ + 231, + 671, + 379, + 689 + ], + "score": 0.93, + "content": "\\epsilon | \\mathbf { x } \\ { \\overset { f _ { 1 } | \\mathbf { x } } { \\longleftrightarrow } } \\ \\mathbf { h } _ { 1 } | \\mathbf { x } \\ { \\overset { f _ { 2 } | \\mathbf { x } } { \\longleftrightarrow } } \\ \\mathbf { h } _ { 2 } | \\mathbf { x } \\cdot \\cdot \\cdot \\ { \\overset { f _ { n } | \\mathbf { x } } { \\longleftrightarrow } } \\ \\mathbf { z } | \\mathbf { x } .", + "type": "interline_equation", + "image_path": "fade58b55d4a057c4cec9e33d737e9d031328233887eb30aeb71f4b16627e059.jpg" + } + ] + } + ], + "index": 44, + "virtual_lines": [ + { + "bbox": [ + 231, + 671, + 379, + 689 + ], + "spans": [], + "index": 44 + } + ] + }, + { + "type": "text", + "bbox": [ + 107, + 698, + 505, + 732 + ], + "lines": [ + { + "bbox": [ + 106, + 699, + 506, + 711 + ], + "spans": [ + { + "bbox": [ + 106, + 699, + 506, + 711 + ], + "score": 1.0, + "content": "Further, in contrast to prior work (Lu & Huang, 2019; Atanov et al., 2019; Ardizzone et al., 2019)", + "type": "text" + } + ], + "index": 45 + }, + { + "bbox": [ + 106, + 710, + 506, + 722 + ], + "spans": [ + { + "bbox": [ + 106, + 710, + 200, + 722 + ], + "score": 1.0, + "content": "which use affine flows", + "type": "text" + }, + { + "bbox": [ + 200, + 710, + 216, + 721 + ], + "score": 0.87, + "content": "( f _ { i } )", + "type": "inline_equation" + }, + { + "bbox": [ + 216, + 710, + 506, + 722 + ], + "score": 1.0, + "content": ", we build upon (Ziegler & Rush, 2019) and introduce conditional non-", + "type": "text" + } + ], + "index": 46 + }, + { + "bbox": [ + 105, + 720, + 505, + 734 + ], + "spans": [ + { + "bbox": [ + 105, + 720, + 505, + 734 + ], + "score": 1.0, + "content": "linear normalizing flows with split coupling. 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Finally, due to the expressive power of our conditional", + "type": "text" + } + ], + "index": 9 + }, + { + "bbox": [ + 106, + 202, + 473, + 214 + ], + "spans": [ + { + "bbox": [ + 106, + 202, + 473, + 214 + ], + "score": 1.0, + "content": "non-linear normalizing flows, simple spherical Gaussians base distributions were sufficient.", + "type": "text" + } + ], + "index": 10 + } + ], + "index": 8 + }, + { + "type": "title", + "bbox": [ + 108, + 226, + 499, + 238 + ], + "lines": [ + { + "bbox": [ + 105, + 225, + 501, + 239 + ], + "spans": [ + { + "bbox": [ + 105, + 225, + 501, + 239 + ], + "score": 1.0, + "content": "3.2 VARIATIONAL INFERENCE USING CONDITIONAL NORMALIZING FLOWS BASED PRIORS", + "type": "text" + } + ], + "index": 11 + } + ], + "index": 11 + }, + { + "type": "text", + "bbox": [ + 106, + 246, + 505, + 313 + ], + "lines": [ + { + "bbox": [ + 105, + 246, + 506, + 260 + ], + "spans": [ + { + "bbox": [ + 105, + 246, + 506, + 260 + ], + "score": 1.0, + "content": "Here, we derive the ELBO (1) for our regularized CF-VAE with our conditional flow based prior.", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 105, + 257, + 506, + 270 + ], + "spans": [ + { + "bbox": [ + 105, + 257, + 506, + 270 + ], + "score": 1.0, + "content": "In case of the standard CVAE with the Gaussian prior, the KL divergence term in the ELBO has a", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 105, + 267, + 506, + 283 + ], + "spans": [ + { + "bbox": [ + 105, + 267, + 506, + 283 + ], + "score": 1.0, + "content": "simple closed form expression. 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D _ { \\mathrm { K L } } ( q _ { \\phi } ( \\mathbf { z } | \\mathbf { x } , \\mathbf { y } ) | | p _ { \\psi } ( \\mathbf { z } | \\mathbf { x } ) ) = - \\mathbb { E } _ { q _ { \\phi } ( \\mathbf { z } | \\mathbf { x } , \\mathbf { y } ) } \\log ( q _ { \\phi } ( \\mathbf { z } | \\mathbf { x } , \\mathbf { y } ) ) + \\mathbb { E } _ { q _ { \\phi } ( \\mathbf { z } | \\mathbf { x } , \\mathbf { y } ) } \\log ( p _ { \\psi } ( \\mathbf { z } | \\mathbf { x } ) ) } } \\\\ & { } & { = \\mathcal { H } ( q _ { \\phi } ) + \\mathbb { E } _ { q _ { \\phi } ( \\mathbf { z } | \\mathbf { x } , \\mathbf { y } ) } \\log ( p ( \\boldsymbol { \\epsilon } | \\mathbf { x } ) ) + \\sum _ { i = 1 } ^ { n } \\log ( | \\operatorname* { d e t } J _ { i } | ) . } \\end{array}", + "type": "interline_equation", + "image_path": "fe15e4072947f3f7cb883ab41bd455afe3e030066f854e78c19ea39885db0f63.jpg" + } + ] + } + ], + "index": 23, + "virtual_lines": [ + { + "bbox": [ + 137, + 387, + 471, + 403.6666666666667 + ], + "spans": [], + "index": 22 + }, + { + "bbox": [ + 137, + 403.6666666666667, + 471, + 420.33333333333337 + ], + "spans": [], + "index": 23 + }, + { + "bbox": [ + 137, + 420.33333333333337, + 471, + 437.00000000000006 + ], + "spans": [], + "index": 24 + } + ] + }, + { + "type": "text", + "bbox": [ + 104, + 446, + 505, + 459 + ], + "lines": [ + { + "bbox": [ + 105, + 444, + 507, + 461 + ], + "spans": [ + { + "bbox": [ + 105, + 444, + 135, + 461 + ], + "score": 1.0, + "content": "where,", + "type": "text" + }, + { + "bbox": [ + 135, + 447, + 162, + 459 + ], + "score": 0.93, + "content": "\\mathcal { H } ( q _ { \\phi } )", + "type": "inline_equation" + }, + { + "bbox": [ + 162, + 444, + 507, + 461 + ], + "score": 1.0, + "content": "is the entropy of the variational distribution. 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D _ { \\mathrm { K L } } ( q _ { \\phi } ( \\mathbf { z } | \\mathbf { x } , \\mathbf { y } ) | | p _ { \\psi } ( \\mathbf { z } | \\mathbf { x } ) ) = - \\mathbb { E } _ { q _ { \\phi } ( \\mathbf { z } | \\mathbf { x } , \\mathbf { y } ) } \\log ( q _ { \\phi } ( \\mathbf { z } | \\mathbf { x } , \\mathbf { y } ) ) + \\mathbb { E } _ { q _ { \\phi } ( \\mathbf { z } | \\mathbf { x } , \\mathbf { y } ) } \\log ( p _ { \\psi } ( \\mathbf { z } | \\mathbf { x } ) ) } } \\\\ & { } & { = \\mathcal { H } ( q _ { \\phi } ) + \\mathbb { E } _ { q _ { \\phi } ( \\mathbf { z } | \\mathbf { x } , \\mathbf { y } ) } \\log ( p ( \\boldsymbol { \\epsilon } | \\mathbf { x } ) ) + \\sum _ { i = 1 } ^ { n } \\log ( | \\operatorname* { d e t } J _ { i } | ) . } \\end{array}", + "type": "interline_equation", + "image_path": "fe15e4072947f3f7cb883ab41bd455afe3e030066f854e78c19ea39885db0f63.jpg" + } + ] + } + ], + "index": 23, + "virtual_lines": [ + { + "bbox": [ + 137, + 387, + 471, + 403.6666666666667 + ], + "spans": [], + "index": 22 + }, + { + "bbox": [ + 137, + 403.6666666666667, + 471, + 420.33333333333337 + ], + "spans": [], + "index": 23 + }, + { + "bbox": [ + 137, + 420.33333333333337, + 471, + 437.00000000000006 + ], + "spans": [], + "index": 24 + } + ] + }, + { + "type": "text", + "bbox": [ + 104, + 446, + 505, + 459 + ], + "lines": [ + { + "bbox": [ + 105, + 444, + 507, + 461 + ], + "spans": [ + { + "bbox": [ + 105, + 444, + 135, + 461 + ], + "score": 1.0, + "content": "where,", + "type": "text" + }, + { + "bbox": [ + 135, + 447, + 162, + 459 + ], + "score": 0.93, + "content": "\\mathcal { H } ( q _ { \\phi } )", + "type": "inline_equation" + }, + { + "bbox": [ + 162, + 444, + 507, + 461 + ], + "score": 1.0, + "content": "is the entropy of the variational distribution. 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This would al-", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 105, + 539, + 338, + 551 + ], + "spans": [ + { + "bbox": [ + 105, + 539, + 223, + 551 + ], + "score": 1.0, + "content": "low the variational posterior", + "type": "text" + }, + { + "bbox": [ + 224, + 542, + 234, + 551 + ], + "score": 0.84, + "content": "q _ { \\theta }", + "type": "inline_equation" + }, + { + "bbox": [ + 234, + 539, + 338, + 551 + ], + "score": 1.0, + "content": "to match the conditional", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 105, + 550, + 338, + 562 + ], + "spans": [ + { + "bbox": [ + 105, + 550, + 338, + 562 + ], + "score": 1.0, + "content": "prior and vice-versa so that the ELBO (7) is maximized.", + "type": "text" + } + ], + "index": 33 + }, + { + "bbox": [ + 105, + 561, + 338, + 573 + ], + "spans": [ + { + "bbox": [ + 105, + 561, + 338, + 573 + ], + "score": 1.0, + "content": "However, in practice we observe instabilities during train-", + "type": "text" + } + ], + "index": 34 + }, + { + "bbox": [ + 106, + 572, + 337, + 585 + ], + "spans": [ + { + "bbox": [ + 106, + 572, + 337, + 585 + ], + "score": 1.0, + "content": "ing and posterior collapse. Next, we introduce our novel", + "type": "text" + } + ], + "index": 35 + }, + { + "bbox": [ + 105, + 582, + 336, + 595 + ], + "spans": [ + { + "bbox": [ + 105, + 582, + 336, + 595 + ], + "score": 1.0, + "content": "regularization schemes to deal with both these problems.", + "type": "text" + } + ], + "index": 36 + } + ], + "index": 32.5, + "bbox_fs": [ + 105, + 506, + 338, + 595 + ] + }, + { + "type": "text", + "bbox": [ + 106, + 600, + 338, + 655 + ], + "lines": [ + { + "bbox": [ + 106, + 600, + 338, + 612 + ], + "spans": [ + { + "bbox": [ + 106, + 600, + 276, + 612 + ], + "score": 1.0, + "content": "Posterior Regularization for Stability", + "type": "text" + }, + { + "bbox": [ + 276, + 600, + 296, + 612 + ], + "score": 0.39, + "content": "\\mathbf { \\Pi } ( \\mathbf { p } \\mathbf { R } )", + "type": "inline_equation" + }, + { + "bbox": [ + 296, + 600, + 338, + 612 + ], + "score": 1.0, + "content": ". The en-", + "type": "text" + } + ], + "index": 37 + }, + { + "bbox": [ + 106, + 610, + 337, + 624 + ], + "spans": [ + { + "bbox": [ + 106, + 610, + 337, + 624 + ], + "score": 1.0, + "content": "tropy and the log-Jacobian of the CF-VAE objective (7)", + "type": "text" + } + ], + "index": 38 + }, + { + "bbox": [ + 106, + 622, + 337, + 633 + ], + "spans": [ + { + "bbox": [ + 106, + 622, + 337, + 633 + ], + "score": 1.0, + "content": "are at odds with each other. The log-Jacobian favours the", + "type": "text" + } + ], + "index": 39 + }, + { + "bbox": [ + 106, + 632, + 336, + 645 + ], + "spans": [ + { + "bbox": [ + 106, + 632, + 336, + 645 + ], + "score": 1.0, + "content": "contraction of the base density. Therefore, log-Jacobian", + "type": "text" + } + ], + "index": 40 + }, + { + "bbox": [ + 105, + 644, + 336, + 655 + ], + "spans": [ + { + "bbox": [ + 105, + 644, + 336, + 655 + ], + "score": 1.0, + "content": "at the right of (7) is maximized when the conditional flow", + "type": "text" + } + ], + "index": 41 + }, + { + "bbox": [ + 106, + 655, + 506, + 667 + ], + "spans": [ + { + "bbox": [ + 106, + 655, + 217, + 667 + ], + "score": 1.0, + "content": "maps the base distribution", + "type": "text" + }, + { + "bbox": [ + 217, + 656, + 243, + 665 + ], + "score": 0.87, + "content": "( \\epsilon z", + "type": "inline_equation" + }, + { + "bbox": [ + 243, + 655, + 506, + 667 + ], + "score": 1.0, + "content": "in Figure 2) to a low entropy conditional prior and thus a low en-", + "type": "text" + } + ], + "index": 51 + }, + { + "bbox": [ + 104, + 665, + 506, + 680 + ], + "spans": [ + { + "bbox": [ + 104, + 665, + 220, + 680 + ], + "score": 1.0, + "content": "tropy variational distribution", + "type": "text" + }, + { + "bbox": [ + 220, + 666, + 260, + 678 + ], + "score": 0.92, + "content": "q _ { \\phi } ( \\mathbf { z } | \\mathbf { x } , \\mathbf { y } )", + "type": "inline_equation" + }, + { + "bbox": [ + 260, + 665, + 506, + 680 + ], + "score": 1.0, + "content": ". Therefore, in practice we observe instabilities during training.", + "type": "text" + } + ], + "index": 52 + }, + { + "bbox": [ + 105, + 676, + 506, + 690 + ], + "spans": [ + { + "bbox": [ + 105, + 676, + 506, + 690 + ], + "score": 1.0, + "content": "We observe that either the entropy or the log-Jacobian term dominates and the data log-likelihood", + "type": "text" + } + ], + "index": 53 + }, + { + "bbox": [ + 104, + 686, + 506, + 701 + ], + "spans": [ + { + "bbox": [ + 104, + 686, + 374, + 701 + ], + "score": 1.0, + "content": "is fully or partially ignored. Therefore, we regularize the posterior", + "type": "text" + }, + { + "bbox": [ + 374, + 687, + 414, + 700 + ], + "score": 0.93, + "content": "q _ { \\phi } ( \\mathbf { z } | \\mathbf { x } , \\mathbf { y } )", + "type": "inline_equation" + }, + { + "bbox": [ + 415, + 686, + 506, + 701 + ], + "score": 1.0, + "content": "by fixing the variance", + "type": "text" + } + ], + "index": 54 + }, + { + "bbox": [ + 105, + 699, + 506, + 711 + ], + "spans": [ + { + "bbox": [ + 105, + 699, + 506, + 711 + ], + "score": 1.0, + "content": "to C. This leads to a constant entropy term which in turn bounds the maximum possible amount of", + "type": "text" + } + ], + "index": 55 + }, + { + "bbox": [ + 105, + 710, + 506, + 722 + ], + "spans": [ + { + "bbox": [ + 105, + 710, + 506, + 722 + ], + "score": 1.0, + "content": "contraction, thus upper bounding the log-Jacobian. This encourages our model to concentrate on", + "type": "text" + } + ], + "index": 56 + }, + { + "bbox": [ + 106, + 720, + 505, + 734 + ], + "spans": [ + { + "bbox": [ + 106, + 720, + 464, + 734 + ], + "score": 1.0, + "content": "explaining the data and leads better fit to the target data distribution. Note that, although", + "type": "text" + }, + { + "bbox": [ + 465, + 720, + 505, + 733 + ], + "score": 0.93, + "content": "q _ { \\phi } ( \\mathbf { z } | \\mathbf { x } , \\mathbf { y } )", + "type": "inline_equation" + } + ], + "index": 57 + } + ], + "index": 39, + "bbox_fs": [ + 105, + 600, + 338, + 655 + ] + }, + { + "type": "image", + "bbox": [ + 344, + 523, + 504, + 613 + ], + "blocks": [ + { + "type": "image_body", + "bbox": [ + 344, + 523, + 504, + 613 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 344, + 523, + 504, + 613 + ], + "spans": [ + { + "bbox": [ + 344, + 523, + 504, + 613 + ], + "score": 0.795, + "type": "image", + "image_path": "86b295e9ae3398cb690828a8b3a03114f9ecb10a4d0d6a2ef3882dfcfed39582.jpg" + } + ] + } + ], + "index": 44.5, + "virtual_lines": [ + { + "bbox": [ + 344, + 523, + 504, + 538.0 + ], + "spans": [], + "index": 42 + }, + { + "bbox": [ + 344, + 538.0, + 504, + 553.0 + ], + "spans": [], + "index": 43 + }, + { + "bbox": [ + 344, + 553.0, + 504, + 568.0 + ], + "spans": [], + "index": 44 + }, + { + "bbox": [ + 344, + 568.0, + 504, + 583.0 + ], + "spans": [], + "index": 45 + }, + { + "bbox": [ + 344, + 583.0, + 504, + 598.0 + ], + "spans": [], + "index": 46 + }, + { + "bbox": [ + 344, + 598.0, + 504, + 613.0 + ], + "spans": [], + "index": 47 + } + ] + }, + { + "type": "image_caption", + "bbox": [ + 344, + 614, + 505, + 647 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 343, + 613, + 506, + 626 + ], + "spans": [ + { + "bbox": [ + 343, + 613, + 506, + 626 + ], + "score": 1.0, + "content": "Figure 2: CF-VAE. The decoder is regu-", + "type": "text" + } + ], + "index": 48 + }, + { + "bbox": [ + 343, + 623, + 505, + 637 + ], + "spans": [ + { + "bbox": [ + 343, + 623, + 505, + 637 + ], + "score": 1.0, + "content": "larized by removing conditioning (grey", + "type": "text" + } + ], + "index": 49 + }, + { + "bbox": [ + 343, + 635, + 490, + 649 + ], + "spans": [ + { + "bbox": [ + 343, + 635, + 490, + 649 + ], + "score": 1.0, + "content": "arrow) to prevent posterior collapse.", + "type": "text" + } + ], + "index": 50 + } + ], + "index": 49 + } + ], + "index": 46.75 + }, + { + "type": "text", + "bbox": [ + 106, + 655, + 506, + 732 + ], + "lines": [], + "index": 54, + "bbox_fs": [ + 104, + 655, + 506, + 734 + ], + "lines_deleted": true + } + ] + }, + { + "preproc_blocks": [ + { + "type": "text", + "bbox": [ + 108, + 82, + 504, + 116 + ], + "lines": [ + { + "bbox": [ + 105, + 82, + 506, + 95 + ], + "spans": [ + { + "bbox": [ + 105, + 82, + 444, + 95 + ], + "score": 1.0, + "content": "has fixed variance, this does not significantly effect sample quality as the marginal", + "type": "text" + }, + { + "bbox": [ + 444, + 83, + 474, + 95 + ], + "score": 0.93, + "content": "q _ { \\phi } ( \\mathbf { z } | \\mathbf { x } )", + "type": "inline_equation" + }, + { + "bbox": [ + 475, + 82, + 506, + 95 + ], + "score": 1.0, + "content": "can be", + "type": "text" + } + ], + "index": 0 + }, + { + "bbox": [ + 105, + 93, + 506, + 106 + ], + "spans": [ + { + "bbox": [ + 105, + 93, + 506, + 106 + ], + "score": 1.0, + "content": "arbitrarily complex due to our conditional flow prior. Moreover, we observe that the LSTM based", + "type": "text" + } + ], + "index": 1 + }, + { + "bbox": [ + 106, + 105, + 502, + 117 + ], + "spans": [ + { + "bbox": [ + 106, + 105, + 436, + 117 + ], + "score": 1.0, + "content": "decoders employed demonstrate robust performance across a wide range of values", + "type": "text" + }, + { + "bbox": [ + 436, + 105, + 502, + 117 + ], + "score": 0.89, + "content": "\\mathbf { C } = [ 0 . 0 5 , 0 . 2 5 ]", + "type": "inline_equation" + } + ], + "index": 2 + } + ], + "index": 1 + }, + { + "type": "text", + "bbox": [ + 106, + 121, + 505, + 253 + ], + "lines": [ + { + "bbox": [ + 106, + 120, + 505, + 134 + ], + "spans": [ + { + "bbox": [ + 106, + 120, + 505, + 134 + ], + "score": 1.0, + "content": "Condition Regularization for Posterior Collapse (cR). We observe missing modes when the target", + "type": "text" + } + ], + "index": 3 + }, + { + "bbox": [ + 105, + 132, + 505, + 145 + ], + "spans": [ + { + "bbox": [ + 105, + 132, + 505, + 145 + ], + "score": 1.0, + "content": "conditional data distribution has a major mode(s) and one or more minor modes (corresponding to", + "type": "text" + } + ], + "index": 4 + }, + { + "bbox": [ + 105, + 143, + 505, + 155 + ], + "spans": [ + { + "bbox": [ + 105, + 143, + 505, + 155 + ], + "score": 1.0, + "content": "rare events). This is because the condition x on the decoder is already enough to model the main", + "type": "text" + } + ], + "index": 5 + }, + { + "bbox": [ + 105, + 154, + 505, + 167 + ], + "spans": [ + { + "bbox": [ + 105, + 154, + 505, + 167 + ], + "score": 1.0, + "content": "mode(s). If the cost of ignoring the minor modes is out-weighed by the cost of encoding a more", + "type": "text" + } + ], + "index": 6 + }, + { + "bbox": [ + 105, + 165, + 506, + 177 + ], + "spans": [ + { + "bbox": [ + 105, + 165, + 506, + 177 + ], + "score": 1.0, + "content": "complex latent distribution reflecting all modes, the minor modes and the latent variables are ignored.", + "type": "text" + } + ], + "index": 7 + }, + { + "bbox": [ + 106, + 176, + 505, + 188 + ], + "spans": [ + { + "bbox": [ + 106, + 176, + 411, + 188 + ], + "score": 1.0, + "content": "We propose a regularization scheme by removing the additional conditioning", + "type": "text" + }, + { + "bbox": [ + 412, + 180, + 417, + 186 + ], + "score": 0.41, + "content": "\\mathbf { X }", + "type": "inline_equation" + }, + { + "bbox": [ + 418, + 176, + 505, + 188 + ], + "score": 1.0, + "content": "on the decoder, when", + "type": "text" + } + ], + "index": 8 + }, + { + "bbox": [ + 105, + 187, + 505, + 199 + ], + "spans": [ + { + "bbox": [ + 105, + 187, + 505, + 199 + ], + "score": 1.0, + "content": "the dataset in question has a dominating mode(s). This enabled by our conditional flow prior, which", + "type": "text" + } + ], + "index": 9 + }, + { + "bbox": [ + 105, + 198, + 505, + 211 + ], + "spans": [ + { + "bbox": [ + 105, + 198, + 389, + 211 + ], + "score": 1.0, + "content": "ensures that conditioning information is encoded in the latent space and", + "type": "text" + }, + { + "bbox": [ + 389, + 200, + 419, + 210 + ], + "score": 0.93, + "content": "p _ { \\theta } ( \\mathbf { y } | \\mathbf { z } )", + "type": "inline_equation" + }, + { + "bbox": [ + 420, + 198, + 463, + 211 + ], + "score": 1.0, + "content": "can match", + "type": "text" + }, + { + "bbox": [ + 464, + 200, + 503, + 210 + ], + "score": 0.93, + "content": "p _ { \\theta } ( \\mathbf { y } | \\mathbf { x } , \\mathbf { z } )", + "type": "inline_equation" + }, + { + "bbox": [ + 503, + 198, + 505, + 211 + ], + "score": 1.0, + "content": ".", + "type": "text" + } + ], + "index": 10 + }, + { + "bbox": [ + 106, + 209, + 505, + 222 + ], + "spans": [ + { + "bbox": [ + 106, + 209, + 251, + 221 + ], + "score": 1.0, + "content": "Leading to a simpler factorization,", + "type": "text" + }, + { + "bbox": [ + 251, + 210, + 375, + 222 + ], + "score": 0.93, + "content": "\\begin{array} { r } { p _ { \\theta } ( \\mathbf { y } | \\mathbf { x } ) = \\int p _ { \\theta } ( \\mathbf { y } | \\mathbf { z } ) p _ { \\psi } ( \\mathbf { z } | \\mathbf { x } ) d \\mathbf { z } } \\end{array}", + "type": "inline_equation" + }, + { + "bbox": [ + 375, + 209, + 505, + 221 + ], + "score": 1.0, + "content": ". Equivalently, this ensures that", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 106, + 221, + 505, + 231 + ], + "spans": [ + { + "bbox": [ + 106, + 221, + 505, + 231 + ], + "score": 1.0, + "content": "the latent variable z cannot be ignored by the CF-VAE and thus must encode useful information.", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 105, + 230, + 505, + 243 + ], + "spans": [ + { + "bbox": [ + 105, + 230, + 505, + 243 + ], + "score": 1.0, + "content": "Note that this regularization scheme is only possible due to our conditional prior, the unconditional", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 106, + 242, + 387, + 254 + ], + "spans": [ + { + "bbox": [ + 106, + 242, + 387, + 254 + ], + "score": 1.0, + "content": "Gaussian prior of CVAE would always need to condition the decoder.", + "type": "text" + } + ], + "index": 14 + } + ], + "index": 8.5 + }, + { + "type": "text", + "bbox": [ + 108, + 259, + 503, + 292 + ], + "lines": [ + { + "bbox": [ + 106, + 258, + 505, + 271 + ], + "spans": [ + { + "bbox": [ + 106, + 258, + 505, + 271 + ], + "score": 1.0, + "content": "The parallel work of Klushyn et al. (2019) also proposes a similar regularization scheme. However, we", + "type": "text" + } + ], + "index": 15 + }, + { + "bbox": [ + 106, + 270, + 505, + 281 + ], + "spans": [ + { + "bbox": [ + 106, + 270, + 505, + 281 + ], + "score": 1.0, + "content": "employ this regularization to deal with posterior collapse only in case of distributions with dominant", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 105, + 280, + 459, + 293 + ], + "spans": [ + { + "bbox": [ + 105, + 280, + 459, + 293 + ], + "score": 1.0, + "content": "modes. We also provide a more detailed analysis of their proposed prior in Appendix E.", + "type": "text" + } + ], + "index": 17 + } + ], + "index": 16 + }, + { + "type": "text", + "bbox": [ + 107, + 298, + 504, + 320 + ], + "lines": [ + { + "bbox": [ + 106, + 297, + 505, + 310 + ], + "spans": [ + { + "bbox": [ + 106, + 297, + 505, + 310 + ], + "score": 1.0, + "content": "Finally, we discuss the integration of diverse sources of contextual information into the conditional", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 105, + 308, + 460, + 321 + ], + "spans": [ + { + "bbox": [ + 105, + 308, + 128, + 321 + ], + "score": 1.0, + "content": "prior", + "type": "text" + }, + { + "bbox": [ + 129, + 309, + 160, + 321 + ], + "score": 0.92, + "content": "p _ { \\psi } ( { \\boldsymbol { \\mathbf { z } } } | { \\boldsymbol { \\mathbf { x } } } )", + "type": "inline_equation" + }, + { + "bbox": [ + 160, + 308, + 460, + 321 + ], + "score": 1.0, + "content": "for even richer conditional latent distributions of our regularized CF-VAE.", + "type": "text" + } + ], + "index": 19 + } + ], + "index": 18.5 + }, + { + "type": "title", + "bbox": [ + 108, + 333, + 372, + 344 + ], + "lines": [ + { + "bbox": [ + 105, + 332, + 374, + 346 + ], + "spans": [ + { + "bbox": [ + 105, + 332, + 374, + 346 + ], + "score": 1.0, + "content": "3.3 CONDITIONING PRIORS ON CONTEXTUAL INFORMATION", + "type": "text" + } + ], + "index": 20 + } + ], + "index": 20 + }, + { + "type": "text", + "bbox": [ + 107, + 354, + 505, + 387 + ], + "lines": [ + { + "bbox": [ + 105, + 353, + 506, + 367 + ], + "spans": [ + { + "bbox": [ + 105, + 353, + 506, + 367 + ], + "score": 1.0, + "content": "For prediction tasks, it is often crucial to integrate sources of contextual information e.g. past", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 106, + 365, + 507, + 377 + ], + "spans": [ + { + "bbox": [ + 106, + 365, + 507, + 377 + ], + "score": 1.0, + "content": "trajectories or environmental information for accurate predictions. As these sources are heterogeneous,", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 105, + 375, + 447, + 389 + ], + "spans": [ + { + "bbox": [ + 105, + 375, + 447, + 389 + ], + "score": 1.0, + "content": "we employ source specific networks to extract fixed length vectors from each source.", + "type": "text" + } + ], + "index": 23 + } + ], + "index": 22 + }, + { + "type": "text", + "bbox": [ + 107, + 393, + 504, + 415 + ], + "lines": [ + { + "bbox": [ + 106, + 393, + 505, + 405 + ], + "spans": [ + { + "bbox": [ + 106, + 393, + 473, + 405 + ], + "score": 1.0, + "content": "Past Trajectory. We encode the past trajectories using a LSTM to an fixed length vector", + "type": "text" + }, + { + "bbox": [ + 473, + 394, + 483, + 404 + ], + "score": 0.84, + "content": "\\mathbf { X } _ { t }", + "type": "inline_equation" + }, + { + "bbox": [ + 483, + 393, + 505, + 405 + ], + "score": 1.0, + "content": ". For", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 106, + 403, + 497, + 416 + ], + "spans": [ + { + "bbox": [ + 106, + 403, + 497, + 416 + ], + "score": 1.0, + "content": "efficiency we share the condition encoder between the conditional flow and the CF-VAE decoder.", + "type": "text" + } + ], + "index": 25 + } + ], + "index": 24.5 + }, + { + "type": "text", + "bbox": [ + 108, + 420, + 503, + 453 + ], + "lines": [ + { + "bbox": [ + 106, + 420, + 505, + 433 + ], + "spans": [ + { + "bbox": [ + 106, + 420, + 505, + 433 + ], + "score": 1.0, + "content": "Environmental Map. We use a CNN to encode environmental information to a set of region specific", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 105, + 431, + 505, + 444 + ], + "spans": [ + { + "bbox": [ + 105, + 431, + 505, + 444 + ], + "score": 1.0, + "content": "feature vectors. We apply attention conditioned on the past trajectory to extract a fixed length", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 105, + 442, + 470, + 456 + ], + "spans": [ + { + "bbox": [ + 105, + 442, + 186, + 456 + ], + "score": 1.0, + "content": "conditioning vector", + "type": "text" + }, + { + "bbox": [ + 186, + 444, + 200, + 453 + ], + "score": 0.87, + "content": "\\mathbf { X } _ { m }", + "type": "inline_equation" + }, + { + "bbox": [ + 200, + 442, + 242, + 456 + ], + "score": 1.0, + "content": ", such that", + "type": "text" + }, + { + "bbox": [ + 242, + 444, + 256, + 453 + ], + "score": 0.86, + "content": "\\mathbf { X } _ { m }", + "type": "inline_equation" + }, + { + "bbox": [ + 257, + 442, + 470, + 456 + ], + "score": 1.0, + "content": "contains information relevant to the future trajectory.", + "type": "text" + } + ], + "index": 28 + } + ], + "index": 27 + }, + { + "type": "text", + "bbox": [ + 107, + 459, + 505, + 559 + ], + "lines": [ + { + "bbox": [ + 106, + 459, + 505, + 471 + ], + "spans": [ + { + "bbox": [ + 106, + 459, + 505, + 471 + ], + "score": 1.0, + "content": "Interacting Agents. To encode information of interacting traffic participants/agents, we build on Deo", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 105, + 471, + 505, + 483 + ], + "spans": [ + { + "bbox": [ + 105, + 471, + 505, + 483 + ], + "score": 1.0, + "content": "& Trivedi (2018) and propose a fully convolutional social pooling layer. We aggregate information of", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 105, + 481, + 506, + 495 + ], + "spans": [ + { + "bbox": [ + 105, + 481, + 506, + 495 + ], + "score": 1.0, + "content": "interacting agents using a grid overlayed on the environment. This grid is represented using a tensor,", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 105, + 492, + 506, + 505 + ], + "spans": [ + { + "bbox": [ + 105, + 492, + 506, + 505 + ], + "score": 1.0, + "content": "where the past trajectory information of traffic participants are aggregated into the tensor indexed", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 105, + 504, + 506, + 516 + ], + "spans": [ + { + "bbox": [ + 105, + 504, + 506, + 516 + ], + "score": 1.0, + "content": "corresponding to the grid in the environment. In Deo & Trivedi (2018) past trajectory information is", + "type": "text" + } + ], + "index": 33 + }, + { + "bbox": [ + 105, + 514, + 505, + 528 + ], + "spans": [ + { + "bbox": [ + 105, + 514, + 481, + 528 + ], + "score": 1.0, + "content": "aggregated using a LSTM. We aggregate the past trajectory information into the tensor using", + "type": "text" + }, + { + "bbox": [ + 482, + 514, + 505, + 525 + ], + "score": 0.88, + "content": "1 \\times 1", + "type": "inline_equation" + } + ], + "index": 34 + }, + { + "bbox": [ + 105, + 525, + 506, + 538 + ], + "spans": [ + { + "bbox": [ + 105, + 525, + 506, + 538 + ], + "score": 1.0, + "content": "convolutions as it allows for stable learning and is computationally efficient. Finally, we apply several", + "type": "text" + } + ], + "index": 35 + }, + { + "bbox": [ + 105, + 536, + 504, + 549 + ], + "spans": [ + { + "bbox": [ + 105, + 536, + 143, + 549 + ], + "score": 1.0, + "content": "layers of", + "type": "text" + }, + { + "bbox": [ + 143, + 536, + 167, + 546 + ], + "score": 0.9, + "content": "k \\times k", + "type": "inline_equation" + }, + { + "bbox": [ + 168, + 536, + 408, + 549 + ], + "score": 1.0, + "content": "convolutions to capture interaction aware contextual features", + "type": "text" + }, + { + "bbox": [ + 408, + 538, + 419, + 548 + ], + "score": 0.86, + "content": "\\mathbf { X } _ { p }", + "type": "inline_equation" + }, + { + "bbox": [ + 420, + 536, + 504, + 549 + ], + "score": 1.0, + "content": "of traffic participants", + "type": "text" + } + ], + "index": 36 + }, + { + "bbox": [ + 105, + 546, + 159, + 560 + ], + "spans": [ + { + "bbox": [ + 105, + 546, + 159, + 560 + ], + "score": 1.0, + "content": "in the scene.", + "type": "text" + } + ], + "index": 37 + } + ], + "index": 33 + }, + { + "type": "text", + "bbox": [ + 107, + 564, + 504, + 586 + ], + "lines": [ + { + "bbox": [ + 106, + 564, + 505, + 577 + ], + "spans": [ + { + "bbox": [ + 106, + 564, + 505, + 577 + ], + "score": 1.0, + "content": "Due to the expressive power of our conditional non-linear normalizing flows, simple concatenation", + "type": "text" + } + ], + "index": 38 + }, + { + "bbox": [ + 105, + 575, + 458, + 588 + ], + "spans": [ + { + "bbox": [ + 105, + 575, + 185, + 588 + ], + "score": 1.0, + "content": "into a single vector", + "type": "text" + }, + { + "bbox": [ + 185, + 575, + 253, + 587 + ], + "score": 0.94, + "content": "\\mathbf { x } = \\left\\{ { \\mathbf { x } } _ { t } , { \\mathbf { x } } _ { m } , { \\mathbf { x } } _ { t } \\right\\}", + "type": "inline_equation" + }, + { + "bbox": [ + 253, + 575, + 458, + 588 + ], + "score": 1.0, + "content": "was sufficient to learn powerful conditional priors.", + "type": "text" + } + ], + "index": 39 + } + ], + "index": 38.5 + }, + { + "type": "title", + "bbox": [ + 108, + 602, + 200, + 614 + ], + "lines": [ + { + "bbox": [ + 105, + 601, + 201, + 617 + ], + "spans": [ + { + "bbox": [ + 105, + 601, + 201, + 617 + ], + "score": 1.0, + "content": "4 EXPERIMENTS", + "type": "text" + } + ], + "index": 40 + } + ], + "index": 40 + }, + { + "type": "text", + "bbox": [ + 106, + 627, + 504, + 649 + ], + "lines": [ + { + "bbox": [ + 105, + 626, + 505, + 640 + ], + "spans": [ + { + "bbox": [ + 105, + 626, + 505, + 640 + ], + "score": 1.0, + "content": "We evaluate our CF-VAE on three popular and highly multi-modal sequence prediction datasets. We", + "type": "text" + } + ], + "index": 41 + }, + { + "bbox": [ + 105, + 638, + 403, + 650 + ], + "spans": [ + { + "bbox": [ + 105, + 638, + 403, + 650 + ], + "score": 1.0, + "content": "begin with a description of our evaluation metrics and model architecture.", + "type": "text" + } + ], + "index": 42 + } + ], + "index": 41.5 + }, + { + "type": "text", + "bbox": [ + 107, + 654, + 505, + 732 + ], + "lines": [ + { + "bbox": [ + 105, + 654, + 506, + 668 + ], + "spans": [ + { + "bbox": [ + 105, + 654, + 506, + 668 + ], + "score": 1.0, + "content": "Evaluation Metrics. In line with prior work (Lee et al., 2017; Bhattacharyya et al., 2018; Pa-", + "type": "text" + } + ], + "index": 43 + }, + { + "bbox": [ + 105, + 666, + 505, + 678 + ], + "spans": [ + { + "bbox": [ + 105, + 666, + 505, + 678 + ], + "score": 1.0, + "content": "jouheshgar & Lampert, 2018; Deo & Trivedi, 2019; Bhattacharyya et al., 2019), we use the negative", + "type": "text" + } + ], + "index": 44 + }, + { + "bbox": [ + 105, + 677, + 506, + 689 + ], + "spans": [ + { + "bbox": [ + 105, + 677, + 436, + 689 + ], + "score": 1.0, + "content": "conditional log-likelihood (-CLL) and mean Euclidean distances of the oracle Top", + "type": "text" + }, + { + "bbox": [ + 437, + 677, + 452, + 687 + ], + "score": 0.87, + "content": "n \\%", + "type": "inline_equation" + }, + { + "bbox": [ + 453, + 677, + 464, + 689 + ], + "score": 1.0, + "content": "of", + "type": "text" + }, + { + "bbox": [ + 465, + 677, + 475, + 687 + ], + "score": 0.8, + "content": "N", + "type": "inline_equation" + }, + { + "bbox": [ + 475, + 677, + 506, + 689 + ], + "score": 1.0, + "content": "predic-", + "type": "text" + } + ], + "index": 45 + }, + { + "bbox": [ + 105, + 687, + 505, + 700 + ], + "spans": [ + { + "bbox": [ + 105, + 687, + 195, + 700 + ], + "score": 1.0, + "content": "tions. The oracle Top", + "type": "text" + }, + { + "bbox": [ + 195, + 688, + 210, + 698 + ], + "score": 0.85, + "content": "n \\%", + "type": "inline_equation" + }, + { + "bbox": [ + 211, + 687, + 505, + 700 + ], + "score": 1.0, + "content": "metric measures not only the coverage of all modes but also discourages", + "type": "text" + } + ], + "index": 46 + }, + { + "bbox": [ + 105, + 699, + 505, + 711 + ], + "spans": [ + { + "bbox": [ + 105, + 699, + 297, + 711 + ], + "score": 1.0, + "content": "random guessing for a reasonably large value of", + "type": "text" + }, + { + "bbox": [ + 297, + 700, + 304, + 709 + ], + "score": 0.77, + "content": "n", + "type": "inline_equation" + }, + { + "bbox": [ + 304, + 699, + 325, + 711 + ], + "score": 1.0, + "content": "(e.g.", + "type": "text" + }, + { + "bbox": [ + 325, + 699, + 364, + 709 + ], + "score": 0.89, + "content": "n = 1 0 \\%", + "type": "inline_equation" + }, + { + "bbox": [ + 364, + 699, + 505, + 711 + ], + "score": 1.0, + "content": "). This is because, a model can only", + "type": "text" + } + ], + "index": 47 + }, + { + "bbox": [ + 106, + 710, + 506, + 722 + ], + "spans": [ + { + "bbox": [ + 106, + 710, + 506, + 722 + ], + "score": 1.0, + "content": "improve this metric by moving randomly guessed samples from an overestimated mode to the correct", + "type": "text" + } + ], + "index": 48 + }, + { + "bbox": [ + 106, + 721, + 272, + 732 + ], + "spans": [ + { + "bbox": [ + 106, + 721, + 272, + 732 + ], + "score": 1.0, + "content": "modes (detailed analysis in Appendix F).", + "type": "text" + } + ], + "index": 49 + } + ], + "index": 46 + } + ], + "page_idx": 4, + "page_size": [ + 612, + 792 + ], + "discarded_blocks": [ + { + "type": "discarded", + "bbox": [ + 107, + 27, + 308, + 37 + ], + "lines": [ + { + "bbox": [ + 107, + 26, + 308, + 38 + ], + "spans": [ + { + "bbox": [ + 107, + 26, + 308, + 38 + ], + "score": 1.0, + "content": "Under review as a conference paper at ICLR 2020", + "type": "text" + } + ] + } + ] + }, + { + "type": "discarded", + "bbox": [ + 302, + 751, + 308, + 760 + ], + "lines": [ + { + "bbox": [ + 302, + 750, + 309, + 763 + ], + "spans": [ + { + "bbox": [ + 302, + 750, + 309, + 763 + ], + "score": 1.0, + "content": "5", + "type": "text" + } + ] + } + ] + } + ], + "para_blocks": [ + { + "type": "text", + "bbox": [ + 108, + 82, + 504, + 116 + ], + "lines": [ + { + "bbox": [ + 105, + 82, + 506, + 95 + ], + "spans": [ + { + "bbox": [ + 105, + 82, + 444, + 95 + ], + "score": 1.0, + "content": "has fixed variance, this does not significantly effect sample quality as the marginal", + "type": "text" + }, + { + "bbox": [ + 444, + 83, + 474, + 95 + ], + "score": 0.93, + "content": "q _ { \\phi } ( \\mathbf { z } | \\mathbf { x } )", + "type": "inline_equation" + }, + { + "bbox": [ + 475, + 82, + 506, + 95 + ], + "score": 1.0, + "content": "can be", + "type": "text" + } + ], + "index": 0 + }, + { + "bbox": [ + 105, + 93, + 506, + 106 + ], + "spans": [ + { + "bbox": [ + 105, + 93, + 506, + 106 + ], + "score": 1.0, + "content": "arbitrarily complex due to our conditional flow prior. Moreover, we observe that the LSTM based", + "type": "text" + } + ], + "index": 1 + }, + { + "bbox": [ + 106, + 105, + 502, + 117 + ], + "spans": [ + { + "bbox": [ + 106, + 105, + 436, + 117 + ], + "score": 1.0, + "content": "decoders employed demonstrate robust performance across a wide range of values", + "type": "text" + }, + { + "bbox": [ + 436, + 105, + 502, + 117 + ], + "score": 0.89, + "content": "\\mathbf { C } = [ 0 . 0 5 , 0 . 2 5 ]", + "type": "inline_equation" + } + ], + "index": 2 + } + ], + "index": 1, + "bbox_fs": [ + 105, + 82, + 506, + 117 + ] + }, + { + "type": "text", + "bbox": [ + 106, + 121, + 505, + 253 + ], + "lines": [ + { + "bbox": [ + 106, + 120, + 505, + 134 + ], + "spans": [ + { + "bbox": [ + 106, + 120, + 505, + 134 + ], + "score": 1.0, + "content": "Condition Regularization for Posterior Collapse (cR). We observe missing modes when the target", + "type": "text" + } + ], + "index": 3 + }, + { + "bbox": [ + 105, + 132, + 505, + 145 + ], + "spans": [ + { + "bbox": [ + 105, + 132, + 505, + 145 + ], + "score": 1.0, + "content": "conditional data distribution has a major mode(s) and one or more minor modes (corresponding to", + "type": "text" + } + ], + "index": 4 + }, + { + "bbox": [ + 105, + 143, + 505, + 155 + ], + "spans": [ + { + "bbox": [ + 105, + 143, + 505, + 155 + ], + "score": 1.0, + "content": "rare events). This is because the condition x on the decoder is already enough to model the main", + "type": "text" + } + ], + "index": 5 + }, + { + "bbox": [ + 105, + 154, + 505, + 167 + ], + "spans": [ + { + "bbox": [ + 105, + 154, + 505, + 167 + ], + "score": 1.0, + "content": "mode(s). If the cost of ignoring the minor modes is out-weighed by the cost of encoding a more", + "type": "text" + } + ], + "index": 6 + }, + { + "bbox": [ + 105, + 165, + 506, + 177 + ], + "spans": [ + { + "bbox": [ + 105, + 165, + 506, + 177 + ], + "score": 1.0, + "content": "complex latent distribution reflecting all modes, the minor modes and the latent variables are ignored.", + "type": "text" + } + ], + "index": 7 + }, + { + "bbox": [ + 106, + 176, + 505, + 188 + ], + "spans": [ + { + "bbox": [ + 106, + 176, + 411, + 188 + ], + "score": 1.0, + "content": "We propose a regularization scheme by removing the additional conditioning", + "type": "text" + }, + { + "bbox": [ + 412, + 180, + 417, + 186 + ], + "score": 0.41, + "content": "\\mathbf { X }", + "type": "inline_equation" + }, + { + "bbox": [ + 418, + 176, + 505, + 188 + ], + "score": 1.0, + "content": "on the decoder, when", + "type": "text" + } + ], + "index": 8 + }, + { + "bbox": [ + 105, + 187, + 505, + 199 + ], + "spans": [ + { + "bbox": [ + 105, + 187, + 505, + 199 + ], + "score": 1.0, + "content": "the dataset in question has a dominating mode(s). This enabled by our conditional flow prior, which", + "type": "text" + } + ], + "index": 9 + }, + { + "bbox": [ + 105, + 198, + 505, + 211 + ], + "spans": [ + { + "bbox": [ + 105, + 198, + 389, + 211 + ], + "score": 1.0, + "content": "ensures that conditioning information is encoded in the latent space and", + "type": "text" + }, + { + "bbox": [ + 389, + 200, + 419, + 210 + ], + "score": 0.93, + "content": "p _ { \\theta } ( \\mathbf { y } | \\mathbf { z } )", + "type": "inline_equation" + }, + { + "bbox": [ + 420, + 198, + 463, + 211 + ], + "score": 1.0, + "content": "can match", + "type": "text" + }, + { + "bbox": [ + 464, + 200, + 503, + 210 + ], + "score": 0.93, + "content": "p _ { \\theta } ( \\mathbf { y } | \\mathbf { x } , \\mathbf { z } )", + "type": "inline_equation" + }, + { + "bbox": [ + 503, + 198, + 505, + 211 + ], + "score": 1.0, + "content": ".", + "type": "text" + } + ], + "index": 10 + }, + { + "bbox": [ + 106, + 209, + 505, + 222 + ], + "spans": [ + { + "bbox": [ + 106, + 209, + 251, + 221 + ], + "score": 1.0, + "content": "Leading to a simpler factorization,", + "type": "text" + }, + { + "bbox": [ + 251, + 210, + 375, + 222 + ], + "score": 0.93, + "content": "\\begin{array} { r } { p _ { \\theta } ( \\mathbf { y } | \\mathbf { x } ) = \\int p _ { \\theta } ( \\mathbf { y } | \\mathbf { z } ) p _ { \\psi } ( \\mathbf { z } | \\mathbf { x } ) d \\mathbf { z } } \\end{array}", + "type": "inline_equation" + }, + { + "bbox": [ + 375, + 209, + 505, + 221 + ], + "score": 1.0, + "content": ". Equivalently, this ensures that", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 106, + 221, + 505, + 231 + ], + "spans": [ + { + "bbox": [ + 106, + 221, + 505, + 231 + ], + "score": 1.0, + "content": "the latent variable z cannot be ignored by the CF-VAE and thus must encode useful information.", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 105, + 230, + 505, + 243 + ], + "spans": [ + { + "bbox": [ + 105, + 230, + 505, + 243 + ], + "score": 1.0, + "content": "Note that this regularization scheme is only possible due to our conditional prior, the unconditional", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 106, + 242, + 387, + 254 + ], + "spans": [ + { + "bbox": [ + 106, + 242, + 387, + 254 + ], + "score": 1.0, + "content": "Gaussian prior of CVAE would always need to condition the decoder.", + "type": "text" + } + ], + "index": 14 + } + ], + "index": 8.5, + "bbox_fs": [ + 105, + 120, + 506, + 254 + ] + }, + { + "type": "text", + "bbox": [ + 108, + 259, + 503, + 292 + ], + "lines": [ + { + "bbox": [ + 106, + 258, + 505, + 271 + ], + "spans": [ + { + "bbox": [ + 106, + 258, + 505, + 271 + ], + "score": 1.0, + "content": "The parallel work of Klushyn et al. (2019) also proposes a similar regularization scheme. However, we", + "type": "text" + } + ], + "index": 15 + }, + { + "bbox": [ + 106, + 270, + 505, + 281 + ], + "spans": [ + { + "bbox": [ + 106, + 270, + 505, + 281 + ], + "score": 1.0, + "content": "employ this regularization to deal with posterior collapse only in case of distributions with dominant", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 105, + 280, + 459, + 293 + ], + "spans": [ + { + "bbox": [ + 105, + 280, + 459, + 293 + ], + "score": 1.0, + "content": "modes. We also provide a more detailed analysis of their proposed prior in Appendix E.", + "type": "text" + } + ], + "index": 17 + } + ], + "index": 16, + "bbox_fs": [ + 105, + 258, + 505, + 293 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 298, + 504, + 320 + ], + "lines": [ + { + "bbox": [ + 106, + 297, + 505, + 310 + ], + "spans": [ + { + "bbox": [ + 106, + 297, + 505, + 310 + ], + "score": 1.0, + "content": "Finally, we discuss the integration of diverse sources of contextual information into the conditional", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 105, + 308, + 460, + 321 + ], + "spans": [ + { + "bbox": [ + 105, + 308, + 128, + 321 + ], + "score": 1.0, + "content": "prior", + "type": "text" + }, + { + "bbox": [ + 129, + 309, + 160, + 321 + ], + "score": 0.92, + "content": "p _ { \\psi } ( { \\boldsymbol { \\mathbf { z } } } | { \\boldsymbol { \\mathbf { x } } } )", + "type": "inline_equation" + }, + { + "bbox": [ + 160, + 308, + 460, + 321 + ], + "score": 1.0, + "content": "for even richer conditional latent distributions of our regularized CF-VAE.", + "type": "text" + } + ], + "index": 19 + } + ], + "index": 18.5, + "bbox_fs": [ + 105, + 297, + 505, + 321 + ] + }, + { + "type": "title", + "bbox": [ + 108, + 333, + 372, + 344 + ], + "lines": [ + { + "bbox": [ + 105, + 332, + 374, + 346 + ], + "spans": [ + { + "bbox": [ + 105, + 332, + 374, + 346 + ], + "score": 1.0, + "content": "3.3 CONDITIONING PRIORS ON CONTEXTUAL INFORMATION", + "type": "text" + } + ], + "index": 20 + } + ], + "index": 20 + }, + { + "type": "text", + "bbox": [ + 107, + 354, + 505, + 387 + ], + "lines": [ + { + "bbox": [ + 105, + 353, + 506, + 367 + ], + "spans": [ + { + "bbox": [ + 105, + 353, + 506, + 367 + ], + "score": 1.0, + "content": "For prediction tasks, it is often crucial to integrate sources of contextual information e.g. past", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 106, + 365, + 507, + 377 + ], + "spans": [ + { + "bbox": [ + 106, + 365, + 507, + 377 + ], + "score": 1.0, + "content": "trajectories or environmental information for accurate predictions. As these sources are heterogeneous,", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 105, + 375, + 447, + 389 + ], + "spans": [ + { + "bbox": [ + 105, + 375, + 447, + 389 + ], + "score": 1.0, + "content": "we employ source specific networks to extract fixed length vectors from each source.", + "type": "text" + } + ], + "index": 23 + } + ], + "index": 22, + "bbox_fs": [ + 105, + 353, + 507, + 389 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 393, + 504, + 415 + ], + "lines": [ + { + "bbox": [ + 106, + 393, + 505, + 405 + ], + "spans": [ + { + "bbox": [ + 106, + 393, + 473, + 405 + ], + "score": 1.0, + "content": "Past Trajectory. We encode the past trajectories using a LSTM to an fixed length vector", + "type": "text" + }, + { + "bbox": [ + 473, + 394, + 483, + 404 + ], + "score": 0.84, + "content": "\\mathbf { X } _ { t }", + "type": "inline_equation" + }, + { + "bbox": [ + 483, + 393, + 505, + 405 + ], + "score": 1.0, + "content": ". For", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 106, + 403, + 497, + 416 + ], + "spans": [ + { + "bbox": [ + 106, + 403, + 497, + 416 + ], + "score": 1.0, + "content": "efficiency we share the condition encoder between the conditional flow and the CF-VAE decoder.", + "type": "text" + } + ], + "index": 25 + } + ], + "index": 24.5, + "bbox_fs": [ + 106, + 393, + 505, + 416 + ] + }, + { + "type": "text", + "bbox": [ + 108, + 420, + 503, + 453 + ], + "lines": [ + { + "bbox": [ + 106, + 420, + 505, + 433 + ], + "spans": [ + { + "bbox": [ + 106, + 420, + 505, + 433 + ], + "score": 1.0, + "content": "Environmental Map. We use a CNN to encode environmental information to a set of region specific", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 105, + 431, + 505, + 444 + ], + "spans": [ + { + "bbox": [ + 105, + 431, + 505, + 444 + ], + "score": 1.0, + "content": "feature vectors. We apply attention conditioned on the past trajectory to extract a fixed length", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 105, + 442, + 470, + 456 + ], + "spans": [ + { + "bbox": [ + 105, + 442, + 186, + 456 + ], + "score": 1.0, + "content": "conditioning vector", + "type": "text" + }, + { + "bbox": [ + 186, + 444, + 200, + 453 + ], + "score": 0.87, + "content": "\\mathbf { X } _ { m }", + "type": "inline_equation" + }, + { + "bbox": [ + 200, + 442, + 242, + 456 + ], + "score": 1.0, + "content": ", such that", + "type": "text" + }, + { + "bbox": [ + 242, + 444, + 256, + 453 + ], + "score": 0.86, + "content": "\\mathbf { X } _ { m }", + "type": "inline_equation" + }, + { + "bbox": [ + 257, + 442, + 470, + 456 + ], + "score": 1.0, + "content": "contains information relevant to the future trajectory.", + "type": "text" + } + ], + "index": 28 + } + ], + "index": 27, + "bbox_fs": [ + 105, + 420, + 505, + 456 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 459, + 505, + 559 + ], + "lines": [ + { + "bbox": [ + 106, + 459, + 505, + 471 + ], + "spans": [ + { + "bbox": [ + 106, + 459, + 505, + 471 + ], + "score": 1.0, + "content": "Interacting Agents. To encode information of interacting traffic participants/agents, we build on Deo", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 105, + 471, + 505, + 483 + ], + "spans": [ + { + "bbox": [ + 105, + 471, + 505, + 483 + ], + "score": 1.0, + "content": "& Trivedi (2018) and propose a fully convolutional social pooling layer. We aggregate information of", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 105, + 481, + 506, + 495 + ], + "spans": [ + { + "bbox": [ + 105, + 481, + 506, + 495 + ], + "score": 1.0, + "content": "interacting agents using a grid overlayed on the environment. 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We", + "type": "text" + } + ], + "index": 41 + }, + { + "bbox": [ + 105, + 638, + 403, + 650 + ], + "spans": [ + { + "bbox": [ + 105, + 638, + 403, + 650 + ], + "score": 1.0, + "content": "begin with a description of our evaluation metrics and model architecture.", + "type": "text" + } + ], + "index": 42 + } + ], + "index": 41.5, + "bbox_fs": [ + 105, + 626, + 505, + 650 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 654, + 505, + 732 + ], + "lines": [ + { + "bbox": [ + 105, + 654, + 506, + 668 + ], + "spans": [ + { + "bbox": [ + 105, + 654, + 506, + 668 + ], + "score": 1.0, + "content": "Evaluation Metrics. In line with prior work (Lee et al., 2017; Bhattacharyya et al., 2018; Pa-", + "type": "text" + } + ], + "index": 43 + }, + { + "bbox": [ + 105, + 666, + 505, + 678 + ], + "spans": [ + { + "bbox": [ + 105, + 666, + 505, + 678 + ], + "score": 1.0, + "content": "jouheshgar & Lampert, 2018; Deo & Trivedi, 2019; Bhattacharyya et al., 2019), we use the negative", + "type": "text" + } + ], + "index": 44 + }, + { + "bbox": [ + 105, + 677, + 506, + 689 + ], + "spans": [ + { + "bbox": [ + 105, + 677, + 436, + 689 + ], + "score": 1.0, + "content": "conditional log-likelihood (-CLL) and mean Euclidean distances of the oracle Top", + "type": "text" + }, + { + "bbox": [ + 437, + 677, + 452, + 687 + ], + "score": 0.87, + "content": "n \\%", + "type": "inline_equation" + }, + { + "bbox": [ + 453, + 677, + 464, + 689 + ], + "score": 1.0, + "content": "of", + "type": "text" + }, + { + "bbox": [ + 465, + 677, + 475, + 687 + ], + "score": 0.8, + "content": "N", + "type": "inline_equation" + }, + { + "bbox": [ + 475, + 677, + 506, + 689 + ], + "score": 1.0, + "content": "predic-", + "type": "text" + } + ], + "index": 45 + }, + { + "bbox": [ + 105, + 687, + 505, + 700 + ], + "spans": [ + { + "bbox": [ + 105, + 687, + 195, + 700 + ], + "score": 1.0, + "content": "tions. The oracle Top", + "type": "text" + }, + { + "bbox": [ + 195, + 688, + 210, + 698 + ], + "score": 0.85, + "content": "n \\%", + "type": "inline_equation" + }, + { + "bbox": [ + 211, + 687, + 505, + 700 + ], + "score": 1.0, + "content": "metric measures not only the coverage of all modes but also discourages", + "type": "text" + } + ], + "index": 46 + }, + { + "bbox": [ + 105, + 699, + 505, + 711 + ], + "spans": [ + { + "bbox": [ + 105, + 699, + 297, + 711 + ], + "score": 1.0, + "content": "random guessing for a reasonably large value of", + "type": "text" + }, + { + "bbox": [ + 297, + 700, + 304, + 709 + ], + "score": 0.77, + "content": "n", + "type": "inline_equation" + }, + { + "bbox": [ + 304, + 699, + 325, + 711 + ], + "score": 1.0, + "content": "(e.g.", + "type": "text" + }, + { + "bbox": [ + 325, + 699, + 364, + 709 + ], + "score": 0.89, + "content": "n = 1 0 \\%", + "type": "inline_equation" + }, + { + "bbox": [ + 364, + 699, + 505, + 711 + ], + "score": 1.0, + "content": "). This is because, a model can only", + "type": "text" + } + ], + "index": 47 + }, + { + "bbox": [ + 106, + 710, + 506, + 722 + ], + "spans": [ + { + "bbox": [ + 106, + 710, + 506, + 722 + ], + "score": 1.0, + "content": "improve this metric by moving randomly guessed samples from an overestimated mode to the correct", + "type": "text" + } + ], + "index": 48 + }, + { + "bbox": [ + 106, + 721, + 272, + 732 + ], + "spans": [ + { + "bbox": [ + 106, + 721, + 272, + 732 + ], + "score": 1.0, + "content": "modes (detailed analysis in Appendix F).", + "type": "text" + } + ], + "index": 49 + } + ], + "index": 46, + "bbox_fs": [ + 105, + 654, + 506, + 732 + ] + } + ] + }, + { + "preproc_blocks": [ + { + "type": "image", + "bbox": [ + 109, + 79, + 500, + 231 + ], + "blocks": [ + { + "type": "image_body", + "bbox": [ + 109, + 79, + 500, + 231 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 109, + 79, + 500, + 231 + ], + "spans": [ + { + "bbox": [ + 109, + 79, + 500, + 231 + ], + "score": 0.862, + "type": "image", + "image_path": "bc15a1a4cd35f188f2ad3cb9c4662d11886de5162e0be0b775766c1ecd61fb15.jpg" + } + ] + } + ], + "index": 1, + "virtual_lines": [ + { + "bbox": [ + 109, + 79, + 500, + 129.66666666666666 + ], + "spans": [], + "index": 0 + }, + { + "bbox": [ + 109, + 129.66666666666666, + 500, + 180.33333333333331 + ], + "spans": [], + "index": 1 + }, + { + "bbox": [ + 109, + 180.33333333333331, + 500, + 230.99999999999997 + ], + "spans": [], + "index": 2 + } + ] + }, + { + "type": "image_caption", + "bbox": [ + 107, + 235, + 505, + 268 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 106, + 234, + 505, + 248 + ], + "spans": [ + { + "bbox": [ + 106, + 234, + 505, + 248 + ], + "score": 1.0, + "content": "Figure 3: Random samples clustered using k-means. The number of clusters is set manually to the", + "type": "text" + } + ], + "index": 3 + }, + { + "bbox": [ + 106, + 245, + 505, + 258 + ], + "spans": [ + { + "bbox": [ + 106, + 246, + 351, + 258 + ], + "score": 1.0, + "content": "number of expected digits. The corresponding priors of our", + "type": "text" + }, + { + "bbox": [ + 351, + 245, + 410, + 256 + ], + "score": 0.5, + "content": "\\mathrm { C F - V A E + p R }", + "type": "inline_equation" + }, + { + "bbox": [ + 411, + 246, + 505, + 258 + ], + "score": 1.0, + "content": "on the right. Note, our", + "type": "text" + } + ], + "index": 4 + }, + { + "bbox": [ + 105, + 255, + 467, + 270 + ], + "spans": [ + { + "bbox": [ + 105, + 255, + 467, + 270 + ], + "score": 1.0, + "content": "64D CF-VAE latent distribution is (approximately) projected to 2D using tSNE and KDE.", + "type": "text" + } + ], + "index": 5 + } + ], + "index": 4 + } + ], + "index": 2.5 + }, + { + "type": "text", + "bbox": [ + 107, + 292, + 505, + 325 + ], + "lines": [ + { + "bbox": [ + 106, + 292, + 506, + 304 + ], + "spans": [ + { + "bbox": [ + 106, + 292, + 506, + 304 + ], + "score": 1.0, + "content": "Conditional Flow Model Architecture. Our conditional flow prior consists of 16 layers of condi-", + "type": "text" + } + ], + "index": 6 + }, + { + "bbox": [ + 106, + 304, + 505, + 316 + ], + "spans": [ + { + "bbox": [ + 106, + 304, + 505, + 316 + ], + "score": 1.0, + "content": "tional non-linear flows with split coupling. Increasing the number of conditional non-linear flows", + "type": "text" + } + ], + "index": 7 + }, + { + "bbox": [ + 105, + 314, + 363, + 327 + ], + "spans": [ + { + "bbox": [ + 105, + 314, + 363, + 327 + ], + "score": 1.0, + "content": "generally led to “over-fitting” on the training latent distribution.", + "type": "text" + } + ], + "index": 8 + } + ], + "index": 7 + }, + { + "type": "title", + "bbox": [ + 107, + 342, + 218, + 353 + ], + "lines": [ + { + "bbox": [ + 105, + 340, + 221, + 355 + ], + "spans": [ + { + "bbox": [ + 105, + 340, + 221, + 355 + ], + "score": 1.0, + "content": "4.1 MNIST SEQUENCES", + "type": "text" + } + ], + "index": 9 + } + ], + "index": 9 + }, + { + "type": "text", + "bbox": [ + 106, + 363, + 505, + 463 + ], + "lines": [ + { + "bbox": [ + 105, + 363, + 506, + 376 + ], + "spans": [ + { + "bbox": [ + 105, + 363, + 506, + 376 + ], + "score": 1.0, + "content": "The MNIST Sequence dataset (D. De Jong, 2016) consists of sequences of handwriting strokes of", + "type": "text" + } + ], + "index": 10 + }, + { + "bbox": [ + 105, + 375, + 506, + 388 + ], + "spans": [ + { + "bbox": [ + 105, + 375, + 506, + 388 + ], + "score": 1.0, + "content": "the MNIST digits. The state-of-the-art approach is the “Best-of-Many”-CVAE (Bhattacharyya et al.,", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 106, + 386, + 506, + 399 + ], + "spans": [ + { + "bbox": [ + 106, + 386, + 506, + 399 + ], + "score": 1.0, + "content": "2018) with a Gaussian prior. We follow the evaluation protocol of Bhattacharyya et al. (2018) and", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 105, + 396, + 506, + 410 + ], + "spans": [ + { + "bbox": [ + 105, + 396, + 506, + 410 + ], + "score": 1.0, + "content": "predict the complete stroke given the first ten steps. We also compare with, 1. A standard CVAE with", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 105, + 407, + 506, + 420 + ], + "spans": [ + { + "bbox": [ + 105, + 407, + 506, + 420 + ], + "score": 1.0, + "content": "uni-modal Gaussian prior; 2. A CVAE with a data dependent conditional mixture of Gaussians (MoG)", + "type": "text" + } + ], + "index": 14 + }, + { + "bbox": [ + 105, + 418, + 506, + 432 + ], + "spans": [ + { + "bbox": [ + 105, + 418, + 506, + 432 + ], + "score": 1.0, + "content": "prior; 3. A CF-VAE without any regularization ; 4. A CF-VAE without the conditional non-linear", + "type": "text" + } + ], + "index": 15 + }, + { + "bbox": [ + 105, + 428, + 506, + 443 + ], + "spans": [ + { + "bbox": [ + 105, + 428, + 506, + 443 + ], + "score": 1.0, + "content": "flow layers (CF-VAE-Affine, replaced with affine flows (Lu & Huang, 2019; Atanov et al., 2019)).", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 106, + 441, + 506, + 453 + ], + "spans": [ + { + "bbox": [ + 106, + 441, + 506, + 453 + ], + "score": 1.0, + "content": "We also experiment with a conditional MoG prior (see Appendix D and E). We use the same model", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 106, + 452, + 350, + 464 + ], + "spans": [ + { + "bbox": [ + 106, + 452, + 350, + 464 + ], + "score": 1.0, + "content": "architecture (Bhattacharyya et al., 2018) across all baselines.", + "type": "text" + } + ], + "index": 18 + } + ], + "index": 14 + }, + { + "type": "text", + "bbox": [ + 107, + 468, + 325, + 600 + ], + "lines": [ + { + "bbox": [ + 106, + 468, + 326, + 480 + ], + "spans": [ + { + "bbox": [ + 106, + 468, + 326, + 480 + ], + "score": 1.0, + "content": "We report the results in Table 1. We see that our CF-", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 105, + 479, + 326, + 492 + ], + "spans": [ + { + "bbox": [ + 105, + 479, + 326, + 492 + ], + "score": 1.0, + "content": "VAE with posterior regularization (pR) performs best.", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 105, + 490, + 326, + 502 + ], + "spans": [ + { + "bbox": [ + 105, + 490, + 271, + 502 + ], + "score": 1.0, + "content": "It has a performance advantage of over", + "type": "text" + }, + { + "bbox": [ + 272, + 491, + 292, + 501 + ], + "score": 0.86, + "content": "20 \\%", + "type": "inline_equation" + }, + { + "bbox": [ + 292, + 490, + 326, + 502 + ], + "score": 1.0, + "content": "against", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 106, + 502, + 325, + 513 + ], + "spans": [ + { + "bbox": [ + 106, + 502, + 325, + 513 + ], + "score": 1.0, + "content": "the state of the art BMS-CVAE. We see that without", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 105, + 513, + 325, + 524 + ], + "spans": [ + { + "bbox": [ + 105, + 513, + 166, + 524 + ], + "score": 1.0, + "content": "regularization", + "type": "text" + }, + { + "bbox": [ + 166, + 513, + 185, + 524 + ], + "score": 0.28, + "content": "\\left( \\mathrm { p R } \\right)", + "type": "inline_equation" + }, + { + "bbox": [ + 186, + 513, + 190, + 524 + ], + "score": 0.0, + "content": "", + "type": "text" + }, + { + "bbox": [ + 190, + 513, + 227, + 523 + ], + "score": 0.85, + "content": "\\mathrm { { C } = 0 . 2 }", + "type": "inline_equation" + }, + { + "bbox": [ + 227, + 513, + 271, + 524 + ], + "score": 1.0, + "content": ") there is a", + "type": "text" + }, + { + "bbox": [ + 271, + 513, + 291, + 523 + ], + "score": 0.88, + "content": "40 \\%", + "type": "inline_equation" + }, + { + "bbox": [ + 292, + 513, + 325, + 524 + ], + "score": 1.0, + "content": "drop in", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 105, + 523, + 326, + 535 + ], + "spans": [ + { + "bbox": [ + 105, + 523, + 326, + 535 + ], + "score": 1.0, + "content": "performance, highlighting the effectiveness of our pro-", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 104, + 534, + 326, + 546 + ], + "spans": [ + { + "bbox": [ + 104, + 534, + 326, + 546 + ], + "score": 1.0, + "content": "posed regularization scheme. 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Method-CLL↓
CVAE (Sohn et al.,2015)96.4
BMS-CVAE (Bhattacharyya et al., 2018)95.6
CVAE+ increased capacity (Ours)94.5
CVAE + conditional prior (Ours)88.9
MoG-CVAE,M= 384.6
CF-VAE -no regularization (Ours)104.3
CF-VAE - Affine + pR, C = 0.2 (Ours)77.2
CF-VAE + pR,C= 0.2 (Ours)74.9
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Note, our", + "type": "text" + } + ], + "index": 4 + }, + { + "bbox": [ + 105, + 255, + 467, + 270 + ], + "spans": [ + { + "bbox": [ + 105, + 255, + 467, + 270 + ], + "score": 1.0, + "content": "64D CF-VAE latent distribution is (approximately) projected to 2D using tSNE and KDE.", + "type": "text" + } + ], + "index": 5 + } + ], + "index": 4 + } + ], + "index": 2.5 + }, + { + "type": "text", + "bbox": [ + 107, + 292, + 505, + 325 + ], + "lines": [ + { + "bbox": [ + 106, + 292, + 506, + 304 + ], + "spans": [ + { + "bbox": [ + 106, + 292, + 506, + 304 + ], + "score": 1.0, + "content": "Conditional Flow Model Architecture. Our conditional flow prior consists of 16 layers of condi-", + "type": "text" + } + ], + "index": 6 + }, + { + "bbox": [ + 106, + 304, + 505, + 316 + ], + "spans": [ + { + "bbox": [ + 106, + 304, + 505, + 316 + ], + "score": 1.0, + "content": "tional non-linear flows with split coupling. 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A CF-VAE without the conditional non-linear", + "type": "text" + } + ], + "index": 15 + }, + { + "bbox": [ + 105, + 428, + 506, + 443 + ], + "spans": [ + { + "bbox": [ + 105, + 428, + 506, + 443 + ], + "score": 1.0, + "content": "flow layers (CF-VAE-Affine, replaced with affine flows (Lu & Huang, 2019; Atanov et al., 2019)).", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 106, + 441, + 506, + 453 + ], + "spans": [ + { + "bbox": [ + 106, + 441, + 506, + 453 + ], + "score": 1.0, + "content": "We also experiment with a conditional MoG prior (see Appendix D and E). We use the same model", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 106, + 452, + 350, + 464 + ], + "spans": [ + { + "bbox": [ + 106, + 452, + 350, + 464 + ], + "score": 1.0, + "content": "architecture (Bhattacharyya et al., 2018) across all baselines.", + "type": "text" + } + ], + "index": 18 + } + ], + "index": 14, + "bbox_fs": [ + 105, + 363, + 506, + 464 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 468, + 325, + 600 + ], + "lines": [ + { + "bbox": [ + 106, + 468, + 326, + 480 + ], + "spans": [ + { + "bbox": [ + 106, + 468, + 326, + 480 + ], + "score": 1.0, + "content": "We report the results in Table 1. We see that our CF-", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 105, + 479, + 326, + 492 + ], + "spans": [ + { + "bbox": [ + 105, + 479, + 326, + 492 + ], + "score": 1.0, + "content": "VAE with posterior regularization (pR) performs best.", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 105, + 490, + 326, + 502 + ], + "spans": [ + { + "bbox": [ + 105, + 490, + 271, + 502 + ], + "score": 1.0, + "content": "It has a performance advantage of over", + "type": "text" + }, + { + "bbox": [ + 272, + 491, + 292, + 501 + ], + "score": 0.86, + "content": "20 \\%", + "type": "inline_equation" + }, + { + "bbox": [ + 292, + 490, + 326, + 502 + ], + "score": 1.0, + "content": "against", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 106, + 502, + 325, + 513 + ], + "spans": [ + { + "bbox": [ + 106, + 502, + 325, + 513 + ], + "score": 1.0, + "content": "the state of the art BMS-CVAE. 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Method-CLL↓
CVAE (Sohn et al.,2015)96.4
BMS-CVAE (Bhattacharyya et al., 2018)95.6
CVAE+ increased capacity (Ours)94.5
CVAE + conditional prior (Ours)88.9
MoG-CVAE,M= 384.6
CF-VAE -no regularization (Ours)104.3
CF-VAE - Affine + pR, C = 0.2 (Ours)77.2
CF-VAE + pR,C= 0.2 (Ours)74.9
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MethodVisualError @1secError@ 2secError @ 3secError@4sec-CLL↓
“Shotgun"(Top 10%)(Pajouheshgar & Lampert,2018)None0.71.73.04.591.6
DESIRE-SI-IT4 (Top 10%) (Lee et al.,2017)RGB1.22.33.45.3X
STCNN (Top 10%)(Pajouheshgar & Lampert, 2018)RGB1.22.13.34.6X
BMS-CVAE(Top 10%)(Bhattacharyya et al.,2018)RGB0.81.73.14.6126.6
MoG-CVAE,M=3(Top 10%)None0.81.72.73.986.1
CF-VAE- no regularization (Ours,Top 10%)None0.91.93.34.796.2
CF-VAE+pR,C= 0.2 (Ours,Top 10%)None0.71.52.53.684.6
CF-VAE+ pR,C= 0.2(Ours,Top 10%)RGB0.71.52.43.584.1
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MethodmADE↓mFDE↓
SocialGAN(Gupta et al., 2018)27.241.4
MATF GAN (Zhao et al., 2019)22.533.5
SoPhie (Sadeghian et al., 2019)16.229.3
Goal Prediction (Deo & Trivedi,2019)15.728.1
CF-VAE+pR,C=0.2(Ours)12.622.3
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MethodVisualError @1secError@ 2secError @ 3secError@4sec-CLL↓
“Shotgun"(Top 10%)(Pajouheshgar & Lampert,2018)None0.71.73.04.591.6
DESIRE-SI-IT4 (Top 10%) (Lee et al.,2017)RGB1.22.33.45.3X
STCNN (Top 10%)(Pajouheshgar & Lampert, 2018)RGB1.22.13.34.6X
BMS-CVAE(Top 10%)(Bhattacharyya et al.,2018)RGB0.81.73.14.6126.6
MoG-CVAE,M=3(Top 10%)None0.81.72.73.986.1
CF-VAE- no regularization (Ours,Top 10%)None0.91.93.34.796.2
CF-VAE+pR,C= 0.2 (Ours,Top 10%)None0.71.52.53.684.6
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MethodmADE↓mFDE↓
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This again", + "type": "text" + } + ], + "index": 3 + }, + { + "bbox": [ + 106, + 127, + 505, + 138 + ], + "spans": [ + { + "bbox": [ + 106, + 127, + 505, + 138 + ], + "score": 1.0, + "content": "reinforces our claim that the standard Gaussian prior induces a strong model bias and data dependent", + "type": "text" + } + ], + "index": 4 + }, + { + "bbox": [ + 105, + 137, + 506, + 150 + ], + "spans": [ + { + "bbox": [ + 105, + 137, + 506, + 150 + ], + "score": 1.0, + "content": "multi-modal priors are needed for best performance. The performance advantage of CF-VAE over", + "type": "text" + } + ], + "index": 5 + }, + { + "bbox": [ + 105, + 149, + 505, + 161 + ], + "spans": [ + { + "bbox": [ + 105, + 149, + 505, + 161 + ], + "score": 1.0, + "content": "the MoG-CVAE again illustrates the advantage of normalizing flows at learning complex conditional", + "type": "text" + } + ], + "index": 6 + }, + { + "bbox": [ + 105, + 159, + 506, + 172 + ], + "spans": [ + { + "bbox": [ + 105, + 159, + 506, + 172 + ], + "score": 1.0, + "content": "multi-modal distributions. The performance advantage over the “Shotgun” baseline shows that our", + "type": "text" + } + ], + "index": 7 + }, + { + "bbox": [ + 106, + 170, + 505, + 183 + ], + "spans": [ + { + "bbox": [ + 106, + 170, + 167, + 182 + ], + "score": 0.37, + "content": "\\mathrm { C F - V A E + p R }", + "type": "inline_equation" + }, + { + "bbox": [ + 167, + 170, + 505, + 183 + ], + "score": 1.0, + "content": "not only learns to capture the correct modes but also generates more fine-grained", + "type": "text" + } + ], + "index": 8 + }, + { + "bbox": [ + 105, + 181, + 505, + 194 + ], + "spans": [ + { + "bbox": [ + 105, + 181, + 505, + 194 + ], + "score": 1.0, + "content": "predictions. The qualitative examples in Figure 5 shows that our CF-VAE is better able to capture", + "type": "text" + } + ], + "index": 9 + }, + { + "bbox": [ + 105, + 192, + 259, + 204 + ], + "spans": [ + { + "bbox": [ + 105, + 192, + 259, + 204 + ], + "score": 1.0, + "content": "complex trajectories with sharp turns.", + "type": "text" + } + ], + "index": 10 + } + ], + "index": 5 + }, + { + "type": "text", + "bbox": [ + 107, + 209, + 505, + 286 + ], + "lines": [ + { + "bbox": [ + 106, + 209, + 506, + 221 + ], + "spans": [ + { + "bbox": [ + 106, + 209, + 506, + 221 + ], + "score": 1.0, + "content": "We report results using the single train/test split of (Robicquet et al., 2016; Sadeghian et al., 2018;", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 106, + 219, + 506, + 232 + ], + "spans": [ + { + "bbox": [ + 106, + 219, + 506, + 232 + ], + "score": 1.0, + "content": "2019; Deo & Trivedi, 2019) in Table 3. We use the minimum Average Displacement Error (mADE)", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 105, + 230, + 506, + 244 + ], + "spans": [ + { + "bbox": [ + 105, + 230, + 506, + 244 + ], + "score": 1.0, + "content": "and minimum Final Displacement Error (mFDE) metrics as in (Deo & Trivedi, 2019). The minimum", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 104, + 241, + 506, + 256 + ], + "spans": [ + { + "bbox": [ + 104, + 241, + 256, + 256 + ], + "score": 1.0, + "content": "is over as set of predictions of size", + "type": "text" + }, + { + "bbox": [ + 257, + 243, + 267, + 252 + ], + "score": 0.73, + "content": "N", + "type": "inline_equation" + }, + { + "bbox": [ + 267, + 241, + 506, + 256 + ], + "score": 1.0, + "content": ". Although this metric is less robust to random guessing", + "type": "text" + } + ], + "index": 14 + }, + { + "bbox": [ + 106, + 252, + 506, + 264 + ], + "spans": [ + { + "bbox": [ + 106, + 252, + 189, + 264 + ], + "score": 1.0, + "content": "compared to the Top", + "type": "text" + }, + { + "bbox": [ + 190, + 253, + 205, + 263 + ], + "score": 0.85, + "content": "n \\%", + "type": "inline_equation" + }, + { + "bbox": [ + 205, + 252, + 493, + 264 + ], + "score": 1.0, + "content": "metric, it avoids rewarding random guessing for a small enough value of", + "type": "text" + }, + { + "bbox": [ + 493, + 253, + 503, + 263 + ], + "score": 0.8, + "content": "N", + "type": "inline_equation" + }, + { + "bbox": [ + 503, + 252, + 506, + 264 + ], + "score": 1.0, + "content": ".", + "type": "text" + } + ], + "index": 15 + }, + { + "bbox": [ + 106, + 263, + 506, + 276 + ], + "spans": [ + { + "bbox": [ + 106, + 263, + 152, + 276 + ], + "score": 1.0, + "content": "We choose", + "type": "text" + }, + { + "bbox": [ + 152, + 264, + 186, + 274 + ], + "score": 0.9, + "content": "N = 2 0", + "type": "inline_equation" + }, + { + "bbox": [ + 186, + 263, + 506, + 276 + ], + "score": 1.0, + "content": "as in (Deo & Trivedi, 2019). Similar to the results with 5 fold cross validation,", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 105, + 275, + 329, + 286 + ], + "spans": [ + { + "bbox": [ + 105, + 275, + 153, + 286 + ], + "score": 1.0, + "content": "we observe", + "type": "text" + }, + { + "bbox": [ + 153, + 275, + 173, + 285 + ], + "score": 0.84, + "content": "20 \\%", + "type": "inline_equation" + }, + { + "bbox": [ + 173, + 275, + 329, + 286 + ], + "score": 1.0, + "content": "improvement over the state-of-the-art.", + "type": "text" + } + ], + "index": 17 + } + ], + "index": 14 + }, + { + "type": "title", + "bbox": [ + 107, + 299, + 162, + 311 + ], + "lines": [ + { + "bbox": [ + 106, + 299, + 163, + 312 + ], + "spans": [ + { + "bbox": [ + 106, + 299, + 163, + 312 + ], + "score": 1.0, + "content": "4.3 HIGHD", + "type": "text" + } + ], + "index": 18 + } + ], + "index": 18 + }, + { + "type": "text", + "bbox": [ + 109, + 320, + 504, + 354 + ], + "lines": [ + { + "bbox": [ + 106, + 320, + 505, + 333 + ], + "spans": [ + { + "bbox": [ + 106, + 320, + 505, + 333 + ], + "score": 1.0, + "content": "The HighD dataset (Krajewski et al., 2018) consists of vehicle trajectories recorded using a drone", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 106, + 331, + 505, + 343 + ], + "spans": [ + { + "bbox": [ + 106, + 331, + 505, + 343 + ], + "score": 1.0, + "content": "over highways. In contrast to other vehicle trajectory datasets e.g. NGSIM it contains minimal false", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 106, + 343, + 367, + 355 + ], + "spans": [ + { + "bbox": [ + 106, + 343, + 367, + 355 + ], + "score": 1.0, + "content": "positive trajectory collisions or physically improvable velocities.", + "type": "text" + } + ], + "index": 21 + } + ], + "index": 20 + }, + { + "type": "text", + "bbox": [ + 107, + 360, + 282, + 469 + ], + "lines": [ + { + "bbox": [ + 106, + 359, + 283, + 371 + ], + "spans": [ + { + "bbox": [ + 106, + 359, + 283, + 371 + ], + "score": 1.0, + "content": "The HighD dataset is challenging because", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 106, + 370, + 282, + 381 + ], + "spans": [ + { + "bbox": [ + 106, + 370, + 252, + 381 + ], + "score": 1.0, + "content": "lane changes or interactions are rare", + "type": "text" + }, + { + "bbox": [ + 252, + 370, + 282, + 381 + ], + "score": 0.86, + "content": "\\sim 1 0 \\%", + "type": "inline_equation" + } + ], + "index": 23 + }, + { + "bbox": [ + 106, + 381, + 282, + 393 + ], + "spans": [ + { + "bbox": [ + 106, + 381, + 282, + 393 + ], + "score": 1.0, + "content": "of all trajectories. The distribution of future", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 106, + 392, + 283, + 404 + ], + "spans": [ + { + "bbox": [ + 106, + 392, + 283, + 404 + ], + "score": 1.0, + "content": "trajectories contain a single main mode (lin-", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 106, + 403, + 283, + 414 + ], + "spans": [ + { + "bbox": [ + 106, + 403, + 283, + 414 + ], + "score": 1.0, + "content": "ear continuations) along with several minor", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 106, + 414, + 283, + 426 + ], + "spans": [ + { + "bbox": [ + 106, + 414, + 283, + 426 + ], + "score": 1.0, + "content": "modes. Thus, approaches which predict a", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 106, + 425, + 282, + 437 + ], + "spans": [ + { + "bbox": [ + 106, + 425, + 282, + 437 + ], + "score": 1.0, + "content": "single mean trajectory (targeting the main", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 106, + 436, + 283, + 448 + ], + "spans": [ + { + "bbox": [ + 106, + 436, + 283, + 448 + ], + "score": 1.0, + "content": "mode) are challenging to outperform. In Ta-", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 106, + 446, + 283, + 458 + ], + "spans": [ + { + "bbox": [ + 106, + 446, + 283, + 458 + ], + "score": 1.0, + "content": "ble 4, we see that the simple Feed Forward", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 106, + 458, + 282, + 470 + ], + "spans": [ + { + "bbox": [ + 106, + 458, + 282, + 470 + ], + "score": 1.0, + "content": "(FF) model performs well and the Graph", + "type": "text" + } + ], + "index": 31 + } + ], + "index": 26.5 + }, + { + "type": "table", + "bbox": [ + 290, + 372, + 504, + 449 + ], + "blocks": [ + { + "type": "table_body", + "bbox": [ + 290, + 372, + 504, + 449 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 290, + 372, + 504, + 449 + ], + "spans": [ + { + "bbox": [ + 290, + 372, + 504, + 449 + ], + "score": 0.977, + "html": "
MethodContextADE↓FDE↓-CLL↓
Constant VelocityNone1.092.66X
FF (Diehl et al.,2019)None0.451.09X
GAT (Diehl et al., 2019)Yes0.471.04X
CVAE(Top 10%)None0.450.965.32
CVAE+Cyclic KL(Top 10%)None0.380.804.80
CF-VAE + pR,(Ours,Top 10%)None0.440.944.71
CF-VAE+{pR,cR},(Ours,Top 10%)None0.300.573.64
CF-VAE+{pR.cR},(Ours,Top 10%)Yes0.290.553.42
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(2019), which captures interactions, only narrowly outper-", + "type": "text" + } + ], + "index": 39 + }, + { + "bbox": [ + 105, + 479, + 506, + 492 + ], + "spans": [ + { + "bbox": [ + 105, + 479, + 506, + 492 + ], + "score": 1.0, + "content": "forms the FF model. This dataset is challenging for CVAE based models as they frequently suffer", + "type": "text" + } + ], + "index": 40 + }, + { + "bbox": [ + 106, + 491, + 505, + 503 + ], + "spans": [ + { + "bbox": [ + 106, + 491, + 505, + 503 + ], + "score": 1.0, + "content": "from posterior collapse when a single mode dominates. This is clearly observed with our CVAE", + "type": "text" + } + ], + "index": 41 + }, + { + "bbox": [ + 106, + 501, + 506, + 514 + ], + "spans": [ + { + "bbox": [ + 106, + 501, + 506, + 514 + ], + "score": 1.0, + "content": "baseline in Table 4. To prevent posterior collapse, we use the cyclic KL annealing scheme proposed", + "type": "text" + } + ], + "index": 42 + }, + { + "bbox": [ + 105, + 513, + 506, + 526 + ], + "spans": [ + { + "bbox": [ + 105, + 513, + 506, + 526 + ], + "score": 1.0, + "content": "in Liu et al. (2019) (using a MoG prior did not help). This already leads to significant improvement", + "type": "text" + } + ], + "index": 43 + }, + { + "bbox": [ + 105, + 524, + 506, + 536 + ], + "spans": [ + { + "bbox": [ + 105, + 524, + 506, + 536 + ], + "score": 1.0, + "content": "over the deterministic FF and GAT baselines. We also observe posterior collapse with our CF-VAE", + "type": "text" + } + ], + "index": 44 + }, + { + "bbox": [ + 105, + 534, + 504, + 548 + ], + "spans": [ + { + "bbox": [ + 105, + 535, + 424, + 548 + ], + "score": 1.0, + "content": "model. Therefore, we regularize by removing additional conditioning (cR). Our", + "type": "text" + }, + { + "bbox": [ + 424, + 534, + 504, + 546 + ], + "score": 0.79, + "content": "\\mathrm { C F - V A E + \\{ p R , c R \\} }", + "type": "inline_equation" + } + ], + "index": 45 + }, + { + "bbox": [ + 105, + 545, + 505, + 558 + ], + "spans": [ + { + "bbox": [ + 105, + 545, + 340, + 558 + ], + "score": 1.0, + "content": "with condition regularization significantly outperforms the", + "type": "text" + }, + { + "bbox": [ + 340, + 546, + 397, + 557 + ], + "score": 0.56, + "content": "\\mathrm { C F - V A E + p R }", + "type": "inline_equation" + }, + { + "bbox": [ + 398, + 545, + 505, + 558 + ], + "score": 1.0, + "content": "and CVAE baselines (with", + "type": "text" + } + ], + "index": 46 + }, + { + "bbox": [ + 105, + 556, + 506, + 569 + ], + "spans": [ + { + "bbox": [ + 105, + 556, + 506, + 569 + ], + "score": 1.0, + "content": "cyclic KL annealing), demonstrating the effectiveness of our condition regularization scheme (cR) in", + "type": "text" + } + ], + "index": 47 + }, + { + "bbox": [ + 104, + 567, + 507, + 581 + ], + "spans": [ + { + "bbox": [ + 104, + 567, + 507, + 581 + ], + "score": 1.0, + "content": "preventing posterior collapse. 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In Ta-", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 106, + 446, + 283, + 458 + ], + "spans": [ + { + "bbox": [ + 106, + 446, + 283, + 458 + ], + "score": 1.0, + "content": "ble 4, we see that the simple Feed Forward", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 106, + 458, + 282, + 470 + ], + "spans": [ + { + "bbox": [ + 106, + 458, + 282, + 470 + ], + "score": 1.0, + "content": "(FF) model performs well and the Graph", + "type": "text" + } + ], + "index": 31 + } + ], + "index": 26.5, + "bbox_fs": [ + 106, + 359, + 283, + 470 + ] + }, + { + "type": "table", + "bbox": [ + 290, + 372, + 504, + 449 + ], + "blocks": [ + { + "type": "table_body", + "bbox": [ + 290, + 372, + 504, + 449 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 290, + 372, + 504, + 449 + ], + "spans": [ + { + "bbox": [ + 290, + 372, + 504, + 449 + ], + "score": 0.977, + "html": "
MethodContextADE↓FDE↓-CLL↓
Constant VelocityNone1.092.66X
FF (Diehl et al.,2019)None0.451.09X
GAT (Diehl et al., 2019)Yes0.471.04X
CVAE(Top 10%)None0.450.965.32
CVAE+Cyclic KL(Top 10%)None0.380.804.80
CF-VAE + pR,(Ours,Top 10%)None0.440.944.71
CF-VAE+{pR,cR},(Ours,Top 10%)None0.300.573.64
CF-VAE+{pR.cR},(Ours,Top 10%)Yes0.290.553.42
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Given x in,p(yx）Cond Affine FlowOur Cond NL Flow
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Given x in,p(yx）Cond Affine FlowOur Cond NL Flow
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", + "type": "table", + "image_path": "a35b8fb6f4fe9fdb5249f4a026ba0f0ea351ee2d79027c06d30b0f525e94860b.jpg" + } + ] + } + ], + "index": 16, + "virtual_lines": [ + { + "bbox": [ + 110, + 307, + 497, + 404.0 + ], + "spans": [], + "index": 15 + }, + { + "bbox": [ + 110, + 404.0, + 497, + 501.0 + ], + "spans": [], + "index": 16 + }, + { + "bbox": [ + 110, + 501.0, + 497, + 598.0 + ], + "spans": [], + "index": 17 + } + ] + } + ], + "index": 14.75 + }, + { + "type": "text", + "bbox": [ + 106, + 665, + 505, + 732 + ], + "lines": [ + { + "bbox": [ + 106, + 665, + 505, + 678 + ], + "spans": [ + { + "bbox": [ + 106, + 665, + 505, + 678 + ], + "score": 1.0, + "content": "We compare conditional affine flows of (Atanov et al., 2019; Lu & Huang, 2019) and our conditional", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 106, + 676, + 505, + 689 + ], + "spans": [ + { + "bbox": [ + 106, + 676, + 478, + 689 + ], + "score": 1.0, + "content": "non-linear (Cond NL) flows in Figure 6 and Figure 7. 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The attention", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 106, + 699, + 504, + 711 + ], + "spans": [ + { + "bbox": [ + 106, + 699, + 504, + 711 + ], + "score": 1.0, + "content": "weighted feature vectors are passed through a final fully connected layer to obtain the final CNN", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 106, + 709, + 505, + 722 + ], + "spans": [ + { + "bbox": [ + 106, + 709, + 505, + 722 + ], + "score": 1.0, + "content": "encoding. Furthermore, we found it helpful to additionally encode the past trajectory as an image (as", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 105, + 720, + 498, + 733 + ], + "spans": [ + { + "bbox": [ + 105, + 720, + 498, + 733 + ], + "score": 1.0, + "content": "in (Pajouheshgar & Lampert, 2018)) as provide this as an additional channel to the CNN encoder.", + "type": "text" + } + ], + "index": 33 + } + ], + "index": 29, + "bbox_fs": [ + 105, + 633, + 506, + 733 + ] + } + ] + }, + { + "preproc_blocks": [ + { + "type": "text", + "bbox": [ + 106, + 82, + 506, + 149 + ], + "lines": [ + { + "bbox": [ + 105, + 81, + 506, + 95 + ], + "spans": [ + { + "bbox": [ + 105, + 81, + 506, + 95 + ], + "score": 1.0, + "content": "HighD. We use the same model architecture with both the CVAE and CF-VAE models. 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The contextual information of interacting traffic participants are encoded into a spatial grid", + "type": "text" + } + ], + "index": 3 + }, + { + "bbox": [ + 105, + 126, + 507, + 139 + ], + "spans": [ + { + "bbox": [ + 105, + 126, + 164, + 139 + ], + "score": 1.0, + "content": "tensor of size", + "type": "text" + }, + { + "bbox": [ + 164, + 126, + 188, + 137 + ], + "score": 0.88, + "content": "1 3 \\times 3", + "type": "inline_equation" + }, + { + "bbox": [ + 189, + 126, + 507, + 139 + ], + "score": 1.0, + "content": "(see Section 3.2 of the main paper). We use a CNN with 5 layers of sizes 64,", + "type": "text" + } + ], + "index": 4 + }, + { + "bbox": [ + 105, + 137, + 317, + 149 + ], + "spans": [ + { + "bbox": [ + 105, + 137, + 317, + 149 + ], + "score": 1.0, + "content": "128, 256, 256 and 256 to extract contextual features.", + "type": "text" + } + ], + "index": 5 + } + ], + "index": 2.5 + }, + { + "type": "title", + "bbox": [ + 106, + 164, + 489, + 178 + ], + "lines": [ + { + "bbox": [ + 105, + 163, + 491, + 180 + ], + "spans": [ + { + "bbox": [ + 105, + 163, + 491, + 180 + ], + "score": 1.0, + "content": "APPENDIX D. DETAILS OF THE MIXTURE OF GAUSSIANS (MOG) BASELINE", + "type": "text" + } + ], + "index": 6 + } + ], + "index": 6 + }, + { + "type": "text", + "bbox": [ + 107, + 189, + 505, + 223 + ], + "lines": [ + { + "bbox": [ + 105, + 190, + 505, + 202 + ], + "spans": [ + { + "bbox": [ + 105, + 190, + 505, + 202 + ], + "score": 1.0, + "content": "In the main paper, we include results on the MNIST Sequence and Stanford Drone dataset with a", + "type": "text" + } + ], + "index": 7 + }, + { + "bbox": [ + 105, + 199, + 505, + 213 + ], + "spans": [ + { + "bbox": [ + 105, + 199, + 505, + 213 + ], + "score": 1.0, + "content": "Mixture of Gaussians (MoG) prior. In detail, instead of a normalizing flow, we set the prior to a MoG", + "type": "text" + } + ], + "index": 8 + }, + { + "bbox": [ + 105, + 210, + 132, + 224 + ], + "spans": [ + { + "bbox": [ + 105, + 210, + 132, + 224 + ], + "score": 1.0, + "content": "form,", + "type": "text" + } + ], + "index": 9 + } + ], + "index": 8 + }, + { + "type": "interline_equation", + "bbox": [ + 231, + 227, + 380, + 261 + ], + "lines": [ + { + "bbox": [ + 231, + 227, + 380, + 261 + ], + "spans": [ + { + "bbox": [ + 231, + 227, + 380, + 261 + ], + "score": 0.95, + "content": "p _ { \\xi } ( \\mathbf { z } | \\mathbf { x } ) = \\sum _ { i = 1 } ^ { M } p ( \\mathbf { c } _ { i } | \\mathbf { x } ) \\mathcal { N } ( \\mathbf { z } ; \\mu _ { i } , \\sigma _ { i } | \\mathbf { x } ) .", + "type": "interline_equation", + "image_path": "940352ac95f34ca5cb68175b8f476ef1c441220411a746b2a2e54b55a72194ad.jpg" + } + ] + } + ], + "index": 10.5, + "virtual_lines": [ + { + "bbox": [ + 231, + 227, + 380, + 244.0 + ], + "spans": [], + "index": 10 + }, + { + "bbox": [ + 231, + 244.0, + 380, + 261.0 + ], + "spans": [], + "index": 11 + } + ] + }, + { + "type": "text", + "bbox": [ + 107, + 271, + 505, + 316 + ], + "lines": [ + { + "bbox": [ + 106, + 272, + 505, + 282 + ], + "spans": [ + { + "bbox": [ + 106, + 272, + 403, + 282 + ], + "score": 1.0, + "content": "We use a simple feed forward neural network that takes in the condition", + "type": "text" + }, + { + "bbox": [ + 403, + 273, + 410, + 281 + ], + "score": 0.63, + "content": "\\mathbf { X }", + "type": "inline_equation" + }, + { + "bbox": [ + 410, + 272, + 505, + 282 + ], + "score": 1.0, + "content": "(see Section 3.4 of the", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 105, + 282, + 506, + 296 + ], + "spans": [ + { + "bbox": [ + 105, + 282, + 322, + 296 + ], + "score": 1.0, + "content": "main paper) and predicts the parameters of the MoG,", + "type": "text" + }, + { + "bbox": [ + 323, + 282, + 466, + 294 + ], + "score": 0.89, + "content": "\\xi = \\{ \\mathbf { c } _ { 1 } , \\mu _ { 1 } , \\sigma _ { 1 } , \\cdots , \\mathbf { c } _ { M } , \\mu _ { M } , \\sigma _ { M } \\}", + "type": "inline_equation" + }, + { + "bbox": [ + 466, + 282, + 506, + 296 + ], + "score": 1.0, + "content": ". Note, to", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 105, + 293, + 505, + 305 + ], + "spans": [ + { + "bbox": [ + 105, + 293, + 505, + 305 + ], + "score": 1.0, + "content": "ensure a reasonable number of parameters, we consider spherical Gaussians. Similar to (5) in the", + "type": "text" + } + ], + "index": 14 + }, + { + "bbox": [ + 106, + 305, + 282, + 317 + ], + "spans": [ + { + "bbox": [ + 106, + 305, + 282, + 317 + ], + "score": 1.0, + "content": "main paper, the ELBO can be expressed as,", + "type": "text" + } + ], + "index": 15 + } + ], + "index": 13.5 + }, + { + "type": "interline_equation", + "bbox": [ + 152, + 337, + 458, + 353 + ], + "lines": [ + { + "bbox": [ + 152, + 337, + 458, + 353 + ], + "spans": [ + { + "bbox": [ + 152, + 337, + 458, + 353 + ], + "score": 0.88, + "content": "\\begin{array} { r } { \\log \\bigl ( p _ { \\theta } ( \\mathbf { y } | \\mathbf { x } ) \\bigr ) \\geq \\mathbb { E } _ { q _ { \\phi } ( z | \\mathbf { x } , \\mathbf { y } ) } \\log \\bigl ( p _ { \\theta } ( \\mathbf { y } | \\mathbf { z } , \\mathbf { x } ) \\bigr ) + \\mathcal { H } ( q _ { \\phi } ) + \\mathbb { E } _ { q _ { \\phi } ( z | \\mathbf { x } , \\mathbf { y } ) } \\log \\bigl ( p _ { \\xi } ( z | \\mathbf { x } ) \\bigr ) . } \\end{array}", + "type": "interline_equation", + "image_path": "a5ab0a771610df40da0dcf5cdda4c29013663aa9ba77743db2d73aea56f6c629.jpg" + } + ] + } + ], + "index": 16, + "virtual_lines": [ + { + "bbox": [ + 152, + 337, + 458, + 353 + ], + "spans": [], + "index": 16 + } + ] + }, + { + "type": "text", + "bbox": [ + 107, + 362, + 392, + 374 + ], + "lines": [ + { + "bbox": [ + 105, + 360, + 392, + 376 + ], + "spans": [ + { + "bbox": [ + 105, + 360, + 332, + 376 + ], + "score": 1.0, + "content": "Note that we fix the entropy of the posterior distribution", + "type": "text" + }, + { + "bbox": [ + 332, + 364, + 343, + 374 + ], + "score": 0.85, + "content": "q _ { \\phi }", + "type": "inline_equation" + }, + { + "bbox": [ + 343, + 360, + 392, + 376 + ], + "score": 1.0, + "content": "for stability", + "type": "text" + } + ], + "index": 17 + } + ], + "index": 17 + }, + { + "type": "title", + "bbox": [ + 108, + 388, + 505, + 402 + ], + "lines": [ + { + "bbox": [ + 106, + 389, + 505, + 404 + ], + "spans": [ + { + "bbox": [ + 106, + 389, + 505, + 404 + ], + "score": 1.0, + "content": "APPENDIX E. ADDITIONAL EVALUATION ON THE MNIST SEQUENCE DATASET", + "type": "text" + } + ], + "index": 18 + } + ], + "index": 18 + }, + { + "type": "text", + "bbox": [ + 106, + 413, + 506, + 480 + ], + "lines": [ + { + "bbox": [ + 105, + 413, + 507, + 426 + ], + "spans": [ + { + "bbox": [ + 105, + 413, + 507, + 426 + ], + "score": 1.0, + "content": "Here, we perform a comprehensive evaluation using the MoG prior with varying mixture components,", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 106, + 425, + 506, + 436 + ], + "spans": [ + { + "bbox": [ + 106, + 425, + 506, + 436 + ], + "score": 1.0, + "content": "a CVAE with unconditional non-linear flow based prior (NL-CVAE), our CF-VAE with Volume-", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 105, + 435, + 506, + 448 + ], + "spans": [ + { + "bbox": [ + 105, + 435, + 506, + 448 + ], + "score": 1.0, + "content": "preserving constant Jacobian conditional NICE flows based on Dinh et al. (2015), a CVAE with the", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 105, + 446, + 506, + 459 + ], + "spans": [ + { + "bbox": [ + 105, + 446, + 506, + 459 + ], + "score": 1.0, + "content": "conditional VampPrior (CDV) of (Klushyn et al., 2019), our CF-VAE with varying hyper-parameters", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 107, + 456, + 506, + 470 + ], + "spans": [ + { + "bbox": [ + 107, + 458, + 175, + 470 + ], + "score": 0.83, + "content": "C = [ 0 . 0 5 , 0 . 2 5 ]", + "type": "inline_equation" + }, + { + "bbox": [ + 175, + 456, + 506, + 470 + ], + "score": 1.0, + "content": "of our posterior regularization (pR) scheme and finally analyze the effect of our", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 105, + 469, + 424, + 480 + ], + "spans": [ + { + "bbox": [ + 105, + 469, + 424, + 480 + ], + "score": 1.0, + "content": "posterior regularization (pR) scheme in detail. We report the results in Table 5.", + "type": "text" + } + ], + "index": 24 + } + ], + "index": 21.5 + }, + { + "type": "table", + "bbox": [ + 196, + 490, + 415, + 667 + ], + "blocks": [ + { + "type": "table_body", + "bbox": [ + 196, + 490, + 415, + 667 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 196, + 490, + 415, + 667 + ], + "spans": [ + { + "bbox": [ + 196, + 490, + 415, + 667 + ], + "score": 0.973, + "html": "
Method -CLL↓
NL-CVAE 107.6±1.2CVAE(M = 1) (Sohn et al., 2015) 96.4±0.2
MoG-CVAE, M = 2 85.3±0.4MoG-CVAE, M = 3 84.6±0.5MoG-CVAE, M = 4 85.7±0.4MoG-CVAE, M = 5 86.3±0.6CDV (Klushyn et al., 2019), M = 12 99.4±0.7
CF-VAE - NICE (Ours) 78.9±0.2
CF-VAE+ pR.C=0.05,(Ours）75.9±0.5
CF-VAE + pR,(,C = 0.10,(Ours)
7
75.4±0.3
CF-VAE + pR,C: = 0.15, (Ours) 75.1±0.3CF-VAE + pR,C= 0.20,(Ours) 74.9±0.2CF-VAE + pR, C = 0.25,(Ours) 75.8±0.4
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The contextual information of interacting traffic participants are encoded into a spatial grid", + "type": "text" + } + ], + "index": 3 + }, + { + "bbox": [ + 105, + 126, + 507, + 139 + ], + "spans": [ + { + "bbox": [ + 105, + 126, + 164, + 139 + ], + "score": 1.0, + "content": "tensor of size", + "type": "text" + }, + { + "bbox": [ + 164, + 126, + 188, + 137 + ], + "score": 0.88, + "content": "1 3 \\times 3", + "type": "inline_equation" + }, + { + "bbox": [ + 189, + 126, + 507, + 139 + ], + "score": 1.0, + "content": "(see Section 3.2 of the main paper). We use a CNN with 5 layers of sizes 64,", + "type": "text" + } + ], + "index": 4 + }, + { + "bbox": [ + 105, + 137, + 317, + 149 + ], + "spans": [ + { + "bbox": [ + 105, + 137, + 317, + 149 + ], + "score": 1.0, + "content": "128, 256, 256 and 256 to extract contextual features.", + "type": "text" + } + ], + "index": 5 + } + ], + "index": 2.5, + "bbox_fs": [ + 105, + 81, + 507, + 149 + ] + }, + { + "type": "title", + "bbox": [ + 106, + 164, + 489, + 178 + ], + "lines": [ + { + "bbox": [ + 105, + 163, + 491, + 180 + ], + "spans": [ + { + "bbox": [ + 105, + 163, + 491, + 180 + ], + "score": 1.0, + "content": "APPENDIX D. DETAILS OF THE MIXTURE OF GAUSSIANS (MOG) BASELINE", + "type": "text" + } + ], + "index": 6 + } + ], + "index": 6 + }, + { + "type": "text", + "bbox": [ + 107, + 189, + 505, + 223 + ], + "lines": [ + { + "bbox": [ + 105, + 190, + 505, + 202 + ], + "spans": [ + { + "bbox": [ + 105, + 190, + 505, + 202 + ], + "score": 1.0, + "content": "In the main paper, we include results on the MNIST Sequence and Stanford Drone dataset with a", + "type": "text" + } + ], + "index": 7 + }, + { + "bbox": [ + 105, + 199, + 505, + 213 + ], + "spans": [ + { + "bbox": [ + 105, + 199, + 505, + 213 + ], + "score": 1.0, + "content": "Mixture of Gaussians (MoG) prior. In detail, instead of a normalizing flow, we set the prior to a MoG", + "type": "text" + } + ], + "index": 8 + }, + { + "bbox": [ + 105, + 210, + 132, + 224 + ], + "spans": [ + { + "bbox": [ + 105, + 210, + 132, + 224 + ], + "score": 1.0, + "content": "form,", + "type": "text" + } + ], + "index": 9 + } + ], + "index": 8, + "bbox_fs": [ + 105, + 190, + 505, + 224 + ] + }, + { + "type": "interline_equation", + "bbox": [ + 231, + 227, + 380, + 261 + ], + "lines": [ + { + "bbox": [ + 231, + 227, + 380, + 261 + ], + "spans": [ + { + "bbox": [ + 231, + 227, + 380, + 261 + ], + "score": 0.95, + "content": "p _ { \\xi } ( \\mathbf { z } | \\mathbf { x } ) = \\sum _ { i = 1 } ^ { M } p ( \\mathbf { c } _ { i } | \\mathbf { x } ) \\mathcal { N } ( \\mathbf { z } ; \\mu _ { i } , \\sigma _ { i } | \\mathbf { x } ) .", + "type": "interline_equation", + "image_path": "940352ac95f34ca5cb68175b8f476ef1c441220411a746b2a2e54b55a72194ad.jpg" + } + ] + } + ], + "index": 10.5, + "virtual_lines": [ + { + "bbox": [ + 231, + 227, + 380, + 244.0 + ], + "spans": [], + "index": 10 + }, + { + "bbox": [ + 231, + 244.0, + 380, + 261.0 + ], + "spans": [], + "index": 11 + } + ] + }, + { + "type": "text", + "bbox": [ + 107, + 271, + 505, + 316 + ], + "lines": [ + { + "bbox": [ + 106, + 272, + 505, + 282 + ], + "spans": [ + { + "bbox": [ + 106, + 272, + 403, + 282 + ], + "score": 1.0, + "content": "We use a simple feed forward neural network that takes in the condition", + "type": "text" + }, + { + "bbox": [ + 403, + 273, + 410, + 281 + ], + "score": 0.63, + "content": "\\mathbf { X }", + "type": "inline_equation" + }, + { + "bbox": [ + 410, + 272, + 505, + 282 + ], + "score": 1.0, + "content": "(see Section 3.4 of the", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 105, + 282, + 506, + 296 + ], + "spans": [ + { + "bbox": [ + 105, + 282, + 322, + 296 + ], + "score": 1.0, + "content": "main paper) and predicts the parameters of the MoG,", + "type": "text" + }, + { + "bbox": [ + 323, + 282, + 466, + 294 + ], + "score": 0.89, + "content": "\\xi = \\{ \\mathbf { c } _ { 1 } , \\mu _ { 1 } , \\sigma _ { 1 } , \\cdots , \\mathbf { c } _ { M } , \\mu _ { M } , \\sigma _ { M } \\}", + "type": "inline_equation" + }, + { + "bbox": [ + 466, + 282, + 506, + 296 + ], + "score": 1.0, + "content": ". Note, to", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 105, + 293, + 505, + 305 + ], + "spans": [ + { + "bbox": [ + 105, + 293, + 505, + 305 + ], + "score": 1.0, + "content": "ensure a reasonable number of parameters, we consider spherical Gaussians. Similar to (5) in the", + "type": "text" + } + ], + "index": 14 + }, + { + "bbox": [ + 106, + 305, + 282, + 317 + ], + "spans": [ + { + "bbox": [ + 106, + 305, + 282, + 317 + ], + "score": 1.0, + "content": "main paper, the ELBO can be expressed as,", + "type": "text" + } + ], + "index": 15 + } + ], + "index": 13.5, + "bbox_fs": [ + 105, + 272, + 506, + 317 + ] + }, + { + "type": "interline_equation", + "bbox": [ + 152, + 337, + 458, + 353 + ], + "lines": [ + { + "bbox": [ + 152, + 337, + 458, + 353 + ], + "spans": [ + { + "bbox": [ + 152, + 337, + 458, + 353 + ], + "score": 0.88, + "content": "\\begin{array} { r } { \\log \\bigl ( p _ { \\theta } ( \\mathbf { y } | \\mathbf { x } ) \\bigr ) \\geq \\mathbb { E } _ { q _ { \\phi } ( z | \\mathbf { x } , \\mathbf { y } ) } \\log \\bigl ( p _ { \\theta } ( \\mathbf { y } | \\mathbf { z } , \\mathbf { x } ) \\bigr ) + \\mathcal { H } ( q _ { \\phi } ) + \\mathbb { E } _ { q _ { \\phi } ( z | \\mathbf { x } , \\mathbf { y } ) } \\log \\bigl ( p _ { \\xi } ( z | \\mathbf { x } ) \\bigr ) . } \\end{array}", + "type": "interline_equation", + "image_path": "a5ab0a771610df40da0dcf5cdda4c29013663aa9ba77743db2d73aea56f6c629.jpg" + } + ] + } + ], + "index": 16, + "virtual_lines": [ + { + "bbox": [ + 152, + 337, + 458, + 353 + ], + "spans": [], + "index": 16 + } + ] + }, + { + "type": "text", + "bbox": [ + 107, + 362, + 392, + 374 + ], + "lines": [ + { + "bbox": [ + 105, + 360, + 392, + 376 + ], + "spans": [ + { + "bbox": [ + 105, + 360, + 332, + 376 + ], + "score": 1.0, + "content": "Note that we fix the entropy of the posterior distribution", + "type": "text" + }, + { + "bbox": [ + 332, + 364, + 343, + 374 + ], + "score": 0.85, + "content": "q _ { \\phi }", + "type": "inline_equation" + }, + { + "bbox": [ + 343, + 360, + 392, + 376 + ], + "score": 1.0, + "content": "for stability", + "type": "text" + } + ], + "index": 17 + } + ], + "index": 17, + "bbox_fs": [ + 105, + 360, + 392, + 376 + ] + }, + { + "type": "title", + "bbox": [ + 108, + 388, + 505, + 402 + ], + "lines": [ + { + "bbox": [ + 106, + 389, + 505, + 404 + ], + "spans": [ + { + "bbox": [ + 106, + 389, + 505, + 404 + ], + "score": 1.0, + "content": "APPENDIX E. ADDITIONAL EVALUATION ON THE MNIST SEQUENCE DATASET", + "type": "text" + } + ], + "index": 18 + } + ], + "index": 18 + }, + { + "type": "text", + "bbox": [ + 106, + 413, + 506, + 480 + ], + "lines": [ + { + "bbox": [ + 105, + 413, + 507, + 426 + ], + "spans": [ + { + "bbox": [ + 105, + 413, + 507, + 426 + ], + "score": 1.0, + "content": "Here, we perform a comprehensive evaluation using the MoG prior with varying mixture components,", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 106, + 425, + 506, + 436 + ], + "spans": [ + { + "bbox": [ + 106, + 425, + 506, + 436 + ], + "score": 1.0, + "content": "a CVAE with unconditional non-linear flow based prior (NL-CVAE), our CF-VAE with Volume-", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 105, + 435, + 506, + 448 + ], + "spans": [ + { + "bbox": [ + 105, + 435, + 506, + 448 + ], + "score": 1.0, + "content": "preserving constant Jacobian conditional NICE flows based on Dinh et al. (2015), a CVAE with the", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 105, + 446, + 506, + 459 + ], + "spans": [ + { + "bbox": [ + 105, + 446, + 506, + 459 + ], + "score": 1.0, + "content": "conditional VampPrior (CDV) of (Klushyn et al., 2019), our CF-VAE with varying hyper-parameters", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 107, + 456, + 506, + 470 + ], + "spans": [ + { + "bbox": [ + 107, + 458, + 175, + 470 + ], + "score": 0.83, + "content": "C = [ 0 . 0 5 , 0 . 2 5 ]", + "type": "inline_equation" + }, + { + "bbox": [ + 175, + 456, + 506, + 470 + ], + "score": 1.0, + "content": "of our posterior regularization (pR) scheme and finally analyze the effect of our", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 105, + 469, + 424, + 480 + ], + "spans": [ + { + "bbox": [ + 105, + 469, + 424, + 480 + ], + "score": 1.0, + "content": "posterior regularization (pR) scheme in detail. We report the results in Table 5.", + "type": "text" + } + ], + "index": 24 + } + ], + "index": 21.5, + "bbox_fs": [ + 105, + 413, + 507, + 480 + ] + }, + { + "type": "table", + "bbox": [ + 196, + 490, + 415, + 667 + ], + "blocks": [ + { + "type": "table_body", + "bbox": [ + 196, + 490, + 415, + 667 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 196, + 490, + 415, + 667 + ], + "spans": [ + { + "bbox": [ + 196, + 490, + 415, + 667 + ], + "score": 0.973, + "html": "
Method -CLL↓
NL-CVAE 107.6±1.2CVAE(M = 1) (Sohn et al., 2015) 96.4±0.2
MoG-CVAE, M = 2 85.3±0.4MoG-CVAE, M = 3 84.6±0.5MoG-CVAE, M = 4 85.7±0.4MoG-CVAE, M = 5 86.3±0.6CDV (Klushyn et al., 2019), M = 12 99.4±0.7
CF-VAE - NICE (Ours) 78.9±0.2
CF-VAE+ pR.C=0.05,(Ours）75.9±0.5
CF-VAE + pR,(,C = 0.10,(Ours)
7
75.4±0.3
CF-VAE + pR,C: = 0.15, (Ours) 75.1±0.3CF-VAE + pR,C= 0.20,(Ours) 74.9��0.2CF-VAE + pR, C = 0.25,(Ours) 75.8±0.4
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As mentioned in the main paper, we see that the MoG-CVAE outperforms the plain", + "type": "text" + } + ], + "index": 39 + }, + { + "bbox": [ + 106, + 710, + 505, + 722 + ], + "spans": [ + { + "bbox": [ + 106, + 710, + 505, + 722 + ], + "score": 1.0, + "content": "CVAE. This again reinforces our claim that the standard Gaussian prior induces a strong model", + "type": "text" + } + ], + "index": 40 + }, + { + "bbox": [ + 106, + 721, + 505, + 733 + ], + "spans": [ + { + "bbox": [ + 106, + 721, + 206, + 733 + ], + "score": 1.0, + "content": "bias. We see that using", + "type": "text" + }, + { + "bbox": [ + 206, + 721, + 239, + 731 + ], + "score": 0.9, + "content": "M = 3", + "type": "inline_equation" + }, + { + "bbox": [ + 239, + 721, + 505, + 733 + ], + "score": 1.0, + "content": "components with the variance of the posterior distribution fixed", + "type": "text" + } + ], + "index": 41 + }, + { + "bbox": [ + 105, + 274, + 506, + 287 + ], + "spans": [ + { + "bbox": [ + 105, + 274, + 117, + 287 + ], + "score": 1.0, + "content": "to", + "type": "text", + "cross_page": true + }, + { + "bbox": [ + 117, + 275, + 154, + 285 + ], + "score": 0.88, + "content": "C = 0 . 2", + "type": "inline_equation", + "cross_page": true + }, + { + "bbox": [ + 155, + 274, + 506, + 287 + ], + "score": 1.0, + "content": "leads to the best performance. This is expected as 3 is the most frequent number of", + "type": "text", + "cross_page": true + } + ], + "index": 13 + }, + { + "bbox": [ + 104, + 284, + 506, + 299 + ], + "spans": [ + { + "bbox": [ + 104, + 284, + 506, + 299 + ], + "score": 1.0, + "content": "possible strokes in the MNIST Sequence dataset. Also note that the results with the MoG prior are", + "type": "text", + "cross_page": true + } + ], + "index": 14 + }, + { + "bbox": [ + 106, + 295, + 505, + 308 + ], + "spans": [ + { + "bbox": [ + 106, + 295, + 221, + 308 + ], + "score": 1.0, + "content": "also relatively robust across", + "type": "text", + "cross_page": true + }, + { + "bbox": [ + 222, + 296, + 289, + 308 + ], + "score": 0.87, + "content": "\\mathbf { C } = [ 0 . 0 5 , 0 . 2 5 ]", + "type": "inline_equation", + "cross_page": true + }, + { + "bbox": [ + 289, + 295, + 505, + 308 + ], + "score": 1.0, + "content": "as we learn the variance of the prior (see the section", + "type": "text", + "cross_page": true + } + ], + "index": 15 + }, + { + "bbox": [ + 105, + 307, + 506, + 320 + ], + "spans": [ + { + "bbox": [ + 105, + 307, + 190, + 320 + ], + "score": 1.0, + "content": "above). Finally, our", + "type": "text", + "cross_page": true + }, + { + "bbox": [ + 190, + 307, + 250, + 318 + ], + "score": 0.27, + "content": "\\mathrm { C F - V A E + p R }", + "type": "inline_equation", + "cross_page": true + }, + { + "bbox": [ + 251, + 307, + 506, + 320 + ], + "score": 1.0, + "content": "still significantly outperforms the MoG-CVAE (74.9 vs 84.6).", + "type": "text", + "cross_page": true + } + ], + "index": 16 + }, + { + "bbox": [ + 105, + 317, + 506, + 331 + ], + "spans": [ + { + "bbox": [ + 105, + 317, + 506, + 331 + ], + "score": 1.0, + "content": "This is expected as normalizing flows are more powerful compared to MoG at learning complex", + "type": "text", + "cross_page": true + } + ], + "index": 17 + }, + { + "bbox": [ + 105, + 328, + 405, + 342 + ], + "spans": [ + { + "bbox": [ + 105, + 328, + 405, + 342 + ], + "score": 1.0, + "content": "multi-modal distributions (Kingma & Dhariwal, 2018) (also see Figure 8).", + "type": "text", + "cross_page": true + } + ], + "index": 18 + } + ], + "index": 40, + "bbox_fs": [ + 105, + 698, + 505, + 733 + ] + } + ] + }, + { + "preproc_blocks": [ + { + "type": "image", + "bbox": [ + 187, + 79, + 423, + 183 + ], + "blocks": [ + { + "type": "image_body", + "bbox": [ + 187, + 79, + 423, + 183 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 187, + 79, + 423, + 183 + ], + "spans": [ + { + "bbox": [ + 187, + 79, + 423, + 183 + ], + "score": 0.963, + "type": "image", + "image_path": "50a15d633cd65996bc46084a5bd7bce523dc1a79afdd807f07ca89c64a1e2b37.jpg" + } + ] + } + ], + "index": 3.5, + "virtual_lines": [ + { + "bbox": [ + 187, + 79, + 423, + 92.0 + ], + "spans": [], + "index": 0 + }, + { + "bbox": [ + 187, + 92.0, + 423, + 105.0 + ], + "spans": [], + "index": 1 + }, + { + "bbox": [ + 187, + 105.0, + 423, + 118.0 + ], + "spans": [], + "index": 2 + }, + { + "bbox": [ + 187, + 118.0, + 423, + 131.0 + ], + "spans": [], + "index": 3 + }, + { + "bbox": [ + 187, + 131.0, + 423, + 144.0 + ], + "spans": [], + "index": 4 + }, + { + "bbox": [ + 187, + 144.0, + 423, + 157.0 + ], + "spans": [], + "index": 5 + }, + { + "bbox": [ + 187, + 157.0, + 423, + 170.0 + ], + "spans": [], + "index": 6 + }, + { + "bbox": [ + 187, + 170.0, + 423, + 183.0 + ], + "spans": [], + "index": 7 + } + ] + }, + { + "type": "image_caption", + "bbox": [ + 106, + 195, + 506, + 250 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 106, + 195, + 506, + 207 + ], + "spans": [ + { + "bbox": [ + 106, + 195, + 467, + 207 + ], + "score": 1.0, + "content": "Figure 9: Random samples using the CDV Prior of (Klushyn et al., 2019) clustered using", + "type": "text" + }, + { + "bbox": [ + 467, + 196, + 474, + 205 + ], + "score": 0.27, + "content": "\\mathbf { k } .", + "type": "inline_equation" + }, + { + "bbox": [ + 475, + 195, + 506, + 207 + ], + "score": 1.0, + "content": "-means.", + "type": "text" + } + ], + "index": 8 + }, + { + "bbox": [ + 105, + 204, + 505, + 218 + ], + "spans": [ + { + "bbox": [ + 105, + 204, + 505, + 218 + ], + "score": 1.0, + "content": "The number of clusters is set manually to the number of expected digits. The CDV Prior latent", + "type": "text" + } + ], + "index": 9 + }, + { + "bbox": [ + 105, + 214, + 506, + 231 + ], + "spans": [ + { + "bbox": [ + 105, + 214, + 506, + 231 + ], + "score": 1.0, + "content": "distribution on the right. Note, the 64D latent distribution is (approximately) projected to 2D using", + "type": "text" + } + ], + "index": 10 + }, + { + "bbox": [ + 105, + 226, + 505, + 242 + ], + "spans": [ + { + "bbox": [ + 105, + 226, + 505, + 242 + ], + "score": 1.0, + "content": "tSNE and KDE. In comparison to the samples and latent spaces of our CF-VAE (Figure 3) we see", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 105, + 237, + 407, + 252 + ], + "spans": [ + { + "bbox": [ + 105, + 237, + 407, + 252 + ], + "score": 1.0, + "content": "that the latent spaces are more simplistic and samples are of poorer quality.", + "type": "text" + } + ], + "index": 12 + } + ], + "index": 10 + } + ], + "index": 6.75 + }, + { + "type": "text", + "bbox": [ + 106, + 274, + 505, + 340 + ], + "lines": [ + { + "bbox": [ + 105, + 274, + 506, + 287 + ], + "spans": [ + { + "bbox": [ + 105, + 274, + 117, + 287 + ], + "score": 1.0, + "content": "to", + "type": "text" + }, + { + "bbox": [ + 117, + 275, + 154, + 285 + ], + "score": 0.88, + "content": "C = 0 . 2", + "type": "inline_equation" + }, + { + "bbox": [ + 155, + 274, + 506, + 287 + ], + "score": 1.0, + "content": "leads to the best performance. This is expected as 3 is the most frequent number of", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 104, + 284, + 506, + 299 + ], + "spans": [ + { + "bbox": [ + 104, + 284, + 506, + 299 + ], + "score": 1.0, + "content": "possible strokes in the MNIST Sequence dataset. Also note that the results with the MoG prior are", + "type": "text" + } + ], + "index": 14 + }, + { + "bbox": [ + 106, + 295, + 505, + 308 + ], + "spans": [ + { + "bbox": [ + 106, + 295, + 221, + 308 + ], + "score": 1.0, + "content": "also relatively robust across", + "type": "text" + }, + { + "bbox": [ + 222, + 296, + 289, + 308 + ], + "score": 0.87, + "content": "\\mathbf { C } = [ 0 . 0 5 , 0 . 2 5 ]", + "type": "inline_equation" + }, + { + "bbox": [ + 289, + 295, + 505, + 308 + ], + "score": 1.0, + "content": "as we learn the variance of the prior (see the section", + "type": "text" + } + ], + "index": 15 + }, + { + "bbox": [ + 105, + 307, + 506, + 320 + ], + "spans": [ + { + "bbox": [ + 105, + 307, + 190, + 320 + ], + "score": 1.0, + "content": "above). Finally, our", + "type": "text" + }, + { + "bbox": [ + 190, + 307, + 250, + 318 + ], + "score": 0.27, + "content": "\\mathrm { C F - V A E + p R }", + "type": "inline_equation" + }, + { + "bbox": [ + 251, + 307, + 506, + 320 + ], + "score": 1.0, + "content": "still significantly outperforms the MoG-CVAE (74.9 vs 84.6).", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 105, + 317, + 506, + 331 + ], + "spans": [ + { + "bbox": [ + 105, + 317, + 506, + 331 + ], + "score": 1.0, + "content": "This is expected as normalizing flows are more powerful compared to MoG at learning complex", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 105, + 328, + 405, + 342 + ], + "spans": [ + { + "bbox": [ + 105, + 328, + 405, + 342 + ], + "score": 1.0, + "content": "multi-modal distributions (Kingma & Dhariwal, 2018) (also see Figure 8).", + "type": "text" + } + ], + "index": 18 + } + ], + "index": 15.5 + }, + { + "type": "text", + "bbox": [ + 107, + 346, + 505, + 390 + ], + "lines": [ + { + "bbox": [ + 105, + 346, + 505, + 359 + ], + "spans": [ + { + "bbox": [ + 105, + 346, + 505, + 359 + ], + "score": 1.0, + "content": "NL-CVAE. We also see that using an unconditional non-linear flow based prior actually harms", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 105, + 357, + 505, + 370 + ], + "spans": [ + { + "bbox": [ + 105, + 357, + 505, + 370 + ], + "score": 1.0, + "content": "performance (107.6 vs 96.4). This is because the latent distribution is highly dependent upon the", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 105, + 368, + 505, + 380 + ], + "spans": [ + { + "bbox": [ + 105, + 368, + 505, + 380 + ], + "score": 1.0, + "content": "condition. Therefore, without conditioning information the non-linear conditional flow learns a global", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 105, + 379, + 486, + 392 + ], + "spans": [ + { + "bbox": [ + 105, + 379, + 486, + 392 + ], + "score": 1.0, + "content": "representation of the latent space which leads to out-of-distribution samples at prediction time.", + "type": "text" + } + ], + "index": 22 + } + ], + "index": 20.5 + }, + { + "type": "text", + "bbox": [ + 106, + 395, + 505, + 473 + ], + "lines": [ + { + "bbox": [ + 106, + 394, + 506, + 407 + ], + "spans": [ + { + "bbox": [ + 106, + 394, + 506, + 407 + ], + "score": 1.0, + "content": "CF-VAE with conditional NICE flows (Dinh et al., 2015). We have added results with the volume", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 105, + 407, + 506, + 419 + ], + "spans": [ + { + "bbox": [ + 105, + 407, + 506, + 419 + ], + "score": 1.0, + "content": "preserving NICE flows in Table 5. We observe that even without our posterior regularization scheme", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 106, + 417, + 505, + 430 + ], + "spans": [ + { + "bbox": [ + 106, + 417, + 505, + 430 + ], + "score": 1.0, + "content": "(pR) volume preserving NICE flows (Dinh et al., 2015) performs well – because of the constant", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 106, + 430, + 505, + 439 + ], + "spans": [ + { + "bbox": [ + 106, + 430, + 505, + 439 + ], + "score": 1.0, + "content": "Jacobian term. However, our conditional non-linear flows with posterior regularization still perform", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 106, + 439, + 505, + 451 + ], + "spans": [ + { + "bbox": [ + 106, + 439, + 505, + 451 + ], + "score": 1.0, + "content": "significantly better (78.9 vs 74.9 -CLL). This is because of the additional expressive power of our", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 105, + 450, + 505, + 462 + ], + "spans": [ + { + "bbox": [ + 105, + 450, + 505, + 462 + ], + "score": 1.0, + "content": "conditional non-linear flows combined with the stability offered by our posterior regularization", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 106, + 462, + 142, + 474 + ], + "spans": [ + { + "bbox": [ + 106, + 462, + 142, + 474 + ], + "score": 1.0, + "content": "scheme.", + "type": "text" + } + ], + "index": 29 + } + ], + "index": 26 + }, + { + "type": "text", + "bbox": [ + 106, + 478, + 505, + 588 + ], + "lines": [ + { + "bbox": [ + 106, + 478, + 505, + 491 + ], + "spans": [ + { + "bbox": [ + 106, + 478, + 505, + 491 + ], + "score": 1.0, + "content": "Comparison to Klushyn et al. (2019). We also perform additional experiments with the conditional", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 106, + 489, + 506, + 501 + ], + "spans": [ + { + "bbox": [ + 106, + 489, + 309, + 501 + ], + "score": 1.0, + "content": "VampPrior (CDV) of Klushyn et al. (2019) using", + "type": "text" + }, + { + "bbox": [ + 310, + 492, + 345, + 499 + ], + "score": 0.89, + "content": "M = 1 2", + "type": "inline_equation" + }, + { + "bbox": [ + 346, + 489, + 506, + 501 + ], + "score": 1.0, + "content": "components. Using more components", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 106, + 500, + 506, + 513 + ], + "spans": [ + { + "bbox": [ + 106, + 500, + 471, + 513 + ], + "score": 1.0, + "content": "makes training/inference significantly slower in comparison to plain CVAEs, Mog-CVAE (", + "type": "text" + }, + { + "bbox": [ + 471, + 502, + 501, + 511 + ], + "score": 0.82, + "content": "M = 3", + "type": "inline_equation" + }, + { + "bbox": [ + 501, + 500, + 506, + 513 + ], + "score": 1.0, + "content": ")", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 106, + 511, + 504, + 523 + ], + "spans": [ + { + "bbox": [ + 106, + 511, + 250, + 523 + ], + "score": 1.0, + "content": "or our CF-VAE. Furthermore, with", + "type": "text" + }, + { + "bbox": [ + 250, + 514, + 284, + 521 + ], + "score": 0.91, + "content": "M = 1 2", + "type": "inline_equation" + }, + { + "bbox": [ + 285, + 511, + 504, + 523 + ], + "score": 1.0, + "content": "components we observe that it is outperformed by the", + "type": "text" + } + ], + "index": 33 + }, + { + "bbox": [ + 106, + 522, + 505, + 535 + ], + "spans": [ + { + "bbox": [ + 106, + 522, + 416, + 535 + ], + "score": 1.0, + "content": "simpler MoG-CVAE. This is because the mean and variance parameters of the (", + "type": "text" + }, + { + "bbox": [ + 416, + 523, + 451, + 533 + ], + "score": 0.84, + "content": "M = 1 2", + "type": "inline_equation" + }, + { + "bbox": [ + 451, + 522, + 505, + 535 + ], + "score": 1.0, + "content": ") components", + "type": "text" + } + ], + "index": 34 + }, + { + "bbox": [ + 106, + 533, + 505, + 546 + ], + "spans": [ + { + "bbox": [ + 106, + 533, + 287, + 546 + ], + "score": 1.0, + "content": "are obtained using the recognition network", + "type": "text" + }, + { + "bbox": [ + 288, + 538, + 298, + 546 + ], + "score": 0.88, + "content": "q _ { \\phi }", + "type": "inline_equation" + }, + { + "bbox": [ + 298, + 533, + 409, + 546 + ], + "score": 1.0, + "content": ". The recognition network", + "type": "text" + }, + { + "bbox": [ + 409, + 535, + 420, + 546 + ], + "score": 0.85, + "content": "q _ { \\phi }", + "type": "inline_equation" + }, + { + "bbox": [ + 421, + 533, + 505, + 546 + ], + "score": 1.0, + "content": "has to learn to both", + "type": "text" + } + ], + "index": 35 + }, + { + "bbox": [ + 106, + 544, + 505, + 557 + ], + "spans": [ + { + "bbox": [ + 106, + 544, + 505, + 557 + ], + "score": 1.0, + "content": "reconstruct the data and maintain a latent space representative of full conditional data distribution", + "type": "text" + } + ], + "index": 36 + }, + { + "bbox": [ + 107, + 554, + 505, + 568 + ], + "spans": [ + { + "bbox": [ + 107, + 557, + 133, + 568 + ], + "score": 0.91, + "content": "p ( \\mathbf { y } | \\mathbf { x } )", + "type": "inline_equation" + }, + { + "bbox": [ + 133, + 554, + 505, + 568 + ], + "score": 1.0, + "content": ". These objectives are at odds with each other. In practice, we find that this leads to simplistic", + "type": "text" + } + ], + "index": 37 + }, + { + "bbox": [ + 106, + 566, + 506, + 578 + ], + "spans": [ + { + "bbox": [ + 106, + 566, + 506, + 578 + ], + "score": 1.0, + "content": "latent spaces along with lower overall data log-likelihood in comparison with our CF-VAE (Figure 3).", + "type": "text" + } + ], + "index": 38 + }, + { + "bbox": [ + 106, + 576, + 412, + 589 + ], + "spans": [ + { + "bbox": [ + 106, + 576, + 412, + 589 + ], + "score": 1.0, + "content": "This can be seen in the samples and corresponding latent spaces in Figure 9.", + "type": "text" + } + ], + "index": 39 + } + ], + "index": 34.5 + }, + { + "type": "text", + "bbox": [ + 107, + 594, + 505, + 650 + ], + "lines": [ + { + "bbox": [ + 105, + 594, + 505, + 605 + ], + "spans": [ + { + "bbox": [ + 105, + 594, + 505, + 605 + ], + "score": 1.0, + "content": "Hyper-parameter analysis of our posterior regularization scheme (pR). We provide additional", + "type": "text" + } + ], + "index": 40 + }, + { + "bbox": [ + 105, + 604, + 505, + 618 + ], + "spans": [ + { + "bbox": [ + 105, + 604, + 505, + 618 + ], + "score": 1.0, + "content": "analysis of our posterior regularization scheme in Table 5. We observe that our CF-VAE is relatively", + "type": "text" + } + ], + "index": 41 + }, + { + "bbox": [ + 105, + 615, + 505, + 628 + ], + "spans": [ + { + "bbox": [ + 105, + 615, + 160, + 628 + ], + "score": 1.0, + "content": "robust across", + "type": "text" + }, + { + "bbox": [ + 160, + 618, + 223, + 628 + ], + "score": 0.88, + "content": "C = [ 0 . 0 5 , 0 2 5 ]", + "type": "inline_equation" + }, + { + "bbox": [ + 224, + 615, + 505, + 628 + ], + "score": 1.0, + "content": ", with only small variance in performance. This is because our posterior", + "type": "text" + } + ], + "index": 42 + }, + { + "bbox": [ + 105, + 626, + 506, + 639 + ], + "spans": [ + { + "bbox": [ + 105, + 626, + 506, + 639 + ], + "score": 1.0, + "content": "regularization scheme encourages our CF-VAE to focus on explaining the data well. We explain this", + "type": "text" + } + ], + "index": 43 + }, + { + "bbox": [ + 105, + 637, + 246, + 651 + ], + "spans": [ + { + "bbox": [ + 105, + 637, + 246, + 651 + ], + "score": 1.0, + "content": "further in the following paragraph.", + "type": "text" + } + ], + "index": 44 + } + ], + "index": 42 + }, + { + "type": "text", + "bbox": [ + 107, + 655, + 505, + 732 + ], + "lines": [ + { + "bbox": [ + 106, + 654, + 506, + 667 + ], + "spans": [ + { + "bbox": [ + 106, + 654, + 506, + 667 + ], + "score": 1.0, + "content": "Analysis of our posterior regularization scheme (pR). We provide additional analysis of our", + "type": "text" + } + ], + "index": 45 + }, + { + "bbox": [ + 106, + 666, + 505, + 678 + ], + "spans": [ + { + "bbox": [ + 106, + 666, + 505, + 678 + ], + "score": 1.0, + "content": "posterior regularization scheme (pR) in Figure 10. We show each term of our objective (7) in", + "type": "text" + } + ], + "index": 46 + }, + { + "bbox": [ + 106, + 676, + 505, + 689 + ], + "spans": [ + { + "bbox": [ + 106, + 676, + 505, + 689 + ], + "score": 1.0, + "content": "Figure 10. First, we see that with our posterior regularization scheme, our CF-VAE focuses on", + "type": "text" + } + ], + "index": 47 + }, + { + "bbox": [ + 106, + 687, + 505, + 700 + ], + "spans": [ + { + "bbox": [ + 106, + 687, + 505, + 700 + ], + "score": 1.0, + "content": "explaining the data well – the data log-likelihood is best with our posterior regularization (pR)", + "type": "text" + } + ], + "index": 48 + }, + { + "bbox": [ + 106, + 698, + 505, + 711 + ], + "spans": [ + { + "bbox": [ + 106, + 698, + 210, + 711 + ], + "score": 1.0, + "content": "scheme Figure 10a, with", + "type": "text" + }, + { + "bbox": [ + 210, + 701, + 244, + 709 + ], + "score": 0.9, + "content": "C = 0 . 2", + "type": "inline_equation" + }, + { + "bbox": [ + 245, + 698, + 347, + 711 + ], + "score": 1.0, + "content": "having a advantage over", + "type": "text" + }, + { + "bbox": [ + 348, + 700, + 415, + 711 + ], + "score": 0.89, + "content": "C = \\{ 0 . 0 5 , 0 . 1 \\}", + "type": "inline_equation" + }, + { + "bbox": [ + 415, + 698, + 505, + 711 + ], + "score": 1.0, + "content": ". Furthermore, we see", + "type": "text" + } + ], + "index": 49 + }, + { + "bbox": [ + 106, + 709, + 505, + 722 + ], + "spans": [ + { + "bbox": [ + 106, + 709, + 505, + 722 + ], + "score": 1.0, + "content": "that without our posterior regularization scheme the Jacobian term dominates while entropy term", + "type": "text" + } + ], + "index": 50 + }, + { + "bbox": [ + 106, + 719, + 506, + 734 + ], + "spans": [ + { + "bbox": [ + 106, + 719, + 506, + 734 + ], + "score": 1.0, + "content": "decreases (Figure 10b vs Figure 10d) – the contraction of the base density is favoured. Interestingly,", + "type": "text" + } + ], + "index": 51 + } + ], + "index": 48 + } + ], + "page_idx": 14, + "page_size": [ + 612, + 792 + ], + "discarded_blocks": [ + { + "type": "discarded", + "bbox": [ + 106, + 27, + 308, + 37 + ], + "lines": [ + { + "bbox": [ + 106, + 26, + 308, + 38 + ], + "spans": [ + { + "bbox": [ + 106, + 26, + 308, + 38 + ], + "score": 1.0, + "content": "Under review as a conference paper at ICLR 2020", + "type": "text" + } + ] + } + ] + }, + { + "type": "discarded", + "bbox": [ + 300, + 751, + 310, + 760 + ], + "lines": [ + { + "bbox": [ + 299, + 750, + 312, + 764 + ], + "spans": [ + { + "bbox": [ + 299, + 750, + 312, + 764 + ], + "score": 1.0, + "content": "", + "type": "text", + "height": 14, + "width": 13 + } + ] + } + ] + } + ], + "para_blocks": [ + { + "type": "image", + "bbox": [ + 187, + 79, + 423, + 183 + ], + "blocks": [ + { + "type": "image_body", + "bbox": [ + 187, + 79, + 423, + 183 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 187, + 79, + 423, + 183 + ], + "spans": [ + { + "bbox": [ + 187, + 79, + 423, + 183 + ], + "score": 0.963, + "type": "image", + "image_path": "50a15d633cd65996bc46084a5bd7bce523dc1a79afdd807f07ca89c64a1e2b37.jpg" + } + ] + } + ], + "index": 3.5, + "virtual_lines": [ + { + "bbox": [ + 187, + 79, + 423, + 92.0 + ], + "spans": [], + "index": 0 + }, + { + "bbox": [ + 187, + 92.0, + 423, + 105.0 + ], + "spans": [], + "index": 1 + }, + { + "bbox": [ + 187, + 105.0, + 423, + 118.0 + ], + "spans": [], + "index": 2 + }, + { + "bbox": [ + 187, + 118.0, + 423, + 131.0 + ], + "spans": [], + "index": 3 + }, + { + "bbox": [ + 187, + 131.0, + 423, + 144.0 + ], + "spans": [], + "index": 4 + }, + { + "bbox": [ + 187, + 144.0, + 423, + 157.0 + ], + "spans": [], + "index": 5 + }, + { + "bbox": [ + 187, + 157.0, + 423, + 170.0 + ], + "spans": [], + "index": 6 + }, + { + "bbox": [ + 187, + 170.0, + 423, + 183.0 + ], + "spans": [], + "index": 7 + } + ] + }, + { + "type": "image_caption", + "bbox": [ + 106, + 195, + 506, + 250 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 106, + 195, + 506, + 207 + ], + "spans": [ + { + "bbox": [ + 106, + 195, + 467, + 207 + ], + "score": 1.0, + "content": "Figure 9: Random samples using the CDV Prior of (Klushyn et al., 2019) clustered using", + "type": "text" + }, + { + "bbox": [ + 467, + 196, + 474, + 205 + ], + "score": 0.27, + "content": "\\mathbf { k } .", + "type": "inline_equation" + }, + { + "bbox": [ + 475, + 195, + 506, + 207 + ], + "score": 1.0, + "content": "-means.", + "type": "text" + } + ], + "index": 8 + }, + { + "bbox": [ + 105, + 204, + 505, + 218 + ], + "spans": [ + { + "bbox": [ + 105, + 204, + 505, + 218 + ], + "score": 1.0, + "content": "The number of clusters is set manually to the number of expected digits. The CDV Prior latent", + "type": "text" + } + ], + "index": 9 + }, + { + "bbox": [ + 105, + 214, + 506, + 231 + ], + "spans": [ + { + "bbox": [ + 105, + 214, + 506, + 231 + ], + "score": 1.0, + "content": "distribution on the right. Note, the 64D latent distribution is (approximately) projected to 2D using", + "type": "text" + } + ], + "index": 10 + }, + { + "bbox": [ + 105, + 226, + 505, + 242 + ], + "spans": [ + { + "bbox": [ + 105, + 226, + 505, + 242 + ], + "score": 1.0, + "content": "tSNE and KDE. In comparison to the samples and latent spaces of our CF-VAE (Figure 3) we see", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 105, + 237, + 407, + 252 + ], + "spans": [ + { + "bbox": [ + 105, + 237, + 407, + 252 + ], + "score": 1.0, + "content": "that the latent spaces are more simplistic and samples are of poorer quality.", + "type": "text" + } + ], + "index": 12 + } + ], + "index": 10 + } + ], + "index": 6.75 + }, + { + "type": "text", + "bbox": [ + 106, + 274, + 505, + 340 + ], + "lines": [], + "index": 15.5, + "bbox_fs": [ + 104, + 274, + 506, + 342 + ], + "lines_deleted": true + }, + { + "type": "text", + "bbox": [ + 107, + 346, + 505, + 390 + ], + "lines": [ + { + "bbox": [ + 105, + 346, + 505, + 359 + ], + "spans": [ + { + "bbox": [ + 105, + 346, + 505, + 359 + ], + "score": 1.0, + "content": "NL-CVAE. We also see that using an unconditional non-linear flow based prior actually harms", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 105, + 357, + 505, + 370 + ], + "spans": [ + { + "bbox": [ + 105, + 357, + 505, + 370 + ], + "score": 1.0, + "content": "performance (107.6 vs 96.4). This is because the latent distribution is highly dependent upon the", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 105, + 368, + 505, + 380 + ], + "spans": [ + { + "bbox": [ + 105, + 368, + 505, + 380 + ], + "score": 1.0, + "content": "condition. Therefore, without conditioning information the non-linear conditional flow learns a global", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 105, + 379, + 486, + 392 + ], + "spans": [ + { + "bbox": [ + 105, + 379, + 486, + 392 + ], + "score": 1.0, + "content": "representation of the latent space which leads to out-of-distribution samples at prediction time.", + "type": "text" + } + ], + "index": 22 + } + ], + "index": 20.5, + "bbox_fs": [ + 105, + 346, + 505, + 392 + ] + }, + { + "type": "text", + "bbox": [ + 106, + 395, + 505, + 473 + ], + "lines": [ + { + "bbox": [ + 106, + 394, + 506, + 407 + ], + "spans": [ + { + "bbox": [ + 106, + 394, + 506, + 407 + ], + "score": 1.0, + "content": "CF-VAE with conditional NICE flows (Dinh et al., 2015). We have added results with the volume", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 105, + 407, + 506, + 419 + ], + "spans": [ + { + "bbox": [ + 105, + 407, + 506, + 419 + ], + "score": 1.0, + "content": "preserving NICE flows in Table 5. We observe that even without our posterior regularization scheme", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 106, + 417, + 505, + 430 + ], + "spans": [ + { + "bbox": [ + 106, + 417, + 505, + 430 + ], + "score": 1.0, + "content": "(pR) volume preserving NICE flows (Dinh et al., 2015) performs well – because of the constant", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 106, + 430, + 505, + 439 + ], + "spans": [ + { + "bbox": [ + 106, + 430, + 505, + 439 + ], + "score": 1.0, + "content": "Jacobian term. However, our conditional non-linear flows with posterior regularization still perform", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 106, + 439, + 505, + 451 + ], + "spans": [ + { + "bbox": [ + 106, + 439, + 505, + 451 + ], + "score": 1.0, + "content": "significantly better (78.9 vs 74.9 -CLL). This is because of the additional expressive power of our", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 105, + 450, + 505, + 462 + ], + "spans": [ + { + "bbox": [ + 105, + 450, + 505, + 462 + ], + "score": 1.0, + "content": "conditional non-linear flows combined with the stability offered by our posterior regularization", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 106, + 462, + 142, + 474 + ], + "spans": [ + { + "bbox": [ + 106, + 462, + 142, + 474 + ], + "score": 1.0, + "content": "scheme.", + "type": "text" + } + ], + "index": 29 + } + ], + "index": 26, + "bbox_fs": [ + 105, + 394, + 506, + 474 + ] + }, + { + "type": "text", + "bbox": [ + 106, + 478, + 505, + 588 + ], + "lines": [ + { + "bbox": [ + 106, + 478, + 505, + 491 + ], + "spans": [ + { + "bbox": [ + 106, + 478, + 505, + 491 + ], + "score": 1.0, + "content": "Comparison to Klushyn et al. (2019). We also perform additional experiments with the conditional", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 106, + 489, + 506, + 501 + ], + "spans": [ + { + "bbox": [ + 106, + 489, + 309, + 501 + ], + "score": 1.0, + "content": "VampPrior (CDV) of Klushyn et al. (2019) using", + "type": "text" + }, + { + "bbox": [ + 310, + 492, + 345, + 499 + ], + "score": 0.89, + "content": "M = 1 2", + "type": "inline_equation" + }, + { + "bbox": [ + 346, + 489, + 506, + 501 + ], + "score": 1.0, + "content": "components. Using more components", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 106, + 500, + 506, + 513 + ], + "spans": [ + { + "bbox": [ + 106, + 500, + 471, + 513 + ], + "score": 1.0, + "content": "makes training/inference significantly slower in comparison to plain CVAEs, Mog-CVAE (", + "type": "text" + }, + { + "bbox": [ + 471, + 502, + 501, + 511 + ], + "score": 0.82, + "content": "M = 3", + "type": "inline_equation" + }, + { + "bbox": [ + 501, + 500, + 506, + 513 + ], + "score": 1.0, + "content": ")", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 106, + 511, + 504, + 523 + ], + "spans": [ + { + "bbox": [ + 106, + 511, + 250, + 523 + ], + "score": 1.0, + "content": "or our CF-VAE. Furthermore, with", + "type": "text" + }, + { + "bbox": [ + 250, + 514, + 284, + 521 + ], + "score": 0.91, + "content": "M = 1 2", + "type": "inline_equation" + }, + { + "bbox": [ + 285, + 511, + 504, + 523 + ], + "score": 1.0, + "content": "components we observe that it is outperformed by the", + "type": "text" + } + ], + "index": 33 + }, + { + "bbox": [ + 106, + 522, + 505, + 535 + ], + "spans": [ + { + "bbox": [ + 106, + 522, + 416, + 535 + ], + "score": 1.0, + "content": "simpler MoG-CVAE. This is because the mean and variance parameters of the (", + "type": "text" + }, + { + "bbox": [ + 416, + 523, + 451, + 533 + ], + "score": 0.84, + "content": "M = 1 2", + "type": "inline_equation" + }, + { + "bbox": [ + 451, + 522, + 505, + 535 + ], + "score": 1.0, + "content": ") components", + "type": "text" + } + ], + "index": 34 + }, + { + "bbox": [ + 106, + 533, + 505, + 546 + ], + "spans": [ + { + "bbox": [ + 106, + 533, + 287, + 546 + ], + "score": 1.0, + "content": "are obtained using the recognition network", + "type": "text" + }, + { + "bbox": [ + 288, + 538, + 298, + 546 + ], + "score": 0.88, + "content": "q _ { \\phi }", + "type": "inline_equation" + }, + { + "bbox": [ + 298, + 533, + 409, + 546 + ], + "score": 1.0, + "content": ". The recognition network", + "type": "text" + }, + { + "bbox": [ + 409, + 535, + 420, + 546 + ], + "score": 0.85, + "content": "q _ { \\phi }", + "type": "inline_equation" + }, + { + "bbox": [ + 421, + 533, + 505, + 546 + ], + "score": 1.0, + "content": "has to learn to both", + "type": "text" + } + ], + "index": 35 + }, + { + "bbox": [ + 106, + 544, + 505, + 557 + ], + "spans": [ + { + "bbox": [ + 106, + 544, + 505, + 557 + ], + "score": 1.0, + "content": "reconstruct the data and maintain a latent space representative of full conditional data distribution", + "type": "text" + } + ], + "index": 36 + }, + { + "bbox": [ + 107, + 554, + 505, + 568 + ], + "spans": [ + { + "bbox": [ + 107, + 557, + 133, + 568 + ], + "score": 0.91, + "content": "p ( \\mathbf { y } | \\mathbf { x } )", + "type": "inline_equation" + }, + { + "bbox": [ + 133, + 554, + 505, + 568 + ], + "score": 1.0, + "content": ". These objectives are at odds with each other. In practice, we find that this leads to simplistic", + "type": "text" + } + ], + "index": 37 + }, + { + "bbox": [ + 106, + 566, + 506, + 578 + ], + "spans": [ + { + "bbox": [ + 106, + 566, + 506, + 578 + ], + "score": 1.0, + "content": "latent spaces along with lower overall data log-likelihood in comparison with our CF-VAE (Figure 3).", + "type": "text" + } + ], + "index": 38 + }, + { + "bbox": [ + 106, + 576, + 412, + 589 + ], + "spans": [ + { + "bbox": [ + 106, + 576, + 412, + 589 + ], + "score": 1.0, + "content": "This can be seen in the samples and corresponding latent spaces in Figure 9.", + "type": "text" + } + ], + "index": 39 + } + ], + "index": 34.5, + "bbox_fs": [ + 106, + 478, + 506, + 589 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 594, + 505, + 650 + ], + "lines": [ + { + "bbox": [ + 105, + 594, + 505, + 605 + ], + "spans": [ + { + "bbox": [ + 105, + 594, + 505, + 605 + ], + "score": 1.0, + "content": "Hyper-parameter analysis of our posterior regularization scheme (pR). We provide additional", + "type": "text" + } + ], + "index": 40 + }, + { + "bbox": [ + 105, + 604, + 505, + 618 + ], + "spans": [ + { + "bbox": [ + 105, + 604, + 505, + 618 + ], + "score": 1.0, + "content": "analysis of our posterior regularization scheme in Table 5. We observe that our CF-VAE is relatively", + "type": "text" + } + ], + "index": 41 + }, + { + "bbox": [ + 105, + 615, + 505, + 628 + ], + "spans": [ + { + "bbox": [ + 105, + 615, + 160, + 628 + ], + "score": 1.0, + "content": "robust across", + "type": "text" + }, + { + "bbox": [ + 160, + 618, + 223, + 628 + ], + "score": 0.88, + "content": "C = [ 0 . 0 5 , 0 2 5 ]", + "type": "inline_equation" + }, + { + "bbox": [ + 224, + 615, + 505, + 628 + ], + "score": 1.0, + "content": ", with only small variance in performance. This is because our posterior", + "type": "text" + } + ], + "index": 42 + }, + { + "bbox": [ + 105, + 626, + 506, + 639 + ], + "spans": [ + { + "bbox": [ + 105, + 626, + 506, + 639 + ], + "score": 1.0, + "content": "regularization scheme encourages our CF-VAE to focus on explaining the data well. We explain this", + "type": "text" + } + ], + "index": 43 + }, + { + "bbox": [ + 105, + 637, + 246, + 651 + ], + "spans": [ + { + "bbox": [ + 105, + 637, + 246, + 651 + ], + "score": 1.0, + "content": "further in the following paragraph.", + "type": "text" + } + ], + "index": 44 + } + ], + "index": 42, + "bbox_fs": [ + 105, + 594, + 506, + 651 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 655, + 505, + 732 + ], + "lines": [ + { + "bbox": [ + 106, + 654, + 506, + 667 + ], + "spans": [ + { + "bbox": [ + 106, + 654, + 506, + 667 + ], + "score": 1.0, + "content": "Analysis of our posterior regularization scheme (pR). We provide additional analysis of our", + "type": "text" + } + ], + "index": 45 + }, + { + "bbox": [ + 106, + 666, + 505, + 678 + ], + "spans": [ + { + "bbox": [ + 106, + 666, + 505, + 678 + ], + "score": 1.0, + "content": "posterior regularization scheme (pR) in Figure 10. We show each term of our objective (7) in", + "type": "text" + } + ], + "index": 46 + }, + { + "bbox": [ + 106, + 676, + 505, + 689 + ], + "spans": [ + { + "bbox": [ + 106, + 676, + 505, + 689 + ], + "score": 1.0, + "content": "Figure 10. First, we see that with our posterior regularization scheme, our CF-VAE focuses on", + "type": "text" + } + ], + "index": 47 + }, + { + "bbox": [ + 106, + 687, + 505, + 700 + ], + "spans": [ + { + "bbox": [ + 106, + 687, + 505, + 700 + ], + "score": 1.0, + "content": "explaining the data well – the data log-likelihood is best with our posterior regularization (pR)", + "type": "text" + } + ], + "index": 48 + }, + { + "bbox": [ + 106, + 698, + 505, + 711 + ], + "spans": [ + { + "bbox": [ + 106, + 698, + 210, + 711 + ], + "score": 1.0, + "content": "scheme Figure 10a, with", + "type": "text" + }, + { + "bbox": [ + 210, + 701, + 244, + 709 + ], + "score": 0.9, + "content": "C = 0 . 2", + "type": "inline_equation" + }, + { + "bbox": [ + 245, + 698, + 347, + 711 + ], + "score": 1.0, + "content": "having a advantage over", + "type": "text" + }, + { + "bbox": [ + 348, + 700, + 415, + 711 + ], + "score": 0.89, + "content": "C = \\{ 0 . 0 5 , 0 . 1 \\}", + "type": "inline_equation" + }, + { + "bbox": [ + 415, + 698, + 505, + 711 + ], + "score": 1.0, + "content": ". Furthermore, we see", + "type": "text" + } + ], + "index": 49 + }, + { + "bbox": [ + 106, + 709, + 505, + 722 + ], + "spans": [ + { + "bbox": [ + 106, + 709, + 505, + 722 + ], + "score": 1.0, + "content": "that without our posterior regularization scheme the Jacobian term dominates while entropy term", + "type": "text" + } + ], + "index": 50 + }, + { + "bbox": [ + 106, + 719, + 506, + 734 + ], + "spans": [ + { + "bbox": [ + 106, + 719, + 506, + 734 + ], + "score": 1.0, + "content": "decreases (Figure 10b vs Figure 10d) – the contraction of the base density is favoured. Interestingly,", + "type": "text" + } + ], + "index": 51 + }, + { + "bbox": [ + 106, + 469, + 505, + 480 + ], + "spans": [ + { + "bbox": [ + 106, + 469, + 505, + 480 + ], + "score": 1.0, + "content": "the likelihood under the prior Figure 10c is similar across methods – with our posterior regularization", + "type": "text", + "cross_page": true + } + ], + "index": 7 + }, + { + "bbox": [ + 105, + 479, + 505, + 491 + ], + "spans": [ + { + "bbox": [ + 105, + 479, + 505, + 491 + ], + "score": 1.0, + "content": "providing additional stability. We also experimented with re-weighting these terms (although its no", + "type": "text", + "cross_page": true + } + ], + "index": 8 + }, + { + "bbox": [ + 106, + 490, + 505, + 502 + ], + "spans": [ + { + "bbox": [ + 106, + 490, + 505, + 502 + ], + "score": 1.0, + "content": "longer a valid lower bound on the true data log-likelihood). This leads to the opposite behaviour – the", + "type": "text", + "cross_page": true + } + ], + "index": 9 + }, + { + "bbox": [ + 106, + 501, + 505, + 513 + ], + "spans": [ + { + "bbox": [ + 106, + 501, + 505, + 513 + ], + "score": 1.0, + "content": "entropy term dominates over the Jacobian term at the cost of the data log-likelihood. On the other", + "type": "text", + "cross_page": true + } + ], + "index": 10 + }, + { + "bbox": [ + 106, + 511, + 507, + 525 + ], + "spans": [ + { + "bbox": [ + 106, + 511, + 507, + 525 + ], + "score": 1.0, + "content": "hand, we observe that all terms of our objective are stable with our posterior regularization scheme,", + "type": "text", + "cross_page": true + } + ], + "index": 11 + }, + { + "bbox": [ + 106, + 522, + 367, + 536 + ], + "spans": [ + { + "bbox": [ + 106, + 522, + 367, + 536 + ], + "score": 1.0, + "content": "illustrating the advantage of our posterior regularization scheme.", + "type": "text", + "cross_page": true + } + ], + "index": 12 + } + ], + "index": 48, + "bbox_fs": [ + 106, + 654, + 506, + 734 + ] + } + ] + }, + { + "preproc_blocks": [ + { + "type": "image", + "bbox": [ + 122, + 82, + 488, + 383 + ], + "blocks": [ + { + "type": "image_body", + "bbox": [ + 122, + 82, + 488, + 383 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 122, + 82, + 488, + 383 + ], + "spans": [ + { + "bbox": [ + 122, + 82, + 488, + 383 + ], + "score": 0.977, + "type": "image", + "image_path": "ddecc9ab2431b6098f5848ee87462eb50e266afb273c9704a024c0b3a63f769b.jpg" + } + ] + } + ], + "index": 1, + "virtual_lines": [ + { + "bbox": [ + 122, + 82, + 488, + 182.33333333333331 + ], + "spans": [], + "index": 0 + }, + { + "bbox": [ + 122, + 182.33333333333331, + 488, + 282.66666666666663 + ], + "spans": [], + "index": 1 + }, + { + "bbox": [ + 122, + 282.66666666666663, + 488, + 382.99999999999994 + ], + "spans": [], + "index": 2 + } + ] + }, + { + "type": "image_caption", + "bbox": [ + 106, + 392, + 505, + 436 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 106, + 391, + 505, + 404 + ], + "spans": [ + { + "bbox": [ + 106, + 391, + 482, + 404 + ], + "score": 1.0, + "content": "Figure 10: Analysis of all four terms of our CF-VAE objective (7) at training time, with", + "type": "text" + }, + { + "bbox": [ + 482, + 392, + 505, + 403 + ], + "score": 0.79, + "content": "C =", + "type": "inline_equation" + } + ], + "index": 3 + }, + { + "bbox": [ + 107, + 403, + 506, + 415 + ], + "spans": [ + { + "bbox": [ + 107, + 403, + 182, + 415 + ], + "score": 0.82, + "content": "\\{ 0 . \\bar { 0 5 } , 0 . 1 0 , 0 . 2 0 \\bar { \\} } )", + "type": "inline_equation" + }, + { + "bbox": [ + 182, + 403, + 506, + 415 + ], + "score": 1.0, + "content": "and without our posterior regularization (pR) scheme. We observe better data", + "type": "text" + } + ], + "index": 4 + }, + { + "bbox": [ + 106, + 413, + 506, + 426 + ], + "spans": [ + { + "bbox": [ + 106, + 413, + 506, + 426 + ], + "score": 1.0, + "content": "log-likelihoods and stable training with our posterior regularization (pR) scheme. Without pR, we", + "type": "text" + } + ], + "index": 5 + }, + { + "bbox": [ + 106, + 425, + 407, + 436 + ], + "spans": [ + { + "bbox": [ + 106, + 425, + 407, + 436 + ], + "score": 1.0, + "content": "observe that the Jacobian term dominates at the cost of data log-likelihood.", + "type": "text" + } + ], + "index": 6 + } + ], + "index": 4.5 + } + ], + "index": 2.75 + }, + { + "type": "text", + "bbox": [ + 107, + 468, + 505, + 534 + ], + "lines": [ + { + "bbox": [ + 106, + 469, + 505, + 480 + ], + "spans": [ + { + "bbox": [ + 106, + 469, + 505, + 480 + ], + "score": 1.0, + "content": "the likelihood under the prior Figure 10c is similar across methods – with our posterior regularization", + "type": "text" + } + ], + "index": 7 + }, + { + "bbox": [ + 105, + 479, + 505, + 491 + ], + "spans": [ + { + "bbox": [ + 105, + 479, + 505, + 491 + ], + "score": 1.0, + "content": "providing additional stability. We also experimented with re-weighting these terms (although its no", + "type": "text" + } + ], + "index": 8 + }, + { + "bbox": [ + 106, + 490, + 505, + 502 + ], + "spans": [ + { + "bbox": [ + 106, + 490, + 505, + 502 + ], + "score": 1.0, + "content": "longer a valid lower bound on the true data log-likelihood). This leads to the opposite behaviour – the", + "type": "text" + } + ], + "index": 9 + }, + { + "bbox": [ + 106, + 501, + 505, + 513 + ], + "spans": [ + { + "bbox": [ + 106, + 501, + 505, + 513 + ], + "score": 1.0, + "content": "entropy term dominates over the Jacobian term at the cost of the data log-likelihood. On the other", + "type": "text" + } + ], + "index": 10 + }, + { + "bbox": [ + 106, + 511, + 507, + 525 + ], + "spans": [ + { + "bbox": [ + 106, + 511, + 507, + 525 + ], + "score": 1.0, + "content": "hand, we observe that all terms of our objective are stable with our posterior regularization scheme,", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 106, + 522, + 367, + 536 + ], + "spans": [ + { + "bbox": [ + 106, + 522, + 367, + 536 + ], + "score": 1.0, + "content": "illustrating the advantage of our posterior regularization scheme.", + "type": "text" + } + ], + "index": 12 + } + ], + "index": 9.5 + }, + { + "type": "title", + "bbox": [ + 107, + 562, + 484, + 575 + ], + "lines": [ + { + "bbox": [ + 106, + 562, + 486, + 576 + ], + "spans": [ + { + "bbox": [ + 106, + 562, + 420, + 576 + ], + "score": 1.0, + "content": "APPENDIX F. 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MethodKError @1secError @ 2secError @ 3secError @ 4sec
Top 1 (Best Guess)
“Shotgun"-u90°500.91.93.14.4
“Shotgun"-u90°1000.91.93.04.3
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Top 10%
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“Shotgun"-u90°1001.22.53.95.4
“Shotgun"-u90°5001.22.53.95.4
Top 1 (Best Guess)
“Shotgun"-u135°500.92.03.14.5
“Shotgun"-u135°1000.91.93.04.3
“Shotgun"-u135°5000.91.93.04.2
Top 10%
“Shotgun"-u135°501.42.94.56.2
"Shotgun"-u135°1001.42.94.56.2
"Shotgun"-u135°5001.42.94.56.2
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Euclidean error at", + "type": "text" + }, + { + "bbox": [ + 441, + 329, + 459, + 341 + ], + "score": 0.81, + "content": "( 1 / 5 )", + "type": "inline_equation" + }, + { + "bbox": [ + 459, + 327, + 504, + 342 + ], + "score": 1.0, + "content": "resolution.", + "type": "text" + } + ], + "index": 3 + } + ], + "index": 3 + }, + { + "type": "table_caption", + "bbox": [ + 108, + 361, + 442, + 374 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 106, + 360, + 444, + 377 + ], + "spans": [ + { + "bbox": [ + 106, + 360, + 444, + 377 + ], + "score": 1.0, + "content": "APPENDIX G. QUALITATIVE EXAMPLES ON THE HIGHD DATASET", + "type": "text" + } + ], + "index": 4 + } + ], + "index": 4 + } + ], + "index": 3 + }, + { + "type": "image", + "bbox": [ + 109, + 390, + 502, + 496 + ], + "blocks": [ + { + "type": "image_body", + "bbox": [ + 109, + 390, + 502, + 496 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 109, + 390, + 502, + 496 + ], + "spans": [ + { + "bbox": [ + 109, + 390, + 502, + 496 + ], + "score": 0.966, + "type": "image", + "image_path": "d834c03a140771003f59337ab88e45dab1c004e269af3abbd0cc11c101285b6d.jpg" + } + ] + } + ], + "index": 6, + "virtual_lines": [ + { + "bbox": [ + 109, + 390, + 502, + 425.3333333333333 + ], + "spans": [], + "index": 5 + }, + { + "bbox": [ + 109, + 425.3333333333333, + 502, + 460.66666666666663 + ], + "spans": [], + "index": 6 + }, + { + "bbox": [ + 109, + 460.66666666666663, + 502, + 495.99999999999994 + ], + "spans": [], + "index": 7 + } + ] + }, + { + "type": "image_caption", + "bbox": [ + 106, + 507, + 506, + 562 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 105, + 506, + 506, + 520 + ], + "spans": [ + { + "bbox": [ + 105, + 506, + 506, + 520 + ], + "score": 1.0, + "content": "Figure 11: Predictions on the HighD dataset. 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In the left of Figure 11 we show", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 105, + 585, + 505, + 599 + ], + "spans": [ + { + "bbox": [ + 105, + 585, + 505, + 599 + ], + "score": 1.0, + "content": "128 random samples from the HighD test set. In the middle we show predictions on these samples by", + "type": "text" + } + ], + "index": 14 + }, + { + "bbox": [ + 105, + 595, + 507, + 612 + ], + "spans": [ + { + "bbox": [ + 105, + 595, + 507, + 612 + ], + "score": 1.0, + "content": "the CVAE (with cyclic KL annealing (Liu et al., 2019)). We see that even with cyclic KL annealing,", + "type": "text" + } + ], + "index": 15 + }, + { + "bbox": [ + 105, + 608, + 505, + 621 + ], + "spans": [ + { + "bbox": [ + 105, + 608, + 505, + 621 + ], + "score": 1.0, + "content": "we observe posterior collapse. 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MethodKError @1secError @ 2secError @ 3secError @ 4sec
Top 1 (Best Guess)
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Top 1 (Best Guess)
“Shotgun"-u135°500.92.03.14.5
“Shotgun"-u135°1000.91.93.04.3
“Shotgun"-u135°5000.91.93.04.2
Top 10%
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