Christopher Beckham

Jae Hyun Lim, Nikola B. Kovachki, Ricardo Baptista et al.

Diffusion models have recently emerged as a powerful framework for generative modeling. They consist of a forward process that perturbs input data with Gaussian white noise and a reverse process that learns a score function to generate samples by denoising. Despite their tremendous success, they are mostly formulated on finite-dimensional spaces, e.g., Euclidean, limiting their applications to many domains where the data has a functional form, such as in scientific computing and 3D geometric data analysis. This work introduces a mathematically rigorous framework called Denoising Diffusion Operators (DDOs) for training diffusion models in function space. In DDOs, the forward process perturbs input functions gradually using a Gaussian process. The generative process is formulated by a function-valued annealed Langevin dynamic. Our approach requires an appropriate notion of the score for the perturbed data distribution, which we obtain by generalizing denoising score matching to function spaces that can be infinite-dimensional. We show that the corresponding discretized algorithm generates accurate samples at a fixed cost independent of the data resolution. We theoretically and numerically verify the applicability of our approach on a set of function-valued problems, including generating solutions to the Navier-Stokes equation viewed as the push-forward distribution of forcings from a Gaussian Random Field (GRF), as well as volcano InSAR and MNIST-SDF.

Christopher Beckham, Martin Weiss, Florian Golemo et al.

Different types of mental rotation tests have been used extensively in psychology to understand human visual reasoning and perception. Understanding what an object or visual scene would look like from another viewpoint is a challenging problem that is made even harder if it must be performed from a single image. We explore a controlled setting whereby questions are posed about the properties of a scene if that scene was observed from another viewpoint. To do this we have created a new version of the CLEVR dataset that we call CLEVR Mental Rotation Tests (CLEVR-MRT). Using CLEVR-MRT we examine standard methods, show how they fall short, then explore novel neural architectures that involve inferring volumetric representations of a scene. These volumes can be manipulated via camera-conditioned transformations to answer the question. We examine the efficacy of different model variants through rigorous ablations and demonstrate the efficacy of volumetric representations.

Christopher Beckham, Christopher Pal

In this work we theoretically show that conservative objective models (COMs) for offline model-based optimisation (MBO) are a special kind of contrastive divergence-based energy model, one where the energy function represents both the unconditional probability of the input and the conditional probability of the reward variable. While the initial formulation only samples modes from its learned distribution, we propose a simple fix that replaces its gradient ascent sampler with a Langevin MCMC sampler. This gives rise to a special probabilistic model where the probability of sampling an input is proportional to its predicted reward. Lastly, we show that better samples can be obtained if the model is decoupled so that the unconditional and conditional probabilities are modelled separately.

Zhi Hao Luo, Luis Lara, Ge Ya Luo et al.

Text conditioned generative models for images have yielded impressive results. Text conditioned floorplan generation as a special type of raster image generation task also received particular attention. However there are many use cases in floorpla generation where numerical properties of the generated result are more important than the aesthetics. For instance, one might want to specify sizes for certain rooms in a floorplan and compare the generated floorplan with given specifications Current approaches, datasets and commonly used evaluations do not support these kinds of constraints. As such, an attractive strategy is to generate an intermediate data structure that contains numerical properties of a floorplan which can be used to generate the final floorplan image. To explore this setting we (1) construct a new dataset for this data-structure to data-structure formulation of floorplan generation using two popular image based floorplan datasets RPLAN and ProcTHOR-10k, and provide the tools to convert further procedurally generated ProcTHOR floorplan data into our format. (2) We explore the task of floorplan generation given a partial or complete set of constraints and we design a series of metrics and benchmarks to enable evaluating how well samples generated from models respect the constraints. (3) We create multiple baselines by finetuning a large language model (LLM), Llama3, and demonstrate the feasibility of using floorplan data structure conditioned LLMs for the problem of floorplan generation respecting numerical constraints. We hope that our new datasets and benchmarks will encourage further research on different ways to improve the performance of LLMs and other generative modelling techniques for generating designs where quantitative constraints are only partially specified, but must be respected.

Christopher Beckham, Alexandre Piche, David Vazquez et al.

In model-based optimisation (MBO) we are interested in using machine learning to design candidates that maximise some measure of reward with respect to a black box function called the (ground truth) oracle, which is expensive to compute since it involves executing a real world process. In offline MBO we wish to do so without assuming access to such an oracle during training or validation, with makes evaluation non-straightforward. While an approximation to the ground oracle can be trained and used in place of it during model validation to measure the mean reward over generated candidates, the evaluation is approximate and vulnerable to adversarial examples. Measuring the mean reward of generated candidates over this approximation is one such `validation metric', whereas we are interested in a more fundamental question which is finding which validation metrics correlate the most with the ground truth. This involves proposing validation metrics and quantifying them over many datasets for which the ground truth is known, for instance simulated environments. This is encapsulated under our proposed evaluation framework which is also designed to measure extrapolation, which is the ultimate goal behind leveraging generative models for MBO. While our evaluation framework is model agnostic we specifically evaluate denoising diffusion models due to their state-of-the-art performance, as well as derive interesting insights such as ranking the most effective validation metrics as well as discussing important hyperparameters.

Luis Lara, Aristides Milios, Zhi Hao Luo et al.

An AI system for professional floor plan design must precisely control room dimensions and areas while respecting the desired connectivity between rooms and maintaining functional and aesthetic quality. Existing generative approaches focus primarily on respecting the requested connectivity between rooms, but do not support generating floor plans that respect numerical constraints. We introduce a text-based floor plan generation approach that fine-tunes a large language model (LLM) on real plans and then applies reinforcement learning with verifiable rewards (RLVR) to improve adherence to topological and numerical constraints while discouraging invalid or overlapping outputs. Furthermore, we design a set of constraint adherence metrics to systematically measure how generated floor plans align with user-defined constraints. Our model generates floor plans that satisfy user-defined connectivity and numerical constraints and outperforms existing methods on Realism, Compatibility, and Diversity metrics. Across all tasks, our approach achieves at least a 94% relative reduction in Compatibility compared with existing methods. Our results demonstrate that LLMs can effectively handle constraints in this setting, suggesting broader applications for text-based generative modeling.

Evan Racah, Christopher Beckham, Tegan Maharaj et al.

Then detection and identification of extreme weather events in large-scale climate simulations is an important problem for risk management, informing governmental policy decisions and advancing our basic understanding of the climate system. Recent work has shown that fully supervised convolutional neural networks (CNNs) can yield acceptable accuracy for classifying well-known types of extreme weather events when large amounts of labeled data are available. However, many different types of spatially localized climate patterns are of interest including hurricanes, extra-tropical cyclones, weather fronts, and blocking events among others. Existing labeled data for these patterns can be incomplete in various ways, such as covering only certain years or geographic areas and having false negatives. This type of climate data therefore poses a number of interesting machine learning challenges. We present a multichannel spatiotemporal CNN architecture for semi-supervised bounding box prediction and exploratory data analysis. We demonstrate that our approach is able to leverage temporal information and unlabeled data to improve the localization of extreme weather events. Further, we explore the representations learned by our model in order to better understand this important data. We present a dataset, ExtremeWeather, to encourage machine learning research in this area and to help facilitate further work in understanding and mitigating the effects of climate change. The dataset is available at extremeweatherdataset.github.io and the code is available at https://github.com/eracah/hur-detect.

Christopher Beckham, Issam Laradji, Pau Rodriguez et al.

In this paper, we explore the use of GAN-based few-shot data augmentation as a method to improve few-shot classification performance. We perform an exploration into how a GAN can be fine-tuned for such a task (one of which is in a class-incremental manner), as well as a rigorous empirical investigation into how well these models can perform to improve few-shot classification. We identify issues related to the difficulty of training such generative models under a purely supervised regime with very few examples, as well as issues regarding the evaluation protocols of existing works. We also find that in this regime, classification accuracy is highly sensitive to how the classes of the dataset are randomly split. Therefore, we propose a semi-supervised fine-tuning approach as a more pragmatic way forward to address these problems.

Eugene Vorontsov, Pavlo Molchanov, Christopher Beckham et al.

Often in medical imaging, it is prohibitively challenging to produce enough boundary annotations to train deep neural networks for accurate tumor segmentation. We propose the use of weak labels about whether an image presents tumor or whether it is absent to extend training over images that lack these annotations. Specifically, we propose a semi-supervised framework that employs unpaired image-to-image translation between two domains, presence vs. absence of cancer, as the unsupervised objective. We conjecture that translation helps segmentation -- both require the target to be separated from the background. We encode images into two codes: one that is common to both domains and one that is unique to the presence domain. Decoding from the common code yields healthy images; decoding with the addition of the unique code produces a residual change to this image that adds cancer. Translation proceeds from presence to absence and vice versa. In the first case, the tumor is re-added to the image and we successfully exploit the residual decoder to also perform segmentation. In the second case, unique codes are sampled, producing a distribution of possible tumors. To validate the method, we created challenging synthetic tasks and tumor segmentation datasets from public BRATS (brain, MRI) and LitS (liver, CT) datasets. We show a clear improvement (0.83 Dice on brain, 0.74 on liver) over baseline semi-supervised training with autoencoding (0.73, 0.66) and a mean teacher approach (0.75, 0.69), demonstrating the ability to generalize from smaller distributions of annotated samples.

Christopher Beckham, Sina Honari, Vikas Verma et al.

In this paper, we explore new approaches to combining information encoded within the learned representations of auto-encoders. We explore models that are capable of combining the attributes of multiple inputs such that a resynthesised output is trained to fool an adversarial discriminator for real versus synthesised data. Furthermore, we explore the use of such an architecture in the context of semi-supervised learning, where we learn a mixing function whose objective is to produce interpolations of hidden states, or masked combinations of latent representations that are consistent with a conditioned class label. We show quantitative and qualitative evidence that such a formulation is an interesting avenue of research.

Vikas Verma, Alex Lamb, Christopher Beckham et al.

Deep neural networks excel at learning the training data, but often provide incorrect and confident predictions when evaluated on slightly different test examples. This includes distribution shifts, outliers, and adversarial examples. To address these issues, we propose Manifold Mixup, a simple regularizer that encourages neural networks to predict less confidently on interpolations of hidden representations. Manifold Mixup leverages semantic interpolations as additional training signal, obtaining neural networks with smoother decision boundaries at multiple levels of representation. As a result, neural networks trained with Manifold Mixup learn class-representations with fewer directions of variance. We prove theory on why this flattening happens under ideal conditions, validate it on practical situations, and connect it to previous works on information theory and generalization. In spite of incurring no significant computation and being implemented in a few lines of code, Manifold Mixup improves strong baselines in supervised learning, robustness to single-step adversarial attacks, and test log-likelihood.

Joel Ruben Antony Moniz, Christopher Beckham, Simon Rajotte et al.

We present an unsupervised approach for learning to estimate three dimensional (3D) facial structure from a single image while also predicting 3D viewpoint transformations that match a desired pose and facial geometry. We achieve this by inferring the depth of facial keypoints of an input image in an unsupervised manner, without using any form of ground-truth depth information. We show how it is possible to use these depths as intermediate computations within a new backpropable loss to predict the parameters of a 3D affine transformation matrix that maps inferred 3D keypoints of an input face to the corresponding 2D keypoints on a desired target facial geometry or pose. Our resulting approach, called DepthNets, can therefore be used to infer plausible 3D transformations from one face pose to another, allowing faces to be frontalized, transformed into 3D models or even warped to another pose and facial geometry. Lastly, we identify certain shortcomings with our formulation, and explore adversarial image translation techniques as a post-processing step to re-synthesize complete head shots for faces re-targeted to different poses or identities.

Christopher Beckham, Christopher Pal

Procedural terrain generation for video games has been traditionally been done with smartly designed but handcrafted algorithms that generate heightmaps. We propose a first step toward the learning and synthesis of these using recent advances in deep generative modelling with openly available satellite imagery from NASA.

Christopher Beckham, Christopher Pal

Probability distributions produced by the cross-entropy loss for ordinal classification problems can possess undesired properties. We propose a straightforward technique to constrain discrete ordinal probability distributions to be unimodal via the use of the Poisson and binomial probability distributions. We evaluate this approach in the context of deep learning on two large ordinal image datasets, obtaining promising results.

Christopher Beckham, Christopher Pal

In this paper, we explore ordinal classification (in the context of deep neural networks) through a simple modification of the squared error loss which not only allows it to not only be sensitive to class ordering, but also allows the possibility of having a discrete probability distribution over the classes. Our formulation is based on the use of a softmax hidden layer, which has received relatively little attention in the literature. We empirically evaluate its performance on the Kaggle diabetic retinopathy dataset, an ordinal and high-resolution dataset and show that it outperforms all of the baselines employed.