BAIT: Benchmarking (Embedding) Architectures for Interactive Theorem-Proving

Artificial Intelligence for Theorem Proving has given rise to a plethora of benchmarks and methodologies, particularly in Interactive Theorem Proving (ITP). Research in the area is fragmented, with a diverse set of approaches being spread across several ITP systems. This presents a significant challenge to the comparison of methods, which are often complex and difficult to replicate. Addressing this, we present BAIT, a framework for fair and streamlined comparison of learning approaches in ITP. We demonstrate BAIT's capabilities with an in-depth comparison, across several ITP benchmarks, of state-of-the-art architectures applied to the problem of formula embedding. We find that Structure Aware Transformers perform particularly well, improving on techniques associated with the original problem sets. BAIT also allows us to assess the end-to-end proving performance of systems built on interactive environments. This unified perspective reveals a novel end-to-end system that improves on prior work. We also provide a qualitative analysis, illustrating that improved performance is associated with more semantically-aware embeddings. By streamlining the implementation and comparison of Machine Learning algorithms in the ITP context, we anticipate BAIT will be a springboard for future research.

Latent Optimal Paths by Gumbel Propagation for Variational Bayesian Dynamic Programming

We propose a unified approach to obtain structured sparse optimal paths in the latent space of a variational autoencoder (VAE) using dynamic programming and Gumbel propagation. We solve the classical optimal path problem by a probability softening solution, called the stochastic optimal path, and transform a wide range of DP problems into directed acyclic graphs in which all possible paths follow a Gibbs distribution. We show the equivalence of the Gibbs distribution to a message-passing algorithm by the properties of the Gumbel distribution and give all the ingredients required for variational Bayesian inference. Our approach obtaining latent optimal paths enables end-to-end training for generative tasks in which models rely on the information of unobserved structural features. We validate the behavior of our approach and showcase its applicability in two real-world applications: text-to-speech and singing voice synthesis.

DualVAE: Controlling Colours of Generated and Real Images

Colour controlled image generation and manipulation are of interest to artists and graphic designers. Vector Quantised Variational AutoEncoders (VQ-VAEs) with autoregressive (AR) prior are able to produce high quality images, but lack an explicit representation mechanism to control colour attributes. We introduce DualVAE, a hybrid representation model that provides such control by learning disentangled representations for colour and geometry. The geometry is represented by an image intensity mapping that identifies structural features. The disentangled representation is obtained by two novel mechanisms: (i) a dual branch architecture that separates image colour attributes from geometric attributes, and (ii) a new ELBO that trains the combined colour and geometry representations. DualVAE can control the colour of generated images, and recolour existing images by transferring the colour latent representation obtained from an exemplar image. We demonstrate that DualVAE generates images with FID nearly two times better than VQ-GAN on a diverse collection of datasets, including animated faces, logos and artistic landscapes.

R-U-SURE? Uncertainty-Aware Code Suggestions By Maximizing Utility Across Random User Intents

Large language models show impressive results at predicting structured text such as code, but also commonly introduce errors and hallucinations in their output. When used to assist software developers, these models may make mistakes that users must go back and fix, or worse, introduce subtle bugs that users may miss entirely. We propose Randomized Utility-driven Synthesis of Uncertain REgions (R-U-SURE), an approach for building uncertainty-aware suggestions based on a decision-theoretic model of goal-conditioned utility, using random samples from a generative model as a proxy for the unobserved possible intents of the end user. Our technique combines minimum-Bayes-risk decoding, dual decomposition, and decision diagrams in order to efficiently produce structured uncertainty summaries, given only sample access to an arbitrary generative model of code and an optional AST parser. We demonstrate R-U-SURE on three developer-assistance tasks, and show that it can be applied different user interaction patterns without retraining the model and leads to more accurate uncertainty estimates than token-probability baselines.

Sampled Transformer for Point Sets

The sparse transformer can reduce the computational complexity of the self-attention layers to $O(n)$, whilst still being a universal approximator of continuous sequence-to-sequence functions. However, this permutation variant operation is not appropriate for direct application to sets. In this paper, we proposed an $O(n)$ complexity sampled transformer that can process point set elements directly without any additional inductive bias. Our sampled transformer introduces random element sampling, which randomly splits point sets into subsets, followed by applying a shared Hamiltonian self-attention mechanism to each subset. The overall attention mechanism can be viewed as a Hamiltonian cycle in the complete attention graph, and the permutation of point set elements is equivalent to randomly sampling Hamiltonian cycles. This mechanism implements a Monte Carlo simulation of the $O(n^2)$ dense attention connections. We show that it is a universal approximator for continuous set-to-set functions. Experimental results on point-clouds show comparable or better accuracy with significantly reduced computational complexity compared to the dense transformer or alternative sparse attention schemes.

LegendreTron: Uprising Proper Multiclass Loss Learning

Loss functions serve as the foundation of supervised learning and are often chosen prior to model development. To avoid potentially ad hoc choices of losses, statistical decision theory describes a desirable property for losses known as \emph{properness}, which asserts that Bayes' rule is optimal. Recent works have sought to \emph{learn losses} and models jointly. Existing methods do this by fitting an inverse canonical link function which monotonically maps $\mathbb{R}$ to $[0,1]$ to estimate probabilities for binary problems. In this paper, we extend monotonicity to maps between $\mathbb{R}^{C-1}$ and the projected probability simplex $\tilde{\Delta}^{C-1}$ by using monotonicity of gradients of convex functions. We present {\sc LegendreTron} as a novel and practical method that jointly learns \emph{proper canonical losses} and probabilities for multiclass problems. Tested on a benchmark of domains with up to 1,000 classes, our experimental results show that our method consistently outperforms the natural multiclass baseline under a $t$-test at 99% significance on all datasets with greater than 10 classes.

Determinantal Point Process Likelihoods for Sequential Recommendation

Sequential recommendation is a popular task in academic research and close to real-world application scenarios, where the goal is to predict the next action(s) of the user based on his/her previous sequence of actions. In the training process of recommender systems, the loss function plays an essential role in guiding the optimization of recommendation models to generate accurate suggestions for users. However, most existing sequential recommendation techniques focus on designing algorithms or neural network architectures, and few efforts have been made to tailor loss functions that fit naturally into the practical application scenario of sequential recommender systems. Ranking-based losses, such as cross-entropy and Bayesian Personalized Ranking (BPR) are widely used in the sequential recommendation area. We argue that such objective functions suffer from two inherent drawbacks: i) the dependencies among elements of a sequence are overlooked in these loss formulations; ii) instead of balancing accuracy (quality) and diversity, only generating accurate results has been over emphasized. We therefore propose two new loss functions based on the Determinantal Point Process (DPP) likelihood, that can be adaptively applied to estimate the subsequent item or items. The DPP-distributed item set captures natural dependencies among temporal actions, and a quality vs. diversity decomposition of the DPP kernel pushes us to go beyond accuracy-oriented loss functions. Experimental results using the proposed loss functions on three real-world datasets show marked improvements over state-of-the-art sequential recommendation methods in both quality and diversity metrics.

SPA-VAE: Similar-Parts-Assignment for Unsupervised 3D Point Cloud Generation

This paper addresses the problem of unsupervised parts-aware point cloud generation with learned parts-based self-similarity. Our SPA-VAE infers a set of latent canonical candidate shapes for any given object, along with a set of rigid body transformations for each such candidate shape to one or more locations within the assembled object. In this way, noisy samples on the surface of, say, each leg of a table, are effectively combined to estimate a single leg prototype. When parts-based self-similarity exists in the raw data, sharing data among parts in this way confers numerous advantages: modeling accuracy, appropriately self-similar generative outputs, precise in-filling of occlusions, and model parsimony. SPA-VAE is trained end-to-end using a variational Bayesian approach which uses the Gumbel-softmax trick for the shared part assignments, along with various novel losses to provide appropriate inductive biases. Quantitative and qualitative analyses on ShapeNet demonstrate the advantage of SPA-VAE.

EditVAE: Unsupervised Part-Aware Controllable 3D Point Cloud Shape Generation

This paper tackles the problem of parts-aware point cloud generation. Unlike existing works which require the point cloud to be segmented into parts a priori, our parts-aware editing and generation is performed in an unsupervised manner. We achieve this with a simple modification of the Variational Auto-Encoder which yields a joint model of the point cloud itself along with a schematic representation of it as a combination of shape primitives. In particular, we introduce a latent representation of the point cloud which can be decomposed into a disentangled representation for each part of the shape. These parts are in turn disentangled into both a shape primitive and a point cloud representation, along with a standardising transformation to a canonical coordinate system. The dependencies between our standardising transformations preserve the spatial dependencies between the parts in a manner which allows meaningful parts-aware point cloud generation and shape editing. In addition to the flexibility afforded by our disentangled representation, the inductive bias introduced by our joint modelling approach yields the state-of-the-art experimental results on the ShapeNet dataset.

Dense Uncertainty Estimation

Deep neural networks can be roughly divided into deterministic neural networks and stochastic neural networks.The former is usually trained to achieve a mapping from input space to output space via maximum likelihood estimation for the weights, which leads to deterministic predictions during testing. In this way, a specific weights set is estimated while ignoring any uncertainty that may occur in the proper weight space. The latter introduces randomness into the framework, either by assuming a prior distribution over model parameters (i.e. Bayesian Neural Networks) or including latent variables (i.e. generative models) to explore the contribution of latent variables for model predictions, leading to stochastic predictions during testing. Different from the former that achieves point estimation, the latter aims to estimate the prediction distribution, making it possible to estimate uncertainty, representing model ignorance about its predictions. We claim that conventional deterministic neural network based dense prediction tasks are prone to overfitting, leading to over-confident predictions, which is undesirable for decision making. In this paper, we investigate stochastic neural networks and uncertainty estimation techniques to achieve both accurate deterministic prediction and reliable uncertainty estimation. Specifically, we work on two types of uncertainty estimations solutions, namely ensemble based methods and generative model based methods, and explain their pros and cons while using them in fully/semi/weakly-supervised framework. Due to the close connection between uncertainty estimation and model calibration, we also introduce how uncertainty estimation can be used for deep model calibration to achieve well-calibrated models, namely dense model calibration. Code and data are available at https://github.com/JingZhang617/UncertaintyEstimation.