A Universal Sets-level Optimization Framework for Next Set Recommendation

Next Set Recommendation (NSRec), encompassing related tasks such as next basket recommendation and temporal sets prediction, stands as a trending research topic. Although numerous attempts have been made on this topic, there are certain drawbacks: (i) Existing studies are still confined to utilizing objective functions commonly found in Next Item Recommendation (NIRec), such as binary cross entropy and BPR, which are calculated based on individual item comparisons; (ii) They place emphasis on building sophisticated learning models to capture intricate dependency relationships across sequential sets, but frequently overlook pivotal dependency in their objective functions; (iii) Diversity factor within sequential sets is frequently overlooked. In this research, we endeavor to unveil a universal and S ets-level optimization framework for N ext Set Recommendation (SNSRec), offering a holistic fusion of diversity distribution and intricate dependency relationships within temporal sets. To realize this, the following contributions are made: (i) We directly model the temporal set in a sequence as a cohesive entity, leveraging the Structured Determinantal Point Process (SDPP), wherein the probabilistic DPP distribution prioritizes collections of structures (sequential sets) instead of individual items; (ii) We introduce a co-occurrence representation to discern and acknowledge the importance of different sets; (iii) We propose a sets-level optimization criterion, which integrates the diversity distribution and dependency relations across the entire sequence of sets, guiding the model to recommend relevant and diversified set. Extensive experiments on real-world datasets show that our approach consistently outperforms previous methods on both relevance and diversity.

3D-Prover: Diversity Driven Theorem Proving With Determinantal Point Processes

A key challenge in automated formal reasoning is the intractable search space, which grows exponentially with the depth of the proof. This branching is caused by the large number of candidate proof tactics which can be applied to a given goal. Nonetheless, many of these tactics are semantically similar or lead to an execution error, wasting valuable resources in both cases. We address the problem of effectively pruning this search, using only synthetic data generated from previous proof attempts. We first demonstrate that it is possible to generate semantically aware tactic representations which capture the effect on the proving environment, likelihood of success and execution time. We then propose a novel filtering mechanism which leverages these representations to select semantically diverse and high quality tactics, using Determinantal Point Processes. Our approach, 3D-Prover, is designed to be general, and to augment any underlying tactic generator. We demonstrate the effectiveness of 3D-Prover on the miniF2F-valid and miniF2F-test benchmarks by augmenting the ReProver LLM. We show that our approach leads to an increase in the overall proof rate, as well as a significant improvement in the tactic success rate, execution time and diversity.

Learning k-Determinantal Point Processes for Personalized Ranking

The key to personalized recommendation is to predict a personalized ranking on a catalog of items by modeling the user's preferences. There are many personalized ranking approaches for item recommendation from implicit feedback like Bayesian Personalized Ranking (BPR) and listwise ranking. Despite these methods have shown performance benefits, there are still limitations affecting recommendation performance. First, none of them directly optimize ranking of sets, causing inadequate exploitation of correlations among multiple items. Second, the diversity aspect of recommendations is insufficiently addressed compared to relevance. In this work, we present a new optimization criterion LkP based on set probability comparison for personalized ranking that moves beyond traditional ranking-based methods. It formalizes set-level relevance and diversity ranking comparisons through a Determinantal Point Process (DPP) kernel decomposition. To confer ranking interpretability to the DPP set probabilities and prioritize the practicality of LkP, we condition the standard DPP on the cardinality k of the DPP-distributed set, known as k-DPP, a less-explored extension of DPP. The generic stochastic gradient descent based technique can be directly applied to optimizing models that employ LkP. We implement LkP in the context of both Matrix Factorization (MF) and neural networks approaches, on three real-world datasets, obtaining improved relevance and diversity performances. LkP is broadly applicable, and when applied to existing recommendation models it also yields strong performance improvements, suggesting that LkP holds significant value to the field of recommender systems.

SoundLoCD: An Efficient Conditional Discrete Contrastive Latent Diffusion Model for Text-to-Sound Generation

We present SoundLoCD, a novel text-to-sound generation framework, which incorporates a LoRA-based conditional discrete contrastive latent diffusion model. Unlike recent large-scale sound generation models, our model can be efficiently trained under limited computational resources. The integration of a contrastive learning strategy further enhances the connection between text conditions and the generated outputs, resulting in coherent and high-fidelity performance. Our experiments demonstrate that SoundLoCD outperforms the baseline with greatly reduced computational resources. A comprehensive ablation study further validates the contribution of each component within SoundLoCD. Demo page: \url{https://XinleiNIU.github.io/demo-SoundLoCD/}.

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.