arXiv subjects

Christian Walder

Publications and source records attributed to Christian Walder.

At least 19 recordsLinked to original sources

arXiv2026

Free Lunch for Pass@$k$? Low Cost Diverse Sampling for Diffusion Language Models

Diverse outputs in text generation are necessary for effective exploration in complex reasoning tasks, such as code generation and mathematical problem solving. Such Pass@$k$ problems benefit from distinct candidates covering the solution space. However, traditional sampling approaches often waste computational resources on repetitive failure modes. While Diffusion Language Models have emerged as a competitive alternative to the prevailing Autoregressive paradigm, they remain susceptible to this redundancy, with independent samples frequently collapsing into similar modes. To address this, we propose a training free, low cost intervention to enhance generative diversity in Diffusion Language Models. Our approach modifies intermediate samples in a batch sequentially, where each sample is repelled from the feature space of previous samples, actively penalising redundancy. Unlike prior methods that require retraining or beam search, our strategy incurs negligible computational overhead, while ensuring that each sample contributes a unique perspective to the batch. We evaluate our method on the HumanEval and GSM8K benchmarks using the LLaDA-8B-Instruct model. Our results demonstrate significantly improved diversity and Pass@$k$ performance across various temperature settings. As a simple modification to the sampling process, our method offers an immediate, low-cost improvement for current and future Diffusion Language Models in tasks that benefit from diverse solution search. We make our code available at https://github.com/sean-lamont/odd.

cs.CL↗

arXiv2025

Pass@K Policy Optimization: Solving Harder Reinforcement Learning Problems

Reinforcement Learning (RL) algorithms sample multiple n>1 solution attempts for each problem and reward them independently. This optimizes for pass@1 performance and prioritizes the strength of isolated samples at the expense of the diversity and collective utility of sets of samples. This under-utilizes the sampling capacity, limiting exploration and eventual improvement on harder examples. As a fix, we propose Pass-at-k Policy Optimization (PKPO), a transformation on the final rewards which leads to direct optimization of pass@k performance, thus optimizing for sets of samples that maximize reward when considered jointly. Our contribution is to derive novel low variance unbiased estimators for pass@k and its gradient, in both the binary and continuous reward settings. We show optimization with our estimators reduces to standard RL with rewards that have been jointly transformed by a stable and efficient transformation function. While previous efforts are restricted to k=n, ours is the first to enable robust optimization of pass@k for any arbitrary k <= n. Moreover, instead of trading off pass@1 performance for pass@k gains, our method allows annealing k during training, optimizing both metrics and often achieving strong pass@1 numbers alongside significant pass@k gains. We validate our reward transformations on toy experiments, which reveal the variance reducing properties of our formulations. We also include real-world examples using the open-source LLM, GEMMA-2. We find that our transformation effectively optimizes for the target k. Furthermore, higher k values enable solving more and harder problems, while annealing k boosts both the pass@1 and pass@k . Crucially, for challenging task sets where conventional pass@1 optimization stalls, our pass@k approach unblocks learning, likely due to better exploration by prioritizing joint utility over the utility of individual samples.

cs.LG↗

arXiv2024

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.

cs.IR↗

arXiv2024

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 and LeanDojo benchmarks by augmenting popular open source proving LLMs. 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. We make our code available at https://github.com/sean-lamont/3D-Prover.

cs.AI↗

arXiv2024

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.

cs.IR↗

arXiv2024

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/}.

cs.SD↗

arXiv2024

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.

cs.AI↗

arXiv2023

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 $\tildeΔ^{C-1}$ 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.

stat.ML↗

arXiv2023

Latent Optimal Paths by Gumbel Propagation for Variational Bayesian Dynamic Programming

We propose the stochastic optimal path which solves the classical optimal path problem by a probability-softening solution. This unified approach transforms a wide range of DP problems into directed acyclic graphs in which all 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 of a latent path, namely Bayesian dynamic programming (BDP). We demonstrate the usage of BDP in the latent space of variational autoencoders (VAEs) and propose the BDP-VAE which captures structured sparse optimal paths as latent variables. This enables end-to-end training for generative tasks in which models rely on unobserved structural information. At last, we validate the behavior of our approach and showcase its applicability in two real-world applications: text-to-speech and singing voice synthesis. Our implementation code is available at \url{https://github.com/XinleiNIU/LatentOptimalPathsBayesianDP}.

stat.ML↗

arXiv2023

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.

cs.CV↗

arXiv2023

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. We also release our implementation as an open-source library at https://github.com/google-research/r_u_sure.

cs.LG↗

arXiv2023

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.

cs.LG↗

arXiv2022

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.

cs.CV↗

arXiv2022

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.

cs.IR↗

arXiv2022

Efficient Non-parametric Bayesian Hawkes Processes

In this paper, we develop an efficient nonparametric Bayesian estimation of the kernel function of Hawkes processes. The non-parametric Bayesian approach is important because it provides flexible Hawkes kernels and quantifies their uncertainty. Our method is based on the cluster representation of Hawkes processes. Utilizing the finite support assumption of the Hawkes process, we efficiently sample random branching structures and thus, we split the Hawkes process into clusters of Poisson processes. We derive two algorithms -- a block Gibbs sampler and a maximum a posteriori estimator based on expectation maximization -- and we show that our methods have a linear time complexity, both theoretically and empirically. On synthetic data, we show our methods to be able to infer flexible Hawkes triggering kernels. On two large-scale Twitter diffusion datasets, we show that our methods outperform the current state-of-the-art in goodness-of-fit and that the time complexity is linear in the size of the dataset. We also observe that on diffusions related to online videos, the learned kernels reflect the perceived longevity for different content types such as music or pets videos.

cs.LG↗

arXiv2022

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 are 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 that 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 modeling approach yields state-of-the-art experimental results on the ShapeNet dataset.

cs.CV↗

arXiv2021

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.

cs.LG↗

arXiv2021

Humanly Certifying Superhuman Classifiers

Estimating the performance of a machine learning system is a longstanding challenge in artificial intelligence research. Today, this challenge is especially relevant given the emergence of systems which appear to increasingly outperform human beings. In some cases, this "superhuman" performance is readily demonstrated; for example by defeating legendary human players in traditional two player games. On the other hand, it can be challenging to evaluate classification models that potentially surpass human performance. Indeed, human annotations are often treated as a ground truth, which implicitly assumes the superiority of the human over any models trained on human annotations. In reality, human annotators can make mistakes and be subjective. Evaluating the performance with respect to a genuine oracle may be more objective and reliable, even when querying the oracle is expensive or impossible. In this paper, we first raise the challenge of evaluating the performance of both humans and models with respect to an oracle which is unobserved. We develop a theory for estimating the accuracy compared to the oracle, using only imperfect human annotations for reference. Our analysis provides a simple recipe for detecting and certifying superhuman performance in this setting, which we believe will assist in understanding the stage of current research on classification. We validate the convergence of the bounds and the assumptions of our theory on carefully designed toy experiments with known oracles. Moreover, we demonstrate the utility of our theory by meta-analyzing large-scale natural language processing tasks, for which an oracle does not exist, and show that under our assumptions a number of models from recent years are with high probability superhuman.

cs.LG↗