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Causality

Yuanyuan Wang, Biwei Huang, Wei Huang, Xi Geng, Mingming Gong

The identifiability analysis of linear Ordinary Differential Equation (ODE) systems is a necessary prerequisite for making reliable causal inferences about these systems. While identifiability has been well studied in scenarios where the system is fully observable, the conditions for identifiability remain unexplored when latent variables interact with the system. This paper aims to address this gap by presenting a systematic analysis of identifiability in linear ODE systems incorporating hidden confounders. Specifically, we investigate two cases of such systems. In the first case, latent confounders exhibit no causal relationships, yet their evolution adheres to specific functional forms, such as polynomial functions of time $t$. Subsequently, we extend this analysis to encompass scenarios where hidden confounders exhibit causal dependencies, with the causal structure of latent variables described by a Directed Acyclic Graph (DAG). The second case represents a more intricate variation of the first case, prompting a more comprehensive identifiability analysis. Accordingly, we conduct detailed identifiability analyses of the second system under various observation conditions, including both continuous and discrete observations from single or multiple trajectories. To validate our theoretical results, we perform a series of simulations, which support and substantiate our findings.

Probabilistic Methods

Tiago Silva, Daniel Augusto de Souza, Diego Mesquita

Bayes' rule naturally allows for inference refinement in a streaming fashion, without the need to recompute posteriors from scratch whenever new data arrives. In principle, Bayesian streaming is straightforward: we update our prior with the available data and use the resulting posterior as a prior when processing the next data chunk. In practice, however, this recipe entails i) approximating an intractable posterior at each time step; and ii) encapsulating results appropriately to allow for posterior propagation. For continuous state spaces, variational inference (VI) is particularly convenient due to its scalability and the tractability of variational posteriors, For discrete state spaces, however, state-of-the-art VI results in analytically intractable approximations that are ill-suited for streaming settings. To enable streaming Bayesian inference over discrete parameter spaces, we propose streaming Bayes GFlowNets (abbreviated as SB-GFlowNets) by leveraging the recently proposed GFlowNets --- a powerful class of amortized samplers for discrete compositional objects. Notably, SB-GFlowNet approximates the initial posterior using a standard GFlowNet and subsequently updates it using a tailored procedure that requires only the newly observed data. Our case studies in linear preference learning and phylogenetic inference showcase the effectiveness of SB-GFlowNets in sampling from an unnormalized posterior in a streaming setting. As expected, we also observe that SB-GFlowNets is significantly faster than repeatedly training a GFlowNet from scratch to sample from the full posterior.

Generative Models · Diffusion models

Marcin Sendera, Minsu Kim, Sarthak Mittal, Pablo Lemos, Luca Scimeca, Jarrid Rector-Brooks, Alexandre Adam, Yoshua Bengio, Nikolay Malkin

We study the problem of training diffusion models to sample from a distribution with a given unnormalized density or energy function. We benchmark several diffusion-structured inference methods, including simulation-based variational approaches and off-policy methods (continuous generative flow networks). Our results shed light on the relative advantages of existing algorithms while bringing into question some claims from past work. We also propose a novel exploration strategy for off-policy methods, based on local search in the target space with the use of a replay buffer, and show that it improves the quality of samples on a variety of target distributions. Our code for the sampling methods and benchmarks studied is made public at [this link](https://github.com/GFNOrg/gfn-diffusion) as a base for future work on diffusion models for amortized inference.

Ming Yin, Minshuo Chen, Kaixuan Huang, Mengdi Wang

Transformer-based autoregressive sampling has been the major bottleneck for slowing down large language model inferences. One effective way to accelerate inference is Speculative Decoding, which employs a small model to sample a sequence of draft tokens and a large model to validate. Given its empirical effectiveness, the theoretical understanding of Speculative Decoding is falling behind. This paper tackles this gap by conceptualizing the decoding problem via markov chain abstraction and studying the key properties, output quality and inference acceleration, from a theoretical perspective. Our analysis covers the theoretical limits of speculative decoding, batch algorithms, and output quality-inference acceleration tradeoffs. Our results reveal the fundamental connections between different components of LLMs via total variation distances and show how they jointly affect the efficiency of decoding algorithms.

Francesco Tonolini, Nikolaos Aletras, Jordan Massiah, Gabriella Kazai

An important requirement for the reliable deployment of pre-trained large language models (LLMs) is the well-calibrated quantification of the uncertainty in their outputs. While the likelihood of predicting the next token is a practical surrogate of the data uncertainty learned during training, model uncertainty is challenging to estimate, i.e., due to lack of knowledge acquired during training. Prior efforts to quantify uncertainty of neural networks require specific architectures or (re-)training strategies, which are impractical to apply to LLMs with several billion parameters, or for black-box models where the architecture and parameters are not available. In this paper, we propose Bayesian Prompts Ensembles (BayesPE), a novel approach to effectively obtain well-calibrated uncertainty for the output of pre-trained LLMs. BayesPE computes output probabilities through a weighted ensemble of different, but semantically equivalent, task instruction prompts. The relative weights of the different prompts in the ensemble are estimated through approximate Bayesian variational inference over a small labeled validation set. We demonstrate that BayesPE approximates a Bayesian input layer for the LLM, providing a lower bound on the expected model error. In our extensive experiments, we show that BayesPE achieves significantly superior uncertainty calibration compared to several baselines over a range of natural language classification tasks, both in zero- and few-shot settings.

Arda Uzunoğlu, Abdulfattah Safa, Gözde Gül Şahin

Recently, there has been growing interest within the community regarding whether large language models are capable of planning or executing plans. However, most prior studies use LLMs to generate high-level plans for simplified scenarios lacking linguistic complexity and domain diversity, limiting analysis of their planning abilities. These setups constrain evaluation methods (e.g., predefined action space), architectural choices (e.g., only generative models), and overlook the linguistic nuances essential for realistic analysis. To tackle this, we present PARADISE, an abductive reasoning task using Q&A format on practical procedural text sourced from wikiHow. It involves tip and warning inference tasks directly associated with goals, excluding intermediary steps, with the aim of testing the ability of the models to infer implicit knowledge of the plan solely from the given goal. Our experiments, utilizing fine-tuned language models and zero-shot prompting, reveal the effectiveness of task-specific small models over large language models in most scenarios. Despite advancements, all models fall short of human performance. Notably, our analysis uncovers intriguing insights, such as variations in model behavior with dropped keywords, struggles of BERT-family and GPT-4 with physical and abstract goals, and the proposed tasks offering valuable prior knowledge for other unseen procedural tasks. The PARADISE dataset and associated resources are publicly available for further research exploration with https://anonymous.4open.science/r/paradise-53BD/README.md.

Gabriele Picco, Leopold Fuchs, Marcos Martínez Galindo, Alberto Purpura, Vanessa López, Hoang Thanh Lam

Zero-shot entity and relation classification models leverage available external information of unseen classes – e.g., textual descriptions – to annotate input text data. Thanks to the minimum data requirement, Zero-Shot Learning (ZSL) methods have high value in practice, especially in applications where labeled data is scarce. Even though recent research in ZSL has demonstrated significant results, our analysis reveals that those methods are sensitive to provided textual descriptions of entities (or relations). Even a minor modification of descriptions can lead to a change in the decision boundary between entity (or relation) classes. In this paper, we formally define the problem of identifying effective descriptions for zero shot inference. We propose a strategy for generating variations of an initial description, a heuristic for ranking them and an ensemble method capable of boosting the predictions of zero-shot models through description enhancement. Empirical results on four different entity and relation classification datasets show that our proposed method outperform existing approaches and achieve new SOTA results on these datasets under the ZSL settings. The source code of the proposed solutions and the evaluation framework are open-sourced.

Miles Williams, Nikolaos Aletras

Quantization and pruning form the foundation of compression for neural networks, enabling efficient inference for large language models (LLMs). Recently, various quantization and pruning techniques have demonstrated remarkable performance in a post-training setting. They rely upon calibration data, a small set of unlabeled examples that are used to generate layer activations. However, no prior work has systematically investigated how the calibration data impacts the effectiveness of model compression methods. In this paper, we present the first extensive empirical study on the effect of calibration data upon LLM performance. We trial a variety of quantization and pruning methods, datasets, tasks, and models. Surprisingly, we find substantial variations in downstream task performance, contrasting existing work that suggests a greater level of robustness to the calibration data. Finally, we make a series of recommendations for the effective use of calibration data in LLM quantization and pruning.

Siddhartha Jain, Xiaofei Ma, Anoop Deoras, Bing Xiang

Large Language Models (LLMs) can exhibit considerable variation in the quality of their sampled outputs. Reranking and selecting the best generation from the sampled set is a popular way of obtaining strong gains in generation quality. In this paper, we present a novel approach for reranking LLM generations. Unlike other techniques that might involve additional inferences or training a specialized reranker, our approach relies on easy to compute pairwise statistics between the generations that have minimal compute overhead. We show that our approach can be formalized as an extension of self-consistency and analyze its performance in that framework, theoretically as well as via simulations. We show strong improvements for selecting the best k generations for code generation tasks as well as robust improvements for the best generation for the tasks of autoformalization, summarization, and translation. While our approach only assumes black-box access to LLMs, we show that additional access to token probabilities can improve performance even further.

Probabilistic Methods · Variational Inference

Yuesong Shen, Nico Daheim, Bai Cong, Peter Nickl, Gian Maria Marconi, Bazan Raoul, Rio Yokota, Iryna Gurevych, Daniel Cremers, Khan Emtiyaz 等

We give extensive empirical evidence against the common belief that variational learning is ineffective for large neural networks. We show that an optimizer called Improved Variational Online Newton (IVON) consistently matches or outperforms Adam for training large networks such as GPT-2 and ResNets from scratch. IVON's computational costs are nearly identical to Adam but its predictive uncertainty is better. We show several new use cases of IVON where we improve finetuning and model merging in Large Language Models, accurately predict generalization error, and faithfully estimate sensitivity to data. We find overwhelming evidence that variational learning is effective. Code is available at https://github.com/team-approx-bayes/ivon.

Social Aspects · Trustworthy Machine Learning

YANRAN WANG, QIUCHEN QIAN, David Boyle

Reinforcement learning can provide effective reasoning for sequential decision-making problems with variable dynamics. Such reasoning in practical implementation, however, poses a persistent challenge in interpreting the reward function and the corresponding optimal policy. Consequently, representing sequential decision-making problems as probabilistic inference can have considerable value, as, in principle, the inference offers diverse and powerful mathematical tools to infer the stochastic dynamics whilst suggesting a probabilistic interpretation of policy optimization. In this study, we propose a novel Adaptive Wasserstein Variational Optimization, namely AWaVO, to tackle these interpretability challenges. Our approach uses formal methods to achieve the interpretability: convergence guarantee, training transparency, and intrinsic decision-interpretation. To demonstrate its practicality, we showcase guaranteed interpretability including a global convergence rate $\Theta(1/\sqrt{T})$ not only in simulation but also in real-world quadrotor tasks. In comparison with state-of-the-art benchmarks, including TRPO-IPO, PCPO, and CRPO, we empirically verify that AWaVO offers a reasonable trade-off between high performance and sufficient interpretability.

Probabilistic Methods · Variational Inference

Alexandra Hotti, Oskar Kviman, Ricky Molén, Víctor Elvira, Jens Lagergren

Mixture variational distributions in black box variational inference (BBVI) have demonstrated impressive results in challenging density estimation tasks. However, currently scaling the number of mixture components can lead to a linear increase in the number of learnable parameters and a quadratic increase in inference time due to the evaluation of the evidence lower bound (ELBO). Our two key contributions address these limitations. First, we introduce the novel Multiple Importance Sampling Variational Autoencoder (MISVAE), which amortizes the mapping from input to mixture-parameter space using one-hot encodings. Fortunately, with MISVAE, each additional mixture component incurs a negligible increase in network parameters. Second, we construct two new estimators of the ELBO for mixtures in BBVI, enabling a tremendous reduction in inference time with marginal or even improved impact on performance. Collectively, our contributions enable scalability to hundreds of mixture components and provide superior estimation performance in shorter time, with fewer network parameters compared to previous Mixture VAEs. Experimenting with MISVAE, we achieve astonishing, SOTA results on MNIST. Furthermore, we empirically validate our estimators in other BBVI settings, including Bayesian phylogenetic inference, where we improve inference times for the SOTA mixture model on eight data sets.

Deep Learning · Generative Models and Autoencoders

Wei Deng, Weijian Luo, Yixin Tan, Marin Biloš, Yu Chen, Yuriy Nevmyvaka, Ricky T. Q. Chen

Schrödinger bridge (SB) has emerged as the go-to method for optimizing transportation plans in diffusion models. However, SB requires estimating the intractable forward score functions, inevitably resulting in the (costly) implicit training loss based on simulated trajectories. To improve the scalability while preserving efficient transportation plans, we leverage variational inference to linearize the forward score functions (variational scores) of SB and restore *simulation-free* properties in training backward scores. We propose the variational Schrödinger diffusion model (VSDM), where the forward process is a multivariate diffusion and the variational scores are adaptively optimized for efficient transport. Theoretically, we use stochastic approximation to prove the convergence of the variational scores and show the convergence of the adaptively generated samples based on the optimal variational scores. Empirically, we test the algorithm in simulated examples and observe that VSDM is efficient in generations of anisotropic shapes and yields straighter sample trajectories compared to the single-variate diffusion. We also verify the scalability of the algorithm in real-world data and achieve competitive unconditional generation performance in CIFAR10 and conditional generation in time series modeling. Notably, VSDM no longer depends on warm-up initializations required by SB.

Social Aspects

Gary Cheng, Moritz Hardt, Celestine Mendler-Dünner

Regulators and academics are increasingly interested in the causal effect that algorithmic actions of a digital platform have on user consumption. In pursuit of estimating this effect from observational data, we identify a set of assumptions that permit causal identifiability without assuming randomized platform actions. Our results are applicable to platforms that rely on machine-learning-powered predictions and leverage knowledge from historical data. The key novelty of our approach is to explicitly model the dynamics of consumption over time, exploiting the repeated interaction of digital platforms with their participants to prove our identifiability results. By viewing the platform as a controller acting on a dynamical system, we can show that exogenous variation in consumption and appropriately responsive algorithmic control actions are sufficient for identifying the causal effect of interest. We complement our claims with an analysis of ready-to-use finite sample estimators and empirical investigations. More broadly, our results deriving identifiability conditions tailored to digital platform settings illustrate a fruitful interplay of control theory and causal inference.

Deep Learning · Generative Models and Autoencoders

Zach Evans, CJ Carr, Josiah Taylor, Scott Hawley, Jordi Pons

Generating long-form 44.1kHz stereo audio from text prompts can be computationally demanding. Further, most previous works do not tackle that music and sound effects naturally vary in their duration. Our research focuses on the efficient generation of long-form, variable-length stereo music and sounds at 44.1kHz using text prompts with a generative model. It is based on latent diffusion, with its latent defined by a fully-convolutional variational autoencoder. The generative model is conditioned on text prompts as well as timing embeddings, allowing for fine control over both the content and length of the generated music and sounds. It is capable of rendering stereo signals of up to 95 sec at 44.1kHz in 8 sec on an A100 GPU. Despite its compute efficiency and fast inference, the proposed model is one of the best in two public text-to-music and -audio benchmarks and, differently from state-of-the-art models, can generate music with structure and stereo sounds.

Probabilistic Methods · Variational Inference

Michael Komodromos, Marina Evangelou, Sarah Filippi

Variational logistic regression is a popular method for approximate Bayesian inference seeing wide-spread use in many areas of machine learning including: Bayesian optimization, reinforcement learning and multi-instance learning to name a few. However, due to the intractability of the Evidence Lower Bound, authors have turned to the use of Monte Carlo, quadrature or bounds to perform inference, methods which are costly or give poor approximations to the true posterior. In this paper we introduce a new bound for the expectation of softplus function and subsequently show how this can be applied to variational logistic regression and Gaussian process classification. Unlike other bounds, our proposal does not rely on extending the variational family, or introducing additional parameters to ensure the bound is tight. In fact, we show that this bound is tighter than the state-of-the-art, and that the resulting variational posterior achieves state-of-the-art performance, whilst being significantly faster to compute than Monte-Carlo methods.

Probabilistic Methods · Bayesian Models and Methods

Mingzhou Fan, Ruida Zhou, Chao Tian, Xiaoning Qian

Particle-based Bayesian inference methods by sampling from a partition-free target (posterior) distribution, e.g., Stein variational gradient descent (SVGD), have attracted significant attention. We propose a path-guided particle-based sampling (PGPS) method based on a novel Log-weighted Shrinkage (LwS) density path linking an initial distribution to the target distribution. We propose to utilize a Neural network to learn a vector field motivated by the Fokker-Planck equation of the designed density path. Particles, initiated from the initial distribution, evolve according to the ordinary differential equation defined by the vector field. The distribution of these particles is guided along a density path from the initial distribution to the target distribution. The proposed LwS density path allows for an efficient search of modes of the target distribution while canonical methods fail. We theoretically analyze the Wasserstein distance of the distribution of the PGPS-generated samples and the target distribution due to approximation and discretization errors. Practically, the proposed PGPS-LwS method demonstrates higher Bayesian inference accuracy and better calibration ability in experiments conducted on both synthetic and real-world Bayesian learning tasks, compared to baselines, such as SVGD and Langevin dynamics, etc.

Applications

Xiao Luo, Yiyang Gu, Huiyu Jiang, Hang Zhou, Jinsheng Huang, Wei Ju, Zhiping Xiao, Ming Zhang, Yizhou Sun

This paper studies the problem of modeling multi-agent dynamical systems, where agents could interact mutually to influence their behaviors. Recent research predominantly uses geometric graphs to depict these mutual interactions, which are then captured by powerful graph neural networks (GNNs). However, predicting interacting dynamics in challenging scenarios such as out-of-distribution shift and complicated underlying rules remains unsolved. In this paper, we propose a new approach named Prototypical Graph ODE (PGODE) to address the problem. The core of PGODE is to incorporate prototype decomposition from contextual knowledge into a continuous graph ODE framework. Specifically, PGODE employs representation disentanglement and system parameters to extract both object-level and system-level contexts from historical trajectories, which allows us to explicitly model their independent influence and thus enhances the generalization capability under system changes. Then, we integrate these disentangled latent representations into a graph ODE model, which determines a combination of various interacting prototypes for enhanced model expressivity. The entire model is optimized using an end-to-end variational inference framework to maximize the likelihood. Extensive experiments in both in-distribution and out-of-distribution settings validate the superiority of PGODE compared to various baselines.

Probabilistic Methods · Variational Inference

Brooks(Ruijia) Niu, Dongxia Wu, Kai Kim, Yian Ma, Duncan Watson-Parris, Rose Yu

Multi-fidelity surrogate modeling aims to learn an accurate surrogate at the highest fidelity level by combining data from multiple sources. Traditional methods relying on Gaussian processes can hardly scale to high-dimensional data. Deep learning approaches utilize neural network based encoders and decoders to improve scalability. These approaches share encoded representations across fidelities without including corresponding decoder parameters. This hinders inference performance, especially in out-of-distribution scenarios when the highest fidelity data has limited domain coverage. To address these limitations, we propose Multi-fidelity Residual Neural Processes (MFRNP), a novel multi-fidelity surrogate modeling framework. MFRNP explicitly models the residual between the aggregated output from lower fidelities and ground truth at the highest fidelity. The aggregation introduces decoders into the information sharing step and optimizes lower fidelity decoders to accurately capture both in-fidelity and cross-fidelity information. We show that MFRNP significantly outperforms state-of-the-art in learning partial differential equations and a real-world climate modeling task. Our code is published at: https://github.com/Rose-STL-Lab/MFRNP

Reinforcement Learning

Mattie Fellows, Brandon Kaplowitz, Christian Schroeder de Witt, Shimon Whiteson

Bayesian reinforcement learning (RL) offers a principled and elegant approach for sequential decision making under uncertainty. Most notably, Bayesian agents do not face an exploration/exploitation dilemma, a major pathology of frequentist methods. However theoretical understanding of model-free approaches is lacking. In this paper, we introduce a novel Bayesian model-free formulation and the first analysis showing that model-free approaches can yield Bayes-optimal policies. We show all existing model-free approaches make approximations that yield policies that can be arbitrarily Bayes-suboptimal. As a first step towards model-free Bayes optimality, we introduce the Bayesian exploration network (BEN) which uses normalising flows to model both the aleatoric uncertainty (via density estimation) and epistemic uncertainty (via variational inference) in the Bellman operator. In the limit of complete optimisation, BEN learns true Bayes-optimal policies, but like in variational expectation-maximisation, partial optimisation renders our approach tractable. Empirical results demonstrate that BEN can learn true Bayes-optimal policies in tasks where existing model-free approaches fail.