Diffusion bridge models have recently become a powerful tool in the field of generative modeling. In this work, we leverage their power to address another important problem in machine learning and information theory, the estimation of the mutual information (MI) between two random variables. We show that by using the theory of diffusion bridges, one can construct an unbiased estimator for data posing difficulties for conventional MI estimators. We showcase the performance of our estimator on two standard MI estimation benchmarks, i.e., low-dimensional and image-based, and on real-world data, i.e., protein language model embeddings.
We employ a unified framework for computing the information capacity of biological signaling systems using Fisher Information. By deriving closed-form or easily computable information capacity formulas, we quantify how well different signaling models, including binomial, multinomial, Poisson, Gaussian, and Gamma distributions, can discriminate among input signals. These expressions clarify how key features such as signal range, noise scaling, pathway length, and receivers' diversity shape the theoretical limits of sensing. In particular, we show how signal-to-noise ratio and fold-change sensitivity arise naturally within the Fisher formalism, and how signal degradation in cascades imposes linear information loss. Our results provide intuitive, analytically grounded tools to benchmark and guide the analysis of real signaling systems, without requiring computationally expensive mutual information estimation. While motivated by cellular communication, the framework generalizes to any system where noisy input-output relationships constrain transmission fidelity, including synthetic biology, sensor networks, and engineered communication channels.
Session-based recommendation (SBR) predicts the next item based on anonymous sessions. Traditional SBR explores user intents based on ID collaborations or auxiliary content. To further alleviate data sparsity and cold-start issues, recent Multimodal SBR (MSBR) methods utilize simplistic pre-trained models for modality learning but have limitations in semantic richness. Considering semantic reasoning abilities of Large Language Models (LLM), we focus on the LLM-enhanced MSBR scenario in this paper, which leverages LLM cognition for comprehensive multimodal representation generation, to enhance downstream MSBR. Tackling this problem faces two challenges: i) how to obtain LLM cognition on both transitional patterns and inherent multimodal knowledge, ii) how to align both features into one unified LLM, minimize discrepancy while maximizing representation utility. To this end, we propose a multimodal LLM-enhanced framework TPAD, which extends a distillation paradigm to decouple and align transitional patterns for promoting MSBR. TPAD establishes parallel Knowledge-MLLM and Transfer-MLLM, where the former interprets item knowledge-reflected features and the latter extracts transition-aware features underneath sessions. A transitional pattern alignment module harnessing mutual information estimation theory unites two MLLMs, alleviating distribution discrepancy and distilling transitional patterns into modal representations. Extensive experiments on real-world datasets demonstrate the effectiveness of our framework.
Mutual Information (MI) is a crucial measure for capturing dependencies between variables, but exact computation is challenging in high dimensions with intractable likelihoods, impacting accuracy and robustness. One idea is to use an auxiliary neural network to train an MI estimator; however, methods based on the empirical distribution function (EDF) can introduce sharp fluctuations in the MI loss due to poor out-of-sample performance, destabilizing convergence. We present a Bayesian nonparametric (BNP) solution for training an MI estimator by constructing the MI loss with a finite representation of the Dirichlet process posterior to incorporate regularization in the training process. With this regularization, the MI loss integrates both prior knowledge and empirical data to reduce the loss sensitivity to fluctuations and outliers in the sample data, especially in small sample settings like mini-batches. This approach addresses the challenge of balancing accuracy and low variance by effectively reducing variance, leading to stabilized and robust MI loss gradients during training and enhancing the convergence of the MI approximation while offering stronger theoretical guarantees for convergence. We explore the application of our estimator in maximizing MI between the data space and the latent space of a variational autoencoder. Experimental results demonstrate significant improvements in convergence over EDF-based methods, with applications across synthetic and real datasets, notably in 3D CT image generation, yielding enhanced structure discovery and reduced overfitting in data synthesis. While this paper focuses on generative models in application, the proposed estimator is not restricted to this setting and can be applied more broadly in various BNP learning procedures.
This work demonstrates that the tools and principles driving the success of large language models (LLMs) can be repurposed to tackle distribution-level tasks, where the goal is to predict properties of the data-generating distribution rather than labels for individual datapoints. These tasks encompass statistical inference problems such as parameter estimation, hypothesis testing, or mutual information estimation. Framing these tasks within traditional machine learning pipelines is challenging, as supervision is typically tied to individual datapoint. We propose meta-statistical learning, a framework inspired by multi-instance learning that reformulates statistical inference tasks as supervised learning problems. In this approach, entire datasets are treated as single inputs to neural networks, which predict distribution-level parameters. Transformer-based architectures, without positional encoding, provide a natural fit due to their permutation-invariance properties. By training on large-scale synthetic datasets, meta-statistical models can leverage the scalability and optimization infrastructure of Transformer-based LLMs. We demonstrate the framework's versatility with applications in hypothesis testing and mutual information estimation, showing strong performance, particularly for small datasets where traditional neural methods struggle.
In this paper, we introduce fastHDMI, a Python package designed for efficient variable screening in high-dimensional datasets, particularly neuroimaging data. This work pioneers the application of three mutual information estimation methods for neuroimaging variable selection, a novel approach implemented via fastHDMI. These advancements enhance our ability to analyze the complex structures of neuroimaging datasets, providing improved tools for variable selection in high-dimensional spaces. Using the preprocessed ABIDE dataset, we evaluate the performance of these methods through extensive simulations. The tests cover a range of conditions, including linear and nonlinear associations, as well as continuous and binary outcomes. Our results highlight the superiority of the FFTKDE-based mutual information estimation for feature screening in continuous nonlinear outcomes, while binning-based methods outperform others for binary outcomes with nonlinear probability preimages. For linear simulations, both Pearson correlation and FFTKDE-based methods show comparable performance for continuous outcomes, while Pearson excels in binary outcomes with linear probability preimages. A comprehensive case study using the ABIDE dataset further demonstrates fastHDMI's practical utility, showcasing the predictive power of models built from variables selected using our screening techniques. This research affirms the computational efficiency and methodological strength of fastHDMI, significantly enriching the toolkit available for neuroimaging analysis.
Cross-modal retrieval is crucial in understanding latent correspondences across modalities. However, existing methods implicitly assume well-matched training data, which is impractical as real-world data inevitably involves imperfect alignments, i.e., noisy correspondences. Although some works explore similarity-based strategies to address such noise, they suffer from sub-optimal similarity predictions influenced by modality-exclusive information (MEI), e.g., background noise in images and abstract definitions in texts. This issue arises as MEI is not shared across modalities, thus aligning it in training can markedly mislead similarity predictions. Moreover, although intuitive, directly applying previous cross-modal disentanglement methods suffers from limited noise tolerance and disentanglement efficacy. Inspired by the robustness of information bottlenecks against noise, we introduce DisNCL, a novel information-theoretic framework for feature Disentanglement in Noisy Correspondence Learning, to adaptively balance the extraction of MII and MEI with certifiable optimal cross-modal disentanglement efficacy. DisNCL then enhances similarity predictions in modality-invariant subspace, thereby greatly boosting similarity-based alleviation strategy for noisy correspondences. Furthermore, DisNCL introduces soft matching targets to model noisy many-to-many relationships inherent in multi-modal input for noise-robust and accurate cross-modal alignment. Extensive experiments confirm DisNCL's efficacy by 2% average recall improvement. Mutual information estimation and visualization results show that DisNCL learns meaningful MII/MEI subspaces, validating our theoretical analyses.
In the era of AIGC, the fast development of visual content generation technologies, such as diffusion models, bring potential security risks to our society. Existing generated image detection methods suffer from performance drop when faced with out-of-domain generators and image scenes. To relieve this problem, we propose Artifact Purification Network (APN) to facilitate the artifact extraction from generated images through the explicit and implicit purification processes. For the explicit one, a suspicious frequency-band proposal method and a spatial feature decomposition method are proposed to extract artifact-related features. For the implicit one, a training strategy based on mutual information estimation is proposed to further purify the artifact-related features. Experiments show that for cross-generator detection, the average accuracy of APN is 5.6% ~ 16.4% higher than the previous 10 methods on GenImage dataset and 1.7% ~ 50.1% on DiffusionForensics dataset. For cross-scene detection, APN maintains its high performance. Via visualization analysis, we find that the proposed method extracts flexible forgery patterns and condenses the forgery information diluted in irrelevant features. We also find that the artifact features APN focuses on across generators and scenes are global and diverse. The code will be available on GitHub.
We propose a novel approach to the problem of mutual information (MI) estimation via introducing a family of estimators based on normalizing flows. The estimator maps original data to the target distribution, for which MI is easier to estimate. We additionally explore the target distributions with known closed-form expressions for MI. Theoretical guarantees are provided to demonstrate that our approach yields MI estimates for the original data. Experiments with high-dimensional data are conducted to highlight the practical advantages of the proposed method.
Ensuring the trustworthiness of large language models (LLMs) is crucial. Most studies concentrate on fully pre-trained LLMs to better understand and improve LLMs' trustworthiness. In this paper, to reveal the untapped potential of pre-training, we pioneer the exploration of LLMs' trustworthiness during this period, focusing on five key dimensions: reliability, privacy, toxicity, fairness, and robustness. To begin with, we apply linear probing to LLMs. The high probing accuracy suggests that \textit{LLMs in early pre-training can already distinguish concepts in each trustworthiness dimension}. Therefore, to further uncover the hidden possibilities of pre-training, we extract steering vectors from a LLM's pre-training checkpoints to enhance the LLM's trustworthiness. Finally, inspired by~\citet{choi2023understanding} that mutual information estimation is bounded by linear probing accuracy, we also probe LLMs with mutual information to investigate the dynamics of trustworthiness during pre-training. We are the first to observe a similar two-phase phenomenon: fitting and compression~\citep{shwartz2017opening}. This research provides an initial exploration of trustworthiness modeling during LLM pre-training, seeking to unveil new insights and spur further developments in the field. We will make our code publicly accessible at \url{https://github.com/ChnQ/TracingLLM}.
Recent advances in large language models (LLMs) have promoted generative error correction (GER) for automatic speech recognition (ASR), which leverages the rich linguistic knowledge and powerful reasoning ability of LLMs to improve recognition results. The latest work proposes a GER benchmark with HyPoradise dataset to learn the mapping from ASR N-best hypotheses to ground-truth transcription by efficient LLM finetuning, which shows great effectiveness but lacks specificity on noise-robust ASR. In this work, we extend the benchmark to noisy conditions and investigate if we can teach LLMs to perform denoising for GER just like what robust ASR do}, where one solution is introducing noise information as a conditioner into LLM. However, directly incorporating noise embeddings from audio encoder could harm the LLM tuning due to cross-modality gap. To this end, we propose to extract a language-space noise embedding from the N-best list to represent the noise conditions of source speech, which can promote the denoising process in GER. Furthermore, in order to enhance its representation ability of audio noise, we design a knowledge distillation (KD) approach via mutual information estimation to distill the real noise information in audio embeddings to our language embedding. Experiments on various latest LLMs demonstrate our approach achieves a new breakthrough with up to 53.9% correction improvement in terms of word error rate while with limited training data. Analysis shows that our language-space noise embedding can well represent the noise conditions of source speech, under which off-the-shelf LLMs show strong ability of language-space denoising.
The pointwise mutual information profile, or simply profile, is the distribution of pointwise mutual information for a given pair of random variables. One of its important properties is that its expected value is precisely the mutual information between these random variables. In this paper, we analytically describe the profiles of multivariate normal distributions and introduce a novel family of distributions, Bend and Mix Models, for which the profile can be accurately estimated using Monte Carlo methods. We then show how Bend and Mix Models can be used to study the limitations of existing mutual information estimators, investigate the behavior of neural critics used in variational estimators, and understand the effect of experimental outliers on mutual information estimation. Finally, we show how Bend and Mix Models can be used to obtain model-based Bayesian estimates of mutual information, suitable for problems with available domain expertise in which uncertainty quantification is necessary.
In this work we present a new method for the estimation of Mutual Information (MI) between random variables. Our approach is based on an original interpretation of the Girsanov theorem, which allows us to use score-based diffusion models to estimate the Kullback Leibler divergence between two densities as a difference between their score functions. As a by-product, our method also enables the estimation of the entropy of random variables. Armed with such building blocks, we present a general recipe to measure MI, which unfolds in two directions: one uses conditional diffusion process, whereas the other uses joint diffusion processes that allow simultaneous modelling of two random variables. Our results, which derive from a thorough experimental protocol over all the variants of our approach, indicate that our method is more accurate than the main alternatives from the literature, especially for challenging distributions. Furthermore, our methods pass MI self-consistency tests, including data processing and additivity under independence, which instead are a pain-point of existing methods.
Recently, contrastive learning has become a key component in fine-tuning code search models for software development efficiency and effectiveness. It pulls together positive code snippets while pushing negative samples away given search queries. Among contrastive learning, InfoNCE is the most widely used loss function due to its better performance. However, the following problems in negative samples of InfoNCE may deteriorate its representation learning: 1) The existence of false negative samples in large code corpora due to duplications. 2). The failure to explicitly differentiate between the potential relevance of negative samples. As an example, a bubble sorting algorithm example is less ``negative'' than a file saving function for the quick sorting algorithm query. In this paper, we tackle the above problems by proposing a simple yet effective Soft-InfoNCE loss that inserts weight terms into InfoNCE. In our proposed loss function, we apply three methods to estimate the weights of negative pairs and show that the vanilla InfoNCE loss is a special case of Soft-InfoNCE. Theoretically, we analyze the effects of Soft-InfoNCE on controlling the distribution of learnt code representations and on deducing a more precise mutual information estimation. We furthermore discuss the superiority of proposed loss functions with other design alternatives. Extensive experiments demonstrate the effectiveness of Soft-InfoNCE and weights estimation methods under state-of-the-art code search models on a large-scale public dataset consisting of six programming languages. Source code is available at \url{https://github.com/Alex-HaochenLi/Soft-InfoNCE}.
We discuss the problem of estimating Radon-Nikodym derivatives. This problem appears in various applications, such as covariate shift adaptation, likelihood-ratio testing, mutual information estimation, and conditional probability estimation. To address the above problem, we employ the general regularization scheme in reproducing kernel Hilbert spaces. The convergence rate of the corresponding regularized algorithm is established by taking into account both the smoothness of the derivative and the capacity of the space in which it is estimated. This is done in terms of general source conditions and the regularized Christoffel functions. We also find that the reconstruction of Radon-Nikodym derivatives at any particular point can be done with high order of accuracy. Our theoretical results are illustrated by numerical simulations.
Zero-shot skeleton-based action recognition aims to recognize actions of unseen categories after training on data of seen categories. The key is to build the connection between visual and semantic space from seen to unseen classes. Previous studies have primarily focused on encoding sequences into a singular feature vector, with subsequent mapping the features to an identical anchor point within the embedded space. Their performance is hindered by 1) the ignorance of the global visual/semantic distribution alignment, which results in a limitation to capture the true interdependence between the two spaces. 2) the negligence of temporal information since the frame-wise features with rich action clues are directly pooled into a single feature vector. We propose a new zero-shot skeleton-based action recognition method via mutual information (MI) estimation and maximization. Specifically, 1) we maximize the MI between visual and semantic space for distribution alignment; 2) we leverage the temporal information for estimating the MI by encouraging MI to increase as more frames are observed. Extensive experiments on three large-scale skeleton action datasets confirm the effectiveness of our method. Code: https://github.com/YujieOuO/SMIE.
Graph contrastive learning (GCL), as a self-supervised learning method, can solve the problem of annotated data scarcity. It mines explicit features in unannotated graphs to generate favorable graph representations for downstream tasks. Most existing GCL methods focus on the design of graph augmentation strategies and mutual information estimation operations. Graph augmentation produces augmented views by graph perturbations. These views preserve a locally similar structure and exploit explicit features. However, these methods have not considered the interaction existing in subgraphs. To explore the impact of substructure interactions on graph representations, we propose a novel framework called subgraph network-based contrastive learning (SGNCL). SGNCL applies a subgraph network generation strategy to produce augmented views. This strategy converts the original graph into an Edge-to-Node mapping network with both topological and attribute features. The single-shot augmented view is a first-order subgraph network that mines the interaction between nodes, node-edge, and edges. In addition, we also investigate the impact of the second-order subgraph augmentation on mining graph structure interactions, and further, propose a contrastive objective that fuses the first-order and second-order subgraph information. We compare SGNCL with classical and state-of-the-art graph contrastive learning methods on multiple benchmark datasets of different domains. Extensive experiments show that SGNCL achieves competitive or better performance (top three) on all datasets in unsupervised learning settings. Furthermore, SGNCL achieves the best average gain of 6.9\% in transfer learning compared to the best method. Finally, experiments also demonstrate that mining substructure interactions have positive implications for graph contrastive learning.
Estimating the mutual information from samples from a joint distribution is a challenging problem in both science and engineering. In this work, we realize a variational bound that generalizes both discriminative and generative approaches. Using this bound, we propose a hybrid method to mitigate their respective shortcomings. Further, we propose Predictive Quantization (PQ): a simple generative method that can be easily combined with discriminative estimators for minimal computational overhead. Our propositions yield a tighter bound on the information thanks to the reduced variance of the estimator. We test our methods on a challenging task of correlated high-dimensional Gaussian distributions and a stochastic process involving a system of free particles subjected to a fixed energy landscape. Empirical results show that hybrid methods consistently improved mutual information estimates when compared to the corresponding discriminative counterpart.
Estimating mutual information accurately is pivotal across diverse applications, from machine learning to communications and biology, enabling us to gain insights into the inner mechanisms of complex systems. Yet, dealing with high-dimensional data presents a formidable challenge, due to its size and the presence of intricate relationships. Recently proposed neural methods employing variational lower bounds on the mutual information have gained prominence. However, these approaches suffer from either high bias or high variance, as the sample size and the structure of the loss function directly influence the training process. In this paper, we propose a novel class of discriminative mutual information estimators based on the variational representation of the $f$-divergence. We investigate the impact of the permutation function used to obtain the marginal training samples and present a novel architectural solution based on derangements. The proposed estimator is flexible since it exhibits an excellent bias/variance trade-off. The comparison with state-of-the-art neural estimators, through extensive experimentation within established reference scenarios, shows that our approach offers higher accuracy and lower complexity.
Computing optimal transport (OT) for general high-dimensional data has been a long-standing challenge. Despite much progress, most of the efforts including neural network methods have been focused on the static formulation of the OT problem. The current work proposes to compute the dynamic OT between two arbitrary distributions $P$ and $Q$ by optimizing a flow model, where both distributions are only accessible via finite samples. Our method learns the dynamic OT by finding an invertible flow that minimizes the transport cost. The trained optimal transport flow subsequently allows for performing many downstream tasks, including infinitesimal density ratio estimation (DRE) and domain adaptation by interpolating distributions in the latent space. The effectiveness of the proposed model on high-dimensional data is demonstrated by strong empirical performance on OT baselines, image-to-image translation, and high-dimensional DRE.