Causal discovery from observational data, especially for count data, is essential across scientific and industrial contexts, such as biology, economics, and network operation maintenance.

Vision-Language Models (VLMs) perform well on multimodal benchmarks but lag behind humans and specialized models on visual perception tasks like depth estimation or object counting. Finetuning on one task can unpredictably affect performance on others, making task-specific finetuning challenging. In this paper, we address this challenge through a systematic study of task transferability. We examine how finetuning a VLM on one perception task affects its zero-shot performance on others. To quantify these effects, we introduce Perfection Gap Factor (PGF), a metric that captures both the breadth and magnitude of transfer. Using three open-weight VLMs evaluated across 13 perception tasks, we construct a task-transfer graph that reveals previously unobserved relationships among perception tasks. Our analysis uncovers patterns of positive and negative transfer, identifies groups of tasks that mutually influence each other, organizes tasks into personas based on their transfer behavior and demonstrates how PGF can guide data selection for more efficient training. These findings highlight both opportunities for positive transfer and risks of negative interference, offering actionable guidance for advancing VLMs.

Graphical models with latent count variables arise in a number of fields.

However, the Bayesian network and ordinal modeling ignore the inherent branching structure among the counting relationship, which is frequently encountered in real world (Weiß [2018]).

We introduce PGF-Net (Progressive Gated-Fusion Network), a novel deep learning framework designed for efficient and interpretable multimodal sentiment analysis. Our framework incorporates three primary innovations. Firstly, we propose a Progressive Intra-Layer Fusion paradigm, where a Cross-Attention mechanism empowers the textual representation to dynamically query and integrate non-linguistic features from audio and visual streams within the deep layers of a Transformer encoder. This enables a deeper, context-dependent fusion process. Secondly, the model incorporates an Adaptive Gated Arbitration mechanism, which acts as a dynamic controller to balance the original linguistic information against the newly fused multimodal context, ensuring stable and meaningful integration while preventing noise from overwhelming the signal. Lastly, a hybrid Parameter-Efficient Fine-Tuning (PEFT) strategy is employed, synergistically combining global adaptation via LoRA with local refinement through Post-Fusion Adapters. This significantly reduces trainable parameters, making the model lightweight and suitable for resource-limited scenarios. These innovations are integrated into a hierarchical encoder architecture, enabling PGF-Net to perform deep, dynamic, and interpretable multimodal sentiment analysis while maintaining exceptional parameter efficiency. Experimental results on MOSI dataset demonstrate that our proposed PGF-Net achieves state-of-the-art performance, with a Mean Absolute Error (MAE) of 0.691 and an F1-Score of 86.9%. Notably, our model achieves these results with only 3.09M trainable parameters, showcasing a superior balance between performance and computational efficiency.

Causal discovery from observational data, especially for count data, is essential across scientific and industrial contexts, such as biology, economics, and network operation maintenance. However, they overlook the inherent branching structures that are frequently encountered, e.g., a browsing event might trigger an adding cart or purchasing event. This can be modeled by a binomial thinning operator (for branching) and an additive independent Poisson distribution (for noising), known as Poisson Branching Structure Causal Model (PB-SCM). There is a provably sound cumulant-based causal discovery method that allows the identification of the causal structure under a branching structure. However, we show that there still remains a gap in that there exist causal directions that are identifiable while the algorithm fails to identify them. In this work, we address this gap by exploring the identifiability of PB-SCM using the Probability Generating Function (PGF).

Graphical models with latent count variables arise in a number of fields. Standard exact inference techniques such as variable elimination and belief propagation do not apply to these models because the latent variables have countably infinite support. As a result, approximations such as truncation or MCMC are employed. We present the first exact inference algorithms for a class of models with latent count variables by developing a novel representation of countably infinite factors as probability generating functions, and then performing variable elimination with generating functions. Our approach is exact, runs in pseudo-polynomial time, and is much faster than existing approximate techniques. It leads to better parameter estimates for problems in population ecology by avoiding error introduced by approximate likelihood computations.

This paper makes two contributions. Firstly, it introduces mixed compositional kernels and mixed neural network Gaussian processes (NGGPs). Mixed compositional kernels are generated by composition of probability generating functions (PGFs). A mixed NNGP is a Gaussian process (GP) with a mixed compositional kernel, arising in the infinite-width limit of multilayer perceptrons (MLPs) that have a different activation function for each layer. Secondly, $\theta$ activation functions for neural networks and $\theta$ compositional kernels are introduced by building upon the theory of branching processes, and more specifically upon $\theta$ PGFs. While $\theta$ compositional kernels are recursive, they are expressed in closed form. It is shown that $\theta$ compositional kernels have non-degenerate asymptotic properties under certain conditions. Thus, GPs with $\theta$ compositional kernels do not require non-explicit recursive kernel evaluations and have controllable infinite-depth asymptotic properties. An open research question is whether GPs with $\theta$ compositional kernels are limits of infinitely-wide MLPs with $\theta$ activation functions.

Temperature monitoring during the life time of heat source components in engineering systems becomes essential to guarantee the normal work and the working life of these components. However, prior methods, which mainly use the interpolate estimation to reconstruct the temperature field from limited monitoring points, require large amounts of temperature tensors for an accurate estimation. This may decrease the availability and reliability of the system and sharply increase the monitoring cost. To solve this problem, this work develops a novel physics-informed deep reversible regression models for temperature field reconstruction of heat-source systems (TFR-HSS), which can better reconstruct the temperature field with limited monitoring points unsupervisedly. First, we define the TFR-HSS task mathematically, and numerically model the task, and hence transform the task as an image-to-image regression problem. Then this work develops the deep reversible regression model which can better learn the physical information, especially over the boundary. Finally, considering the physical characteristics of heat conduction as well as the boundary conditions, this work proposes the physics-informed reconstruction loss including four training losses and jointly learns the deep surrogate model with these losses unsupervisedly. Experimental studies have conducted over typical two-dimensional heat-source systems to demonstrate the effectiveness of the proposed method.