Granger causality (GC) [15] is a time series causal discovery framework that uses predictive modeling to identify the underlying causal structure of a time series system. Relying on the assumption that cause precedes effect, GC assesses whether including the lagged information from one time series in the autoregressive model of a second time series enhances its predictions. This improvement indicates a predictive relationship between the time series variables, where one time series provides supplemental information about the future of another time series, thereby signifying the presence of a (Granger) causal relationship. GC requires only observational data, and has been used for time series causal discovery across diverse domains, including climate science [33], political and social sciences [17], econometrics [4], and biological systems studies [13]. The original formulation of GC requires several assumptions to be satisfied for causal identifiability. In regards to the candidate time series system, it is assumed that the time series variables are stationary, and that all variables are observed (absence of latent confounders). GC was initially proposed for bivariate time series systems, but was generalised for the multivariate setting to accommodate the assumption that all relevant variables are included in the analysis [15]. Additional assumptions are made with regard to the types of causal relationships that can be identified within the time series system. GC cannot estimate a causal relationship between time series at an instantaneous time point, relying on the relationship between the lags and predicted values to determine a GC relationship.

Semi-supervised learning on real-world graphs is frequently challenged by heterophily, where the observed graph is unreliable or label-disassortative. Many existing graph neural networks either rely on a fixed adjacency structure or attempt to handle structural noise through regularization. In this work, we explicitly capture structural uncertainty by modeling a posterior distribution over signed adjacency matrices, allowing each edge to be positive, negative, or absent. We propose a sparse signed message passing network that is naturally robust to edge noise and heterophily, which can be interpreted from a Bayesian perspective. By combining (i) posterior marginalization over signed graph structures with (ii) sparse signed message aggregation, our approach offers a principled way to handle both edge noise and heterophily. Experimental results demonstrate that our method outperforms strong baseline models on heterophilic benchmarks under both synthetic and real-world structural noise. We provide an anonymous repository at: https://anonymous.4open.science/r/SpaM-F2C8

Recent advancements in State Space Models, notably Mamba, have demonstrated superior performance over the dominant Transformer models, particularly in reducing the computational complexity from quadratic to linear. Yet, difficulties in adapting Mamba from language to vision tasks arise due to the distinct characteristics of visual data, such as the spatial locality and adjacency within images and large variations in information granularity across visual tokens. Existing vision Mamba approaches either flatten tokens into sequences in a raster scan fashion, which breaks the local adjacency of images, or manually partition tokens into windows, which limits their long-range modeling and generalization capabilities. To address these limitations, we present a new vision Mamba model, coined QuadMamba, that effectively captures local dependencies of varying granularities via quadtree-based image partition and scan. Concretely, our lightweight quadtree-based scan module learns to preserve the 2D locality of spatial regions within learned window quadrants.

As major progress in LLM-based long-form text generation enables paradigms such as retrieval-augmented generation (RAG) and inference-time scaling, safely incorporating private information into the generation remains a critical open question. We present InvisibleInk, a highly scalable long-form text generation framework satisfying rigorous differential privacy guarantees with respect to the sensitive reference texts. It interprets sampling from the LLM's next-token-distribution as the exponential mechanism over the LLM logits with two innovations. First, we reduce the privacy cost by isolating and clipping only the sensitive information in the model logits (relative to the public logits). Second, we improve text quality by sampling without any privacy cost from a small superset of the top-$k$ private tokens. Empirical evaluations demonstrate a consistent $8\times$ (or more) reduction in computation cost over state-of-the-art baselines to generate long-form private text of the same utility across privacy levels. InvisibleInk is able to generate, for the first time, high-quality private long-form text at less than $4$-$8\times$ times the computation cost of non-private generation, paving the way for its practical use. We open-source a pip-installable Python package (invink) for InvisibleInk at https://github.com/cerai-iitm/invisibleink.

Training machine learning models with differential privacy (DP) limits an adversary's ability to infer sensitive information about the training data. It can be interpreted as a bound on adversary's capability to distinguish two adjacent datasets according to chosen adjacency relation. In practice, most DP implementations use the add/remove adjacency relation, where two datasets are adjacent if one can be obtained from the other by adding or removing a single record, thereby protecting membership. In many ML applications, however, the goal is to protect attributes of individual records (e.g., labels used in supervised fine-tuning). We show that privacy accounting under add/remove overstates attribute privacy compared to accounting under the substitute adjacency relation, which permits substituting one record. To demonstrate this gap, we develop novel attacks to audit DP under substitute adjacency, and show empirically that audit results are inconsistent with DP guarantees reported under add/remove, yet remain consistent with the budget accounted under the substitute adjacency relation. Our results highlight that the choice of adjacency when reporting DP guarantees is critical when the protection target is per-record attributes rather than membership.

Taking into account the regional characteristics of intrinsic and extrinsic properties of space is an essential issue in architectural design and urban renewal, which is often achieved step by step using image and graph-based GANs. However, each model nesting and data conversion may cause information loss, and it is necessary to streamline the tools to facilitate architects and users to participate in the design. Therefore, this study hopes to prove that I2I GAN also has the potential to recognize topological relationships autonomously. Therefore, this research proposes a method for quickly detecting the ability of pix2pix to learn topological relationships, which is achieved by adding two Grasshopper-based detection modules before and after GAN. At the same time, quantitative data is provided and its learning process is visualized, and changes in different input modes such as greyscale and RGB affect its learning efficiency. There are two innovations in this paper: 1) It proves that pix2pix can automatically learn spatial topological relationships and apply them to architectural design. 2) It fills the gap in detecting the performance of Image-based Generation GAN from a topological perspective. Moreover, the detection method proposed in this study takes a short time and is simple to operate. The two detection modules can be widely used for customizing image datasets with the same topological structure and for batch detection of topological relationships of images. In the future, this paper may provide a theoretical foundation and data support for the application of architectural design and urban renewal that use GAN to preserve spatial topological characteristics.

We would like to thank the reviewers for their comments and constructive feedback. Below, we address the main issues raised and clarify some misunderstandings. Also, the work of Y ang et al. (2018) characterizes soft interventions in systems without latent variables. Mooij et al. (2013) discussed interventions of this nature in the context of equilibrium in cyclic causal models. Usage of MAGs: The reviewer's observation only holds for hard interventions.

It is also of interest in addressing class imbalance and federated learning. Current computable guarantees for fixed-size subsampling are not tight and do not consider both add/remove and replace-one adjacency relationships.