Beyond Do-Calculus: Standard Probability Powers Causal Inference
![The study demonstrates that varying the assigned aspirin dose-specifically through interventions denoted as [latex]t^{\*} [/latex]-directly influences the distribution of headache duration within a log-normal aspirin model.](https://arxiv.org/html/2512.23408v1/x2.png)
New research shows that traditional probabilistic modeling techniques, like Bayesian Networks, are surprisingly capable of handling complex causal questions, including those involving interventions and counterfactual reasoning.
![A novel multimodal fact-checking workflow leverages an agent-based architecture to rigorously assess information veracity, enabling a systematic decomposition of claims and evidence for enhanced reliability-a process fundamentally reliant on the logical consistency of [latex] p \land q [/latex], where <i>p</i> represents the claim and <i>q</i> the supporting evidence.](https://arxiv.org/html/2512.22933v1/x5.png)





![Generated molecules exhibit a nuanced relationship between structural distance from seed compounds and predicted odor probabilities, as evidenced by a UMAP visualization of the latent space and a statistically significant correlation-demonstrated through [latex]\sigma\_{\phi}(z|X)[/latex] distance metrics and QSAR modeling-between generated compounds, existing ChemBL molecules, and known odorants from the Good Scents database.](https://arxiv.org/html/2512.23080v1/Fig_5.png)
