A.1 MONet To segment each w hframe Ft into No object representations, MONet uses a recurrent attention network to obtain No attention masks Ati [0,1]w h for i = 1,...,No that represent the probability of each pixel in Ft belonging to the i-th object, with This attention network is coupled with a component VAE with latents zti Rd for i= 1,...,No that reconstructs Ati Ft, the i-th object in the image. The latent posterior distribution q(zt|Ft,Ati)is a diagonal Gaussian with mean µti, and we use µti as the representation of the i-th object. When these representations are fed into the transformer, we use a linear projection to map the raw object/word embeddings, which lie in Rd, to a vector in RdNH, where NH is the number of selfattention heads. This step is necessary as generally the latent dimensionality of MONet, d, is less than NH whereas a transformer expects the embedding size to be divisible by NH. A.2 Self-supervised training Recall in the main text that we wrote the auxiliary self-supervised loss as auxiliary loss = X A comparison of these losses and the masking schemes is given in Figure 4. We also tested a few variations of the contrastive loss inspired by literature and tested all combinations of variations.

Building upon Miller's framework of explanations derived from research in multiple

We propose a post hoc saliency-based explanation framework for counterfactual reasoning in probabilistic multivariate time-series forecasting (regression) settings. Building upon Miller's framework of explanations derived from research in multiple social science disciplines, we establish a conceptual link between counterfactual reasoning and saliency-based explanation techniques. To address the lack of a principled notion of saliency, we leverage a unifying definition of information-theoretic saliency grounded in preattentive human visual cognition and extend it to forecasting settings. Specifically, we obtain a closed-form expression for commonly used density functions to identify which observed timesteps appear salient to an underlying model in making its probabilistic forecasts. We empirically validate our framework in a principled manner using synthetic data to establish ground-truth saliency that is unavailable for real-world data. Finally, using real-world data and forecasting models, we demonstrate how our framework can assist domain experts in forming new data-driven hypotheses about the causal relationships between features in the wild.

There has been recent interest in exploring generative goals for counterfactual reasoning, such as individualized treatment effect (ITE) estimation. However, existing solutions often fail to address issues that are unique to causal inference, such as covariate balancing and (infeasible) counterfactual validation. As a step towards more flexible, scalable and accurate ITE estimation, we present a novel generative Bayesian estimation framework that integrates representation learning, adversarial matching and causal estimation. By appealing to the Robinson decomposition, we derive a reformulated variational bound that explicitly targets the causal effect estimation rather than specific predictive goals. Our procedure acknowledges the uncertainties in representation and solves a Fenchel mini-max game to resolve the representation imbalance for better counterfactual generalization, justified by new theory. Further, the latent variable formulation employed enables robustness to unobservable latent confounders, extending the scope of its applicability. The utility of the proposed solution is demonstrated via an extensive set of tests against competing solutions, both under various simulation setups and to real-world datasets, with encouraging results reported.

Large Language Models (LLMs) have transformed natural language processing and hold growing promise for advancing science, healthcare, and decision-making. Yet their training paradigms remain dominated by affirmation-based inference, akin to \textit{modus ponens}, where accepted premises yield predicted consequents. While effective for generative fluency, this one-directional approach leaves models vulnerable to logical fallacies, adversarial manipulation, and failures in causal reasoning. This paper makes two contributions. First, it demonstrates how existing LLMs from major platforms exhibit systematic weaknesses when reasoning in scientific domains with negation, counterexamples, or faulty premises \footnote{Code to recreate these experiments are at https://github.com/hannahdavidsoncollege-maker/ScientificReasoningForEnvironment-MedicineWithLLMs. Second, it introduces a dual-reasoning training framework that integrates affirmative generation with structured counterfactual denial. Grounded in formal logic, cognitive science, and adversarial training, this training paradigm formalizes a computational analogue of ``denying the antecedent'' as a mechanism for disconfirmation and robustness. By coupling generative synthesis with explicit negation-aware objectives, the framework enables models that not only affirm valid inferences but also reject invalid ones, yielding systems that are more resilient, interpretable, and aligned with human reasoning.

Vision Language Models (VLMs) have recently shown significant advancements in video understanding, especially in feature alignment, event reasoning, and instruction-following tasks. However, their capability for counterfactual reasoning, inferring alternative outcomes under hypothetical conditions, remains underexplored. This capability is essential for robust video understanding, as it requires identifying underlying causal structures and reasoning about unobserved possibilities, rather than merely recognizing observed patterns. To systematically evaluate this capability, we introduce CounterVQA, a video-based benchmark featuring three progressive difficulty levels that assess different aspects of counterfactual reasoning. Through comprehensive evaluation of both state-of-the-art open-source and closed-source models, we uncover a substantial performance gap: while these models achieve reasonable accuracy on simple counterfactual questions, performance degrades significantly on complex multi-hop causal chains. To address these limitations, we develop a post-training method, CFGPT, that enhances a model's visual counterfactual reasoning ability by distilling its counterfactual reasoning capability from the language modality, yielding consistent improvements across all CounterVQA difficulty levels. Dataset and code will be further released.

Large-scale neural language models exhibit remarkable performance in in-context learning: the ability to learn and reason about the input context on the fly. This work studies in-context counterfactual reasoning in language models, that is, the ability to predict consequences of a hypothetical scenario. We focus on a well-defined, synthetic linear regression task that requires noise abduction. Accurate prediction is based on (1) inferring an unobserved latent concept and (2) copying contextual noise from factual observations. We show that language models are capable of counterfactual reasoning. Further, we enhance existing identifiability results and reduce counterfactual reasoning for a broad class of functions to a transformation on in-context observations. In Transformers, we find that self-attention, model depth and pre-training data diversity drive performance. Moreover, we provide mechanistic evidence that the latent concept is linearly represented in the residual stream and we introduce designated \textit{noise abduction heads} central to performing counterfactual reasoning. Lastly, our findings extend to counterfactual reasoning under SDE dynamics and reflect that Transformers can perform noise abduction on sequential data, providing preliminary evidence on the potential for counterfactual story generation. Our code is available under https://github.com/mrtzmllr/iccr.

Explainable recommendation through counterfactual reasoning seeks to identify the influential aspects of items in recommendations, which can then be used as explanations. However, state-of-the-art approaches, which aim to minimize changes in product aspects while reversing their recommended decisions according to an aggregated decision boundary score, often lead to factual inaccuracies in explanations. To solve this problem, in this work we propose a novel method of Comparative Counterfactual Explanations for Recommendation (CoCountER). CoCountER creates counterfactual data based on soft swap operations, enabling explanations for recommendations of arbitrary pairs of comparative items. Empirical experiments validate the effectiveness of our approach.