Uncovering the underlying causal mechanisms of complex real-world systems remains a significant challenge, as these systems often entail high data collection costs and involve unknown interventions. We introduce MetaCaDI, the first framework to cast the joint discovery of a causal graph and unknown interventions as a meta-learning problem. MetaCaDI is a Bayesian framework that learns a shared causal graph structure across multiple experiments and is optimized to rapidly adapt to new, few-shot intervention target prediction tasks. A key innovation is our model's analytical adaptation, which uses a closed-form solution to bypass expensive and potentially unstable gradient-based bilevel optimization. Extensive experiments on synthetic and complex gene expression data demonstrate that MetaCaDI significantly outperforms state-of-the-art methods. It excels at both causal graph recovery and identifying intervention targets from as few as 10 data instances, proving its robustness in data-scarce scenarios.

This paper studies prediction with multiple candidate models, where the goal is to combine their outputs. This task is especially challenging in heterogeneous settings, where different models may be better suited to different inputs. We propose input adaptive Bayesian Model Averaging (IA-BMA), a Bayesian method that assigns model weights conditional on the input. IA-BMA employs an input adaptive prior, and yields a posterior distribution that adapts to each prediction, which we estimate with amortized variational inference. We derive formal guarantees for its performance, relative to any single predictor selected per input. We evaluate IABMA across regression and classification tasks, studying data from personalized cancer treatment, credit-card fraud detection, and UCI datasets. IA-BMA consistently delivers more accurate and better-calibrated predictions than both non-adaptive baselines and existing adaptive methods. Many applications require adaptive predictions. In personalized medicine, different patients respond differently to the same treatment (Mahajan et al., 2023); in fairness-sensitive domains, predictions need to adapt to subpopulations (Wang et al., 2019; Grother et al., 2019); and in fraud detection, behavioral data is often heteroskedastic and varies substantially across inputs (V armedja et al., 2019).

Quantum channel discrimination has been studied from an information-theoretic perspective, wherein one is interested in the optimal decay rate of error probabilities as a function of the number of unknown channel accesses. In this paper, we study the query complexity of quantum channel discrimination, wherein the goal is to determine the minimum number of channel uses needed to reach a desired error probability. To this end, we show that the query complexity of binary channel discrimination depends logarithmically on the inverse error probability and inversely on the negative logarithm of the (geometric and Holevo) channel fidelity. As a special case of these findings, we precisely characterize the query complexity of discriminating two classical channels and two classical-quantum channels. Furthermore, by obtaining an optimal characterization of the sample complexity of quantum hypothesis testing, including prior probabilities, we provide a more precise characterization of query complexity when the error probability does not exceed a fixed threshold. We also provide lower and upper bounds on the query complexity of binary asymmetric channel discrimination and multiple quantum channel discrimination. For the former, the query complexity depends on the geometric Rényi and Petz Rényi channel divergences, while for the latter, it depends on the negative logarithm of the (geometric and Uhlmann) channel fidelity. For multiple channel discrimination, the upper bound scales as the logarithm of the number of channels.

Cross-linguistically, native words and loanwords follow different phonological rules. In English, for example, words of Germanic and Latinate origin exhibit different stress patterns, and a certain syntactic structure, double-object datives, is predominantly associated with Germanic verbs rather than Latinate verbs. As a cognitive model, however, such etymology-based generalizations face challenges in terms of learnability, since the historical origins of words are presumably inaccessible information for general language learners. In this study, we present computational evidence indicating that the Germanic-Latinate distinction in the English lexicon is learnable from the phonotactic information of individual words. Specifically, we performed an unsupervised clustering on corpus-extracted words, and the resulting word clusters largely aligned with the etymological distinction. The model-discovered clusters also recovered various linguistic generalizations documented in the previous literature regarding the corresponding etymological classes. Moreover, our findings also uncovered previously unrecognized features of the quasi-etymological clusters.

A fundamental challenge in probabilistic modeling is to balance expressivity and inference efficiency. Tractable probabilistic models (TPMs) aim to directly address this tradeoff by imposing constraints that guarantee efficient inference of certain queries while maintaining expressivity. In particular, probabilistic circuits (PCs) provide a unifying framework for many TPMs, by characterizing families of models as circuits satisfying different structural properties. Because the complexity of inference on PCs is a function of the circuit size, understanding the size requirements of different families of PCs is fundamental in mapping the trade-off between tractability and expressive efficiency. However, the study of expressive efficiency of circuits are often concerned with exact representations, which may not align with model learning, where we look to approximate the underlying data distribution closely by some distance measure. Moreover, due to hardness of inference tasks, exactly representing distributions while supporting tractable inference often incurs exponential size blow-ups. In this paper, we consider a natural, yet so far underexplored, question: can we avoid such size blow-up by allowing for some small approximation error? We study approximating distributions with probabilistic circuits with guarantees based on $f$-divergences, and analyze which inference queries remain well-approximated under this framework. We show that approximating an arbitrary distribution with bounded $f$-divergence is $\mathsf{NP}$-hard for any model that can tractably compute marginals. In addition, we prove an exponential size gap for approximation between the class of decomposable PCs and that of decomposable and deterministic PCs.

World models predict state transitions in response to actions and are increasingly developed across diverse modalities. However, standard training objectives such as maximum likelihood estimation (MLE) often misalign with task-specific goals of world models, i.e., transition prediction metrics like accuracy or perceptual quality. In this paper, we present RLVR-World, a unified framework that leverages reinforcement learning with verifiable rewards (RLVR) to directly optimize world models for such metrics. Despite formulating world modeling as autoregressive prediction of tokenized sequences, RLVR-World evaluates metrics of decoded predictions as verifiable rewards. We demonstrate substantial performance gains on both language- and video-based world models across domains, including text games, web navigation, and robot manipulation. Our work indicates that, beyond recent advances in reasoning language models, RLVR offers a promising post-training paradigm for enhancing the utility of generative models more broadly. Code, datasets, models, and video samples are available at the project website: https://thuml.github.io/RLVR-World.

We introduce the Schrodinger Neural Network (SNN), a principled architecture for conditional density estimation and uncertainty quantification inspired by quantum mechanics. The SNN maps each input to a normalized wave function on the output domain and computes predictive probabilities via the Born rule. The SNN departs from standard parametric likelihood heads by learning complex coefficients of a spectral expansion (e . g ., Chebyshev polynomials) whose squared modulus yields the conditional density $p(y|x)=\left| ψ_x(y)\right| {}^2$ with analytic normalization. This representation confers three practical advantages: positivity and exact normalization by construction, native multimodality through interference among basis modes without explicit mixture bookkeeping, and yields closed-form (or efficiently computable) functionals$-$such as moments and several calibration diagnostics$-$as quadratic forms in coefficient space. We develop the statistical and computational foundations of the SNN, including (i) training by exact maximum-likelihood with unit-sphere coefficient parameterization, (ii) physics-inspired quadratic regularizers (kinetic and potential energies) motivated by uncertainty relations between localization and spectral complexity, (iii) scalable low-rank and separable extensions for multivariate outputs, (iv) operator-based extensions that represent observables, constraints, and weak labels as self-adjoint matrices acting on the amplitude space, and (v) a comprehensive framework for evaluating multimodal predictions. The SNN provides a coherent, tractable framework to elevate probabilistic prediction from point estimates to physically inspired amplitude-based distributions.

This thesis works to address a pivotal challenge in medical image analysis: the reliance on extensive labeled datasets, which are often limited due to the need for expert annotation and constrained by privacy and legal issues. By focusing on the development of self-supervised learning techniques and domain adaptation methods, this research aims to circumvent these limitations, presenting a novel approach to enhance the utility and efficacy of deep learning in medical imaging. Central to this thesis is the development of the Medformer, an innovative neural network architecture designed for multitask learning and deep domain adaptation. This model is adept at pre-training on diverse medical image datasets, handling varying sizes and modalities, and is equipped with a dynamic input-output adaptation mechanism. This enables efficient processing and integration of a wide range of medical image types, from 2D X-rays to complex 3D MRIs, thus mitigating the dependency on large labeled datasets. Further, the thesis explores the current state of self-supervised learning in medical imaging. It introduces novel pretext tasks that are capable of extracting meaningful information from unlabeled data, significantly advancing the model's interpretative abilities. This approach is validated through rigorous experimentation, including the use of the MedMNIST dataset, demonstrating the model's proficiency in learning generalized features applicable to various downstream tasks. In summary, this thesis contributes to the advancement of medical image analysis by offering a scalable, adaptable framework that reduces reliance on labeled data. It paves the way for more accurate, efficient diagnostic tools in healthcare, signifying a major step forward in the application of deep learning in medical imaging.

Machine learning has achieved remarkable successes, yet its deployment in safety-critical domains remains hindered by an inherent inability to manage uncertainty, resulting in overconfident and unreliable predictions when models encounter out-of-distribution data, adversarial perturbations, or naturally fluctuating environments. This thesis, titled Epistemic Deep Learning: Enabling Machine Learning Models to 'Know When They Do Not Know', addresses these critical challenges by advancing the paradigm of Epistemic Artificial Intelligence, which explicitly models and quantifies epistemic uncertainty: the uncertainty arising from limited, biased, or incomplete training data, as opposed to the irreducible randomness of aleatoric uncertainty, thereby empowering models to acknowledge their limitations and refrain from overconfident decisions when uncertainty is high. Central to this work is the development of the Random-Set Neural Network (RS-NN), a novel methodology that leverages random set theory to predict belief functions over sets of classes, capturing the extent of epistemic uncertainty through the width of associated credal sets, applications of RS-NN, including its adaptation to Large Language Models (LLMs) and its deployment in weather classification for autonomous racing. In addition, the thesis proposes a unified evaluation framework for uncertainty-aware classifiers. Extensive experiments validate that integrating epistemic awareness into deep learning not only mitigates the risks associated with overconfident predictions but also lays the foundation for a paradigm shift in artificial intelligence, where the ability to 'know when it does not know' becomes a hallmark of robust and dependable systems. The title encapsulates the core philosophy of this work, emphasizing that true intelligence involves recognizing and managing the limits of one's own knowledge.

Cognitive studies and artificial intelligence have developed distinct models for various inferential mechanisms (categorization, induction, abduction, causal inference, contrast, merge, ...). Yet, both natural and artificial views on cognition lack apparently a unifying framework. This paper formulates a speculative answer attempting to respond to this gap. To postulate on higher-level activation processes from a material perspective, we consider inferential mechanisms informed by symbolic AI modelling techniques, through the simplistic lenses of electronic circuits based on logic gates. We observe that a logic gate view entails a different treatment of implication and negation compared to standard logic and logic programming. Then, by combinatorial exploration, we identify four main forms of dependencies that can be realized by these inferential circuits. Looking at how these forms are generally used in the context of logic programs, we identify eight common inferential patterns, exposing traditionally distinct inferential mechanisms in an unifying framework. Finally, following a probabilistic interpretation of logic programs, we unveil inner functional dependencies. The paper concludes elaborating in what sense, even if our arguments are mostly informed by symbolic means and digital systems infrastructures, our observations may pinpoint to more generally applicable structures.