Low-Rank Adaptation (LoRA) enables parameter-efficient fine-tuning of large language models by decomposing weight updates into low-rank matrices, significantly reducing storage and computational overhead. While effective, standard LoRA lacks mechanisms for uncertainty quantification, leading to overconfident and poorly calibrated models. Bayesian variants of LoRA address this limitation, but at the cost of a significantly increased number of trainable parameters, partially offsetting the original efficiency gains. Additionally, these models are harder to train and may suffer from unstable convergence. In this work, we propose a novel parameter-efficient Bayesian LoRA, demonstrating that effective uncertainty quantification can be achieved in very low-dimensional parameter spaces. The proposed method achieves strong performance with improved calibration and generalization while maintaining computational efficiency. Our empirical findings show that, with the appropriate projection of the weight space: (1) uncertainty can be effectively modeled in a low-dimensional space, and (2) weight covariances exhibit low ranks.

Modern machine learning approaches often prioritize performance at the cost of increased complexity, computational demands, and reduced interpretability. This paper introduces a novel framework that challenges this trend by reinterpreting learning from an information-theoretic perspective, viewing it as a search for encoding schemes that capture intrinsic data structures through compact representations. Rather than following the conventional approach of fitting data to complex models, we propose a fundamentally different method that maps data to intervals of initial conditions in a dynamical system. Our GLS (Generalized L\"uroth Series) coding compression classifier employs skew tent maps - a class of chaotic maps - both for encoding data into initial conditions and for subsequent recovery. The effectiveness of this simple framework is noteworthy, with performance closely approaching that of well-established machine learning methods. On the breast cancer dataset, our approach achieves 92.98\% accuracy, comparable to Naive Bayes at 94.74\%. While these results do not exceed state-of-the-art performance, the significance of our contribution lies not in outperforming existing methods but in demonstrating that a fundamentally simpler, more interpretable approach can achieve competitive results.

Recent advances in imitation learning, particularly using generative modelling techniques like diffusion, have enabled policies to capture complex multi-modal action distributions. However, these methods often require large datasets and multiple inference steps for action generation, posing challenges in robotics where the cost for data collection is high and computation resources are limited. To address this, we introduce IMLE Policy, a novel behaviour cloning approach based on Implicit Maximum Likelihood Estimation (IMLE). IMLE Policy excels in low-data regimes, effectively learning from minimal demonstrations and requiring 38\% less data on average to match the performance of baseline methods in learning complex multi-modal behaviours. Its simple generator-based architecture enables single-step action generation, improving inference speed by 97.3\% compared to Diffusion Policy, while outperforming single-step Flow Matching. We validate our approach across diverse manipulation tasks in simulated and real-world environments, showcasing its ability to capture complex behaviours under data constraints. Videos and code are provided on our project page: https://imle-policy.github.io/.

In this paper, we propose an improved online confidence bound for multinomial logistic (MNL) models and apply this result to MNL bandits, achieving variance-dependent optimal regret. Recently, Lee & Oh (2024) established an online confidence bound for MNL models and achieved nearly minimax-optimal regret in MNL bandits. However, their results still depend on the norm-boundedness of the unknown parameter $B$ and the maximum size of possible outcomes $K$. To address this, we first derive an online confidence bound of $O\left(\sqrt{d \log t} + B \right)$, which is a significant improvement over the previous bound of $O (B \sqrt{d} \log t \log K )$ (Lee & Oh, 2024). This is mainly achieved by establishing tighter self-concordant properties of the MNL loss and introducing a novel intermediary term to bound the estimation error. Using this new online confidence bound, we propose a constant-time algorithm, OFU-MNL++, which achieves a variance-dependent regret bound of $O \Big( d \log T \sqrt{ \smash[b]{\sum_{t=1}^T} \sigma_t^2 } \Big) $ for sufficiently large $T$, where $\sigma_t^2$ denotes the variance of the rewards at round $t$, $d$ is the dimension of the contexts, and $T$ is the total number of rounds. Furthermore, we introduce a Maximum Likelihood Estimation (MLE)-based algorithm, OFU-MN$^2$L, which achieves an anytime poly(B)-free regret of $O \Big( d \log (BT) \sqrt{ \smash[b]{\sum_{t=1}^T} \sigma_t^2 } \Big) $.

Bayesian and frequentist inference are two fundamental paradigms in statistical estimation. Bayesian methods treat hypotheses as random variables, incorporating priors and updating beliefs via Bayes' theorem, whereas frequentist methods assume fixed but unknown hypotheses, relying on estimators like maximum likelihood. While extensive research has compared these approaches, the frequentist paradigm of obtaining point estimates has become predominant in deep learning, as Bayesian inference is challenging due to the computational complexity and the approximation gap of posterior estimation methods. However, a good understanding of trade-offs between the two approaches is lacking in the regime of amortized estimators, where in-context learners are trained to estimate either point values via maximum likelihood or maximum a posteriori estimation, or full posteriors using normalizing flows, score-based diffusion samplers, or diagonal Gaussian approximations, conditioned on observations. To help resolve this, we conduct a rigorous comparative analysis spanning diverse problem settings, from linear models to shallow neural networks, with a robust evaluation framework assessing both in-distribution and out-of-distribution generalization on tractable tasks. Our experiments indicate that amortized point estimators generally outperform posterior inference, though the latter remain competitive in some low-dimensional problems, and we further discuss why this might be the case.

The foundation model enables general-purpose problem-solving and enjoys desirable rapid adaptation due to its adopted cross-task generalization paradigms, e.g., pretraining, meta-training, and finetuning. Recent advances in these paradigms show the crucial role of challenging tasks' prioritized sampling in enhancing adaptation robustness. However, ranking task difficulties exhausts massive task queries to evaluate, thus computation and annotation intensive, which is typically unaffordable in practice. This work underscores the criticality of both adaptation robustness and learning efficiency, especially in scenarios where tasks are risky or costly to evaluate, e.g., policy evaluations in Markov decision processes (MDPs) or inference with large models. To this end, we present Model Predictive Task Sampling (MPTS) to establish connections between the task space and adaptation risk landscape to form a theoretical guideline in robust active task sampling. MPTS characterizes the task episodic information with a generative model and directly predicts task-specific adaptation risk values from posterior inference. The developed risk learner can amortize expensive evaluation and provably approximately rank task difficulties in the pursuit of task robust adaptation. MPTS can be seamlessly integrated into zero-shot, few-shot, and many-shot learning paradigms. Extensive experimental results are conducted to exhibit the superiority of the proposed framework, remarkably increasing task adaptation robustness and retaining learning efficiency in contrast to existing state-of-the-art (SOTA) methods. The code is available at the project site https://github.com/thu-rllab/MPTS.

Explainable AI (XAI) aims to provide insights into the decisions made by AI models. To date, most XAI approaches provide only one-time, static explanations, which cannot cater to users' diverse knowledge levels and information needs. Conversational explanations have been proposed as an effective method to customize XAI explanations. However, building conversational explanation systems is hindered by the scarcity of training data. Training with synthetic data faces two main challenges: lack of data diversity and hallucination in the generated data. To alleviate these issues, we introduce a repetition penalty to promote data diversity and exploit a hallucination detector to filter out untruthful synthetic conversation turns. We conducted both automatic and human evaluations on the proposed system, fEw-shot Multi-round ConvErsational Explanation (EMCEE). For automatic evaluation, EMCEE achieves relative improvements of 81.6% in BLEU and 80.5% in ROUGE compared to the baselines. EMCEE also mitigates the degeneration of data quality caused by training on synthetic data. In human evaluations (N=60), EMCEE outperforms baseline models and the control group in improving users' comprehension, acceptance, trust, and collaboration with static explanations by large margins. Through a fine-grained analysis of model responses, we further demonstrate that training on self-generated synthetic data improves the model's ability to generate more truthful and understandable answers, leading to better user interactions. To the best of our knowledge, this is the first conversational explanation method that can answer free-form user questions following static explanations.

Classification with imbalanced data is a common challenge in data analysis, where certain classes (minority classes) account for a small fraction of the training data compared with other classes (majority classes). Classical statistical theory based on large-sample asymptotics and finite-sample corrections is often ineffective for high-dimensional data, leaving many overfitting phenomena in empirical machine learning unexplained. In this paper, we develop a statistical theory for high-dimensional imbalanced classification by investigating support vector machines and logistic regression. We find that dimensionality induces truncation or skewing effects on the logit distribution, which we characterize via a variational problem under high-dimensional asymptotics. In particular, for linearly separable data generated from a two-component Gaussian mixture model, the logits from each class follow a normal distribution $\mathsf{N}(0,1)$ on the testing set, but asymptotically follow a rectified normal distribution $\max\{\kappa, \mathsf{N}(0,1)\}$ on the training set -- which is a pervasive phenomenon we verified on tabular data, image data, and text data. This phenomenon explains why the minority class is more severely affected by overfitting. Further, we show that margin rebalancing, which incorporates class sizes into the loss function, is crucial for mitigating the accuracy drop for the minority class. Our theory also provides insights into the effects of overfitting on calibration and other uncertain quantification measures.

Causal discovery is a structured prediction task that aims to predict causal relations among variables based on their data samples. Supervised Causal Learning (SCL) is an emerging paradigm in this field. Existing Deep Neural Network (DNN)-based methods commonly adopt the "Node-Edge approach", in which the model first computes an embedding vector for each variable-node, then uses these variable-wise representations to concurrently and independently predict for each directed causal-edge. In this paper, we first show that this architecture has some systematic bias that cannot be mitigated regardless of model size and data size. We then propose SiCL, a DNN-based SCL method that predicts a skeleton matrix together with a v-tensor (a third-order tensor representing the v-structures). According to the Markov Equivalence Class (MEC) theory, both the skeleton and the v-structures are identifiable causal structures under the canonical MEC setting, so predictions about skeleton and v-structures do not suffer from the identifiability limit in causal discovery, thus SiCL can avoid the systematic bias in Node-Edge architecture, and enable consistent estimators for causal discovery. Moreover, SiCL is also equipped with a specially designed pairwise encoder module with a unidirectional attention layer to model both internal and external relationships of pairs of nodes. Experimental results on both synthetic and real-world benchmarks show that SiCL significantly outperforms other DNN-based SCL approaches.

Across many domains of science, stochastic models are an essential tool to understand the mechanisms underlying empirically observed data. Models can be of different levels of detail and accuracy, with models of high-fidelity (i.e., high accuracy) to the phenomena under study being often preferable. However, inferring parameters of high-fidelity models via simulation-based inference is challenging, especially when the simulator is computationally expensive. We introduce MF-NPE, a multifidelity approach to neural posterior estimation that leverages inexpensive low-fidelity simulations to infer parameters of high-fidelity simulators within a limited simulation budget. MF-NPE performs neural posterior estimation with limited high-fidelity resources by virtue of transfer learning, with the ability to prioritize individual observations using active learning. On one statistical task with analytical ground-truth and two real-world tasks, MF-NPE shows comparable performance to current approaches while requiring up to two orders of magnitude fewer high-fidelity simulations. Overall, MF-NPE opens new opportunities to perform efficient Bayesian inference on computationally expensive simulators.