We study the problem of designing minimax procedures in linear regression under the quantile risk. We start by considering the realizable setting with independent Gaussian noise, where for any given noise level and distribution of inputs, we obtain the exact minimax quantile risk for a rich family of error functions and establish the minimaxity of OLS. This improves on the lower bounds obtained by Lecué and Mendelson (2016) and Mendelson (2017) for the special case of square error, and provides us with a lower bound on the minimax quantile risk over larger sets of distributions. Under the square error and a fourth moment assumption on the distribution of inputs, we show that this lower bound is tight over a larger class of problems. Specifically, we prove a matching upper bound on the worst-case quantile risk of a variant of the procedure proposed by Lecué and Lerasle (2020), thereby establishing its minimaxity, up to absolute constants. We illustrate the usefulness of our approach by extending this result to all p-th power error functions for p (2,). Along the way, we develop a generic analogue to the classical Bayesian method for lower bounding the minimax risk when working with the quantile risk, as well as a tight characterization of the quantiles of the smallest eigenvalue of the sample covariance matrix.

Real-world applications of machine learning models are often subject to legal or policy-based regulations. Some of these regulations require ensuring the validity of the model, i.e., the approximation error being smaller than a threshold. A global metric is generally too insensitive to determine the validity of a specific prediction, whereas evaluating local validity is costly since it requires gathering additional data.We propose learning the model error to acquire a local validity estimate while reducing the amount of required data through active learning. Using model validation benchmarks, we provide empirical evidence that the proposed method can lead to an error model with sufficient discriminative properties using a relatively small amount of data. Furthermore, an increased sensitivity to local changes of the validity bounds compared to alternative approaches is demonstrated.

The last decade has seen blossoming research in deep learning theory attempting to answer, "Why does deep learning generalize?" A powerful shift in perspective precipitated this progress: the study of overparametrized models in the interpolation regime. In this paper, we argue that another perspective shift is due, since some of the desirable qualities of LLMs are not a consequence of good statistical generalization and require a separate theoretical explanation. Our core argument relies on the observation that AR probabilistic models are inherently non-identifiable: models zero or near-zero KL divergence apart -- thus, equivalent test loss -- can exhibit markedly different behaviors. We support our position with mathematical examples and empirical observations, illustrating why non-identifiability has practical relevance through three case studies: (1) the non-identifiability of zero-shot rule extrapolation; (2) the approximate non-identifiability of in-context learning; and (3) the non-identifiability of fine-tunability. We review promising research directions focusing on LLM-relevant generalization measures, transferability, and inductive biases.

Large language models (LLMs) can adapt to new tasks through in-context learning (ICL) based on a few examples presented in dialogue history without any model parameter update. Despite such convenience, the performance of ICL heavily depends on the quality of the in-context examples presented, which makes the in-context example selection approach a critical choice. This paper proposes a novel Bayesian in-Context example Selection method (ByCS) for ICL. Extending the inference probability conditioned on in-context examples based on Bayes' theorem, ByCS focuses on the inverse inference conditioned on test input. Following the assumption that accurate inverse inference probability (likelihood) will result in accurate inference probability (posterior), in-context examples are selected based on their inverse inference results. Diverse and extensive cross-tasking and cross-modality experiments are performed with speech, text, and image examples. Experimental results show the efficacy and robustness of our ByCS method on various models, tasks and modalities.

Instruction Fine-Tuning enhances pre-trained language models from basic next-word prediction to complex instruction-following. However, existing One-off Instruction Fine-Tuning (One-off IFT) method, applied on a diverse instruction, may not effectively boost models' adherence to instructions due to the simultaneous handling of varying instruction complexities. To improve this, Phased Instruction Fine-Tuning (Phased IFT) is proposed, based on the idea that learning to follow instructions is a gradual process. It assesses instruction difficulty using GPT-4, divides the instruction data into subsets of increasing difficulty, and uptrains the model sequentially on these subsets. Experiments with Llama-2 7B/13B/70B, Llama3 8/70B and Mistral-7B models using Alpaca data show that Phased IFT significantly outperforms One-off IFT, supporting the progressive alignment hypothesis and providing a simple and efficient way to enhance large language models. Codes and datasets from our experiments are freely available at https://github.com/xubuvd/PhasedSFT.

Causal discovery is crucial for understanding complex systems and informing decisions. While observational data can uncover causal relationships under certain assumptions, it often falls short, making active interventions necessary. Current methods, such as Bayesian and graph-theoretical approaches, do not prioritize decision-making and often rely on ideal conditions or information gain, which is not directly related to hypothesis testing. We propose a novel Bayesian optimization-based method inspired by Bayes factors that aims to maximize the probability of obtaining decisive and correct evidence. Our approach uses observational data to estimate causal models under different hypotheses, evaluates potential interventions pre-experimentally, and iteratively updates priors to refine interventions. We demonstrate the effectiveness of our method through various experiments. Our contributions provide a robust framework for efficient causal discovery through active interventions, enhancing the practical application of theoretical advancements.

Diffusion models have become the de-facto approach for generating visual data, which are trained to match the distribution of the training dataset. In addition, we also want to control generation to fulfill desired properties such as alignment to a text description, which can be specified with a black-box reward function. Prior works fine-tune pretrained diffusion models to achieve this goal through reinforcement learning-based algorithms. Nonetheless, they suffer from issues including slow credit assignment as well as low quality in their generated samples. In this work, we explore techniques that do not directly maximize the reward but rather generate high-reward images with relatively high probability -- a natural scenario for the framework of generative flow networks (GFlowNets). To this end, we propose the Diffusion Alignment with GFlowNet (DAG) algorithm to post-train diffusion models with black-box property functions. Extensive experiments on Stable Diffusion and various reward specifications corroborate that our method could effectively align large-scale text-to-image diffusion models with given reward information.

Learning predictive world models is essential for enhancing the planning capabilities of reinforcement learning agents. Notably, the MuZero-style algorithms, based on the value equivalence principle and Monte Carlo Tree Search (MCTS), have achieved superhuman performance in various domains. However, in environments that require capturing long-term dependencies, MuZero's performance deteriorates rapidly. We identify that this is partially due to the \textit{entanglement} of latent representations with historical information, which results in incompatibility with the auxiliary self-supervised state regularization. To overcome this limitation, we present \textit{UniZero}, a novel approach that \textit{disentangles} latent states from implicit latent history using a transformer-based latent world model. By concurrently predicting latent dynamics and decision-oriented quantities conditioned on the learned latent history, UniZero enables joint optimization of the long-horizon world model and policy, facilitating broader and more efficient planning in latent space. We demonstrate that UniZero, even with single-frame inputs, matches or surpasses the performance of MuZero-style algorithms on the Atari 100k benchmark. Furthermore, it significantly outperforms prior baselines in benchmarks that require long-term memory. Lastly, we validate the effectiveness and scalability of our design choices through extensive ablation studies, visual analyses, and multi-task learning results. The code is available at \textcolor{magenta}{https://github.com/opendilab/LightZero}.

The study of intelligent systems explains behaviour in terms of economic rationality. This results in an optimization principle involving a function or utility, which states that the system will evolve until the configuration of maximum utility is achieved. Recently, this theory has incorporated constraints, i.e., the optimum is achieved when the utility is maximized while respecting some information-processing constraints. This is reminiscent of thermodynamic systems. As such, the study of intelligent systems has benefited from the tools of thermodynamics. The first aim of this thesis is to clarify the applicability of these results in the study of intelligent systems. We can think of the local transition steps in thermodynamic or intelligent systems as being driven by uncertainty. In fact, the transitions in both systems can be described in terms of majorization. Hence, real-valued uncertainty measures like Shannon entropy are simply a proxy for their more involved behaviour. More in general, real-valued functions are fundamental to study optimization and complexity in the order-theoretic approach to several topics, including economics, thermodynamics, and quantum mechanics. The second aim of this thesis is to improve on this classification. The basic similarity between thermodynamic and intelligent systems is based on an uncertainty notion expressed by a preorder. We can also think of the transitions in the steps of a computational process as a decision-making procedure. In fact, by adding some requirements on the considered order structures, we can build an abstract model of uncertainty reduction that allows to incorporate computability, that is, to distinguish the objects that can be constructed by following a finite set of instructions from those that cannot. The third aim of this thesis is to clarify the requirements on the order structure that allow such a framework.

Identifying gene splicing is a core and significant task confronted in modern collaboration between artificial intelligence and bioinformatics. Past decades have witnessed great efforts on this concern, such as the bio-plausible splicing pattern AT-CG and the famous SpliceAI. In this paper, we propose a novel framework for the task of gene splicing identification, named Horizon-wise Gene Splicing Identification (H-GSI). The proposed H-GSI follows the horizon-wise identification paradigm and comprises four components: the pre-processing procedure transforming string data into tensors, the sliding window technique handling long sequences, the SeqLab model, and the predictor. In contrast to existing studies that process gene information with a truncated fixed-length sequence, H-GSI employs a horizon-wise identification paradigm in which all positions in a sequence are predicted with only one forward computation, improving accuracy and efficiency. The experiments conducted on the real-world Human dataset show that our proposed H-GSI outperforms SpliceAI and achieves the best accuracy of 97.20\%. The source code is available from this link.