Yu Bai

Shuaiyu Zhang, Xun Lin, Rongxiang Zhang et al.

The integration of pathologic images and genomic data for survival analysis has gained increasing attention with advances in multimodal learning. However, current methods often ignore biological characteristics, such as heterogeneity and sparsity, both within and across modalities, ultimately limiting their adaptability to clinical practice. To address these challenges, we propose AdaMHF: Adaptive Multimodal Hierarchical Fusion, a framework designed for efficient, comprehensive, and tailored feature extraction and fusion. AdaMHF is specifically adapted to the uniqueness of medical data, enabling accurate predictions with minimal resource consumption, even under challenging scenarios with missing modalities. Initially, AdaMHF employs an experts expansion and residual structure to activate specialized experts for extracting heterogeneous and sparse features. Extracted tokens undergo refinement via selection and aggregation, reducing the weight of non-dominant features while preserving comprehensive information. Subsequently, the encoded features are hierarchically fused, allowing multi-grained interactions across modalities to be captured. Furthermore, we introduce a survival prediction benchmark designed to resolve scenarios with missing modalities, mirroring real-world clinical conditions. Extensive experiments on TCGA datasets demonstrate that AdaMHF surpasses current state-of-the-art (SOTA) methods, showcasing exceptional performance in both complete and incomplete modality settings.

Tengyang Xie, Nan Jiang, Huan Wang et al.

Recent theoretical work studies sample-efficient reinforcement learning (RL) extensively in two settings: learning interactively in the environment (online RL), or learning from an offline dataset (offline RL). However, existing algorithms and theories for learning near-optimal policies in these two settings are rather different and disconnected. Towards bridging this gap, this paper initiates the theoretical study of policy finetuning, that is, online RL where the learner has additional access to a "reference policy" $μ$ close to the optimal policy $π_\star$ in a certain sense. We consider the policy finetuning problem in episodic Markov Decision Processes (MDPs) with $S$ states, $A$ actions, and horizon length $H$. We first design a sharp offline reduction algorithm -- which simply executes $μ$ and runs offline policy optimization on the collected dataset -- that finds an $\varepsilon$ near-optimal policy within $\widetilde{O}(H^3SC^\star/\varepsilon^2)$ episodes, where $C^\star$ is the single-policy concentrability coefficient between $μ$ and $π_\star$. This offline result is the first that matches the sample complexity lower bound in this setting, and resolves a recent open question in offline RL. We then establish an $Ω(H^3S\min\{C^\star, A\}/\varepsilon^2)$ sample complexity lower bound for any policy finetuning algorithm, including those that can adaptively explore the environment. This implies that -- perhaps surprisingly -- the optimal policy finetuning algorithm is either offline reduction or a purely online RL algorithm that does not use $μ$. Finally, we design a new hybrid offline/online algorithm for policy finetuning that achieves better sample complexity than both vanilla offline reduction and purely online RL algorithms, in a relaxed setting where $μ$ only satisfies concentrability partially up to a certain time step.

Yu Bai, Song Mei, Huan Wang et al.

Modern machine learning models with high accuracy are often miscalibrated -- the predicted top probability does not reflect the actual accuracy, and tends to be over-confident. It is commonly believed that such over-confidence is mainly due to over-parametrization, in particular when the model is large enough to memorize the training data and maximize the confidence. In this paper, we show theoretically that over-parametrization is not the only reason for over-confidence. We prove that logistic regression is inherently over-confident, in the realizable, under-parametrized setting where the data is generated from the logistic model, and the sample size is much larger than the number of parameters. Further, this over-confidence happens for general well-specified binary classification problems as long as the activation is symmetric and concave on the positive part. Perhaps surprisingly, we also show that over-confidence is not always the case -- there exists another activation function (and a suitable loss function) under which the learned classifier is under-confident at some probability values. Overall, our theory provides a precise characterization of calibration in realizable binary classification, which we verify on simulations and real data experiments.

Ming Yin, Yu Bai, Yu-Xiang Wang

We consider the problem of offline reinforcement learning (RL) -- a well-motivated setting of RL that aims at policy optimization using only historical data. Despite its wide applicability, theoretical understandings of offline RL, such as its optimal sample complexity, remain largely open even in basic settings such as \emph{tabular} Markov Decision Processes (MDPs). In this paper, we propose Off-Policy Double Variance Reduction (OPDVR), a new variance reduction based algorithm for offline RL. Our main result shows that OPDVR provably identifies an $ε$-optimal policy with $\widetilde{O}(H^2/d_mε^2)$ episodes of offline data in the finite-horizon stationary transition setting, where $H$ is the horizon length and $d_m$ is the minimal marginal state-action distribution induced by the behavior policy. This improves over the best known upper bound by a factor of $H$. Moreover, we establish an information-theoretic lower bound of $Ω(H^2/d_mε^2)$ which certifies that OPDVR is optimal up to logarithmic factors. Lastly, we show that OPDVR also achieves rate-optimal sample complexity under alternative settings such as the finite-horizon MDPs with non-stationary transitions and the infinite horizon MDPs with discounted rewards.

Yu Bai, Minshuo Chen, Pan Zhou et al.

Meta-learning aims to perform fast adaptation on a new task through learning a "prior" from multiple existing tasks. A common practice in meta-learning is to perform a train-validation split (\emph{train-val method}) where the prior adapts to the task on one split of the data, and the resulting predictor is evaluated on another split. Despite its prevalence, the importance of the train-validation split is not well understood either in theory or in practice, particularly in comparison to the more direct \emph{train-train method}, which uses all the per-task data for both training and evaluation. We provide a detailed theoretical study on whether and when the train-validation split is helpful in the linear centroid meta-learning problem. In the agnostic case, we show that the expected loss of the train-val method is minimized at the optimal prior for meta testing, and this is not the case for the train-train method in general without structural assumptions on the data. In contrast, in the realizable case where the data are generated from linear models, we show that both the train-val and train-train losses are minimized at the optimal prior in expectation. Further, perhaps surprisingly, our main result shows that the train-train method achieves a \emph{strictly better} excess loss in this realizable case, even when the regularization parameter and split ratio are optimally tuned for both methods. Our results highlight that sample splitting may not always be preferable, especially when the data is realizable by the model. We validate our theories by experimentally showing that the train-train method can indeed outperform the train-val method, on both simulations and real meta-learning tasks.

Minshuo Chen, Yu Bai, Jason D. Lee et al.

Deep neural networks can empirically perform efficient hierarchical learning, in which the layers learn useful representations of the data. However, how they make use of the intermediate representations are not explained by recent theories that relate them to "shallow learners" such as kernels. In this work, we demonstrate that intermediate neural representations add more flexibility to neural networks and can be advantageous over raw inputs. We consider a fixed, randomly initialized neural network as a representation function fed into another trainable network. When the trainable network is the quadratic Taylor model of a wide two-layer network, we show that neural representation can achieve improved sample complexities compared with the raw input: For learning a low-rank degree-$p$ polynomial ($p \geq 4$) in $d$ dimension, neural representation requires only $\tilde{O}(d^{\lceil p/2 \rceil})$ samples, while the best-known sample complexity upper bound for the raw input is $\tilde{O}(d^{p-1})$. We contrast our result with a lower bound showing that neural representations do not improve over the raw input (in the infinite width limit), when the trainable network is instead a neural tangent kernel. Our results characterize when neural representations are beneficial, and may provide a new perspective on why depth is important in deep learning.

Wang Haonan, Gao Yang, Bai Yu et al.

Like humans, document summarization models can interpret a document's contents in a number of ways. Unfortunately, the neural models of today are largely black boxes that provide little explanation of how or why they generated a summary in the way they did. Therefore, to begin prying open the black box and to inject a level of control into the substance of the final summary, we developed a novel select-and-generate framework that focuses on explainability. By revealing the latent centrality and interactions between sentences, along with scores for sentence novelty and relevance, users are given a window into the choices a model is making and an opportunity to guide those choices in a more desirable direction. A novel pair-wise matrix captures the sentence interactions, centrality, and attribute scores, and a mask with tunable attribute thresholds allows the user to control which sentences are likely to be included in the extraction. A sentence-deployed attention mechanism in the abstractor ensures the final summary emphasizes the desired content. Additionally, the encoder is adaptable, supporting both Transformer- and BERT-based configurations. In a series of experiments assessed with ROUGE metrics and two human evaluations, ESCA outperformed eight state-of-the-art models on the CNN/DailyMail and NYT50 benchmark datasets.

Yu Bai, Ben Krause, Huan Wang et al.

We propose \emph{Taylorized training} as an initiative towards better understanding neural network training at finite width. Taylorized training involves training the $k$-th order Taylor expansion of the neural network at initialization, and is a principled extension of linearized training---a recently proposed theory for understanding the success of deep learning. We experiment with Taylorized training on modern neural network architectures, and show that Taylorized training (1) agrees with full neural network training increasingly better as we increase $k$, and (2) can significantly close the performance gap between linearized and full training. Compared with linearized training, higher-order training works in more realistic settings such as standard parameterization and large (initial) learning rate. We complement our experiments with theoretical results showing that the approximation error of $k$-th order Taylorized models decay exponentially over $k$ in wide neural networks.