We study the geometry of conditional optimal transport (COT) and prove a dynamical formulation which generalizes the Benamou-Brenier Theorem. Equipped with these tools, we propose a simulation-free flow-based method for conditional generative modeling. Our method couples an arbitrary source distribution to a specified target distribution through a triangular COT plan, and a conditional generative model is obtained by approximating the geodesic path of measures induced by this COT plan. Our theory and methods are applicable in infinite-dimensional settings, making them well suited for a wide class of Bayesian inverse problems. Empirically, we demonstrate that our method is competitive on several challenging conditional generation tasks, including an infinite-dimensional inverse problem.

This paper introduces DiffPuter, an iterative method for missing data imputation that leverages the Expectation-Maximization (EM) algorithm and Diffusion Models. By treating missing data as hidden variables that can be updated during model training, we frame the missing data imputation task as an EM problem. During the M-step, DiffPuter employs a diffusion model to learn the joint distribution of both the observed and currently estimated missing data. In the E-step, DiffPuter re-estimates the missing data based on the conditional probability given the observed data, utilizing the diffusion model learned in the M-step. Starting with an initial imputation, DiffPuter alternates between the M-step and E-step until convergence. Through this iterative process, DiffPuter progressively refines the complete data distribution, yielding increasingly accurate estimations of the missing data. Our theoretical analysis demonstrates that the unconditional training and conditional sampling processes of the diffusion model align precisely with the objectives of the M-step and E-step, respectively. Empirical evaluations across 10 diverse datasets and comparisons with 16 different imputation methods highlight DiffPuter's superior performance. Notably, DiffPuter achieves an average improvement of 8.10% in MAE and 5.64% in RMSE compared to the most competitive existing method.

Recent works have shown the remarkable superiority of transformer models in reinforcement learning (RL), where the decision-making problem is formulated as sequential generation. Transformer-based agents could emerge with self-improvement in online environments by providing task contexts, such as multiple trajectories, called in-context RL. However, due to the quadratic computation complexity of attention in transformers, current in-context RL methods suffer from huge computational costs as the task horizon increases. In contrast, the Mamba model is renowned for its efficient ability to process long-term dependencies, which provides an opportunity for in-context RL to solve tasks that require long-term memory. To this end, we first implement Decision Mamba (DM) by replacing the backbone of Decision Transformer (DT). Then, we propose a Decision Mamba-Hybrid (DM-H) with the merits of transformers and Mamba in high-quality prediction and long-term memory. Specifically, DM-H first generates high-value sub-goals from long-term memory through the Mamba model. Then, we use sub-goals to prompt the transformer, establishing high-quality predictions. Experimental results demonstrate that DM-H achieves state-of-the-art in long and short-term tasks, such as D4RL, Grid World, and Tmaze benchmarks. Regarding efficiency, the online testing of DM-H in the long-term task is 28$\times$ times faster than the transformer-based baselines.

Natural language is structured hierarchically: words are grouped into phrases or constituents, which can be further grouped to form higher-level phrases up to the full sentence. How well do the neural network models trained on language data learn this phrase structure of human language has been a subject of great interest. A flurry of past work have shown that syntax trees can be recovered from recurrent neural network (RNN) and transformer-based models trained on large-scale language corpora (Tenney et al., 2019, Peters et al., 2018, Lin et al., 2019, Wu et al., 2020). While these studies provide useful evidence of the aforementioned phenomenon, they do not shed light on the architectural choices, training paradigms or dataset characteristics that lead models to learn the phrase structure of language. A useful tool to understand these model and dataset specific properties is through the test for hierarchical generalization, i.e., evaluating the capability of a model to generalize to novel syntactic forms, which were unseen during training. A classic problem to test for hierarchical generalization is question formation, where given a declarative sentence, e.g., My walrus does move the dogs that do wait., the task is to transform it into a question: Does my walrus move the dogs that do wait? The task is accomplished by moving one auxiliary verb to the front. The correct choice to move does in this example (rather than do), is predicted both by a hierarchical rule based on the phrase-structure syntax of the sentence, and by a linear rule that says to move the first auxiliary. Hence, as a test for hierarchical generalization, we can ask, for neural networks trained from scratch on data that is consistent with both hierarchical and linear rules (i.e.,

In-context learning is a promising approach for offline reinforcement learning (RL) to handle online tasks, which can be achieved by providing task prompts. Recent works demonstrated that in-context RL could emerge with self-improvement in a trial-and-error manner when treating RL tasks as an across-episodic sequential prediction problem. Despite the self-improvement not requiring gradient updates, current works still suffer from high computational costs when the across-episodic sequence increases with task horizons. To this end, we propose an In-context Decision Transformer (IDT) to achieve self-improvement in a high-level trial-and-error manner. Specifically, IDT is inspired by the efficient hierarchical structure of human decision-making and thus reconstructs the sequence to consist of high-level decisions instead of low-level actions that interact with environments. As one high-level decision can guide multi-step low-level actions, IDT naturally avoids excessively long sequences and solves online tasks more efficiently. Experimental results show that IDT achieves state-of-the-art in long-horizon tasks over current in-context RL methods. In particular, the online evaluation time of our IDT is \textbf{36$\times$} times faster than baselines in the D4RL benchmark and \textbf{27$\times$} times faster in the Grid World benchmark.

This article presents a review of typical techniques used in three distinct aspects of deep learning model development for audio generation. In the first part of the article, we provide an explanation of audio representations, beginning with the fundamental audio waveform. We then progress to the frequency domain, with an emphasis on the attributes of human hearing, and finally introduce a relatively recent development. The main part of the article focuses on explaining basic and extended deep learning architecture variants, along with their practical applications in the field of audio generation. The following architectures are addressed: 1) Autoencoders 2) Generative adversarial networks 3) Normalizing flows 4) Transformer networks 5) Diffusion models. Lastly, we will examine four distinct evaluation metrics that are commonly employed in audio generation. This article aims to offer novice readers and beginners in the field a comprehensive understanding of the current state of the art in audio generation methods as well as relevant studies that can be explored for future research.

Large language models (LLMs) like transformers have impressive in-context learning (ICL) capabilities; they can generate predictions for new queries based on input-output sequences in prompts without parameter updates. While many theories have attempted to explain ICL, they often focus on structured training data similar to ICL tasks, such as regression. In practice, however, these models are trained in an unsupervised manner on unstructured text data, which bears little resemblance to ICL tasks. To this end, we investigate how ICL emerges from unsupervised training on unstructured data. The key observation is that ICL can arise simply by modeling co-occurrence information using classical language models like continuous bag of words (CBOW), which we theoretically prove and empirically validate. Furthermore, we establish the necessity of positional information and noise structure to generalize ICL to unseen data. Finally, we present instances where ICL fails and provide theoretical explanations; they suggest that the ICL ability of LLMs to identify certain tasks can be sensitive to the structure of the training data.

Multiclass neural network classifiers are typically trained using cross-entropy loss. Following training, the performance of this same neural network is evaluated using an application-specific metric based on the multiclass confusion matrix, such as the Macro $F_\beta$-Score. It is questionable whether the use of cross-entropy will yield a classifier that aligns with the intended application-specific performance criteria, particularly in scenarios where there is a need to emphasize one aspect of classifier performance. For example, if greater precision is preferred over recall, the $\beta$ value in the $F_\beta$ evaluation metric can be adjusted accordingly, but the cross-entropy objective remains unaware of this preference during training. We propose a method that addresses this training-evaluation gap for multiclass neural network classifiers such that users can train these models informed by the desired final $F_\beta$-Score. Following prior work in binary classification, we utilize the concepts of the soft-set confusion matrices and a piecewise-linear approximation of the Heaviside step function. Our method extends the $2 \times 2$ binary soft-set confusion matrix to a multiclass $d \times d$ confusion matrix and proposes dynamic adaptation of the threshold value $\tau$, which parameterizes the piecewise-linear Heaviside approximation during run-time. We present a theoretical analysis that shows that our method can be used to optimize for a soft-set based approximation of Macro-$F_\beta$ that is a consistent estimator of Macro-$F_\beta$, and our extensive experiments show the practical effectiveness of our approach.

Reinforcement learning from human feedback (RLHF) has emerged as a central tool for language model alignment. We consider online exploration in RLHF, which exploits interactive access to human or AI feedback by deliberately encouraging the model to produce diverse, maximally informative responses. By allowing RLHF to confidently stray from the pre-trained model, online exploration offers the possibility of novel, potentially super-human capabilities, but its full potential as a paradigm for language model training has yet to be realized, owing to computational and statistical bottlenecks in directly adapting existing reinforcement learning techniques. We propose a new algorithm for online exploration in RLHF, Exploratory Preference Optimization (XPO), which is simple and practical -- a one-line change to (online) Direct Preference Optimization (DPO; Rafailov et al., 2023) -- yet enjoys the strongest known provable guarantees and promising empirical performance. XPO augments the DPO objective with a novel and principled exploration bonus, empowering the algorithm to explore outside the support of the initial model and human feedback data. In theory, we show that XPO is provably sample-efficient and converges to a near-optimal language model policy under natural exploration conditions, irrespective of whether the initial model has good coverage. Our analysis, which builds on the observation that DPO implicitly performs a form of $Q^{\star}$-approximation (or, Bellman error minimization), combines previously disparate techniques from language modeling and theoretical reinforcement learning in a serendipitous fashion through the perspective of KL-regularized Markov decision processes. Empirically, we find that XPO is more sample-efficient than non-exploratory DPO variants in a preliminary evaluation.

The practical use of Bayesian Optimization (BO) in engineering applications imposes special requirements: high sampling efficiency on the one hand and finding a robust solution on the other hand. We address the case of adversarial robustness, where all parameters are controllable during the optimization process, but a subset of them is uncontrollable or even adversely perturbed at the time of application. To this end, we develop an efficient information-based acquisition function that we call Robust Entropy Search (RES). We empirically demonstrate its benefits in experiments on synthetic and real-life data. The results showthat RES reliably finds robust optima, outperforming state-of-the-art algorithms.