The decomposition idea is discussed more extensively by Seita et al. 2017 (for achieving subsampling without any

A.1 HQ-VAE For designing HQ-VAE, we modify the encoder and decoder architectures of VQ-GAN [A1]; we set the stride of the first convolution layer in the encoder and the last transposed convolution layer in the decoder as two as mentioned in the main paper. The encoder takes an image x and returns encoded feature map z. We adopt HQ-VAE equipped with pixel-unshuffle and -shuffle for resampling. We use HQ-VAE (16 16) with f = 16 for the two-level HQ-TVAE implementation, which gives concise visual codes for efficient training of HQ-Transformer. We train HQ-VAE (16 16) for 50 epochs on the ImageNet training split.

We propose a locally hierarchical auto-regressive model with multiple resolutions of discrete codes. In the first stage of our algorithm, we represent an image with a pyramid of codes using Hierarchically Quantized Variational AutoEncoder (HQ-VAE), which disentangles the information contained in the multi-level codes. For an example of two-level codes, we create two separate pathways to carry high-level coarse structures of input images using top codes while compensating for missing fine details by constructing a residual connection for bottom codes. An appropriate selection of resizing operations for code embedding maps enables top codes to capture maximal information within images and the first stage algorithm achieves better performance on both vector quantization and image generation. The second stage adopts Hierarchically Quantized Transformer (HQ-Transformer) to process a sequence of local pyramids, which consist of a single top code and its corresponding bottom codes.

In this work we study the problem of actively learning binary classifiers from a given concept class, i.e., learning by utilizing unlabeled data and submitting targeted queries about their labels to a domain expert. We evaluate the quality of our solutions by considering the learning curves they induce, i.e., the rate of decrease of the misclassification probability as the number of label queries increases. The majority of the literature on active learning has focused on obtaining uniform guarantees on the error rate which are only able to explain the upper envelope of the learning curves over families of different data-generating distributions. We diverge from this line of work and we focus on the distribution-dependent framework of universal learning whose goal is to obtain guarantees that hold for any fixed distribution, but do not apply uniformly over all the distributions. We provide a complete characterization of the optimal learning rates that are achievable by algorithms that have to specify the number of unlabeled examples they use ahead of their execution. Moreover, we identify combinatorial complexity measures that give rise to each case of our tetrachotomic characterization. This resolves an open question that was posed by Balcan et al. (2010). As a byproduct of our main result, we develop an active learning algorithm for partial concept classes that achieves exponential learning rates in the uniform setting.

A core capability of intelligent systems is the ability to quickly learn new tasks by drawing on prior experience. Gradient (or optimization) based meta-learning has recently emerged as an effective approach for few-shot learning. In this formulation, meta-parameters are learned in the outer loop, while task-specific models are learned in the inner-loop, by using only a small amount of data from the current task. A key challenge in scaling these approaches is the need to differentiate through the inner loop learning process, which can impose considerable computational and memory burdens. By drawing upon implicit differentiation, we develop the implicit MAML algorithm, which depends only on the solution to the inner level optimization and not the path taken by the inner loop optimizer.

We thank the reviewers for their careful consideration of our work. R2 suggested that an analysis on non-toy models would be interesting to see. R3 believed that the synthetic experiment was not suited to the model class. We expect our analysis on smaller models to extrapolate to larger ones (R2). We regret that we were not clearer about how our aim differs from these studies [McMurray et al. (2012), ME would aid downstream learning as we propose or as is observed in humans in lifelong learning settings.

Theoretical analysis confirms that the proposed algorithm achieves sub-linear regret in relation to the number of rounds and arms.

Transformers are slow and memory-hungry on long sequences, since the time and memory complexity of self-attention are quadratic in sequence length. Approximate attention methods have attempted to address this problem by trading off model quality to reduce the compute complexity, but often do not achieve wall-clock speedup. We argue that a missing principle is making attention algorithms IO-aware-- accounting for reads and writes between levels of GPU memory.

Virtual Screening is an essential technique in the early phases of drug discovery, aimed at identifying promising drug candidates from vast molecular libraries. Recently, ligand-based virtual screening has garnered significant attention due to its efficacy in conducting extensive database screenings without relying on specific protein-binding site information. Obtaining binding affinity data for complexes is highly expensive, resulting in a limited amount of available data that covers a relatively small chemical space. Moreover, these datasets contain a significant amount of inconsistent noise. It is challenging to identify an inductive bias that consistently maintains the integrity of molecular activity during data augmentation. To tackle these challenges, we propose S-MolSearch, the first framework to our knowledge, that leverages molecular 3D information and affinity information in semi-supervised contrastive learning for ligand-based virtual screening. Drawing on the principles of inverse optimal transport, S-MolSearch efficiently processes both labeled and unlabeled data, training molecular structural encoders while generating soft labels for the unlabeled data. This design allows S-MolSearch to adaptively utilize unlabeled data within the learning process. Empirically, S-MolSearch demonstrates superior performance on widely-used benchmarks LIT-PCBA and DUD-E.

State aggregation is a popular model reduction method rooted in optimal control. It reduces the complexity of engineering systems by mapping the system's states into a small number of meta-states. The choice of aggregation map often depends on the data analysts' knowledge and is largely ad hoc. In this paper, we propose a tractable algorithm that estimates the probabilistic aggregation map from the system's trajectory. We adopt a soft-aggregation model, where each meta-state has a signature raw state, called an anchor state.