Through considerable effort and intuition, several recent works have reverseengineered nontrivial behaviors of transformer models. This paper systematizes the mechanistic interpretability process they followed. First, researchers choose a metric and dataset that elicit the desired model behavior. Then, they apply activation patching to find which abstract neural network units are involved in the behavior. By varying the dataset, metric, and units under investigation, researchers can understand the functionality of each component.

Generative models at times produce "invalid" outputs, such as images with generation artifacts and unnatural sounds. Validity-constrained distribution learning attempts to address this problem by requiring that the learned distribution have a provably small fraction of its mass in invalid parts of space - something which standard loss minimization does not always ensure. To this end, a learner in this model can guide the learning via "validity queries", which allow it to ascertain the validity of individual examples. Prior work on this problem takes a worst-case stance, showing that proper learning requires an exponential number of validity queries, and demonstrating an improper algorithm which - while generating guarantees in a wide-range of settings - makes an atypical polynomial number of validity queries. In this work, we take a first step towards characterizing regimes where guaranteeing validity is easier than in the worst-case. We show that when the data distribution lies in the model class and the log-loss is minimized, the number of samples required to ensure validity has a weak dependence on the validity requirement. Additionally, we show that when the validity region belongs to a VC-class, a limited number of validity queries are often sufficient.

While the conditional sequence modeling with the transformer architecture has demonstrated its effectiveness in dealing with offline reinforcement learning (RL) tasks, it is struggle to handle out-of-distribution states and actions. Existing work attempts to address this issue by data augmentation with the learned policy or adding extra constraints with the value-based RL algorithm. However, these studies still fail to overcome the following challenges: (1) insufficiently utilizing the historical temporal information among inter-steps, (2) overlooking the local intrastep relationships among return-to-gos (RTGs), states and actions, (3) overfitting suboptimal trajectories with noisy labels. To address these challenges, we propose Decision Mamba (DM), a novel multi-grained state space model (SSM) with a selfevolving policy learning strategy. DM explicitly models the historical hidden state to extract the temporal information by using the mamba architecture. To capture the relationship among RTG-state-action triplets, a fine-grained SSM module is designed and integrated into the original coarse-grained SSM in mamba, resulting in a novel mamba architecture tailored for offline RL. Finally, to mitigate the overfitting issue on noisy trajectories, a self-evolving policy is proposed by using progressive regularization. The policy evolves by using its own past knowledge to refine the suboptimal actions, thus enhancing its robustness on noisy demonstrations. Extensive experiments on various tasks show that DM outperforms other baselines substantially.

In this paper, we study the non-asymptotic sample complexity for the pure exploration problem in contextual bandits and tabular reinforcement learning (RL): identifying an ϵ-optimal policy from a set of policies Π with high probability. Existing work in bandits has shown that it is possible to identify the best policy by estimating only the difference between the behaviors of individual policies-which can be substantially cheaper than estimating the behavior of each policy directly --yet the best-known complexities in RL fail to take advantage of this, and instead estimate the behavior of each policy directly. Does it suffice to estimate only the differences in the behaviors of policies in RL? We answer this question positively for contextual bandits, but in the negative for tabular RL, showing a separation between contextual bandits and RL. However, inspired by this, we show that it almost suffices to estimate only the differences in RL: if we can estimate the behavior of a single reference policy, it suffices to only estimate how any other policy deviates from this reference policy. We develop an algorithm which instantiates this principle and obtains, to the best of our knowledge, the tightest known bound on the sample complexity of tabular RL.

Molecule generation ideally in its 3-D form has enjoyed wide applications in material, chemistry, life science, etc. We propose the first quantum parametric circuit for 3-D molecule generation for its potential quantum advantage especially considering the arrival of Noisy Intermediate-Scale Quantum (NISQ) era. We choose the Variational AutoEncoder (VAE) scheme for its simplicity and one-shot generation ability, which we believe is more quantum-friendly compared with the auto-regressive generative models or diffusion models as used in classic approaches. Specifically, we present a quantum encoding scheme designed for 3-D molecules with qubits complexity O(C log n) (n is the number of atoms) and adopt a von Mises-Fisher (vMF) distributed latent space to meet the inherent coherence of the quantum system.

We study the problem of locally private mean estimation of high-dimensional vectors in the Euclidean ball. Existing algorithms for this problem either incur suboptimal error or have high communication and/or run-time complexity. We propose a new algorithmic framework, ProjUnit, for private mean estimation that yields algorithms that are computationally efficient, have low communication complexity, and incur optimal error up to a 1 + o(1)-factor. Our framework is deceptively simple: each randomizer projects its input to a random low-dimensional subspace, normalizes the result, and then runs an optimal algorithm such as PrivUnitG in the lower-dimensional space. In addition, we show that, by appropriately correlating the random projection matrices across devices, we can achieve fast server run-time. We mathematically analyze the error of the algorithm in terms of properties of the random projections, and study two instantiations. Lastly, our experiments for private mean estimation and private federated learning demonstrate that our algorithms empirically obtain nearly the same utility as optimal ones while having significantly lower communication and computational cost.

We adopt the natural assumption that the empirical NTK develops a block structure aligned with the class labels, i.e., samples within the same class have stronger