A popular paradigm for offline Reinforcement Learning (RL) tasks is to first fit the offline trajectories to a sequence model, and then prompt the model for actions that lead to high expected return. In addition to obtaining accurate sequence models, this paper highlights that tractability, the ability to exactly and efficiently answer various probabilistic queries, plays an important role in offline RL. Specifically, due to the fundamental stochasticity from the offline data-collection policies and the environment dynamics, highly non-trivial conditional/constrained generation is required to elicit rewarding actions. While it is still possible to approximate such queries, we observe that such crude estimates undermine the benefits brought by expressive sequence models. To overcome this problem, this paper proposes Trifle (Tractable Inference for Offline RL), which leverages modern tractable generative models to bridge the gap between good sequence models and high expected returns at evaluation time. Empirically, Trifle achieves $7$ state-of-the-art scores and the highest average scores in $9$ Gym-MuJoCo benchmarks against strong baselines. Further, Trifle significantly outperforms prior approaches in stochastic environments and safe RL tasks with minimum algorithmic modifications.

Despite its widespread use in neural networks, error backpropagation has faced criticism for its lack of biological plausibility, suffering from issues such as the backward locking problem and the weight transport problem. These limitations have motivated researchers to explore more biologically plausible learning algorithms that could potentially shed light on how biological neural systems adapt and learn. Inspired by the counter-current exchange mechanisms observed in biological systems, we propose counter-current learning (CCL), a biologically plausible framework for credit assignment in deep learning. This framework employs a feedforward network to process input data and a feedback network to process targets, with each network enhancing the other through anti-parallel signal propagation. By leveraging the more informative signals from the bottom layer of the feedback network to guide the updates of the top layer of the feedforward network and vice versa, CCL enables the simultaneous transformation of source inputs to target outputs and the dynamic mutual influence of these transformations.Experimental results on MNIST, FashionMNIST, CIFAR10, CIFAR100, and STL-10 datasets using multi-layer perceptrons and convolutional neural networks demonstrate that CCL achieves comparable performance to other biological plausible algorithms while offering a more biologically realistic learning mechanism. Furthermore, we showcase the applicability of our approach to an autoencoder task, underscoring its potential for unsupervised representation learning.Our work presents a promising direction for biologically inspired and plausible learning algorithms, offering insights into the mechanisms of learning and adaptation in neural networks.

In steganography, selecting an optimal cover image--referred to as cover selection--is pivotal for effective message concealment. Traditional methods have typically employed exhaustive searches to identify images that conform to specific perceptual or complexity metrics. However, the relationship between these metrics and the actual message hiding efficacy of an image is unclear, often yielding less-than-ideal steganographic outcomes. Inspired by recent advancements in generative models, we introduce a novel cover selection framework, which involves optimizing within the latent space of pretrained generative models to identify the most suitable cover images, distinguishing itself from traditional exhaustive search methods. Our method shows significant advantages in message recovery and image quality. We also conduct an information-theoretic analysis of the generated cover images, revealing that message hiding predominantly occurs in low-variance pixels, reflecting the waterfilling algorithm's principles in parallel Gaussian channels.

We prove that single-parameter natural exponential families with subexponential tails are self-concordant with polynomial-sized parameters. For subgaussian natural exponential families we establish an exact characterization of the growth rate of the self-concordance parameter. Applying these findings to bandits allows us to fill gaps in the literature: We show that optimistic algorithms for generalized linear bandits enjoy regret bounds that are both second-order (scale with the variance of the optimal arm's reward distribution) and free of an exponential dependence on the bound of the problem parameter in the leading term. To the best of our knowledge, ours is the first regret bound for generalized linear bandits with subexponential tails, broadening the class of problems to include Poisson, exponential and gamma bandits.

While finetuning language models from pairwise preferences has proven remarkably effective, the underspecified nature of natural language presents critical challenges. Direct preference feedback is uninterpretable, difficult to provide where multidimensional criteria may apply, and often inconsistent, either because it is based on incomplete instructions or provided by diverse principals. To address these challenges, we consider the two-step preference modeling procedure that first resolves the under-specification by selecting a context, and then evaluates preference with respect to the chosen context. We decompose reward modeling error according to these two steps, which suggests that supervising context in addition to context-specific preference may be a viable approach to aligning models with diverse human preferences. For this to work, the ability of models to evaluate context-specific preference is critical. To this end, we contribute context-conditioned preference datasets and accompanying experiments that investigate the ability of language models to evaluate context-specific preference. Unlike past datasets, where context-specific preference is highly correlated with general preference, our preference reversal datasets disentangle context-specific and general preferences to isolate context-specific capabilities. We use our datasets to (1) show that existing preference models benefit from, but fail to fully consider, added context, (2) finetune a context-aware reward model with context-specific performance exceeding that of GPT-4 and Llama 3 70B, and (3) investigate the potential value of context-aware preference modeling.

Molecular property prediction (MPP) is integral to drug discovery and material science, but often faces the challenge of data scarcity in real-world scenarios. Addressing this, few-shot molecular property prediction (FSMPP) has been developed. Unlike other few-shot tasks, FSMPP typically employs a pre-trained molecular encoder and a context-aware classifier, benefiting from molecular pre-training and molecular context information.

The Procrustes-Wasserstein problem consists in matching two high-dimensional point clouds in an unsupervised setting, and has many applications in natural language processing and computer vision. We consider a planted model with two datasets $X,Y$ that consist of $n$ datapoints in $\mathbb{R}^d$, where $Y$ is a noisy version of $X$, up to an orthogonal transformation and a relabeling of the data points. This setting is related to the graph alignment problem in geometric models.In this work, we focus on the euclidean transport cost between the point clouds as a measure of performance for the alignment. We first establish information-theoretic results, in the high ($d \gg \log n$) and low ($d \ll \log n$) dimensional regimes. We then study computational aspects and propose the'Ping-Pong algorithm', alternatively estimating the orthogonal transformation and the relabeling, initialized via a Franke-Wolfe convex relaxation. We give sufficient conditions for the method to retrieve the planted signal after one single step. We provide experimental results to compare the proposed approach with the state-of-the-art method of Grave et al. (2019).

We study the optimal memorization capacity of modern Hopfield models and Kernelized Hopfield Models (KHMs), a transformer-compatible class of Dense Associative Memories.We present a tight analysis by establishing a connection between the memory configuration of KHMs and spherical codes from information theory. Specifically, we treat the stored memory set as a specialized spherical code.This enables us to cast the memorization problem in KHMs into a point arrangement problem on a hypersphere.We show that the optimal capacity of KHMs occurs when the feature space allows memories to form an optimal spherical code.This unique perspective leads to: 1. An analysis of how KHMs achieve optimal memory capacity, and identify corresponding necessary conditions. Importantly, we establish an upper capacity bound that matches the well-known exponential lower bound in the literature. This provides the first tight and optimal asymptotic memory capacity for modern Hopfield models.2. A sub-linear time algorithm $\mathtt{U}\text{-}\mathtt{Hop}$+ to reach KHMs' optimal capacity. 3. An analysis of the scaling behavior of the required feature dimension relative to the number of stored memories.These efforts improve both the retrieval capability of KHMs and the representation learning of corresponding transformers.Experimentally, we provide thorough numerical results to back up theoretical findings.

Solving parametric partial differential equations (PDEs) presents significant challenges for data-driven methods due to the sensitivity of spatio-temporal dynamics to variations in PDE parameters. Machine learning approaches often struggle to capture this variability. To address this, data-driven approaches learn parametric PDEs by sampling a very large variety of trajectories with varying PDE parameters. We first show that incorporating conditioning mechanisms for learning parametric PDEs is essential and that among them, \textit{adaptive conditioning}, allows stronger generalization. As existing adaptive conditioning methods do not scale well with respect to the number of parameters to adapt in the neural solver, we propose GEPS, a simple adaptation mechanism to boost GEneralization in Pde Solvers via a first-order optimization and low-rank rapid adaptation of a small set of context parameters. We demonstrate the versatility of our approach for both fully data-driven and for physics-aware neural solvers. Validation performed on a whole range of spatio-temporal forecasting problems demonstrates excellent performance for generalizing to unseen conditions including initial conditions, PDE coefficients, forcing terms and solution domain.

We introduce the framework of performative control, where the policy chosen by the controller affects the underlying dynamics of the control system.