Large language models have shown an impressive societal impact owing to their excellent understanding and logical reasoning skills. However, such strong ability relies on a huge amount of computing resources, which makes it difficult to deploy LLMs on computing resource-constrained platforms. Currently, LLMs process each token equivalently, but we argue that not every word is equally important. Some words should not be allocated excessive computing resources, particularly for dispensable terms in simple questions. In this paper, we propose a novel dynamic inference paradigm for LLMs, namely D-LLMs, which adaptively allocate computing resources in token processing. We design a dynamic decision module for each transformer layer that decides whether a network unit should be executed or skipped. Moreover, we tackle the issue of adapting D-LLMs to real-world applications, specifically concerning the missing KV-cache when layers are skipped. To overcome this, we propose a simple yet effective eviction policy to exclude the skipped layers from subsequent attention calculations. The eviction policy not only enables D-LLMs to be compatible with prevalent applications but also reduces considerable storage resources. Experimentally, D-LLMs show superior performance, in terms of computational cost and KV storage utilization. It can reduce up to 45\% computational cost and KV storage on Q\&A, summarization, and math solving tasks, 50\% on commonsense reasoning tasks.

The inversion of diffusion model sampling, which aims to find the corresponding initial noise of a sample, plays a critical role in various tasks. Recently, several heuristic exact inversion samplers have been proposed to address the inexact inversion issue in a training-free manner. However, the theoretical properties of these heuristic samplers remain unknown and they often exhibit mediocre sampling quality. In this paper, we introduce a generic formulation, \emph{Bidirectional Explicit Linear Multi-step} (BELM) samplers, of the exact inversion samplers, which includes all previously proposed heuristic exact inversion samplers as special cases. The BELM formulation is derived from the variable-stepsize-variable-formula linear multi-step method via integrating a bidirectional explicit constraint. We highlight this bidirectional explicit constraint is the key of mathematically exact inversion. We systematically investigate the Local Truncation Error (LTE) within the BELM framework and show that the existing heuristic designs of exact inversion samplers yield sub-optimal LTE. Consequently, we propose the Optimal BELM (O-BELM) sampler through the LTE minimization approach. We conduct additional analysis to substantiate the theoretical stability and global convergence property of the proposed optimal sampler. Comprehensive experiments demonstrate our O-BELM sampler establishes the exact inversion property while achieving high-quality sampling. Additional experiments in image editing and image interpolation highlight the extensive potential of applying O-BELM in varying applications.

In this paper, we propose a provably efficient natural policy gradient algorithm called Spectral Dynamic Embedding Policy Optimization (\SDEPO) for two-player zero-sum stochastic Markov games with continuous state space and finite action space. In the policy evaluation procedure of our algorithm, a novel kernel embedding method is employed to construct a finite-dimensional linear approximations to the state-action value function. We explicitly analyze the approximation error in policy evaluation, and show that \SDEPO\ achieves an $\tilde{O}(\frac{1}{(1-\gamma)^3\epsilon})$ last-iterate convergence to the $\epsilon-$optimal Nash equilibrium, which is independent of the cardinality of the state space. The complexity result matches the best-known results for global convergence of policy gradient algorithms for single agent setting. Moreover, we also propose a practical variant of \SDEPO\ to deal with continuous action space and empirical results demonstrate the practical superiority of the proposed method.

The degradation of salinized land in western Jilin Province and its negative impact on the local and global environment have led to increasing interest in salinization restoration. Satellite remote sensing technology may provide up-to-date information on large-scale land salinization, and provide support for land protection and monitoring planning. In this case, the fusion of optical and radar remote sensing data may be precious because most of the land salinization degradation is located in areas with high cloud cover, which limiting the use of optical data. Radar data can “see-through” clouds, but the experience so far shows that it can't distinguish some types of land cover very well. At present, there are many optical and radar data fusion methods, but there is rare information about how to mapping land salinity using data fusion. To evaluate data fusion's potential, we applied classification method to sentinel-1 and sentinel-2 images for mapping the land salinity cover in Da'an City, Western Jilin Province. Based on our research results, we provide a beneficial method to help people involved in salinized land restoration to utilize the potential of big data.