Search

Current Large Language Models (LLMs) face inherent limitations due to their pre-defined context lengths, which impede their capacity for multi-hop reasoning within extensive textual contexts. While existing techniques like Retrieval-Augmented Generation (RAG) have attempted to bridge this gap by sourcing external information, they fall short when direct answers are not readily available. We introduce a novel approach that re-imagines information retrieval through dynamic in-context editing, inspired by recent breakthroughs in knowledge editing. By treating lengthy contexts as malleable external knowledge, our method interactively gathers and integrates relevant information, thereby enabling LLMs to perform sophisticated reasoning steps. Experimental results demonstrate that our method effectively empowers context-limited LLMs, such as Llama2, to engage in multi-hop reasoning with improved performance, which outperforms state-of-the-art context window extrapolation methods and even compares favorably to more advanced commercial long-context models. Our interactive method not only enhances reasoning capabilities but also mitigates the associated training and computational costs, making it a pragmatic solution for enhancing LLMs' reasoning within expansive contexts.

We prove that a quadratic polynomial with a bounded type Siegel disk and a quadratic post-critically finite polynomial are always mateable., Comment: 20 pages, 5 figures

Real-time semantic segmentation is a crucial research for real-world applications. However, many methods lay particular emphasis on reducing the computational complexity and model size, while largely sacrificing the accuracy. To tackle this problem, we propose a parallel inference network customized for semantic segmentation tasks to achieve a good trade-off between speed and accuracy. We employ a shallow backbone to ensure real-time speed, and propose three core components to compensate for the reduced model capacity to improve accuracy. Specifically, we first design a dual-pyramidal path architecture (Multi-level Feature Aggregation Module, MFAM) to aggregate multi-level features from the encoder to each scale, providing hierarchical clues for subsequent spatial alignment and corresponding in-network inference. Then, we build Recursive Alignment Module (RAM) by combining the flow-based alignment module with recursive upsampling architecture for accurate spatial alignment between multi-scale feature maps with half the computational complexity of the straightforward alignment method. Finally, we perform independent parallel inference on the aligned features to obtain multi-scale scores, and adaptively fuse them through an attention-based Adaptive Scores Fusion Module (ASFM) so that the final prediction can favor objects of multiple scales. Our framework shows a better balance between speed and accuracy than state-of-the-art real-time methods on Cityscapes and CamVid datasets. We also conducted systematic ablation studies to gain insight into our motivation and architectural design. Code is available at: https://github.com/Yanhua-Zhang/MFARANet., Comment: 15 pages, 9 figures and 12 Tables. Manuscript completed on April 30, 2022

In order to estimate qualitatively the influence of nonequilibrium evolution in relativistic heavy ion collisions, we use the three dimensional Ising model with Metropolis algorithm to study the evolution from nonequilibrium to equilibrium on the phase boundary. The evolution of order parameter approaches its equilibrium value exponentially, the same as that given by Langevin equation. The average relaxation time is defined which is demonstrated to well represent the relaxation time in dynamical equations. It is shown that the average relaxation time at critical temperature diverges as the zth power of system size. The third and the fourth cumulants of order parameter during the nonequilibrium evolution could be either positive or negative, depending on the observation time, consistent with dynamical models at T > Tc. It is found that the nonequilibrium evolution at T > Tc lasts very short, and the influence is weaker than that at T < Tc. Those qualitative features are instructive to determine experimentally the critical point and the phase boundary of QCD., Comment: 8 pages, 5 figures; add fig.3 and up date the eq.(9-10), and contents

We prove that a long iteration of rational maps is expanding near boundaries of bounded type Siegel disks. This leads us to extend Petersen's local connectivity result on the Julia sets of quadratic Siegel polynomials to a general case. A new key feature in the proof is that the puzzles are not used., Comment: 46 pages, 12 figures; Some details of the proofs are added

The critical point is a fixed point in finite-size scaling. To quantify the behaviour of such a fixed point, we define, at a given temperature and scaling exponent ratio, the width of scaled observables for different sizes. The minimum of the width reveals the position of fixed point, its corresponding phase transition temperature, and scaling exponent ratio. The value of this ratio tells the nature of fixed point, which can be a critical point, a point of the first order phase transition line, or a point of the crossover region. To demonstrate the effectiveness of this method, we apply it to three typical samples produced by the 3D three-state Potts model. Results show the method to be more precise and effective than conventional methods. Finally, we discuss a possible application at the beam energy scan program of relativistic heavy-Ion collision., Comment: v3: final version. v2: references update. 7 pages, 4 figures. arXiv admin note: text overlap with arXiv:1805.04311