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After Gross, Hacking, Keel, Kontsevich [GHKK18] introduced the theta basis which is shown to be indexed by its highest term exponent in cluster variables of any given seed, we are interested in all the non-vanishing exponents in these cluster variables. We prove that the coefficients of the exponents of any cluster variable of type $A_n$ are log-concave. We show that the cluster monomials of $A_2$ type are log-concave. As for larger generality, we conjecture that the log-concavity of cluster monomials is also true., Comment: 26 pages, 10 figures

The widespread use of large language models (LLMs) has sparked concerns about the potential misuse of AI-generated text, as these models can produce content that closely resembles human-generated text. Current detectors for AI-generated text (AIGT) lack robustness against adversarial perturbations, with even minor changes in characters or words causing a reversal in distinguishing between human-created and AI-generated text. This paper investigates the robustness of existing AIGT detection methods and introduces a novel detector, the Siamese Calibrated Reconstruction Network (SCRN). The SCRN employs a reconstruction network to add and remove noise from text, extracting a semantic representation that is robust to local perturbations. We also propose a siamese calibration technique to train the model to make equally confidence predictions under different noise, which improves the model's robustness against adversarial perturbations. Experiments on four publicly available datasets show that the SCRN outperforms all baseline methods, achieving 6.5\%-18.25\% absolute accuracy improvement over the best baseline method under adversarial attacks. Moreover, it exhibits superior generalizability in cross-domain, cross-genre, and mixed-source scenarios. The code is available at \url{https://github.com/CarlanLark/Robust-AIGC-Detector}., Comment: Accepted to ACL 2024 main conference

In this work, we propose an Implicit Regularization Enhancement (IRE) framework to accelerate the discovery of flat solutions in deep learning, thereby improving generalization and convergence. Specifically, IRE decouples the dynamics of flat and sharp directions, which boosts the sharpness reduction along flat directions while maintaining the training stability in sharp directions. We show that IRE can be practically incorporated with {\em generic base optimizers} without introducing significant computational overload. Experiments show that IRE consistently improves the generalization performance for image classification tasks across a variety of benchmark datasets (CIFAR-10/100, ImageNet) and models (ResNets and ViTs). Surprisingly, IRE also achieves a $2\times$ {\em speed-up} compared to AdamW in the pre-training of Llama models (of sizes ranging from 60M to 229M) on datasets including Wikitext-103, Minipile, and Openwebtext. Moreover, we provide theoretical guarantees, showing that IRE can substantially accelerate the convergence towards flat minima in Sharpness-aware Minimization (SAM)., Comment: 35 pages

We introduce a novel framework of LLM agents named AGILE (AGent that Interacts and Learns from Environments) designed to perform complex conversational tasks with users, leveraging LLMs, memory, tools, and interactions with experts. The agent's abilities include not only conversation but also reflection, utilization of tools, and consultation with experts. We formulate the construction of such an LLM agent as a reinforcement learning problem, in which the LLM serves as the policy model. We fine-tune the LLM using labeled data of actions and the PPO algorithm. We focus on question answering and release a dataset for agents called ProductQA, comprising challenging questions in online shopping. Our extensive experiments on ProductQA and MedMCQA show that AGILE agents based on 13B and 7B LLMs trained with PPO can outperform GPT-4 agents. Our ablation study highlights the indispensability of memory, tools, consultation, reflection, and reinforcement learning in achieving the agent's strong performance.

In this paper, we propose a novel Siamese Adversarial Network (SAN) architecture for automatic speech recognition, which aims at solving the difficulty of fuzzy audio recognition. Specifically, SAN constructs two sub-networks to differentiate the audio feature input and then introduces a loss to unify the output distribution of these sub-networks. Adversarial learning enables the network to capture more essential acoustic features and helps the models achieve better performance when encountering fuzzy audio input. We conduct numerical experiments with the SAN model on several datasets for the automatic speech recognition task. All experimental results show that the siamese adversarial nets significantly reduce the character error rate (CER). Specifically, we achieve a new state of art 4.37 CER without language model on the AISHELL-1 dataset, which leads to around 5% relative CER reduction. To reveal the generality of the siamese adversarial net, we also conduct experiments on the phoneme recognition task, which also shows the superiority of the siamese adversarial network.