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Deep Learning · Algorithms

Vincent Roulet, Atish Agarwala, Jean-Bastien Grill, Grzegorz Swirszcz, Mathieu Blondel, Fabian Pedregosa

Curvature information -- particularly, the largest eigenvalue of the lossHessian, known as the sharpness -- often forms the basis for learning ratetuners. However, recent work has shown that the curvature information undergoescomplex dynamics during training, going from a phase of increasing sharpness toeventual stabilization. We analyze the closed-loop feedback effect betweenlearning rate tuning and curvature. We find that classical learning rate tunersmay yield greater one-step loss reduction, yet they ultimately underperform inthe long term when compared to constant learning rates in the full batch regime.These models break the stabilization of the sharpness, which we explain using asimplified model of the joint dynamics of the learning rate and the curvature.To further investigate these effects, we introduce a new learning rate tuningmethod, Curvature Dynamics Aware Tuning (CDAT), which prioritizes long termcurvature stabilization over instantaneous progress on the objective. In thefull batch regime, CDAT shows behavior akin to prefixed warm-up schedules on deeplearning objectives, outperforming tuned constant learning rates. In the minibatch regime, we observe that stochasticity introduces confounding effects thatexplain the previous success of some learning rate tuners at appropriate batchsizes. Our findings highlight the critical role of understanding the jointdynamics of the learning rate and curvature, beyond greedy minimization, todiagnose failures and design effective adaptive learning rate tuners.

Probabilistic Methods · Bayesian Models and Methods

Trevor Campbell

Bayesian coresets speed up posterior inference in the large-scale data regime by approximating the full-data log-likelihood function with a surrogate log-likelihood based on a small, weighted subset of the data. But while Bayesian coresets and methods for construction are applicable in a wide range of models, existing theoretical analysis of the posterior inferential error incurred by coreset approximations only apply in restrictive settings---i.e., exponential family models, or models with strong log-concavity and smoothness assumptions. This work presents general upper and lower bounds on the Kullback-Leibler (KL) divergence of coreset approximations that reflect the full range of applicability of Bayesian coresets. The lower bounds require only mild model assumptions typical of Bayesian asymptotic analyses, while the upper bounds require the log-likelihood functions to satisfy a generalized subexponentiality criterion that is weaker than conditions used in earlier work. The lower bounds are applied to obtain fundamental limitations on the quality of coreset approximations, and to provide a theoretical explanation for the previously-observed poor empirical performance of importance sampling-based construction methods. The upper bounds are used to analyze the performance of recent subsample-optimize methods. The flexibility of the theory is demonstrated in validation experiments involving multimodal, unidentifiable, heavy-tailed Bayesian posterior distributions.

Language · Generation

Zifan Song, Yudong Wang, Wenwei Zhang, Kuikun Liu, Chengqi Lyu, Demin Song, Qipeng Guo, Hang Yan, Dahua Lin, Kai Chen 等

Open-source Large Language Models (LLMs) and their specialized variants, particularly Code LLMs, have recently delivered impressive performance. However, previous Code LLMs are typically fine-tuned on single-source data with limited quality and diversity, which may insufficiently elicit the potential of pre-trained Code LLMs. In this paper, we present AlchemistCoder, a series of Code LLMs with enhanced code generation and generalization capabilities fine-tuned on multi-source data. To achieve this, we pioneer to unveil inherent conflicts among the various styles and qualities in multi-source code corpora and introduce data-specific prompts with hindsight relabeling, termed AlchemistPrompts, to harmonize different data sources and instruction-response pairs. Additionally, we propose incorporating the data construction process into the fine-tuning data as code comprehension tasks, including instruction evolution, data filtering, and code review. Extensive experiments demonstrate that AlchemistCoder holds a clear lead among all models of the same size (6.7B/7B) and rivals or even surpasses larger models (15B/33B/70B), showcasing the efficacy of our method in refining instruction-following capabilities and advancing the boundaries of code intelligence. Source code and models are available at https://github.com/InternLM/AlchemistCoder.

Deep Learning · Algorithms

Gavia Gray, aman tiwari, Shane Bergsma, Joel Hestness

Per-example gradient norms are a vital ingredient for estimating gradient noise scale (GNS) with minimal variance. Observing the tensor contractions required to compute them, we propose a method with minimal FLOPs in 3D or greater tensor regimes by simultaneously computing the norms while computing the parameter gradients. Using this method we are able to observe the GNS of different layers at higher accuracy than previously possible. We find that the total GNS of contemporary transformer models is predicted well by the GNS of only the normalization layers. As a result, focusing only on the normalization layer, we develop a custom kernel to compute the per-example gradient norms while performing the LayerNorm backward pass with zero throughput overhead. Tracking GNS on only those layers, we are able to guide a practical batch size schedule that reduces training time by 18% on a Chinchilla-optimal language model.

Applications

Lei Huang, Lei Xiong, Na Sun, Zunpeng Liu, Ka-Chun Wong, Manolis Kellis

The rapid advancement of single-cell ATAC sequencing (scATAC-seq) technologies holds great promise for investigating the heterogeneity of epigenetic landscapes at the cellular level. The amplification process in scATAC-seq experiments often introduces noise due to dropout events, which results in extreme sparsity that hinders accurate analysis. Consequently, there is a significant demand for the generation of high-quality scATAC-seq data in silico. Furthermore, current methodologies are typically task-specific, lacking a versatile framework capable of handling multiple tasks within a single model. In this work, we propose ATAC-Diff, a versatile framework, which is based on a diffusion model conditioned on the latent auxiliary variables to adapt for various tasks. ATAC-Diff is the first diffusion model for the scATAC-seq data generation and analysis, composed of auxiliary modules encoding the latent high-level variables to enable the model to learn the semantic information to sample high-quality data. Gaussian Mixture Model (GMM) as the latent prior and auxiliary decoder, the yield variables reserve the refined genomic information beneficial for downstream analyses. Another innovation is the incorporation of mutual information between observed and hidden variables as a regularization term to prevent the model from decoupling from latent variables. Through extensive experiments, we demonstrate that ATAC-Diff achieves high performance in both generation and analysis tasks, outperforming state-of-the-art models.

Computer Vision

JI Yuzhe, Yijie CHEN, Liuqing Yang, Ding Rui, Meng Yang, Xinhu Zheng

Recent advancements in 3D perception have led to a proliferation of network architectures, particularly those involving multi-modal fusion algorithms. While these fusion algorithms improve accuracy, their complexity often impedes real-time performance. This paper introduces VeXKD, an effective and Versatile framework that integrates Cross-Modal Fusion with Knowledge Distillation. VeXKD applies knowledge distillation exclusively to the Bird's Eye View (BEV) feature maps, enabling the transfer of cross-modal insights to single-modal students without additional inference time overhead. It avoids volatile components that can vary across various 3D perception tasks and student modalities, thus improving versatility. The framework adopts a modality-general cross-modal fusion module to bridge the modality gap between the multi-modal teachers and single-modal students. Furthermore, leveraging byproducts generated during fusion, our BEV query guided mask generation network identifies crucial spatial locations across different BEV feature maps in a data-driven manner, significantly enhancing the effectiveness of knowledge distillation. Extensive experiments on the nuScenes dataset demonstrate notable improvements, with up to 6.9\%/4.2\% increase in mAP and NDS for 3D detection tasks and up to 4.3\% rise in mIoU for BEV map segmentation tasks, narrowing the performance gap with multi-modal models.

Computer Vision

Bin Fan, Jiaoyang Yin, Yuchao Dai, Chao Xu, Tiejun Huang, Boxin Shi

The spiking camera is an emerging neuromorphic vision sensor that records high-speed motion scenes by asynchronously firing continuous binary spike streams. Prevailing image reconstruction methods, generating intermediate frames from these spike streams, often rely on complex step-by-step network architectures that overlook the intrinsic collaboration of spatio-temporal complementary information. In this paper, we propose an efficient spatio-temporal interactive reconstruction network to jointly perform inter-frame feature alignment and intra-frame feature filtering in a coarse-to-fine manner. Specifically, it starts by extracting hierarchical features from a concise hybrid spike representation, then refines the motion fields and target frames scale-by-scale, ultimately obtaining a full-resolution output. Meanwhile, we introduce a symmetric interactive attention block and a multi-motion field estimation block to further enhance the interaction capability of the overall network. Experiments on synthetic and real-captured data show that our approach exhibits excellent performance while maintaining low model complexity.

Causality

Feng Xie, Zhen Yao, Lin Xie, Yan Zeng, Zhi Geng

We consider the challenging problem of estimating causal effects from purely observational data in the bi-directional Mendelian randomization (MR), where some invalid instruments, as well as unmeasured confounding, usually exist. To address this problem, most existing methods attempt to find proper valid instrumental variables (IVs) for the target causal effect by expert knowledge or by assuming that the causal model is a one-directional MR model. As such, in this paper, we first theoretically investigate the identification of the bi-directional MR from observational data. In particular, we provide necessary and sufficient conditions under which valid IV sets are correctly identified such that the bi-directional MR model is identifiable, including the causal directions of a pair of phenotypes (i.e., the treatment and outcome).Moreover, based on the identification theory, we develop a cluster fusion-like method to discover valid IV sets and estimate the causal effects of interest.We theoretically demonstrate the correctness of the proposed algorithm.Experimental results show the effectiveness of our method for estimating causal effects in both one-directional and bi-directional MR models.

Neuroscience, Cognitive Science

Dongyang Li, Chen Wei, Shiying Li, Jiachen Zou, Quanying Liu

How to decode human vision through neural signals has attracted a long-standing interest in neuroscience and machine learning. Modern contrastive learning and generative models improved the performance of visual decoding and reconstruction based on functional Magnetic Resonance Imaging (fMRI). However, the high cost and low temporal resolution of fMRI limit their applications in brain-computer interfaces (BCIs), prompting a high need for visual decoding based on electroencephalography (EEG). In this study, we present an end-to-end EEG-based visual reconstruction zero-shot framework, consisting of a tailored brain encoder, called the Adaptive Thinking Mapper (ATM), which projects neural signals from different sources into the shared subspace as the clip embedding, and a two-stage multi-pipe EEG-to-image generation strategy. In stage one, EEG is embedded to align the high-level clip embedding, and then the prior diffusion model refines EEG embedding into image priors. A blurry image also decoded from EEG for maintaining the low-level feature. In stage two, we input both the high-level clip embedding, the blurry image and caption from EEG latent to a pre-trained diffusion model. Furthermore, we analyzed the impacts of different time windows and brain regions on decoding and reconstruction. The versatility of our framework is demonstrated in the magnetoencephalogram (MEG) data modality. The experimental results indicate that our EEG-based visual zero-shot framework achieves SOTA performance in classification, retrieval and reconstruction, highlighting the portability, low cost, and high temporal resolution of EEG, enabling a wide range of BCI applications. Our code is available at https://github.com/ncclab-sustech/EEG_Image_decode.

Miscellaneous Aspects of Machine Learning · Kernel methods

Anna Korba, Francis Bach, Clémentine CHAZAL

In this paper, we study the statistical and geometrical properties of the Kullback-Leibler divergence with kernel covariance operators (KKL) introduced by [Bach, 2022, Information Theory with Kernel Methods]. Unlike the classical Kullback-Leibler (KL) divergence that involves density ratios, the KKL compares probability distributions through covariance operators (embeddings) in a reproducible kernel Hilbert space (RKHS), and compute the Kullback-Leibler quantum divergence. This novel divergence hence shares parallel but different aspects with both the standard Kullback-Leibler between probability distributions and kernel embeddings metrics such as the maximum mean discrepancy. A limitation faced with the original KKL divergence is its inability to be defined for distributions with disjoint supports. To solve this problem, we propose in this paper a regularised variant that guarantees that divergence is well defined for all distributions. We derive bounds that quantify the deviation of the regularised KKL to the original one, as well as concentration bounds. In addition, we provide a closed-form expression for the regularised KKL, specifically applicable when the distributions consist of finite sets of points, which makes it implementable. Furthermore, we derive a Wasserstein gradient descent scheme of the KKL divergence in the case of discrete distributions, and study empirically its properties to transport a set of points to a target distribution.

Theory · Game Theory

Wei Tang, Haifeng Xu, Ruimin Zhang, Derek Zhu

Prophet inequality concerns a basic optimal stopping problem and states that simple threshold stopping policies --- i.e., accepting the first reward larger than a certain threshold --- can achieve tight $\frac{1}{2}$-approximation to the optimal prophet value. Motivated by its economic applications, this paper studies the robustness of this approximation to natural strategic manipulations in which each random reward is associated with a self-interested player who may selectively reveal his realized reward to the searcher in order to maximize his probability of being selected. We say a threshold policy is $\alpha$(-strategically)-robust if it (a) achieves the $\alpha$-approximation to the prophet value for strategic players; and (b) meanwhile remains a $\frac{1}{2}$-approximation in the standard non-strategic setting.Starting with a characterization of each player's optimal information revealing strategy, we demonstrate the intrinsic robustness of prophet inequalities to strategic reward signaling through the following results:(1) for arbitrary reward distributions, there is a threshold policy that is $\frac{1-\frac{1}{e}}{2}$-robust, and this ratio is tight;(2) for i.i.d. reward distributions, there is a threshold policy that is $\frac{1}{2}$-robust, which is tight for the setting; and (3) for log-concave (but non-identical) reward distributions, the $\frac{1}{2}$-robustness can also be achieved under certain regularity assumptions.

Language

Benjamin Minixhofer, Edoardo Maria Ponti, Ivan Vulić

Language models (LMs) are bound to their tokenizer, which maps raw text to a sequence of vocabulary items (tokens). This restricts their flexibility: for example, LMs trained primarily on English may still perform well in other natural and programming languages, but have vastly decreased efficiency due to their English-centric tokenizer. To mitigate this, we should be able to swap the original LM tokenizer with an arbitrary one, on the fly, without degrading performance. Hence, in this work we define a new problem: Zero-Shot Tokenizer Transfer (ZeTT). The challenge at the core of ZeTT is finding embeddings for the tokens in the vocabulary of the new tokenizer. Since prior heuristics for initializing embeddings often perform at chance level in a ZeTT setting, we propose a new solution: we train a hypernetwork taking a tokenizer as input and predicting the corresponding embeddings. We empirically demonstrate that the hypernetwork generalizes to new tokenizers both with encoder (e.g., XLM-R) and decoder LLMs (e.g., Mistral-7B). Our method comes close to the original models' performance in cross-lingual and coding tasks while markedly reducing the length of the tokenized sequence. We also find that the remaining gap can be quickly closed by continued training on less than 1B tokens. Finally, we show that a ZeTT hypernetwork trained for a base (L)LM can also be applied to fine-tuned variants without extra training. Overall, our results make substantial strides toward detaching LMs from their tokenizer.

Generative Models · Diffusion models

Huayang Huang, Yu Wu, Qian Wang

Watermarking generative content serves as a vital tool for authentication, ownership protection, and mitigation of potential misuse. Existing watermarking methods face the challenge of balancing robustness and concealment. They empirically inject a watermark that is both invisible and robust and passively achieve concealment by limiting the strength of the watermark, thus reducing the robustness. In this paper, we propose to explicitly introduce a watermark hiding process to actively achieve concealment, thus allowing the embedding of stronger watermarks. To be specific, we implant a robust watermark in an intermediate diffusion state and then guide the model to hide the watermark in the final generated image. We employ an adversarial optimization algorithm to produce the optimal hiding prompt guiding signal for each watermark. The prompt embedding is optimized to minimize artifacts in the generated image, while the watermark is optimized to achieve maximum strength. The watermark can be verified by reversing the generation process. Experiments on various diffusion models demonstrate the watermark remains verifiable even under significant image tampering and shows superior invisibility compared to other state-of-the-art robust watermarking methods.

Learning Theory

Shuyao Li, Sushrut Karmalkar, Ilias Diakonikolas, Jelena Diakonikolas

We study the problem of learning a single neuron with respect to the $L_2^2$-loss in the presence of adversarial distribution shifts, where the labels can be arbitrary, and the goal is to find a "best-fit" function.More precisely, given training samples from a reference distribution $p_0$, the goal is to approximate the vector $\mathbf{w}^*$which minimizes the squared loss with respect to the worst-case distribution that is close in $\chi^2$-divergence to $p_{0}$.We design a computationally efficient algorithm that recovers a vector $ \hat{\mathbf{w}}$satisfying $\mathbb{E}\_{p^*} (\sigma(\hat{\mathbf{w}} \cdot \mathbf{x}) - y)^2 \leq C \hspace{0.2em} \mathbb{E}\_{p^*} (\sigma(\mathbf{w}^* \cdot \mathbf{x}) - y)^2 + \epsilon$, where $C>1$ is a dimension-independent constant and $(\mathbf{w}^*, p^*)$ is the witness attaining the min-max risk$\min_{\mathbf{w}:\|\mathbf{w}\| \leq W} \max\_{p} \mathbb{E}\_{(\mathbf{x}, y) \sim p} (\sigma(\mathbf{w} \cdot \mathbf{x}) - y)^2 - \nu \chi^2(p, p_0)$.Our algorithm follows the primal-dual framework and is designed by directly bounding the risk with respect to the original, nonconvex $L_2^2$ loss.From an optimization standpoint, our work opens new avenues for the design of primal-dual algorithms under structured nonconvexity.

Trustworthy Machine Learning

Biqing Qi, Yiang Luo, Junqi Gao, Pengfei Li, Kai Tian, Zhiyuan Ma, Bowen Zhou

Deep State Space Models (SSMs) have proven effective in numerous task scenarios but face significant security challenges due to Adversarial Perturbations (APs) in real-world deployments. Adversarial Training (AT) is a mainstream approach to enhancing Adversarial Robustness (AR) and has been validated on various traditional DNN architectures. However, its effectiveness in improving the AR of SSMs remains unclear.While many enhancements in SSM components, such as integrating Attention mechanisms and expanding to data-dependent SSM parameterizations, have brought significant gains in Standard Training (ST) settings, their potential benefits in AT remain unexplored. To investigate this, we evaluate existing structural variants of SSMs with AT to assess their AR performance. We observe that pure SSM structures struggle to benefit from AT, whereas incorporating Attention yields a markedly better trade-off between robustness and generalization for SSMs in AT compared to other components. Nonetheless, the integration of Attention also leads to Robust Overfitting (RO) issues.To understand these phenomena, we empirically and theoretically analyze the output error of SSMs under AP. We find that fixed-parameterized SSMs have output error bounds strictly related to their parameters, limiting their AT benefits, while input-dependent SSMs may face the problem of error explosion. Furthermore, we show that the Attention component effectively scales the output error of SSMs during training, enabling them to benefit more from AT, but at the cost of introducing RO due to its high model complexity.Inspired by this, we propose a simple and effective Adaptive Scaling (AdS) mechanism that brings AT performance close to Attention-integrated SSMs without introducing the issue of RO.

Huaijin Wu, Xinyu Ye, Junchi Yan

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 $\mathcal{O}(C\log n)$ ($n$ 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 further design to encode conditions into quantum circuits for property-specified generation. Experimentally, our model could generate plausible 3-D molecules and achieve competitive quantitative performance with significantly reduced circuit parameters compared with their classic counterparts. The source code will be released upon publication.

Trustworthy Machine Learning

Elias Stengel-Eskin, Peter Hase, Mohit Bansal

When answering questions, large language models (LLMs) can convey not only an answer to the question, but a level of confidence about the answer being correct. This includes explicit markers of confidence (e.g. giving a numeric confidence score) as well as implicit markers, like using an authoritative tone or elaborating with additional knowledge of a subject. For LLMs to be trustworthy sources of knowledge, the confidence they convey should match their actual expertise on a topic; however, this is currently not the case, with most models tending towards overconfidence. To calibrate both implicit and explicit confidence markers, we introduce a pragmatic, listener-aware finetuning method (LACIE) that directly models the listener, considering not only whether an answer is right, but whether it will be accepted by a listener. Specifically, we cast calibration as a preference optimization problem, creating data via a two-agent speaker-listener game, where a speaker model’s outputs are judged by a simulated listener. We then finetune three different LLMs (Mistral-7B, Llama3-8B, Llama3-70B) with LACIE, and show that the models resulting from this multi-agent optimization are better calibrated on TriviaQA with respect to a simulated listener. Crucially, these trends transfer to human listeners, helping them correctly predict model correctness: we conduct a human evaluation where annotators accept or reject an LLM’s answers to trivia questions, finding that training with LACIE results in 47% fewer incorrect answers being accepted while maintaining the same level of acceptance for correct answers. Furthermore, LACIE generalizes to another dataset, resulting in a large increase in truthfulness on TruthfulQA when trained on TriviaQA. Our analysis indicates that LACIE leads to a better separation in confidence between correct and incorrect examples. Qualitatively, we find that a LACIE-trained model hedges more when uncertain and adopts implicit cues to signal certainty when it is correct, such as using an authoritative tone or including details. Finally, finetuning with our listener- aware method leads to an emergent increase in model abstention (e.g. saying “I don’t know”) for answers that are likely to be wrong, trading recall for precision.

Neuroscience, Cognitive Science

Xuan-Hao Liu, Yan-Kai Liu, Yansen Wang, Kan Ren, Hanwen Shi, Zilong Wang, Dongsheng Li, Bao-Liang Lu, Wei-Long Zheng

Our visual experience in daily life are dominated by dynamic change. Decoding such dynamic information from brain activity can enhance the understanding of the brain’s visual processing system. However, previous studies predominately focus on reconstructing static visual stimuli. In this paper, we explore to decode dynamic visual perception from electroencephalography (EEG), a neuroimaging technique able to record brain activity with high temporal resolution (1000 Hz) for capturing rapid changes in brains. Our contributions are threefold: Firstly, we develop a large dataset recording signals from 20 subjects while they were watching 1400 dynamic video clips of 40 concepts. This dataset fills the gap in the lack of EEG-video pairs. Secondly, we annotate each video clips to investigate the potential for decoding some specific meta information (e.g., color, dynamic, human or not) from EEG. Thirdly, we propose a novel baseline EEG2Video for video reconstruction from EEG signals that better aligns dynamic movements with high temporal resolution brain signals by Seq2Seq architecture. EEG2Video achieves a 2-way accuracy of 79.8% in semantic classification tasks and 0.256 in structural similarity index (SSIM). Overall, our works takes an important step towards decoding dynamic visual perception from EEG signals. Our dataset and code will be released soon.

Reinforcement Learning · Everything Else

Daehee Lee, Minjong Yoo, Woo Kyung Kim, Wonje Choi, Honguk Woo

Continual Imitation Learning (CiL) involves extracting and accumulating task knowledge from demonstrations across multiple stages and tasks to achieve a multi-task policy. With recent advancements in foundation models, there has been a growing interest in adapter-based CiL approaches, where adapters are established parameter-efficiently for tasks newly demonstrated. While these approaches isolate parameters for specific tasks and tend to mitigate catastrophic forgetting, they limit knowledge sharing among different demonstrations. We introduce IsCiL, an adapter-based CiL framework that addresses this limitation of knowledge sharing by incrementally learning shareable skills from different demonstrations, thus enabling sample-efficient task adaptation using the skills particularly in non-stationary CiL environments. In IsCiL, demonstrations are mapped into the state embedding space, where proper skills can be retrieved upon input states through prototype-based memory. These retrievable skills are incrementally learned on their corresponding adapters. Our CiL experiments with complex tasks in the Franka-Kitchen and Meta-World demonstrate the robust performance of IsCiL in both task adaptation and sample-efficiency. We also show a simple extension of IsCiL for task unlearning scenarios.

Hongzhan Lin, Ang Lv, yuhan chen, chen zhu, Yang Song, Hengshu Zhu, Rui Yan

Many studies have revealed that large language models (LLMs) exhibit uneven awareness of different contextual positions. Their limited context awareness can lead to overlooking critical information and subsequent task failures. While several approaches have been proposed to enhance LLMs' context awareness, achieving both effectiveness and efficiency remains challenging. In this paper, for LLMs utilizing RoPE as position embeddings, we introduce a novel method called "Mixture of In-Context Experts" (MoICE) to address this challenge. MoICE comprises two key components: a router integrated into each attention head within LLMs and a lightweight router-only training optimization strategy:(1) MoICE views each RoPE angle as an 'in-context' expert, demonstrated to be capable of directing the attention of a head to specific contextual positions. Consequently, each attention head flexibly processes tokens using multiple RoPE angles dynamically selected by the router to attend to the needed positions. This approach mitigates the risk of overlooking essential contextual information. (2) The router-only training strategy entails freezing LLM parameters and exclusively updating routers for only a few steps. When applied to open-source LLMs including Llama and Mistral, MoICE surpasses prior methods across multiple tasks on long context understanding and generation, all while maintaining commendable inference efficiency.