In this paper, we introduce analytic federated learning (AFL), a new training paradigm that brings analytical (i.e., closed- form) solutions to the federated learning (FL) with pre-trained models. Our AFL draws inspiration from analytic learning—a gradient-free technique that trains neural networks with analytical solutions in one epoch. In the local client training stage, the AFL facilitates a one-epoch training, eliminating the necessity for multi-epoch updates. In the aggregation stage, we derive an absolute aggregation (AA) law. This AA law allows a single-round aggregation, reducing heavy communication overhead and achieving fast convergence by removing the need for multiple aggregation rounds. More importantly, the AFL exhibits a property that invariance to data partitioning, meaning that regardless of how the full dataset is distributed among clients, the aggregated result remains identical. This could spawn various potentials, such as data heterogeneity invariance and client-number invariance. We conduct experiments across various FL settings including extremely non-IID ones, and scenarios with a large number of clients (e.g., ≥ 1000). In all these settings, our AFL constantly performs competitively while existing FL techniques encounter various obstacles. Our codes are available at https://github.com/ZHUANGHP/Analytic-federated-learning.

Exemplar-Free Class-Incremental Learning (EFCIL) aims to sequentially learn from distinct categories without retaining exemplars but easily suffers from catastrophic forgetting of learned knowledge. While existing EFCIL methods leverage knowledge distillation to alleviate forgetting, they still face two critical challenges: semantic shift and decision bias. Specifically, the embeddings of old tasks shift in the embedding space after learning new tasks, and the classifier becomes biased towards new tasks due to training solely with new data, hindering the balance between old and new knowledge. To address these issues, we propose the Dual-Projection Shift Estimation and Classifier Reconstruction (DPCR) approach for EFCIL. DPCR effectively estimates semantic shift through a dual-projection, which combines a learnable transformation with a row-space projection to capture both task-wise and category-wise shifts. Furthermore, to mitigate decision bias, DPCR employs ridge regression to reformulate a classifier reconstruction process. This reconstruction exploits previous in covariance and prototype of each class after calibration with estimated shift, thereby reducing decision bias. Extensive experiments demonstrate that, on various datasets, DPCR effectively balances old and new tasks, outperforming state-of-the-art EFCIL methods. Our codes are available at https://github.com/RHe502/ICML25-DPCR.

Class-incremental learning (CIL) enables models to learn new classes continually without forgetting previously acquired knowledge. Multi-label CIL (MLCIL) extends CIL to a real-world scenario where each sample may belong to multiple classes, introducing several challenges: label absence, which leads to incomplete historical information due to missing labels, and class imbalance, which results in the model bias toward majority classes. To address these challenges, we propose Label-Augmented Analytic Adaptation (L3A), an exemplar-free approach without storing past samples. L3A integrates two key modules. The pseudo-label (PL) module implements label augmentation by generating pseudo-labels for current phase samples, addressing the label absence problem. The weighted analytic classifier (WAC) derives a closed-form solution for neural networks. It introduces sample-specific weights to adaptively balance the class contribution and mitigate class imbalance. Experiments on MS-COCO and PASCAL VOC datasets demonstrate that L3A outperforms existing methods in MLCIL tasks. Our code is available at https://github.com/scut-zx/L3A.

Saturated rocks typically contain pores of various geometric shapes. The complex pore structure not only significantly affects the elastic and seismic response characteristics of rocks but also influences the accuracy of petrophysical parameter predictions. Existing rock physics inversion methods struggle to quantitatively describe pore type distributions and their geological implications, and there remains a lack of comprehensive inversion methods for simultaneously determining pore types and petrophysical parameters in porous reservoirs. Porosity, pore structure, and fluid properties collectively reflect the reservoir's physical attributes, pore space complexity, and pore fluid types. Establishing an accurate relationship between seismic parameters and reservoir pore characteristics can enhance the reliability of reservoir predictions. In this paper, taking the oil and gas-bearing sandstone reservoir as an example, the influence of reservoir pore space geometry on rock elastic parameters and seismic AVO reflection coefficients is theoretically considered from the perspective of seismic petrophysics, and the relationship between seismic reflection coefficient and effective pore structure is established. By combining the Biot-Gassmann pore theory and Russell's linear approximation equation, a target functional containing the fluid term and pore structure was derived. Based on the stochastic inversion algorithm, the inversion of the fluid term and pore structure is stably achieved.

Class-incremental learning (CIL) under an exemplar-free constraint has presented a significant challenge. Existing methods adhering to this constraint are prone to catastrophic forgetting, far more so than replay-based techniques that retain access to past samples. In this paper, to solve the exemplar-free CIL problem, we propose a Dual-Stream Analytic Learning (DS-AL) approach. The DS-AL contains a main stream offering an analytical (i.e., closed-form) linear solution, and a compensation stream improving the inherent under-fitting limitation due to adopting linear mapping. The main stream redefines the CIL problem into a Concatenated Recursive Least Squares (C-RLS) task, allowing an equivalence between the CIL and its joint-learning counterpart. The compensation stream is governed by a Dual-Activation Compensation (DAC) module. This module re-activates the embedding with a different activation function from the main stream one, and seeks fitting compensation by projecting the embedding to the null space of the main stream's linear mapping. Empirical results demonstrate that the DS-AL, despite being an exemplar-free technique, delivers performance comparable with or better than that of replay-based methods across various datasets, including CIFAR-100, ImageNet-100 and ImageNet-Full. Additionally, the C-RLS' equivalent property allows the DS-AL to execute CIL in a phase-invariant manner. This is evidenced by a never-before-seen 500-phase CIL ImageNet task, which performs on a level identical to a 5-phase one. Our codes are available at https://github.com/ZHUANGHP/Analytic-continual-learning.

Large language models (LLMs) have shown dominant performance in various language tasks, including code-writing, machine translation, and semantic comprehension. With prompt engineering, LLMs can also comprehend complex tasks and translate them into executable code. These powers offer great potential for controlling the motion of robots. In this paper, we focus on leveraging the ability of LLMs, prompt engineering, and predefined robot action APIs to facilitate high-level motion planning for quadruped robots. With LLMs, we enable the robot to autonomously plan and execute sophisticated actions based on the comprehension of effective prompts. Through various experiments and evaluations, we demonstrate the effectiveness and adaptability of our approach in handling intricate motion tasks. Our research contributes to the advancement of intelligent robotics and paves the way for more versatile quadruped robots in real-world scenarios.

Class incremental learning (CIL) trains a network on sequential tasks with separated categories in each task but suffers from catastrophic forgetting, where models quickly lose previously learned knowledge when acquiring new tasks. The generalized CIL (GCIL) aims to address the CIL problem in a more real-world scenario, where incoming data have mixed data categories and unknown sample size distribution. Existing attempts for the GCIL either have poor performance or invade data privacy by saving exemplars. In this paper, we propose a new exemplar-free GCIL technique named generalized analytic continual learning (GACL). The GACL adopts analytic learning (a gradient-free training technique) and delivers an analytical (i.e., closed-form) solution to the GCIL scenario. This solution is derived via decomposing the incoming data into exposed and unexposed classes, thereby attaining a weight-invariant property, a rare yet valuable property supporting an equivalence between incremental learning and its joint training. Such an equivalence is crucial in GCIL settings as data distributions among different tasks no longer pose challenges to adopting our GACL. Theoretically, this equivalence property is validated through matrix analysis tools. Empirically, we conduct extensive experiments where, compared with existing GCIL methods, our GACL exhibits a consistently leading performance across various datasets and GCIL settings. Source code is available at https://github.com/CHEN-YIZHU/GACL.

Online Class Incremental Learning (OCIL) aims to train models incrementally, where data arrive in mini-batches, and previous data are not accessible. A major challenge in OCIL is Catastrophic Forgetting, i.e., the loss of previously learned knowledge. Among existing baselines, replay-based methods show competitive results but requires extra memory for storing exemplars, while exemplar-free (i.e., data need not be stored for replay in production) methods are resource friendly but often lack accuracy. In this paper, we propose an exemplar-free approach—Forward-only Online Analytic Learning (F-OAL). Unlike traditional methods, F-OAL does not rely on back-propagation and is forward-only, significantly reducing memory usage and computational time. Cooperating with a pre-trained frozen encoder with Feature Fusion, F-OAL only needs to update a linear classifier by recursive least square. This approach simultaneously achieves high accuracy and low resource consumption. Extensive experiments on bench mark datasets demonstrate F-OAL’s robust performance in OCIL scenarios. Code is available at: https://github.com/liuyuchen-cz/F-OAL

Few-shot class incremental learning (FSCIL) aims to address catastrophic forgetting during class incremental learning in a few-shot learning setting. In this paper, we approach the FSCIL by adopting analytic learning, a technique that converts network training into linear problems. This is inspired by the fact that the recursive implementation (batch-by-batch learning) of analytic learning gives identical weights to that produced by training on the entire dataset at once. The recursive implementation and the weight-identical property highly resemble the FSCIL setting (phase-by-phase learning) and its goal of avoiding catastrophic forgetting. By bridging the FSCIL with the analytic learning, we propose a Gaussian kernel embedded analytic learning (GKEAL) for FSCIL. The key components of GKEAL include the kernel analytic module which allows the GKEAL to conduct FSCIL in a recursive manner, and the augmented feature concatenation module that balances the preference between old and new tasks especially effectively under the few-shot setting. Our experiments show that the GKEAL gives state-of-the-art performance on several benchmark datasets.

The essentiality of diffraction wavefront in structural mapping has been perceived, mainly because of its imaging potential for small structural variations and microscopic discontinuities. However, full extraction of ground penetrating radar (GPR) diffractions cannot be done perfectly even in theory as the faint components are typically masked by the more dominant reflections, resulting in a resolution loss of minutiae features. To address these issues, this letter develops a semblance-based coherence analysis framework for GPR diffraction wavefront reconstruction and full waveform inversion (FWI). Specifically, adaptive amplitude restoration is initially performed using the mean instant amplitude for analytic attenuation function derivation, which is followed by modified multitrace coherence stacking. Diffraction reconstruction is then executed with corrective factors determined by EM semblance attributes, while being assessed by quantified indices for reconstruction performance. The proposed framework is tested for validity and practicality with a synthetic model and laboratory experiment by comparing the conventional FWI and the diffraction driven FWI. The results present a high-resolution image of diffraction occurrences even with a homogeneous initial model, and more intuitively show a higher-resolution image even with a suboptimal initial model by diffraction-driven permittivity analysis. These encouraging results could potentially enable a hybrid inversion which benefits from reconstructing both GPR reflections and diffractions.

Diffraction separation is considered of great importance for the full-wavefront reconstruction (FWR) of ground penetrating radar (GPR) and its delicate data processing. In contrast to reflections, GPR diffraction events encode the fully dynamic feature and subwavelength information to identify small-scale heterogeneities, thereby offering enhanced illumination and resolution for GPR imaging. However, fully extracting these faint diffraction components remains a very challenging task. These components are usually ignored because of the strong interference and masking effect of the more dominant reflective components, and in particular, the attenuation of GPR waves accelerates almost exponentially with the frequency. In this article, we developed a coherence analysis (CA) framework for extracting GPR diffractions by considering the kinematic attributes and discontinuity features of GPR wavefronts, as well as the dispersion and attenuation effects of GPR responses. To be specific, the compensation preprocessing and semblance summation are performed sequentially for coherence acquisition, after which a multiscale subtraction is designed toward the coherent fields. In particular, we concentrated on analyzing media losses and multiparameter impacts on diffraction separation performance. To demonstrate the feasibility and practicality of the proposed framework, we tested our algorithm using synthetic and field datasets, both results with quantified metrics showing the elimination of continuities. The comparative results reveal the performance of the framework in preserving the edge components of GPR diffractions, making it potentially attractive for microscopic velocity analysis, refined full wavefield migration (FWM), and well-constrained full waveform inversion in terms of small-scale heterogeneities and discontinuities.