Extracting a flat clustering solution from a hierarchy is a common task in practical cluster analysis and can be formulated as an optimisation problem. Existing approaches focus on finding a single optimal solution. We introduce FOSC-X, a framework for extracting the top-M globally optimal flat clusterings from local, non-horizontal cuts of a hierarchical cluster tree, while optionally enforcing constraints on the number of clusters. This enables automatic identification of multiple high-quality alternative clusterings that capture different aspects of the hierarchical structure. Without constraints, the top-M problem can be solved in polynomial time using dynamic programming, exploiting the property that locally optimal partial candidates within subtrees can be combined to form globally optimal solutions while automatically determining the number of clusters. However, this can lead to solutions with numbers of clusters that are ultimately undesirable -- e.g., too large to be meaningful or practically analysed within a particular application domain. Imposing cluster-count constraints breaks the optimality property underlying the unconstrained dynamic programming approach, since locally optimal partial candidates may no longer combine into feasible globally optimal solutions. FOSC-X addresses this challenge through a dynamic programming strategy that maintains compact sets of feasible candidates using lower and upper feasibility bounds while pruning infeasible or dominated combinations. The resulting method guarantees optimal rankings of the top-M solutions with linear-time complexity in the number of cluster nodes and dataset size, both with and without cluster-count constraints. Experiments show that FOSC-X efficiently reveals alternative clustering structures overlooked by single-solution extraction methods.

The deep neural network is a widely used framework in machine learning that has been widely applied in various fields. However, deep neural networks often involve a large number of parameters and inputs, many of which may be irrelevant to the goal or true output. These parameters and input variables not only increase computational complexity, but also contribute to additional computational cost. One solution to this problem is knockoff methods, which have proven successful in controlling false discovery rates in high-dimensional regression. Building on the knockoff methods and using the regularised neural network, this paper proposes three variable screening methods under the condition of controlling false discovery rates: one layer filter, multiple layers filter, and variable weight aggregation filter. In comparison with existing algorithms, we find that our algorithms show satisfactory performance.

Neural Controlled Differential Equations (NCDE) provide a powerful continuous-time framework for forecasting time series, but standard graph-based extensions typically learn spatial structure purely from data, even in settings where a directed graph structure is known a priori. We introduce Informed Neural controlled Differential EQuationS (INDEQS), a graph-based NCDE forecasting method that incorporates prior knowledge of a directed graph at distinct architectural positions. INDEQS separates inner mixing of hidden states across graph nodes from outer mixing between vector field and control, and offers both a lightweight graph-constrained variant and a more expressive variant, learning additional graph connections from data via adaptive graph convolutions. To systematically study when graph informedness is beneficial in forecasting, we devise a continuous advection simulation on directed graphs, yielding synthetic spatio-temporal datasets with known ground-truth flow structure. We then evaluate INDEQS on two real-world tasks: river discharge forecasting on a hydrological network and traffic flow prediction on PeMS08. Across these synthetic and real-world benchmarks, outer informedness consistently improves mean absolute error over an uninformed NCDE with comparable parameter count, particularly on larger graphs, while inner informedness offers a more parameter-efficient alternative when strict adherence to a known adjacency is desired. A comparison of discrete convolutional and continuous-time decoders further shows that continuous decoders yield better accuracy and greater temporal flexibility on real-world tasks. An implementation of INDEQS and the advection simulation is available at https://github.com/Mitchi1/indeqs.

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Understanding how the human brain progresses from processing simple linguistic inputs to performing high-level reasoning is a fundamental challenge in neuroscience. While modern large language models (LLMs) are increasingly used to model neural responses to language, their internal representations are highly "entangled," mixing information about lexicon, syntax, meaning, and reasoning. This entanglement biases conventional brain encoding analyses toward linguistically shallow features (e.g., lexicon and syntax), making it difficult to isolate the neural substrates of cognitively deeper processes. Here, we introduce a residual disentanglement method that computationally isolates these components. By first probing an LM to identify feature-specific layers, our method iteratively regresses out lower-level representations to produce four nearly orthogonal embeddings for lexicon, syntax, meaning, and, critically, reasoning. We used these disentangled embeddings to model intracranial (ECoG) brain recordings from neurosurgical patients listening to natural speech. We show that: 1) This isolated reasoning embedding exhibits unique predictive power, accounting for variance in neural activity not explained by other linguistic features and even extending to the recruitment of visual regions beyond classical language areas.

Labeling LiDAR point clouds is notoriously time-and-energy-consuming, which spurs recent unsupervised 3D representation learning methods to alleviate the labeling burden in LiDAR perception via pretrained weights. Existing work focus on either masked auto encoding or contrastive learning on LiDAR point clouds, which neglects the temporal LiDAR sequence that naturally accounts for object motion (and their semantics). Instead, we propose TREND, short for Temporal REndering with Neural fielD, to learn 3D representation via forecasting the future observation in an unsupervised manner. TREND integrates forecasting for 3D pretraining through a Recurrent Embedding scheme to generate 3D embeddings across time and a Temporal LiDARNeural Field specifically designed for LiDAR modality to represent the 3D scene, with which we compute the loss using differentiable rendering. We evaluate TREND on 3D object detection and LiDAR semantic segmentation tasks on popular datasets, including Once, Waymo, NuScenes, and SemanticKITTI. TREND generally improves from-scratch models across datasets and tasks and brings gains of 1.77% mAP on Once and 2.11% mAP on NuScenes, which are up to 400%more improvement compared to previous SOTA unsupervised 3D pre-training methods. Codes and models will be available here.

Autonomous driving represents a prominent application of artificial intelligence. Recent approaches have shifted from focusing solely on common scenarios to addressing complex, long-tail situations such as subtle human behaviors, traffic accidents, and non-compliant driving patterns. Given the demonstrated capabilities of large language models (LLMs) in understanding visual and natural language inputs and following instructions, recent methods have integrated LLMs into autonomous driving systems to enhance reasoning, interpretability, and performance across diverse scenarios. However, existing methods typically rely either on realworld data, which is suitable for industrial deployment, or on simulation data tailored to rare or hard case scenarios. Few approaches effectively integrate the complementary advantages of both data sources.

Erasing harmful or proprietary concepts from powerful text-to-image generators is an emerging safety requirement, yet current "concept erasure" techniques either collapse image quality, rely on brittle adversarial losses, or demand prohibitive retraining cycles. We trace these limitations to a myopic view of the denoising trajectories that govern diffusion-based generation. We introduce EraseFlow, the first framework that casts concept unlearning as exploration in the space of denoising paths and optimizes it with GFlowNets equipped with the trajectory-balance objective. By sampling entire trajectories rather than single end states, EraseFlow learns a stochastic policy that steers generation away from target concepts while preserving the model's prior. EraseFloweliminates the need for carefully crafted reward models and by doing this, it generalizes effectively to unseen concepts and avoids hackable rewards while improving the performance. Extensive empirical results demonstrate that EraseFlowoutperforms existing baselines and achieves an optimal trade-off between performance and prior preservation. Warning: This paper may contain content that may seem as offensive in nature.

Clustering is a fundamental task in both machine learning and data mining. Among various methods, edge-colored clustering (ECC) has emerged as a useful approach for handling categorical data. Given a hypergraph with (hyper)edges labeled by colors, ECC aims to assign vertex colors to minimize the number of edges where the vertex color differs from the edge's color. However, traditional ECC has inherent limitations, as it enforces a nonoverlapping and exhaustive clustering. To tackle these limitations, three versions of ECC have been studied: LOCALECC and GLOBALECC, which allow overlapping clusters, and ROBUSTECC, which accounts for vertex outliers.

Retrosynthetic planning is a fundamental task in chemical discovery. Due to the vast combinatorial search space, identifying viable synthetic routes remains a significant challenge-even for expert chemists. Recent advances in Large Language Models (LLMs), particularly equipped with reinforcement learning, have demonstrated strong human-like reasoning and planning abilities, especially in mathematics and code problem solving. This raises a natural question: Can the reasoning capabilities of LLMs be harnessed to develop an AI chemist capable of learning effective policies for multi-step retrosynthesis? In this study, we introduce RETROR1, a novel LLM-based retrosynthesis agent trained via reinforcement learning to design molecular synthesis pathways. Unlike prior approaches, which typically rely on single-turn, question-answering formats, RETRO-R1 interacts dynamically with plug-in single-step retrosynthesis tools and learns from environmental feedback. Experimental results show that RETRO-R1 achieves a 55.79% pass@1 success rate, surpassing the previous state of the art by 8.95%. Notably, RETRO-R1 demonstrates strong generalization to out-of-domain test cases, where existing methods tend to fail despite their high in-domain performance. Our work marks a significant step toward equipping LLMs with advanced, chemist-like reasoning abilities, highlighting the promise of reinforcement learning for enabling data-efficient, generalizable, and sophisticated scientific problem-solving in LLM-based agents.