We introduce PurpCode, the first post-training recipe for training safe code reasoning models towards generating secure code and defending against malicious cyberactivities. PurpCode trains a reasoning model in two stages: (i) Rule Learning, which explicitly teaches the model to reference cybersafety rules to generate vulnerability-free code and to avoid facilitating malicious cyberactivities; and (ii) Reinforcement Learning, which optimizes model safety and preserves model utility through diverse, multi-objective reward mechanisms. To empower the training pipelines with comprehensive cybersafety data, we conduct internal red-teaming to synthesize comprehensive and high-coverage prompts based on real-world tasks for inducing unsafe cyberactivities in the model. Based on PurpCode, we develop a reasoning-based coding model, namely PurpCode-32B, which demonstrates state-of-the-art cybersafety, outperforming various frontier models. Moreover, our alignment method decreases the model overrefusal rates in both general and cybersafety-specific scenarios, while preserving model utility in both code generation and common security knowledge.

Density-based clustering algorithms are widely used for their ability to handle complex datasets; however, their performance often depends on the definition of density and is sensitive to data shapes, density variations, and noise. To address these challenges, we propose a novel parameter-free clustering algorithm named "Bombing", which can automatically determine the number of clusters. The algorithm enhances adaptability to complex data structures by combining global and local density estimations and utilizing dynamically adjusted density measures. By introducing the concept of generalized clusters and employing a "bombing" process that propagates clustering outward from core points, the method effectively mitigates the impact of cluster shapes, overlaps, and noise. Additionally, through the analysis of adjacency degrees, the algorithm can automatically detect the optimal number of clusters without prior knowledge. Experimental results on various synthetic and real datasets show that our proposed algorithm outperforms existing methods in clustering accuracy and robustness. It effectively handles noise and cluster overlap, and excels in identifying the optimal value of K .

With the management of load aggregator (LA), demand-side adjustable resources (DAR) such as electric vehicle (EV) and temperature controlled load can provide tremendous reserve capacity to support the power system. However, DAR users’ decisions are strongly uncertain, which makes it difficult for LA to evaluate reserve capacity accurately. Therefore, a LA-DAR optimal dispatching strategy considering users’ decisions is proposed. First, in view of the spatial mobility characteristics of EV, and influencing factors such as time cost and price incentives, the uncertainty of DAR user's decision under normal and extreme scenarios is characterized. Second, an optimal dispatching model using Stackelberg game is proposed, with LA as the leader and DAR as the follower. To solve the game strategy, we propose an efficient iterative solution method with a transformed decision-making model for participation in LA regulation. It is shown that the proposed optimal strategy significantly improves LA's ability to provide reserve capacity under normal and extreme scenarios, while improving the economy of the LA and DAR users.

Conventional model quantization methods use a fixed quantization scheme to different data samples, which ignores the inherent"recognition difficulty" differences between various samples. We propose to feed different data samples with varying quantization schemes to achieve a data-dependent dynamic inference, at a fine-grained layer level. However, enabling this adaptive inference with changeable layer-wise quantization schemes is challenging because the combination of bit-widths and layers is growing exponentially, making it extremely difficult to train a single model in such a vast searching space and use it in practice. To solve this problem, we present the Arbitrary Bit-width Network (ABN), where the bit-widths of a single deep network can change at runtime for different data samples, with a layer-wise granularity. Specifically, first we build a weight-shared layer-wise quantizable "super-network" in which each layer can be allocated with multiple bit-widths and thus quantized differently on demand. The super-network provides a considerably large number of combinations of bit-widths and layers, each of which can be used during inference without retraining or storing myriad models. Second, based on the well-trained super-network, each layer's runtime bit-width selection decision is modeled as a Markov Decision Process (MDP) and solved by an adaptive inference strategy accordingly. Experiments show that the super-network can be built without accuracy degradation, and the bit-widths allocation of each layer can be adjusted to deal with various inputs on the fly. On ImageNet classification, we achieve 1.1% top1 accuracy improvement while saving 36.2% BitOps.