Training Large Language Models (LLMs) with synthetic data is a prevalent practice in code generation. A key approach is self-training, where LLMs are iteratively trained on self-generated correct code snippets. In this case, the self-generated codes are drawn from a conditional distribution, conditioned on a specific seed description. However, the seed description is not the only valid representation that aligns with its intended meaning. With all valid descriptions and codes forming a joint space, codes drawn from the conditional distribution would lead to an underrepresentation of the full description-code space. As such, we propose Gibbs Fine-Tuning (GiFT), a novel self-training method inspired by Gibbs sampling. GiFT allows self-generated data to be drawn from the marginal distribution of the joint space, thereby mitigating the biases inherent in conditional sampling. We provide a theoretical analysis demonstrating the potential benefits of fine-tuning LLMs with code derived from the marginal distribution. Furthermore, we propose a perplexity-based code selection method to mitigate the imbalanced long-tail distribution of the self-generated codes. Empirical evaluation of two LLMs across four datasets demonstrates that GiFT achieves superior performance, particularly on more challenging benchmarks. Source code is available at https://github.com/Alex-HaochenLi/GiFT.

Spiking Neural Networks (SNNs) offer a promising, biologically inspired approach for processing spatiotemporal data, particularly for time series forecasting. However, conventional neuron models like the Leaky Integrate-and-Fire (LIF) struggle to capture long-term dependencies and effectively process multi-scale temporal dynamics. To overcome these limitations, we introduce the Temporal Segment Leaky Integrate-and-Fire (TS-LIF) model, featuring a novel dual-compartment architecture. The dendritic and somatic compartments specialize in capturing distinct frequency components, providing functional heterogeneity that enhances the neuron's ability to process both low- and high-frequency information. Furthermore, the newly introduced direct somatic current injection reduces information loss during intra-neuronal transmission, while dendritic spike generation improves multi-scale information extraction. We provide a theoretical stability analysis of the TS-LIF model and explain how each compartment contributes to distinct frequency response characteristics. Experimental results show that TS-LIF outperforms traditional SNNs in time series forecasting, demonstrating better accuracy and robustness, even with missing data. TS-LIF advances the application of SNNs in time-series forecasting, providing a biologically inspired approach that captures complex temporal dynamics and offers potential for practical implementation in diverse forecasting scenarios.

Spiking Neural Networks (SNNs) often suffer from high time complexity $O(T)$ due to the sequential processing of $T$ spikes, making training computationally expensive. In this paper, we propose a novel Fixed-point Parallel Training (FPT) method to accelerate SNN training without modifying the network architecture or introducing additional assumptions. FPT reduces the time complexity to $O(K)$, where $K$ is a small constant (usually $K=3$), by using a fixed-point iteration form of Leaky Integrate-and-Fire (LIF) neurons for all $T$ timesteps. We provide a theoretical convergence analysis of FPT and demonstrate that existing parallel spiking neurons can be viewed as special cases of our approach. Experimental results show that FPT effectively simulates the dynamics of original LIF neurons, significantly reducing computational time without sacrificing accuracy. This makes FPT a scalable and efficient solution for real-world applications, particularly for long-duration simulations.

Bandit online multiclass prediction plays an important role in many real-world applications. In this paper, we propose a unified Bandit Online Multiclass Prediction (BOMP) framework. This framework is based on our proposed margin-based gradient descent approach. Its update step provides an unbiased estimate of the surrogate loss gradient and has a lower variance than existing methods. It also enables our algorithms to update even for incorrect predictions by penalizing the wrong classes. The link function of the framework can evolve over time, gradually incorporating online data information including second-order information into the potential functions. Based on the proposed framework, we investigate first-order and second-order bandit online multiclass prediction algorithms. Theoretical analysis demonstrates the superiority of our proposed update rule and bandit online multiclass prediction framework. Finally, we compare our proposed first-order and second-order bandit online multiclass prediction algorithms with several state-of-the-art methods on two synthetic and four real-world datasets. The encouraging results show that our proposed algorithms significantly outperform state-of-the-art techniques.

The exploitation and exploration dilemma is a crucial issue in bandit online multiclass prediction. Conventional algorithms typically resort to either random sample or estimate uncertainty for exploration. In contrast, we propose a novel scheme that focuses solely on exploitation with implicit feedback. To ensure efficient information feedback even when predictions are incorrect, we introduce mixed losses into our proposed scheme. We derive two mixed versions of the multiclass hinge loss and the logistic loss, along with their corresponding algorithms. Context-free and context-aware experiments are conducted to evaluate the performance of our proposed algorithms. Experiment results demonstrate that random sampling are unnecessary if a reasonable loss function is employed. By compared with several state-of-the-art baselines on both synthetic and real-world datasets, our proposed algorithms show their superior performance. Remarkably, they even outperform the Perceptron algorithm with full-information feedback in some cases.