The design of training objective is central to training time-series forecasting models. Existing training objectives such as mean squared error mostly treat each future step as an independent, equally weighted task, which we found leading to the following two issues: (1) overlook the label autocorrelation effect among future steps, leading to biased training objective; (2) fail to set heterogeneous task weights for different forecasting tasks corresponding to varying future steps, limiting the forecasting performance. To fill this gap, we propose a novel quadratic-form weighted training objective, addressing both of the issues simultaneously. Specifically, the off-diagonal elements of the weighting matrix account for the label autocorrelation effect, whereas the non-uniform diagonals are expected to match the most preferable weights of the forecasting tasks with varying future steps. To achieve this, we propose a Quadratic Direct Forecast (QDF) learning algorithm, which trains the forecast model using the adaptively updated quadratic-form weighting matrix. Experiments show that our QDF effectively improves performance of various forecast models, achieving state-of-the-art results. Code is available at https://anonymous.4open.science/r/QDF-8937.

Training time-series forecast models requires aligning the conditional distribution of model forecasts with that of the label sequence. The standard direct forecast (DF) approach resorts to minimize the conditional negative log-likelihood of the label sequence, typically estimated using the mean squared error. However, this estimation proves to be biased in the presence of label autocorrelation. In this paper, we propose DistDF, which achieves alignment by alternatively minimizing a discrepancy between the conditional forecast and label distributions. Because conditional discrepancies are difficult to estimate from finite time-series observations, we introduce a newly proposed joint-distribution Wasserstein discrepancy for time-series forecasting, which provably upper bounds the conditional discrepancy of interest. This discrepancy admits tractable, differentiable estimation from empirical samples and integrates seamlessly with gradient-based training. Extensive experiments show that DistDF improves the performance diverse forecast models and achieves the state-of-the-art forecasting performance. Code is available at https://anonymous.4open.science/r/DistDF-F66B.

Reward machines are an established tool for dealing with reinforcement learning problems in which rewards are sparse and depend on complex sequences of actions. However, existing algorithms for learning reward machines assume an overly idealized setting where rewards have to be free of noise. To overcome this practical limitation, we introduce a novel type of reward machines, called stochastic reward machines, and an algorithm for learning them. Our algorithm, based on constraint solving, learns minimal stochastic reward machines from the explorations of a reinforcement learning agent. This algorithm can easily be paired with existing reinforcement learning algorithms for reward machines and guarantees to converge to an optimal policy in the limit. We demonstrate the effectiveness of our algorithm in two case studies and show that it outperforms both existing methods and a naive approach for handling noisy reward functions.

Training time-series forecast models presents unique challenges in designing effective learning objectives. Existing methods predominantly utilize the temporal mean squared error, which faces two critical challenges: (1) label autocorrelation, which leads to bias from the label sequence likelihood; (2) excessive amount of tasks, which increases with the forecast horizon and complicates optimization. To address these challenges, we propose Time-o1, a transformation-augmented learning objective tailored for time-series forecasting. The central idea is to transform the label sequence into decorrelated components with discriminated significance. Models are then trained to align the most significant components, thereby effectively mitigating label autocorrelation and reducing task amount. Extensive experiments demonstrate that Time-o1 achieves state-of-the-art performance and is compatible with various forecast models. Code is available at https://github.com/Master-PLC/Time-o1.

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Multidimensional recurrent neural networks (MDRNNs) have shown a remarkable performance in the area of speech and handwriting recognition. The performance of an MDRNN is improved by further increasing its depth, and the difficulty of learning the deeper network is overcome by using Hessian-free (HF) optimization. Given that connectionist temporal classification (CTC) is utilized as an objective of learning an MDRNN for sequence labeling, the non-convexity of CTC poses a problem when applying HF to the network. As a solution, a convex approximation of CTC is formulated and its relationship with the EM algorithm and the Fisher information matrix is discussed. An MDRNN up to a depth of 15 layers is successfully trained using HF, resulting in an improved performance for sequence labeling.

With the development of social media networks, rumor detection models have attracted more and more attention. Whereas, these models primarily focus on classifying contexts as rumors or not, lacking the capability to locate and mark specific rumor content. To address this limitation, this paper proposes a novel rumor detection model named Insight Rumors to locate and mark rumor content within textual data. Specifically, we propose the Bidirectional Mamba2 Network with Dot-Product Attention (Att_BiMamba2), a network that constructs a bidirectional Mamba2 model and applies dot-product attention to weight and combine the outputs from both directions, thereby enhancing the representation of high-dimensional rumor features. Simultaneously, a Rumor Locating and Marking module is designed to locate and mark rumors. The module constructs a skip-connection network to project high-dimensional rumor features onto low-dimensional label features. Moreover, Conditional Random Fields (CRF) is employed to impose strong constraints on the output label features, ensuring accurate rumor content location. Additionally, a labeled dataset for rumor locating and marking is constructed, with the effectiveness of the proposed model is evaluated through comprehensive experiments. Extensive experiments indicate that the proposed scheme not only detects rumors accurately but also locates and marks them in context precisely, outperforming state-of-the-art schemes that can only discriminate rumors roughly.

Although connectionist temporal classification (CTC) has the label context independence assumption, it can still implicitly learn a context-dependent internal language model (ILM) due to modern powerful encoders. In this work, we investigate the implicit context dependency modeled in the ILM of CTC. To this end, we propose novel context-dependent ILM estimation methods for CTC based on knowledge distillation (KD) with theoretical justifications. Furthermore, we introduce two regularization methods for KD. We conduct experiments on Librispeech and TED-LIUM Release 2 datasets for in-domain and cross-domain evaluation, respectively. Experimental results show that context-dependent ILMs outperform the context-independent priors in cross-domain evaluation, indicating that CTC learns a context-dependent ILM. The proposed label-level KD with smoothing method surpasses other ILM estimation approaches, with more than 13% relative improvement in word error rate compared to shallow fusion.