BinConv: A Neural Architecture for Ordinal Encoding in Time-Series Forecasting
BinConv uses Cumulative Binary Encoding to model ordinal info, significantly improving time series forecasting accuracy.
Key Findings
Methodology
This paper introduces BinConv, a convolutional architecture that leverages Cumulative Binary Encoding (CBE) to encode target values preserving ordinal and magnitude information. CBE activates all binary bits below or equal to the current value, implicitly encoding order and scale. The model stacks multiple BinConv blocks with residual connections, combining 2D and 1D convolutions to capture local temporal features efficiently. Training employs binary cross-entropy loss on each binary bit, predicting success probabilities via Bernoulli distributions. During inference, the model computes joint probabilities of valid sequences, enabling autoregressive sampling or point estimation. The inverse transformation reconstructs continuous predictions from encoded outputs. Experiments on benchmark datasets demonstrate superior performance over baselines like DLinear and PatchTST, with fewer parameters and faster training.
Key Results
- On M4 Daily, Weekly, and Tourism datasets, BinConv outperformed baselines with a 15% reduction in CRPS and 10% in NMAE, achieving statistically significant improvements (p<0.05).
- On multivariate datasets ETTh1 and ETTh2, BinConv ranked first on average, reducing CRPS by 0.02 and improving NMAE by about 10%.
- Ablation studies confirmed that CBE encoding and convolutional architecture are critical; replacing CBE with one-hot encoding or using transformers degraded performance.
Significance
This work addresses the limitations of one-hot encoding in time series forecasting by introducing an ordinal-preserving binary encoding, enhancing the model’s ability to learn relative distances between target values. The convolutional architecture ensures computational efficiency and scalability, making it suitable for industrial applications requiring high-accuracy, real-time predictions. The probabilistic framework further enables uncertainty quantification, vital for decision-making in finance, climate modeling, and healthcare. Overall, the approach advances deep learning methods by integrating ordinal information directly into the model structure, offering a robust and efficient solution for complex forecasting tasks.
Technical Contribution
The main technical contributions include the development of CBE, a monotonic binary encoding that preserves ordinal and magnitude information, and the design of BinConv, a convolutional neural network optimized for CBE inputs. The model employs residual blocks with DyTanh activation, combining 2D and depthwise 1D convolutions to efficiently capture local temporal features while maintaining parameter efficiency. The probabilistic forecasting leverages Bernoulli success probabilities to compute joint sequence likelihoods, enabling autoregressive sampling. This architecture departs from traditional fully connected or transformer-based models, emphasizing weight sharing and local feature extraction aligned with CBE’s structure, resulting in faster training and better generalization.
Novelty
This study is the first to apply cumulative binary encoding to time series forecasting, explicitly preserving ordinal and magnitude information in a neural network framework. Unlike prior approaches relying solely on one-hot encoding or continuous regression, BinConv integrates a monotonic binary representation with convolutional architecture, enabling efficient, accurate, and uncertainty-aware predictions. This combination of ordinal encoding and convolutional modeling is a novel contribution that addresses the limitations of existing methods, especially in capturing relative target value relationships.
Limitations
- Currently, BinConv is designed for univariate forecasting; extending to multivariate scenarios requires additional mechanisms for joint modeling, which remains future work.
- The fixed binning parameters may not adapt well to datasets with highly non-uniform value distributions, potentially affecting accuracy.
- Model performance can be sensitive to hyperparameter choices such as bin number and network depth, necessitating dataset-specific tuning.
Future Work
Future research will focus on extending BinConv to multivariate time series, exploring adaptive binning strategies, and integrating attention mechanisms to enhance long-range dependency modeling. Additionally, automatic hyperparameter tuning and real-time deployment considerations will be addressed to facilitate industrial adoption. Further, combining CBE with other neural architectures like transformers may be explored, despite current limitations, to leverage their long-term dependency modeling capabilities.
AI Executive Summary
Time series forecasting is vital across sectors like finance, climate, and healthcare, yet traditional models such as ARIMA struggle with complex, nonlinear patterns. Deep learning approaches like Transformers and RNNs have advanced the field but often at the cost of high computational complexity and large parameter counts. Recent efforts to discretize continuous targets into categories, such as tokenization-based models like TiMER and Chronos, have improved stability but overlooked the ordinal relationships inherent in target values. This oversight limits the models’ ability to understand the relative distances between predictions and true values, especially during training.
To address this, the authors propose BinConv, a convolutional neural network architecture that leverages Cumulative Binary Encoding (CBE). CBE transforms target values into a monotonic binary vector, activating all bits below or equal to the current value, thus implicitly encoding the ordinal and magnitude information. This encoding preserves the global order and allows models to learn distance-aware representations within a classification framework. The BinConv architecture stacks residual blocks combining 2D and depthwise 1D convolutions, efficiently capturing local temporal features while maintaining parameter efficiency.
Training involves a binary cross-entropy loss applied to each binary bit, with probabilistic forecasting achieved through Bernoulli success probabilities. During inference, the model computes joint probabilities of valid sequences, enabling both sampling-based and argmax point predictions. Extensive experiments on benchmark datasets, including M4, ETTh1, and ETTh2, demonstrate that BinConv consistently outperforms state-of-the-art baselines like DLinear and PatchTST, with improvements in CRPS and NMAE metrics, while requiring fewer parameters and faster training.
This work significantly advances time series forecasting by integrating ordinal-preserving encoding with convolutional modeling, offering a scalable, accurate, and uncertainty-aware solution. Its implications extend to real-world applications in finance, climate prediction, and industrial automation. Nevertheless, future challenges include extending to multivariate data, adaptive binning, and integrating long-range dependency mechanisms, promising a rich avenue for ongoing research.
Deep Analysis
Background
时间序列预测作为数据分析的重要工具，经历了从传统统计模型到深度学习模型的演变。ARIMA、指数平滑等经典方法在稳定性和解释性方面表现优异，但难以捕获复杂非线性关系。近年来，LSTM、GRU和Transformer等深度模型展现出强大能力，尤其是Transformer在长距离依赖建模方面表现突出，但其参数规模庞大，训练成本高。为了提升效率，卷积神经网络（如TCN）被引入，提供了更快的训练速度和较好的性能。同时，将连续值离散化为类别标签的研究逐渐兴起，如TiMER、Chronos等，利用NLP技术将连续目标转化为token，改善模型稳定性。然而，一热编码忽视了目标值的序数关系，限制了模型对目标值相对距离的理解。本文提出的CBE编码，结合卷积架构，旨在解决这一瓶颈，推动时间序列建模的精度和效率提升。
Core Problem
现有时间序列分类化方法多采用一热编码，忽略了目标值的序数和幅值信息，导致模型难以学习目标值之间的相对关系。此外，Transformer等深度模型虽能捕获长距离依赖，但参数庞大、训练缓慢，限制了实际应用。如何在保持模型表达能力的同时，提高训练效率和预测精度，成为亟待解决的问题。尤其是在高频、长序列场景中，模型的泛化能力和计算成本成为主要瓶颈。本文旨在通过引入序数保持的编码机制和高效卷积架构，突破这一限制，提升时间序列预测性能。
Innovation
核心创新包括：1）引入CBE编码机制，利用二进制激活实现目标值的序数和幅值信息隐式表达，避免一热编码的局限；2）设计多层卷积网络BinConv，有效捕获局部时间依赖，减少参数量，提高训练速度；3）结合贝努利成功概率推导联合分布，实现自回归和概率预测。不同于Transformer的全连接机制，卷积结构具有参数共享和位置不变性，更适合CBE的序数特性。模型在编码和预测两个环节均实现创新，显著提升了时间序列建模的效率和准确性。
Methodology
- �� 数据预处理：对时间序列进行均值缩放，映射到[-5,5]区间。• 编码：将连续值离散化为D个均匀划分的区间，生成CBE向量，激活所有低于或等于当前值的二进制位。• 模型结构：由M个BinConv块组成，每块包括一个2D卷积（捕获局部特征）和两个1D卷积（提取时间依赖），采用DyTanh激活，加入残差连接。• 训练：使用二元交叉熵损失，预测每个二进制位的成功概率。• 预测：输出贝努利成功概率，通过联合概率公式推导目标序列的概率分布，支持自回归采样或最大概率输出。• 逆变换：将预测的CBE向量转化为连续值，反向缩放得到原始预测值。
Experiments
- �� 数据集：包括M4每日、每周、旅游月度，以及ETTh1、ETTh2等多变量数据集。• 基线模型：DLinear、PatchTST、GRU-NVP、TimeGrad。• 评估指标：CRPS和NMAE，衡量点预测和概率预测性能。• 超参数：编码区间[-5,5]，D=1000（单变量）或500（多变量），网络深度3层，学习率0.001。• 实验设计：多次随机种子，统计显著性检验，比较不同编码和架构的影响。
Results
- �� BinConv在所有单变量数据集上均优于基线模型，CRPS平均提升15%，NMAE降低10%，统计显著（p<0.05）。• 在多变量数据集上，平均排名第一，CRPS指标下降0.02，表现优异。• 消融实验显示，CBE编码优于一热编码，卷积架构优于Transformer，验证了序数和局部特征的重要性。
Applications
- �� 立即应用：金融市场预测、能源负荷管理、气象预报等行业可采用此模型提升预测精度和效率。• 长期愿景：推动深度时间序列模型在工业自动化、智能制造等领域的广泛部署，实现高效、稳健的自动决策系统。
Limitations & Outlook
- �� 目前仅支持单变量预测，扩展多变量场景需设计多输出机制。• 在极端尺度变化或非线性动态中，编码策略可能面临信息丢失。• 模型对超参数敏感，需根据数据特性调整参数设置。未来将探索多变量联合建模和自适应编码策略，提升模型泛化能力。
Plain Language Accessible to non-experts
想象你在厨房做饭，食材的量有大、中、小之分。传统的时间序列预测就像只知道食材是否有，没有考虑它们之间的大小关系，比如大于或小于。本文提出的方法像是用一种特殊的标签，把每种食材的大小用二进制的方式标记出来，既告诉你大还是小，还隐含了它们的相对关系。这样，厨师（模型）就能更聪明地判断下一步需要用多少食材，而不是仅仅知道“有”或“没有”。通过这种编码，厨师可以更快、更准确地预测未来的用料量，做出更美味的菜肴。这就像给厨师装上了“智能尺子”，让它知道每个食材的相对大小，做饭变得更科学、更高效。
ELI14 Explained like you're 14
想象你在玩一个游戏，你的任务是猜下一关会出现什么东西。以前的方法就像只知道“有”或“没有”，没有考虑它们的大小关系。现在，这个新方法像是给每个东西都贴上了一个数字标签，用二进制（像电脑用的0和1）表示它们的大小。这样，你不仅知道“有”或“没有”，还能知道哪个更大或更小。游戏里的角色（模型）用这个标签来猜未来会出现的东西，变得更聪明、更快。它就像给你装了一个“智能尺子”，让你能更准确地判断未来会发生什么。这种方法让预测变得更科学，也更可靠，能帮你在游戏中赢得更多！
Abstract
Recent work in time series forecasting has explored reformulating regression as a classification task. By discretizing the continuous target space into bins and predicting over a fixed set of classes, these approaches benefit from more stable training, improved uncertainty modeling, and compatibility with modern deep learning architectures. However, most existing methods rely on one-hot encoding, which ignores the inherent ordinal structure of the target values. As a result, they fail to convey information about the relative distance between predicted and true values during training. In this paper, we address this limitation by applying \textbf{Cumulative Binary Encoding} (CBE), a monotonic binary representation that transforms both model inputs and outputs. CBE implicitly preserves ordinal and magnitude information, allowing models to learn distance aware representations while operating within a classification framework. To leverage CBE effectively, we propose \textbf{BinConv}, a fully convolutional neural network architecture designed for probabilistic forecasting. We demonstrate that standard fully connected layers are not only less computationally efficient than convolutional layers when used with CBE, but also degrade forecasting performance. Our experiments on standard benchmark datasets show that BinConv achieves superior performance compared to widely used baselines in both point and probabilistic forecasting, while requiring fewer parameters and enabling faster training.