Jayant Kalagnanam

Yuqi Nie, Nam H. Nguyen, Phanwadee Sinthong et al.

We propose an efficient design of Transformer-based models for multivariate time series forecasting and self-supervised representation learning. It is based on two key components: (i) segmentation of time series into subseries-level patches which are served as input tokens to Transformer; (ii) channel-independence where each channel contains a single univariate time series that shares the same embedding and Transformer weights across all the series. Patching design naturally has three-fold benefit: local semantic information is retained in the embedding; computation and memory usage of the attention maps are quadratically reduced given the same look-back window; and the model can attend longer history. Our channel-independent patch time series Transformer (PatchTST) can improve the long-term forecasting accuracy significantly when compared with that of SOTA Transformer-based models. We also apply our model to self-supervised pre-training tasks and attain excellent fine-tuning performance, which outperforms supervised training on large datasets. Transferring of masked pre-trained representation on one dataset to others also produces SOTA forecasting accuracy. Code is available at: https://github.com/yuqinie98/PatchTST.

Vijay Ekambaram, Arindam Jati, Nam Nguyen et al.

Transformers have gained popularity in time series forecasting for their ability to capture long-sequence interactions. However, their high memory and computing requirements pose a critical bottleneck for long-term forecasting. To address this, we propose TSMixer, a lightweight neural architecture exclusively composed of multi-layer perceptron (MLP) modules for multivariate forecasting and representation learning on patched time series. Inspired by MLP-Mixer's success in computer vision, we adapt it for time series, addressing challenges and introducing validated components for enhanced accuracy. This includes a novel design paradigm of attaching online reconciliation heads to the MLP-Mixer backbone, for explicitly modeling the time-series properties such as hierarchy and channel-correlations. We also propose a novel Hybrid channel modeling and infusion of a simple gating approach to effectively handle noisy channel interactions and generalization across diverse datasets. By incorporating these lightweight components, we significantly enhance the learning capability of simple MLP structures, outperforming complex Transformer models with minimal computing usage. Moreover, TSMixer's modular design enables compatibility with both supervised and masked self-supervised learning methods, making it a promising building block for time-series Foundation Models. TSMixer outperforms state-of-the-art MLP and Transformer models in forecasting by a considerable margin of 8-60%. It also outperforms the latest strong benchmarks of Patch-Transformer models (by 1-2%) with a significant reduction in memory and runtime (2-3X). The source code of our model is officially released as PatchTSMixer in the HuggingFace. Model: https://huggingface.co/docs/transformers/main/en/model_doc/patchtsmixer Examples: https://github.com/ibm/tsfm/#notebooks-links

Trang H. Tran, Lam M. Nguyen, Kyongmin Yeo et al. · ibm-research

Time series forecasting using historical data has been an interesting and challenging topic, especially when the data is corrupted by missing values. In many industrial problem, it is important to learn the inference function between the auxiliary observations and target variables as it provides additional knowledge when the data is not fully observed. We develop an end-to-end time series model that aims to learn the such inference relation and make a multiple-step ahead forecast. Our framework trains jointly two neural networks, one to learn the feature-wise correlations and the other for the modeling of temporal behaviors. Our model is capable of simultaneously imputing the missing entries and making a multiple-step ahead prediction. The experiments show good overall performance of our framework over existing methods in both imputation and forecasting tasks.

Srideepika Jayaraman, Achille Fokoue, Dhaval Patel et al. · ibm-research

Synthetic Data Generation (SDG), leveraging Large Language Models (LLMs), has recently been recognized and broadly adopted as an effective approach to improve the performance of smaller but more resource and compute efficient LLMs through fine-tuning. A key challenge in SDG is ensuring the quality and diversity of the generated data. In this paper, we analyze the diversity and distribution of generated data in the embedding space, and demonstrate a strong correlation between the density of examples within a specific neighborhood and the accuracy of predictions on examples drawn from that region. Building on this insight, we present a targeted pipeline for embedding-based sampling that enhances data diversity and consistently improves performance across several benchmarks.

Yunshi Wen, Wesley M. Gifford, Chandra Reddy et al.

The recent surge in Time Series Foundation Models has rapidly advanced the field, yet the heterogeneous training setups across studies make it difficult to attribute improvements to architectural innovations versus data engineering. In this work, we investigate the potential of a standard patch Transformer, demonstrating that this generic architecture achieves state-of-the-art zero-shot forecasting performance using a straightforward training protocol. We conduct a comprehensive ablation study that covers model scaling, data composition, and training techniques to isolate the essential ingredients for high performance. Our findings identify the key drivers of performance, while confirming that the generic architecture itself demonstrates excellent scalability. By strictly controlling these variables, we provide comprehensive empirical results on model scaling across multiple dimensions. We release our open-source model and detailed findings to establish a transparent, reproducible baseline for future research.

Santosh Palaskar, Vijay Ekambaram, Arindam Jati et al.

The efficiency of business processes relies on business key performance indicators (Biz-KPIs), that can be negatively impacted by IT failures. Business and IT Observability (BizITObs) data fuses both Biz-KPIs and IT event channels together as multivariate time series data. Forecasting Biz-KPIs in advance can enhance efficiency and revenue through proactive corrective measures. However, BizITObs data generally exhibit both useful and noisy inter-channel interactions between Biz-KPIs and IT events that need to be effectively decoupled. This leads to suboptimal forecasting performance when existing multivariate forecasting models are employed. To address this, we introduce AutoMixer, a time-series Foundation Model (FM) approach, grounded on the novel technique of channel-compressed pretrain and finetune workflows. AutoMixer leverages an AutoEncoder for channel-compressed pretraining and integrates it with the advanced TSMixer model for multivariate time series forecasting. This fusion greatly enhances the potency of TSMixer for accurate forecasts and also generalizes well across several downstream tasks. Through detailed experiments and dashboard analytics, we show AutoMixer's capability to consistently improve the Biz-KPI's forecasting accuracy (by 11-15\%) which directly translates to actionable business insights.

Lam M. Nguyen, Dzung T. Phan, Jayant Kalagnanam

Shuffling strategies for stochastic gradient descent (SGD), including incremental gradient, shuffle-once, and random reshuffling, are supported by rigorous convergence analyses for arbitrary within-epoch permutations. In particular, random reshuffling is known to improve optimization constants relative to cyclic and shuffle-once schemes. However, existing theory offers limited guidance on how to design new data-ordering schemes that further improve optimization constants or stability beyond random reshuffling. In this paper, we design a pipeline using a large language model (LLM)-guided program evolution framework to discover an effective shuffling rule for without-replacement SGD. Abstracting from this instance, we identify two fundamental structural components: block reshuffling and paired reversal. We analyze these components separately and show that block reshuffling strictly reduces prefix-gradient variance constants within the unified shuffling framework, yielding provable improvements over random reshuffling under mild conditions. Separately, we show that paired reversal symmetrizes the epoch map and cancels the leading order-dependent second-order term, reducing order sensitivity from quadratic to cubic in the step size. Numerical experiments with the discovered algorithm validate the theory and demonstrate consistent gains over standard shuffling schemes across convex and nonconvex benchmarks.

Vijay Ekambaram, Arindam Jati, Pankaj Dayama et al.

Large pre-trained models excel in zero/few-shot learning for language and vision tasks but face challenges in multivariate time series (TS) forecasting due to diverse data characteristics. Consequently, recent research efforts have focused on developing pre-trained TS forecasting models. These models, whether built from scratch or adapted from large language models (LLMs), excel in zero/few-shot forecasting tasks. However, they are limited by slow performance, high computational demands, and neglect of cross-channel and exogenous correlations. To address this, we introduce Tiny Time Mixers (TTM), a compact model (starting from 1M parameters) with effective transfer learning capabilities, trained exclusively on public TS datasets. TTM, based on the light-weight TSMixer architecture, incorporates innovations like adaptive patching, diverse resolution sampling, and resolution prefix tuning to handle pre-training on varied dataset resolutions with minimal model capacity. Additionally, it employs multi-level modeling to capture channel correlations and infuse exogenous signals during fine-tuning. TTM outperforms existing popular benchmarks in zero/few-shot forecasting by (4-40%), while reducing computational requirements significantly. Moreover, TTMs are lightweight and can be executed even on CPU-only machines, enhancing usability and fostering wider adoption in resource-constrained environments. The model weights for reproducibility and research use are available at https://huggingface.co/ibm/ttm-research-r2/, while enterprise-use weights under the Apache license can be accessed as follows: the initial TTM-Q variant at https://huggingface.co/ibm-granite/granite-timeseries-ttm-r1, and the latest variants (TTM-B, TTM-E, TTM-A) weights are available at https://huggingface.co/ibm-granite/granite-timeseries-ttm-r2.

Vijay Ekambaram, Subodh Kumar, Arindam Jati et al.

The rise of time-series pre-trained models has advanced temporal representation learning, but current state-of-the-art models are often large-scale, requiring substantial compute. We introduce TSPulse, ultra-compact time-series pre-trained models with only 1M parameters, specialized to perform strongly across classification, anomaly detection, imputation, and retrieval tasks. TSPulse introduces innovations at both the architecture and task levels. At the architecture level, it employs a dual-space masked reconstruction, learning from both time and frequency domains to capture complementary signals. This is further enhanced by a dual-embedding disentanglement, generating both detailed embeddings for fine-grained analysis and high-level semantic embeddings for broader task understanding. Notably, TSPulse's semantic embeddings are robust to shifts in time, magnitude, and noise, which is important for robust retrieval. At the task level, TSPulse incorporates TSLens, a fine-tuning component enabling task-specific feature attention. It also introduces a multi-head triangulation technique that correlates deviations from multiple prediction heads, enhancing anomaly detection by fusing complementary model outputs. Additionally, a hybrid mask pretraining is proposed to improves zero-shot imputation by reducing pre-training bias. These architecture and task innovations collectively contribute to TSPulse's significant performance gains: 5-16% on the UEA classification benchmarks, +20% on the TSB-AD anomaly detection leaderboard, +50% in zero-shot imputation, and +25% in time-series retrieval. Remarkably, these results are achieved with just 1M parameters (10-100X smaller than existing SOTA models) and allow GPU-free inference, setting a new standard for efficient time-series pre-trained models. The models can be accessed from https://huggingface.co/ibm-granite/granite-timeseries-tspulse-r1

Dhaval Patel, Shuxin Lin, James Rayfield et al.

AI for Industrial Asset Lifecycle Management aims to automate complex operational workflows -- such as condition monitoring, maintenance planning, and intervention scheduling -- to reduce human workload and minimize system downtime. Traditional AI/ML approaches have primarily tackled these problems in isolation, solving narrow tasks within the broader operational pipeline. In contrast, the emergence of AI agents and large language models (LLMs) introduces a next-generation opportunity: enabling end-to-end automation across the entire asset lifecycle. This paper envisions a future where AI agents autonomously manage tasks that previously required distinct expertise and manual coordination. To this end, we introduce AssetOpsBench -- a unified framework and environment designed to guide the development, orchestration, and evaluation of domain-specific agents tailored for Industry 4.0 applications. We outline the key requirements for such holistic systems and provide actionable insights into building agents that integrate perception, reasoning, and control for real-world industrial operations. The software is available at https://github.com/IBM/AssetOpsBench.

Christodoulos Constantinides, Dhaval Patel, Shuxin Lin et al.

We introduce FailureSensorIQ, a novel Multi-Choice Question-Answering (MCQA) benchmarking system designed to assess the ability of Large Language Models (LLMs) to reason and understand complex, domain-specific scenarios in Industry 4.0. Unlike traditional QA benchmarks, our system focuses on multiple aspects of reasoning through failure modes, sensor data, and the relationships between them across various industrial assets. Through this work, we envision a paradigm shift where modeling decisions are not only data-driven using statistical tools like correlation analysis and significance tests, but also domain-driven by specialized LLMs which can reason about the key contributors and useful patterns that can be captured with feature engineering. We evaluate the Industrial knowledge of over a dozen LLMs-including GPT-4, Llama, and Mistral-on FailureSensorIQ from different lens using Perturbation-Uncertainty-Complexity analysis, Expert Evaluation study, Asset-Specific Knowledge Gap analysis, ReAct agent using external knowledge-bases. Even though closed-source models with strong reasoning capabilities approach expert-level performance, the comprehensive benchmark reveals a significant drop in performance that is fragile to perturbations, distractions, and inherent knowledge gaps in the models. We also provide a real-world case study of how LLMs can drive the modeling decisions on 3 different failure prediction datasets related to various assets. We release: (a) expert-curated MCQA for various industrial assets, (b) FailureSensorIQ benchmark and Hugging Face leaderboard based on MCQA built from non-textual data found in ISO documents, and (c) LLMFeatureSelector, an LLM-based feature selection scikit-learn pipeline. The software is available at https://github.com/IBM/FailureSensorIQ.

Claudius Krause, Michele Faucci Giannelli, Gregor Kasieczka et al.

We present the results of the "Fast Calorimeter Simulation Challenge 2022" - the CaloChallenge. We study state-of-the-art generative models on four calorimeter shower datasets of increasing dimensionality, ranging from a few hundred voxels to a few tens of thousand voxels. The 31 individual submissions span a wide range of current popular generative architectures, including Variational AutoEncoders (VAEs), Generative Adversarial Networks (GANs), Normalizing Flows, Diffusion models, and models based on Conditional Flow Matching. We compare all submissions in terms of quality of generated calorimeter showers, as well as shower generation time and model size. To assess the quality we use a broad range of different metrics including differences in 1-dimensional histograms of observables, KPD/FPD scores, AUCs of binary classifiers, and the log-posterior of a multiclass classifier. The results of the CaloChallenge provide the most complete and comprehensive survey of cutting-edge approaches to calorimeter fast simulation to date. In addition, our work provides a uniquely detailed perspective on the important problem of how to evaluate generative models. As such, the results presented here should be applicable for other domains that use generative AI and require fast and faithful generation of samples in a large phase space.

Connor Lawless, Jayant Kalagnanam, Lam M. Nguyen et al.

Clustering is a popular unsupervised learning tool often used to discover groups within a larger population such as customer segments, or patient subtypes. However, despite its use as a tool for subgroup discovery and description - few state-of-the-art algorithms provide any rationale or description behind the clusters found. We propose a novel approach for interpretable clustering that both clusters data points and constructs polytopes around the discovered clusters to explain them. Our framework allows for additional constraints on the polytopes - including ensuring that the hyperplanes constructing the polytope are axis-parallel or sparse with integer coefficients. We formulate the problem of constructing clusters via polytopes as a Mixed-Integer Non-Linear Program (MINLP). To solve our formulation we propose a two phase approach where we first initialize clusters and polytopes using alternating minimization, and then use coordinate descent to boost clustering performance. We benchmark our approach on a suite of synthetic and real world clustering problems, where our algorithm outperforms state of the art interpretable and non-interpretable clustering algorithms.

Pavithra Harsha, Ashish Jagmohan, Jayant Kalagnanam et al.

We present a Reinforcement Learning (RL) based framework for optimizing long-term discounted reward problems with large combinatorial action space and state dependent constraints. These characteristics are common to many operations management problems, e.g., network inventory replenishment, where managers have to deal with uncertain demand, lost sales, and capacity constraints that results in more complex feasible action spaces. Our proposed Programmable Actor Reinforcement Learning (PARL) uses a deep-policy iteration method that leverages neural networks (NNs) to approximate the value function and combines it with mathematical programming (MP) and sample average approximation (SAA) to solve the per-step-action optimally while accounting for combinatorial action spaces and state-dependent constraint sets. We show how the proposed methodology can be applied to complex inventory replenishment problems where analytical solutions are intractable. We also benchmark the proposed algorithm against state-of-the-art RL algorithms and commonly used replenishment heuristics and find it considerably outperforms existing methods by as much as 14.7% on average in various complex supply chain settings. We find that this improvement of PARL over benchmark algorithms can be directly attributed to better inventory cost management, especially in inventory constrained settings. Furthermore, in the simpler setting where optimal replenishment policy is tractable or known near optimal heuristics exist, we find that the RL approaches can learn near optimal policies. Finally, to make RL algorithms more accessible for inventory management researchers, we also discuss the development of a modular Python library that can be used to test the performance of RL algorithms with various supply chain structures and spur future research in developing practical and near-optimal algorithms for inventory management problems.

Haoran Zhu, Pavankumar Murali, Dzung T. Phan et al.

Several recent publications report advances in training optimal decision trees (ODT) using mixed-integer programs (MIP), due to algorithmic advances in integer programming and a growing interest in addressing the inherent suboptimality of heuristic approaches such as CART. In this paper, we propose a novel MIP formulation, based on a 1-norm support vector machine model, to train a multivariate ODT for classification problems. We provide cutting plane techniques that tighten the linear relaxation of the MIP formulation, in order to improve run times to reach optimality. Using 36 data-sets from the University of California Irvine Machine Learning Repository, we demonstrate that our formulation outperforms its counterparts in the literature by an average of about 10% in terms of mean out-of-sample testing accuracy across the data-sets. We provide a scalable framework to train multivariate ODT on large data-sets by introducing a novel linear programming (LP) based data selection method to choose a subset of the data for training. Our method is able to routinely handle large data-sets with more than 7,000 sample points and outperform heuristics methods and other MIP based techniques. We present results on data-sets containing up to 245,000 samples. Existing MIP-based methods do not scale well on training data-sets beyond 5,500 samples.

Kyongmin Yeo, Dylan E. C. Grullon, Fan-Keng Sun et al.

We propose a recurrent neural network for a "model-free" simulation of a dynamical system with unknown parameters without prior knowledge. The deep learning model aims to jointly learn the nonlinear time marching operator and the effects of the unknown parameters from a time series dataset. We assume that the time series data set consists of an ensemble of trajectories for a range of the parameters. The learning task is formulated as a statistical inference problem by considering the unknown parameters as random variables. A latent variable is introduced to model the effects of the unknown parameters, and a variational inference method is employed to simultaneously train probabilistic models for the time marching operator and an approximate posterior distribution for the latent variable. Unlike the classical variational inference, where a factorized distribution is used to approximate the posterior, we employ a feedforward neural network supplemented by an encoder recurrent neural network to develop a more flexible probabilistic model. The approximate posterior distribution makes an inference on a trajectory to identify the effects of the unknown parameters. The time marching operator is approximated by a recurrent neural network, which takes a latent state sampled from the approximate posterior distribution as one of the input variables, to compute the time evolution of the probability distribution conditioned on the latent variable. In the numerical experiments, it is shown that the proposed variational inference model makes a more accurate simulation compared to the standard recurrent neural networks. It is found that the proposed deep learning model is capable of correctly identifying the dimensions of the random parameters and learning a representation of complex time series data.

Lam M. Nguyen, Marten van Dijk, Dzung T. Phan et al.

The total complexity (measured as the total number of gradient computations) of a stochastic first-order optimization algorithm that finds a first-order stationary point of a finite-sum smooth nonconvex objective function $F(w)=\frac{1}{n} \sum_{i=1}^n f_i(w)$ has been proven to be at least $Ω(\sqrt{n}/ε)$ for $n \leq \mathcal{O}(ε^{-2})$ where $ε$ denotes the attained accuracy $\mathbb{E}[ \|\nabla F(\tilde{w})\|^2] \leq ε$ for the outputted approximation $\tilde{w}$ (Fang et al., 2018). In this paper, we provide a convergence analysis for a slightly modified version of the SARAH algorithm (Nguyen et al., 2017a;b) and achieve total complexity that matches the lower-bound worst case complexity in (Fang et al., 2018) up to a constant factor when $n \leq \mathcal{O}(ε^{-2})$ for nonconvex problems. For convex optimization, we propose SARAH++ with sublinear convergence for general convex and linear convergence for strongly convex problems; and we provide a practical version for which numerical experiments on various datasets show an improved performance.

Lam M. Nguyen, Phuong Ha Nguyen, Dzung T. Phan et al.

This paper has some inconsistent results, i.e., we made some failed claims because we did some mistakes for using the test criterion for a series. Precisely, our claims on the convergence rate of $\mathcal{O}(1/t)$ of SGD presented in Theorem 1, Corollary 1, Theorem 2 and Corollary 2 are wrongly derived because they are based on Lemma 5. In Lemma 5, we do not correctly use the test criterion for a series. Hence, the result of Lemma 5 is not valid. We would like to thank the community for pointing out this mistake!

Lam M. Nguyen, Nam H. Nguyen, Dzung T. Phan et al.

In this paper, we consider a general stochastic optimization problem which is often at the core of supervised learning, such as deep learning and linear classification. We consider a standard stochastic gradient descent (SGD) method with a fixed, large step size and propose a novel assumption on the objective function, under which this method has the improved convergence rates (to a neighborhood of the optimal solutions). We then empirically demonstrate that these assumptions hold for logistic regression and standard deep neural networks on classical data sets. Thus our analysis helps to explain when efficient behavior can be expected from the SGD method in training classification models and deep neural networks.

Oktay Gunluk, Jayant Kalagnanam, Minhan Li et al.

Decision trees have been a very popular class of predictive models for decades due to their interpretability and good performance on categorical features. However, they are not always robust and tend to overfit the data. Additionally, if allowed to grow large, they lose interpretability. In this paper, we present a mixed integer programming formulation to construct optimal decision trees of a prespecified size. We take the special structure of categorical features into account and allow combinatorial decisions (based on subsets of values of features) at each node. Our approach can also handle numerical features via thresholding. We show that very good accuracy can be achieved with small trees using moderately-sized training sets. The optimization problems we solve are tractable with modern solvers.

Jayant Kalagnanam, Max Henrion

There has long been debate about the relative merits of decision theoretic methods and heuristic rule-based approaches for reasoning under uncertainty. We report an experimental comparison of the performance of the two approaches to troubleshooting, specifically to test selection for fault diagnosis. We use as experimental testbed the problem of diagnosing motorcycle engines. The first approach employs heuristic test selection rules obtained from expert mechanics. We compare it with the optimal decision analytic algorithm for test selection which employs estimated component failure probabilities and test costs. The decision analytic algorithm was found to reduce the expected cost (i.e. time) to arrive at a diagnosis by an average of 14% relative to the expert rules. Sensitivity analysis shows the results are quite robust to inaccuracy in the probability and cost estimates. This difference suggests some interesting implications for knowledge acquisition.