Andrew Wilson

Roman Levin, Valeriia Cherepanova, Avi Schwarzschild et al. · amazon-science

Recent work on deep learning for tabular data demonstrates the strong performance of deep tabular models, often bridging the gap between gradient boosted decision trees and neural networks. Accuracy aside, a major advantage of neural models is that they learn reusable features and are easily fine-tuned in new domains. This property is often exploited in computer vision and natural language applications, where transfer learning is indispensable when task-specific training data is scarce. In this work, we demonstrate that upstream data gives tabular neural networks a decisive advantage over widely used GBDT models. We propose a realistic medical diagnosis benchmark for tabular transfer learning, and we present a how-to guide for using upstream data to boost performance with a variety of tabular neural network architectures. Finally, we propose a pseudo-feature method for cases where the upstream and downstream feature sets differ, a tabular-specific problem widespread in real-world applications. Our code is available at https://github.com/LevinRoman/tabular-transfer-learning .

Shikai Qiu, Tim G. J. Rudner, Sanyam Kapoor et al.

Standard regularized training procedures correspond to maximizing a posterior distribution over parameters, known as maximum a posteriori (MAP) estimation. However, model parameters are of interest only insomuch as they combine with the functional form of a model to provide a function that can make good predictions. Moreover, the most likely parameters under the parameter posterior do not generally correspond to the most likely function induced by the parameter posterior. In fact, we can re-parametrize a model such that any setting of parameters can maximize the parameter posterior. As an alternative, we investigate the benefits and drawbacks of directly estimating the most likely function implied by the model and the data. We show that this procedure leads to pathological solutions when using neural networks and prove conditions under which the procedure is well-behaved, as well as a scalable approximation. Under these conditions, we find that function-space MAP estimation can lead to flatter minima, better generalization, and improved robustness to overfitting.

Abdul Fatir Ansari, Lorenzo Stella, Caner Turkmen et al.

We introduce Chronos, a simple yet effective framework for pretrained probabilistic time series models. Chronos tokenizes time series values using scaling and quantization into a fixed vocabulary and trains existing transformer-based language model architectures on these tokenized time series via the cross-entropy loss. We pretrained Chronos models based on the T5 family (ranging from 20M to 710M parameters) on a large collection of publicly available datasets, complemented by a synthetic dataset that we generated via Gaussian processes to improve generalization. In a comprehensive benchmark consisting of 42 datasets, and comprising both classical local models and deep learning methods, we show that Chronos models: (a) significantly outperform other methods on datasets that were part of the training corpus; and (b) have comparable and occasionally superior zero-shot performance on new datasets, relative to methods that were trained specifically on them. Our results demonstrate that Chronos models can leverage time series data from diverse domains to improve zero-shot accuracy on unseen forecasting tasks, positioning pretrained models as a viable tool to greatly simplify forecasting pipelines.

Luke Bhan, Hanyu Zhang, Andrew Gordon Wilson et al.

Monitoring forecasting systems is critical for customer satisfaction, profitability, and operational efficiency in large-scale retail businesses. We propose The Forecast Critic, a system that leverages Large Language Models (LLMs) for automated forecast monitoring, taking advantage of their broad world knowledge and strong ``reasoning'' capabilities. As a prerequisite for this, we systematically evaluate the ability of LLMs to assess time series forecast quality, focusing on three key questions. (1) Can LLMs be deployed to perform forecast monitoring and identify obviously unreasonable forecasts? (2) Can LLMs effectively incorporate unstructured exogenous features to assess what a reasonable forecast looks like? (3) How does performance vary across model sizes and reasoning capabilities, measured across state-of-the-art LLMs? We present three experiments, including on both synthetic and real-world forecasting data. Our results show that LLMs can reliably detect and critique poor forecasts, such as those plagued by temporal misalignment, trend inconsistencies, and spike errors. The best-performing model we evaluated achieves an F1 score of 0.88, somewhat below human-level performance (F1 score: 0.97). We also demonstrate that multi-modal LLMs can effectively incorporate unstructured contextual signals to refine their assessment of the forecast. Models correctly identify missing or spurious promotional spikes when provided with historical context about past promotions (F1 score: 0.84). Lastly, we demonstrate that these techniques succeed in identifying inaccurate forecasts on the real-world M5 time series dataset, with unreasonable forecasts having an sCRPS at least 10% higher than that of reasonable forecasts. These findings suggest that LLMs, even without domain-specific fine-tuning, may provide a viable and scalable option for automated forecast monitoring and evaluation.

Luca Masserano, Abdul Fatir Ansari, Boran Han et al.

How to best develop foundational models for time series forecasting remains an important open question. Tokenization is a crucial consideration in this effort: what is an effective discrete vocabulary for a real-valued sequential input? To address this question, we develop WaveToken, a wavelet-based tokenizer that allows models to learn complex representations directly in the space of time-localized frequencies. Our method first scales and decomposes the input time series, then thresholds and quantizes the wavelet coefficients, and finally pre-trains an autoregressive model to forecast coefficients for the forecast horizon. By decomposing coarse and fine structures in the inputs, wavelets provide an eloquent and compact language for time series forecasting that simplifies learning. Empirical results on a comprehensive benchmark, including 42 datasets for both in-domain and zero-shot settings, show that WaveToken: i) provides better accuracy than recently proposed foundation models for forecasting while using a much smaller vocabulary (1024 tokens), and performs on par or better than modern deep learning models trained specifically on each dataset; and ii) exhibits superior generalization capabilities, achieving the best average rank across all datasets for three complementary metrics. In addition, we show that our method can easily capture complex temporal patterns of practical relevance that are challenging for other recent pre-trained models, including trends, sparse spikes, and non-stationary time series with varying frequencies evolving over time.

Shikai Qiu, Lechao Xiao, Andrew Gordon Wilson et al.

What scaling limits govern neural network training dynamics when model size and training time grow in tandem? We show that despite the complex interactions between architecture, training algorithms, and data, compute-optimally trained models exhibit a remarkably precise universality. Specifically, loss curves from models of varying sizes collapse onto a single universal curve when training compute and loss are normalized to unity at the end of training. With learning rate decay, the collapse becomes so tight that differences in the normalized curves across models fall below the noise floor of individual loss curves across random seeds, a phenomenon we term supercollapse. We observe supercollapse across learning rate schedules, datasets, and architectures, including transformers trained on next-token prediction, and find it breaks down when hyperparameters are scaled suboptimally, providing a precise and practical indicator of good scaling. We explain these phenomena by connecting collapse to the power-law structure in typical neural scaling laws, and analyzing a simple yet surprisingly effective model of SGD noise dynamics that accurately predicts loss curves across various learning rate schedules and quantitatively explains the origin of supercollapse.

Hanyu Zhang, Chuck Arvin, Dmitry Efimov et al.

Modern time-series forecasting models often fail to make full use of rich unstructured information about the time series themselves. This lack of proper conditioning can lead to obvious model failures; for example, models may be unaware of the details of a particular product, and hence fail to anticipate seasonal surges in customer demand in the lead up to major exogenous events like holidays for clearly relevant products. To address this shortcoming, this paper introduces a novel forecast post-processor -- which we call LLMForecaster -- that fine-tunes large language models (LLMs) to incorporate unstructured semantic and contextual information and historical data to improve the forecasts from an existing demand forecasting pipeline. In an industry-scale retail application, we demonstrate that our technique yields statistically significantly forecast improvements across several sets of products subject to holiday-driven demand surges.

Annan Yu, Danielle C. Maddix, Boran Han et al.

Time series foundation models (TSFMs) are a class of potentially powerful, general-purpose tools for time series forecasting and related temporal tasks, but their behavior is strongly shaped by subtle inductive biases in their design. Rather than developing a new model and claiming that it is better than existing TSFMs, e.g., by winning on existing well-established benchmarks, our objective is to understand how the various ``knobs'' of the training process affect model quality. Using a mix of theory and controlled empirical evaluation, we identify several design choices (patch size, embedding choice, training objective, etc.) and show how they lead to implicit biases in fundamental model properties (temporal behavior, geometric structure, how aggressively or not the model regresses to the mean, etc.); and we show how these biases can be intuitive or very counterintuitive, depending on properties of the model and data. We also illustrate in a case study on outlier handling how multiple biases can interact in complex ways; and we discuss implications of our results for learning the bitter lesson and building TSFMs.

Annan Yu, Danielle C. Maddix, Boran Han et al.

Transformers are widely used across data modalities, and yet the principles distilled from text models often transfer imperfectly to models trained to other modalities. In this paper, we analyze Transformers through the lens of rank structure. Our focus is on the time series setting, where the structural properties of the data differ remarkably from those of text or vision. We show that time-series embeddings, unlike text or vision, exhibit sharply decaying singular value spectra: small patch sizes and smooth continuous mappings concentrate the data into low-rank subspaces. From this, we prove that the associated $Q/K/V$ projections admit accurate low-rank approximations, and that attention layers become compressible in proportion to the decay of the embedding spectrum. We introduce the concept of flow-of-ranks, a phenomenon by which nonlinear mixing across depth inflates the rank, explaining why early layers are most amenable to compression and why ranks grow with depth. Guided by these theoretical and empirical results, we use these insights to compress Chronos, a large time series foundation model, achieving a reduction of $65\%$ in inference time and $81\%$ in memory, without loss of accuracy. Our findings provide principled guidance for allocating width, depth, and heads in time series foundation models, and for exploiting their inherent compressibility.

Ethan Baron, Boris Oreshkin, Ruijun Ma et al.

Many time series applications require access to multi-step forecast trajectories in the form of sample paths. Recently, time series foundation models have leveraged multi-step lookahead predictions to improve the quality and efficiency of multi-step forecasts. However, these models only predict independent marginal distributions for each time step, rather than a full joint predictive distribution. To generate forecast sample paths with realistic correlation structures, one typically resorts to autoregressive sampling, which can be extremely expensive. In this paper, we present a copula-based approach to efficiently generate accurate, correlated sample paths from existing multi-step time series foundation models in one forward pass. Our copula-based approach generates correlated sample paths orders of magnitude faster than autoregressive sampling, and it yields improved sample path quality by mitigating the snowballing error phenomenon.

Yilun Kuang, Noah Amsel, Sanae Lotfi et al.

The core component of attention is the scoring function, which transforms the inputs into low-dimensional queries and keys and takes the dot product of each pair. While the low-dimensional projection improves efficiency, it causes information loss for certain tasks that have intrinsically high-dimensional inputs. Additionally, attention uses the same scoring function for all input pairs, without imposing a distance-dependent compute bias for neighboring tokens in the sequence. In this work, we address these shortcomings by proposing new scoring functions based on computationally efficient structured matrices with high ranks, including Block Tensor-Train (BTT) and Multi-Level Low Rank (MLR) matrices. On in-context regression tasks with high-dimensional inputs, our proposed scoring functions outperform standard attention for any fixed compute budget. On language modeling, a task that exhibits locality patterns, our MLR-based attention method achieves improved scaling laws compared to both standard attention and variants of sliding window attention. Additionally, we show that both BTT and MLR fall under a broader family of efficient structured matrices capable of encoding either full-rank or distance-dependent compute biases, thereby addressing significant shortcomings of standard attention. Finally, we show that MLR attention has promising results for long-range time-series forecasting.