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EEO-TFV: Escape-Explore Optimizer for Web-Scale Time-Series Forecasting and Vision Analysis

Hua Wang, Jinghao Lu, Fan Zhang

TL;DR

EEO-TFV addresses stability and generalization challenges in Transformer-based Web-scale time-series forecasting and vision tasks by pairing a lightweight Transformer with the Escape–Explore Optimizer (EEO). The optimizer combines a sharpness-aware outer update, negative-curvature escape, and SGLD-style stochastic exploration with EMA aggregation to avoid saddle points, entropy collapse, and rank collapse, promoting flatter minima and robust convergence. Across extensive Web-scale benchmarks, EEO-TFV matches or surpasses state-of-the-art baselines on long-horizon forecasting and Synapse medical segmentation, while demonstrating stronger generalization and stability across modalities. The work highlights EEO-TFV as a promising cross-task foundation model for Web-scale data mining and outlines future directions in cross-domain transfer, web-tailored self-supervision, and online robust learning.

Abstract

Transformer-based foundation models have achieved remarkable progress in tasks such as time-series forecasting and image segmentation. However, they frequently suffer from error accumulation in multivariate long-sequence prediction and exhibit vulnerability to out-of-distribution samples in image-related tasks. Furthermore, these challenges become particularly pronounced in large-scale Web data analysis tasks, which typically involve complex temporal patterns and multimodal features. This complexity substantially increases optimization difficulty, rendering models prone to stagnation at saddle points within high-dimensional parameter spaces. To address these issues, we propose a lightweight Transformer architecture in conjunction with a novel Escape-Explore Optimizer (EEO). The optimizer enhances both exploration and generalization while effectively avoiding sharp minima and saddle-point traps. Experimental results show that, in representative Web data scenarios, our method achieves performance on par with state-of-the-art models across 11 time-series benchmark datasets and the Synapse medical image segmentation task. Moreover, it demonstrates superior generalization and stability, thereby validating its potential as a versatile cross-task foundation model for Web-scale data mining and analysis.

EEO-TFV: Escape-Explore Optimizer for Web-Scale Time-Series Forecasting and Vision Analysis

TL;DR

EEO-TFV addresses stability and generalization challenges in Transformer-based Web-scale time-series forecasting and vision tasks by pairing a lightweight Transformer with the Escape–Explore Optimizer (EEO). The optimizer combines a sharpness-aware outer update, negative-curvature escape, and SGLD-style stochastic exploration with EMA aggregation to avoid saddle points, entropy collapse, and rank collapse, promoting flatter minima and robust convergence. Across extensive Web-scale benchmarks, EEO-TFV matches or surpasses state-of-the-art baselines on long-horizon forecasting and Synapse medical segmentation, while demonstrating stronger generalization and stability across modalities. The work highlights EEO-TFV as a promising cross-task foundation model for Web-scale data mining and outlines future directions in cross-domain transfer, web-tailored self-supervision, and online robust learning.

Abstract

Transformer-based foundation models have achieved remarkable progress in tasks such as time-series forecasting and image segmentation. However, they frequently suffer from error accumulation in multivariate long-sequence prediction and exhibit vulnerability to out-of-distribution samples in image-related tasks. Furthermore, these challenges become particularly pronounced in large-scale Web data analysis tasks, which typically involve complex temporal patterns and multimodal features. This complexity substantially increases optimization difficulty, rendering models prone to stagnation at saddle points within high-dimensional parameter spaces. To address these issues, we propose a lightweight Transformer architecture in conjunction with a novel Escape-Explore Optimizer (EEO). The optimizer enhances both exploration and generalization while effectively avoiding sharp minima and saddle-point traps. Experimental results show that, in representative Web data scenarios, our method achieves performance on par with state-of-the-art models across 11 time-series benchmark datasets and the Synapse medical image segmentation task. Moreover, it demonstrates superior generalization and stability, thereby validating its potential as a versatile cross-task foundation model for Web-scale data mining and analysis.
Paper Structure (36 sections, 4 theorems, 12 equations, 5 figures, 6 tables)

This paper contains 36 sections, 4 theorems, 12 equations, 5 figures, 6 tables.

Table of Contents

  1. Introduction
  2. Related Work
  3. Web Scale Foundation Models for Time-Series Forecasting and Medical Image Segmentation
  4. Efficient Transformer Design in Web-Scale Intelligent Environments
  5. Entropy Collapse and Rank Collapse
  6. Optimizers and Convergence: Flatness, Escape, and Stochastic Exploration
  7. Methodology
  8. Notation
  9. Problem Formulation Extension
  10. Motivating Example
  11. Unified Design of the Representation Layer
  12. Transformer Architecture
  13. Escape–Explore Optimizer (EEO)
  14. Sharpness-Aware Outer Update
  15. Negative-Curvature Escape
  16. ...and 21 more sections

Key Result

lemma 1

Consider a single-layer, single-head attention mechanism, where the alignment loss is defined as $L_{\text{att}} = \tfrac{1}{2} \|A(Z) - A^*(Z)\|_F^2$, with $A(Z)$ denoting the attention matrix and $A^*(Z)$ the ideal affinity matrix. Under the main theorem assumptions and appropriate choices of $\et

Figures (5)

  • Figure 1: The architecture of EEO-TFV
  • Figure 2: Left: Rank-collapse diagnostic plot for the Traffic dataset showing no signs of rank degradation. Right: Rank-collapse diagnostic plot for the Synapse medical image segmentation dataset.
  • Figure 3: Left: Singular value spectrum for the Traffic dataset. Right: Singular value spectrum for the Synapse dataset.
  • Figure 4: Nuclear norm of the attention matrix for different models
  • Figure 5: Attention matrices on Web-Weather dataset.

Theorems & Definitions (4)

  • lemma 1: Attention Loss Descent of the Toy Transformer
  • lemma 2: Consistency of Robust Neighborhood and Outer Update
  • lemma 3: Reliable Curvature Estimation and Negative-Curvature Escape
  • lemma 4: Expected Descent of the Robust Objective under EEO