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In this paper, we explore a novel online learning setting, where the online learners are presented with “doubly-streaming” data. Namely, the data instances constantly streaming in are described by feature spaces that over-time evolve, with new features emerging and old features fading away. The main challenge of this problem lies in the fact that the newly emerging features are described by very few samples, resulting in weak learners that tend to make error predictions. A seemingly plausible idea to overcome the challenge is to establish a relationship between the old and new feature spaces, so that an online learner can leverage the knowledge learned from the old features to better the learning performance on the new features. Unfortunately, this idea does not scale up to high-dimensional feature spaces that entail very complex feature interplay. Specifically. a tradeoff between onlineness, which biases shallow learners, and expressiveness, which requires deep models, is inevitable. Motivated by this, we propose a novel paradigm, named Online Learning Deep models from Data of Double Streams (OLD3S), where a shared latent subspace is discovered to summarize information from the old and new feature spaces, building an intermediate feature mapping relationship. A key trait of OLD3S is to treat the model capacity as a learnable semantics, aiming to yield optimal model depth and parameters jointly in accordance with the complexity and non-linearity of the input data streams in an online fashion. To ablate its efficacy and applicability, two variants of OLD3S are proposed namely, OLD-Linear that learns the relationship by a linear function; and OLD-FD learns that two consecutive feature spaces pre-and-post evolution with fixed deep depth. Besides, instead of re-starting the entire learning process from scratch, OLD3S learns multiple newly emerging feature spaces in a lifelong manner, retaining the knowledge from the learned and vanished feature space to enjoy a jump-start of the new features’ learning process. Both theoretical analysis and empirical studies substantiate the viability and effectiveness of our proposed approach.
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This content will become publicly available on October 31, 2026
Feature-Function Curvature Analysis: A Geometric Framework for Explaining Differentiable Models
Explainable AI (XAI) is critical for building trust in complex machine learning models, yet mainstream attribution methods often provide an incomplete, static picture of a model's final state. By collapsing a feature's role into a single score, they are confounded by non-linearity and interactions. To address this, we introduce Feature-Function Curvature Analysis (FFCA), a novel framework that analyzes the geometry of a model's learned function. FFCA produces a 4-dimensional signature for each feature, quantifying its: (1) Impact, (2) Volatility, (3) Non-linearity, and (4) Interaction. Crucially, we extend this framework into Dynamic Archetype Analysis, which tracks the evolution of these signatures throughout the training process. This temporal view moves beyond explaining what a model learned to revealing how it learns. We provide the first direct, empirical evidence of hierarchical learning, showing that models consistently learn simple linear effects before complex interactions. Furthermore, this dynamic analysis provides novel, practical diagnostics for identifying insufficient model capacity and predicting the onset of overfitting. Our comprehensive experiments demonstrate that FFCA, through its static and dynamic components, provides the essential geometric context that transforms model explanation from simple quantification to a nuanced, trustworthy analysis of the entire learning process.
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- Award ID(s):
- 2331908
- PAR ID:
- 10703597
- Publisher / Repository:
- arXiv preprint: https://doi.org/10.48550/arXiv.2510.27207
- Date Published:
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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