ICML 2025

Time Series Representations with Hard-Coded Invariances
Thibaut Germain * 1 Chrysoula Kosma * 1 Laurent Oudre 1
Abstract
Automatically extracting robust representations
from large and complex time series data is becom-
ing imperative for several real-world applications.
Unfortunately, the potential of common neural
network architectures in capturing invariant prop-
erties of time series remains relatively underex-
plored. For instance, convolutional layers often
fail to capture underlying patterns in time series
inputs that encompass strong deformations, such
as trends. Indeed, invariances to some deforma-
tions may be critical for solving complex time se-
ries tasks, such as classification, while guarantee-
ing good generalization performance. To address
these challenges, we mathematically formulate
and technically design efficient and hard-coded
invariant convolutions for specific group actions
applicable to the case of time series. We construct
these convolutions by considering specific sets of
deformations commonly observed in time series,
including scaling, offset shift, and trend. We fur-
ther combine the proposed invariant convolutions
with standard convolutions in single embedding
layers, and we showcase the layer’s capacity to
capture complex invariant time series properties
in several scenarios.
1. Introduction
Recently, there has been a growing interest in applying
machine learning to time series data, further necessitated by
the challenging properties of time series, including varying
modalities, high noise levels, and distribution shifts.
Machine learning for time series has gradually moved from
statistical methods, e. g., autoregressive models (Box et al.,
*Equal contribution 1Universit´e Paris-Saclay, Universit´e Paris
Cit´e, ENS Paris Saclay, CNRS, SSA, INSERM, Centre Borelli,
F-91190, Gif-sur-Yvette, France. Correspondence to: Thibaut Ger-
main <thibaut.germain@ens-paris-saclay.fr>, Chrysoula Kosma
<chrysoula.kosma@ens-paris-saclay.fr>.
Proceedings ...