Analogical transfer infers unknown information by leveraging known similarities between situations. This doctoral research investigates similarity measure learning tailored for analogical transfer, focusing on classification. A unified theoretical framework, called Similarity Measure Learning Architecture (SiMeLAr), is introduced to optimize systematically similarity measures for analogical tasks. Beside this generic question, we focus on the specific case of the method called CoAT (Complexity-based Analogical Transfer). To address its non-continuity, we propose a continuous variant which enables gradient-based optimization. Future work will explore the application of the variant to real-world domains, such as culinary and medical use cases.
Analogical transfer infers information from known similar cases by assuming that their similarity in
certain components implies similarity in others [
Similarity measures thus obviously play a central role to analogical transfer, that can be seen as
essentially transferring similarity knowledge [
This thesis aims at studying the interactions between analogical transfer and metric learning and at
developing a methodology to learn optimized similarity measures for case-based prediction. Validation will
occur in two domains: culinary recipe transfer [
This research lies at the intersection of similarity measure learning and analogical transfer, necessitating an overview of both fields and their interactions.
Similarity Measure Learning Similarity measures quantify how alike two objects are, often derived
from distances transformed by decreasing functions [
More recently, Deep metric learning (DML) employs neural networks projecting data into embedding
spaces, leading to approaches that can be categorized into pair-based methods using contrastive
loss [
In the context of case-based reasoning, some works further propose data-driven approaches to
learning or tuning similarity measures that rely less on expert-driven designs [
Analogical transfer infers new situations’ outcomes from similar known
instances by mapping similarities (see e.g. [
Case based prediction (CBP) considers a case base CB, which is a set of cases where each case is a pair (, ) ∈ × ℛ
, where and ℛ respectively denote the situation and the outcome spaces. They
are respectively equipped with two similarity measures : × →
describe in more details the CoAT [
R+. We promising results in analogical transfer tasks.
CoAT relies on a global indicator, computed on the whole case base instead of evaluating locally similarity between source-target pairs: applying the analogical transfer to CBP, according to which similar situations imply similar outcomes, the incompatibility indicator computes the number of triplets (, , ) in CB that violate this principle, i.e. (, ) ≥ (, ) but ℛ(, ) < ℛ(, ): Γ( , ℛ, CB) :=
Ind (, , ) ∑︁ (,,)∈CB3 (1) ∈
where = ( , ℛ, CB), and Ind (, , ) := 1 { (, ) ≥ (, )} 1 { ℛ(, ) < ℛ(, )}.
As a classifier, for a new situation new, when leveraging the situation similarity to predict its outcome, CoAT then identifies the most plausible outcome, defined as the one minimizing the incompatibility of the case base augmented with the candidate new case (new, ) ˆnew := arg min CoAT(new, ) where CoAT(new, ) := Γ ( , ℛ, CB ∪ {(new, )})
Similarity measure learning and analogical transfer are interdependent: efective analogical transfer requires suitably learned measures, and optimal measures can be guided by analogical prediction tasks. Taking CoAT as an example, the incompatibility indicator Γ enables metric learning beyond classification. In fact, defining parameters
and incompatibility , Badra et al. [
This opens the following questions: Do similarity measures optimized for a specific algorithm, for example CoAT, generalize across analogical classifiers? Can we tailor measures specifically for analogical classifiers or vice versa?
This research investigates how metric learning algorithms influence analogical transfer classifier performance, e.g. measured by their accuracy, and considering in particular the case of CoAT. Challenges include studying classifier-metric interactions, defining mathematical frameworks for analogical similarity learning, and taking into account computational complexity constraints.
The objectives of this research include both theoretical and practical aspects. The former aims to study the relationship between similarity measure learning and analogical transfer, with a focus on the classification task. This involves (1) establishing a theoretical framework that unifies similarity measure learning and analogical transfer, and (2) studying the optimization of similarity measures using a specific analogical transfer model. On the practical side, the analogical transfer model will be applied to diferent domains, including culinary recipe cases and medical use cases.
︁( In order to achieve the first objective in the theoretical part, I propose a unified framework that combines similarity measure learning and analogical transfer, by abstracting the common processes, as measure, interaction and optimization. This work includes the following targets. Firstly, it aims to provide a clear mathematical framework. By doing so, my aim is to identify parts of existing metric learning that can be considered as using components of analogical transfer like . After that, I would like to provide a base of theoretical proofs for the research questions introduced in Section 1.2, for example, whether guarantee can be provided about the prediction accuracy, i.e., studying the probability P arg min∈ ^CoAT(new, )}) = new . Eventually, this work could help to guide the development of new models. This part will be evaluated by a systematic literature survey and mathematical demonstrations: we will investigate models that fit into this framework and characterize formally their expression within this framework. In addition, we will prove the theorems under this ︁) framework using mathematical methods.
After establishing the theoretical framework, the next step is to study the optimization of similarity
measures for the analogical transfer model CoAT [
I would like to explore the use of metric learning methods to optimize for CoAT. This involves a more detailed theoretical analysis the limitations of the original CoAT model, such as its discrete and non-diferentiable nature limiting its optimization capabilities, and proposing a method to overcome these limitations. The proposed method will be evaluated on real datasets to assess its efectiveness in improving the performance of CoAT, using classical supervised learning quality metrics, such as accuracy and algorithmic complexity.
At present, the theoretical part of my study comprises a framework that integrates similarity measure learning with analogical transfer (Section 3.1), and an investigation into optimizing similarity measures for the analogical transfer model CoAT (Section 3.2).
In order to explore the relationship between metric learning and analogical transfer, I first propose a
theoretical framework based on the literature in the state of the art (especially inspired by CoAT [
situation space () and the outcome space (ℛ), establishing intra-space relationships. 1. The measure component defines the similarity measures ( and ℛ) independently within the 2. The interaction component introduces an interaction function linking metrics from the situation and outcome spaces, establishing inter-space relationships. This function ensures consistency, so that similar input features correspond to similar outputs. 3. The optimization component employs a parameterized loss function and an aggregated total loss function to optimize the model parameters. It guides the training process, aligning the interaction of metrics toward efective learning.
Based on this framework I develop several theorems for discussing when the loss function can be guaranteed to be diferentiable and convex, and study the relationship between the loss function and the accuracy of the model.
Beyond the general case, I look at the particular case of CoAT [
To overcome these limitations, I propose a new continuous energy function, which measures the extent of violation of the analogical transfer principle rather than merely counting violations. Specifically, in Ind , I propose to replace the first term of the product with max (0, − (, ) + (, )), where is a margin parameter. It quantifies the degree of violation. By doing so, the proposed method enables gradient-based optimization due to its continuity and diferentiability. Additionally, I propose to modify the number of triplets (, , ) involved in the computation of Γ (see Eq. 1), to reduce the algorithmic complexity, and to introduce a normalization term in order to deal with multi-class classification scenarios.
Experimental Study Ongoing works study the proposed function for metric leaning, combining it
with several common loss functions in energy-based models, such as MCE loss, hinge loss and direct
loss [
Results show that the new continuous energy-based method outperforms the original CoAT in 4 out of the 6 considered datasets, particularly when the similarity measures are optimized. Notably, datasets with purely categorical attributes present challenges, that we are currently investigating in more details.
My research advances the integration of similarity measure learning with analogical transfer for classification tasks. A unified theoretical framework (SiMeLAr) is proposed to clarify structural elements common to metric learning and analogical transfer. The proposed Continuous Complexity-based Analogical Transfer (C-CoAT) resolves discontinuity and zero-gradient limitations of the original CoAT, and opens the way to improving the classification performance via gradient-based optimization of the similarity measure it relies on, validated through empirical evaluations.
Future work will further explore whether the similarity measures optimized for C-CoAT are also efective for other classifiers, and extend to real-world applications such as cooking and medical use cases.
This work is funded by the SMeLT project, ANR-22-CE23-0032-03.
The authors did not use any generative AI during the preparation of this work.