Generalizing Linear Autoencoder Recommenders with Decoupled Expected Quadratic Loss
Ruixin Guo, Xinyu Li, Hao Zhou, Yang Zhou, Ruoming Jin
TL;DR
This paper introduces Decoupled Expected Quadratic Loss (DEQL), a generalization of EDLAE for linear autoencoder recommenders, enabling solutions with better performance and broader hyperparameter flexibility.
Contribution
The paper generalizes EDLAE with DEQL, allowing solutions for a wider hyperparameter range and providing an efficient algorithm for practical implementation.
Findings
DEQL outperforms the original EDLAE baseline on benchmark datasets.
Broader hyperparameter range b > 0 improves model performance.
Efficient algorithm ensures computational tractability for DEQL solutions.
Abstract
Linear autoencoders (LAEs) have gained increasing popularity in recommender systems due to their simplicity and strong empirical performance. Most LAE models, including the Emphasized Denoising Linear Autoencoder (EDLAE) introduced by (Steck, 2020), use quadratic loss during training. However, the original EDLAE only provides closed-form solutions for the hyperparameter choice , which limits its capacity. In this work, we generalize EDLAE objective into a Decoupled Expected Quadratic Loss (DEQL). We show that DEQL simplifies the process of deriving EDLAE solutions and reveals solutions in a broader hyperparameter range , which were not derived in Steck's original paper. Additionally, we propose an efficient algorithm based on Miller's matrix inverse theorem to ensure the computational tractability for the case. Empirical results on benchmark datasets show that the…
Peer Reviews
Decision·ICLR 2026 Poster
1. Clear theoretical generalization of EDLAE. Reformulating EDLAE as an expected loss (DEQL) provides a cleaner statistical foundation and yields closed-form solutions for b>0, which were missing in prior work. 2. Efficient algorithmic adaptation. The use of Miller’s theorem reduces computation from $O(n^4)$ to $O(n^3)$, making the extended solution computable in practice. 3. Empirical improvements. Experimental results show that DEQL with $b>0$ offers consistent but moderate accuracy gains ov
1. Limited novelty in the ICLR context. The main contribution is an extension of an existing model (EDLAE) from $b=0$ to $b>0$. While theoretically meaningful, this is somewhat incremental—more aligned with recommender system venues (KDD, SIGIR, RecSys) than a general ML conference like ICLR. 2. Utilization of existing mathematical tools. The core efficiency improvement relies on Miller’s matrix inverse theorem rather than a new theoretical contribution. The innovation lies in applying this the
The paper successfully generalizes the closed-form solution of the EDLAE objective from the special case of $b=0$ to the more general case of $b>0$, which increases the model’s flexibility. The authors developed a practical algorithm for their proposed solution. They designed a method that reduces the computational complexity from $O(n^4)$ to $O(n^3)$, which makes their approach applicable to the datasets used in their experiments. The claims are supported by experiments on multiple public dat
Limited Motivation for the Chosen Approach: The paper does not explicitly justify why a closed-form solution is preferable to a standard gradient-based optimization for this problem. While experts in the subfield might understand the rationale, a broader audience would benefit from a discussion of the trade-offs (e.g., computational cost, guarantee of finding a global optimum, reproducibility). Lack of Analysis of the Key Hyperparameter: While the authors state in Section 5.2 that they perform
1. The paper clearly identifies a key limitation of the existing EDLAE model, the lack of analytical solutions for the case b>0. By introducing the DEQL formulation, the authors successfully generalize EDLAE and provide new theoretical insights into the design of expected quadratic loss functions. The proposed formulation is both mathematically and conceptually well-grounded. 2. The authors provide detailed derivations, lemmas, and proofs to support the theoretical claims. The transition from th
1. The entire paper contains no figures or diagrams to illustrate the overall framework, problem formulation, or intuition behind DEQL. The heavy use of equations makes it difficult for readers to intuitively understand the workflow and conceptual contribution. Adding schematic diagrams of the model or algorithm would greatly improve readability. 2. As the proposed method is a linear autoencoder-based (LAE-based) method, the most recent baseline considered in the paper is EDLAE (2020). Including
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsRecommender Systems and Techniques · Generative Adversarial Networks and Image Synthesis · Explainable Artificial Intelligence (XAI)