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Nodens Koren

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4 papers

2 author rows

TMLR Journal 2026 Journal Article

Merging Memory and Space: A State Space Neural Operator

Nodens Koren
Samuel Lanthaler

We propose the *State Space Neural Operator* (SS-NO), a compact architecture for learning solution operators of time-dependent partial differential equations (PDEs). Our formulation extends structured state space models (SSMs) to joint spatiotemporal modeling, introducing two key mechanisms: *adaptive damping*, which stabilizes learning by localizing receptive fields, and *learnable frequency modulation*, which enables data-driven spectral selection. These components provide a unified framework for capturing long-range dependencies with parameter efficiency. Theoretically, we establish connections between SSMs and neural operators, proving a universality theorem for convolutional architectures with a full field of view. Empirically, SS-NO achieves strong performance across diverse PDE benchmarks—including 1D Burgers' and Kuramoto–Sivashinsky equations, and 2D Navier–Stokes and compressible Euler flows—while using significantly fewer parameters than competing approaches. Our results demonstrate that state space modeling provides an effective foundation for efficient and accurate neural operator learning.

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ICML Conference 2023 Conference Paper

Reconstructive Neuron Pruning for Backdoor Defense

Yige Li
Xixiang Lyu
Xingjun Ma
Nodens Koren
Lingjuan Lyu
Bo Li 0026
Yu-Gang Jiang 0001

Deep neural networks (DNNs) have been found to be vulnerable to backdoor attacks, raising security concerns about their deployment in mission-critical applications. While existing defense methods have demonstrated promising results, it is still not clear how to effectively remove backdoor-associated neurons in backdoored DNNs. In this paper, we propose a novel defense called Reconstructive Neuron Pruning (RNP) to expose and prune backdoor neurons via an unlearning and then recovering process. Specifically, RNP first unlearns the neurons by maximizing the model’s error on a small subset of clean samples and then recovers the neurons by minimizing the model’s error on the same data. In RNP, unlearning is operated at the neuron level while recovering is operated at the filter level, forming an asymmetric reconstructive learning procedure. We show that such an asymmetric process on only a few clean samples can effectively expose and prune the backdoor neurons implanted by a wide range of attacks, achieving a new state-of-the-art defense performance. Moreover, the unlearned model at the intermediate step of our RNP can be directly used to improve other backdoor defense tasks including backdoor removal, trigger recovery, backdoor label detection, and backdoor sample detection. Code is available at https: //github. com/bboylyg/RNP.

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NeurIPS Conference 2021 Conference Paper

Anti-Backdoor Learning: Training Clean Models on Poisoned Data

Yige Li
Xixiang Lyu
Nodens Koren
Lingjuan Lyu
Bo Li
Xingjun Ma

Backdoor attack has emerged as a major security threat to deep neural networks (DNNs). While existing defense methods have demonstrated promising results on detecting or erasing backdoors, it is still not clear whether robust training methods can be devised to prevent the backdoor triggers being injected into the trained model in the first place. In this paper, we introduce the concept of \emph{anti-backdoor learning}, aiming to train \emph{clean} models given backdoor-poisoned data. We frame the overall learning process as a dual-task of learning the \emph{clean} and the \emph{backdoor} portions of data. From this view, we identify two inherent characteristics of backdoor attacks as their weaknesses: 1) the models learn backdoored data much faster than learning with clean data, and the stronger the attack the faster the model converges on backdoored data; 2) the backdoor task is tied to a specific class (the backdoor target class). Based on these two weaknesses, we propose a general learning scheme, Anti-Backdoor Learning (ABL), to automatically prevent backdoor attacks during training. ABL introduces a two-stage \emph{gradient ascent} mechanism for standard training to 1) help isolate backdoor examples at an early training stage, and 2) break the correlation between backdoor examples and the target class at a later training stage. Through extensive experiments on multiple benchmark datasets against 10 state-of-the-art attacks, we empirically show that ABL-trained models on backdoor-poisoned data achieve the same performance as they were trained on purely clean data. Code is available at \url{https: //github. com/bboylyg/ABL}.

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ICLR Conference 2021 Conference Paper

Neural Attention Distillation: Erasing Backdoor Triggers from Deep Neural Networks

Yige Li
Xixiang Lyu
Nodens Koren
Lingjuan Lyu
Bo Li 0026
Xingjun Ma

Deep neural networks (DNNs) are known vulnerable to backdoor attacks, a training time attack that injects a trigger pattern into a small proportion of training data so as to control the model's prediction at the test time. Backdoor attacks are notably dangerous since they do not affect the model's performance on clean examples, yet can fool the model to make the incorrect prediction whenever the trigger pattern appears during testing. In this paper, we propose a novel defense framework Neural Attention Distillation (NAD) to erase backdoor triggers from backdoored DNNs. NAD utilizes a teacher network to guide the finetuning of the backdoored student network on a small clean subset of data such that the intermediate-layer attention of the student network aligns with that of the teacher network. The teacher network can be obtained by an independent finetuning process on the same clean subset. We empirically show, against 6 state-of-the-art backdoor attacks, NAD can effectively erase the backdoor triggers using only 5\% clean training data without causing obvious performance degradation on clean examples. Our code is available at https://github.com/bboylyg/NAD.

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