arXiv subjects

Patryk Krukowski

Publications and source records attributed to Patryk Krukowski.

7 recordsLinked to original sources

arXiv2026

BARRIER: Bounded Activation Regions for Robust Information Erasure

Machine unlearning has reached a critical bottleneck. As traditional weight-space interventions focus primarily on erasing targeted concepts, they often fail to prevent the unintended suppression of other significant representations. This leads to substantial collateral damage, with essential knowledge being forgotten, because these methods lack formal mathematical guarantees for the preservation of neutral concepts. To avoid degradation, they are frequently forced into conservative updates. We propose BARRIER (Bounded Activation Regions for Robust Information Erasure), a paradigm-shifting framework that shifts the locus of intervention from static model weights to the dynamic geometry of hidden-layer activations. Unlike existing methods, BARRIER employs Interval Arithmetic (IA) on SVD-based projections of the activation space to encapsulate the specific target region within a bounding hypercube. By driving unlearning updates exclusively within this forget interval and mathematically bounding the model response on the complement, we ensure rigorous protection of the retain distribution. This geometric construction transforms the preservation of knowledge from an empirical heuristic into a formal optimization target with a probabilistic tail bound on functional drift. Crucially, this stability permits highly aggressive unlearning updates within the forget region. Empirical evaluations demonstrate that BARRIER matches state-of-the-art trade-offs across classifiers and diffusion models, maximizing targeted concept erasure while safeguarding the integrity of all other representations. Our code is available at https://github.com/OneAndZero24/BARRIER.

cs.CV↗

arXiv2026

Stop Marginalizing My Dreams: Model Inversion via Laplace Kernel for Continual Learning

Data-free continual learning (DFCIL) relies on model inversion to synthesize pseudo-samples and mitigate catastrophic forgetting. However, existing inversion methods are fundamentally limited by a simplifying assumption: they model feature distributions using diagonal covariance, effectively ignoring correlations that define the geometry of learned representations. As a result, synthesized samples often lack fidelity, limiting knowledge retention. In this work, we show that modeling feature dependencies is a key ingredient for effective DFCIL. We introduce REMIX, a structured covariance modeling framework that enables scalable full-covariance modeling without the prohibitive cost of dense matrix inversion and log-determinant computation. By leveraging a Laplace kernel parameterization, REMIX captures structured feature dependencies using memory that scales linearly with the feature dimensionality, while requiring only an additional logarithmic factor in computation. Modeling these correlations produces more coherent synthetic samples and consistently improves performance across standard DFCIL benchmarks. Our results demonstrate that moving beyond diagonal assumptions is essential for effective and scalable data-free continual learning. Our code is available at https://github. com/pkrukowski1/REMIX-Model-Inversion-via-Laplace-Kernel.

cs.LG↗

arXiv2025

InTAct: Interval-based Task Activation Consolidation for Continual Learning

Continual learning is a fundamental challenge in artificial intelligence that requires networks to acquire new knowledge while preserving previously learned representations. Despite the success of various approaches, most existing paradigms do not provide rigorous mathematical guarantees against catastrophic forgetting. Current methods that offer such guarantees primarily focus on analyzing the parameter space using \textit{interval arithmetic (IA)}, as seen in frameworks such as InterContiNet. However, restricting high-dimensional weight updates can be computationally expensive. In this work, we propose InTAct (Interval-based Task Activation Consolidation), a method that mitigates catastrophic forgetting by enforcing functional invariance at the neuron level. We identify specific activation intervals where previous tasks reside and constrain updates within these regions while allowing for flexible adaptation elsewhere. By ensuring that predictions remain stable within these nested activation intervals, we provide a tractable mathematical guarantee of functional invariance. We emphasize that regulating the activation space is significantly more efficient than parameter-based constraints, because the dimensionality of internal signals is much lower than that of the vast space of model weights. While our approach is architecture-agnostic and applicable to various continual learning settings, its integration with prompt-based methods enables it to achieve state-of-the-art performance on challenging benchmarks.

cs.LG↗

arXiv2025

SHIELD: Secure Hypernetworks for Incremental Expansion Learning Defense

Continual learning under adversarial conditions remains an open problem, as existing methods often compromise either robustness, scalability, or both. We propose a novel framework that integrates Interval Bound Propagation (IBP) with a hypernetwork-based architecture to enable certifiably robust continual learning across sequential tasks. Our method, SHIELD, generates task-specific model parameters via a shared hypernetwork conditioned solely on compact task embeddings, eliminating the need for replay buffers or full model copies and enabling efficient over time. To further enhance robustness, we introduce Interval MixUp, a novel training strategy that blends virtual examples represented as $\ell_{\infty}$ balls centered around MixUp points. Leveraging interval arithmetic, this technique guarantees certified robustness while mitigating the wrapping effect, resulting in smoother decision boundaries. We evaluate SHIELD under strong white-box adversarial attacks, including PGD and AutoAttack, across multiple benchmarks. It consistently outperforms existing robust continual learning methods, achieving state-of-the-art average accuracy while maintaining both scalability and certification. These results represent a significant step toward practical and theoretically grounded continual learning in adversarial settings.

cs.LG↗

arXiv2024

Make Interval Bound Propagation great again

In various scenarios motivated by real life, such as medical data analysis, autonomous driving, and adversarial training, we are interested in robust deep networks. A network is robust when a relatively small perturbation of the input cannot lead to drastic changes in output (like change of class, etc.). This falls under the broader scope field of Neural Network Certification (NNC). Two crucial problems in NNC are of profound interest to the scientific community: how to calculate the robustness of a given pre-trained network and how to construct robust networks. The common approach to constructing robust networks is Interval Bound Propagation (IBP). This paper demonstrates that IBP is sub-optimal in the first case due to its susceptibility to the wrapping effect. Even for linear activation, IBP gives strongly sub-optimal bounds. Consequently, one should use strategies immune to the wrapping effect to obtain bounds close to optimal ones. We adapt two classical approaches dedicated to strict computations -- Dubleton Arithmetic and Affine Arithmetic -- to mitigate the wrapping effect in neural networks. These techniques yield precise results for networks with linear activation functions, thus resisting the wrapping effect. As a result, we achieve bounds significantly closer to the optimal level than IBPs.

cs.LG↗

arXiv2024

HINT: Hypernetwork Approach to Training Weight Interval Regions in Continual Learning

Recently, a new Continual Learning (CL) paradigm was presented to control catastrophic forgetting, called Interval Continual Learning (InterContiNet), which relies on enforcing interval constraints on the neural network parameter space. Unfortunately, InterContiNet training is challenging due to the high dimensionality of the weight space, making intervals difficult to manage. To address this issue, we introduce HINT, a technique that employs interval arithmetic within the embedding space and utilizes a hypernetwork to map these intervals to the target network parameter space. We train interval embeddings for consecutive tasks and train a hypernetwork to transform these embeddings into weights of the target network. An embedding for a given task is trained along with the hypernetwork, preserving the response of the target network for the previous task embeddings. Interval arithmetic works with a more manageable, lower-dimensional embedding space rather than directly preparing intervals in a high-dimensional weight space. Our model allows faster and more efficient training. Furthermore, HINT maintains the guarantee of not forgetting. At the end of training, we can choose one universal embedding to produce a single network dedicated to all tasks. In such a framework, hypernetwork is used only for training and, finally, we can utilize one set of weights. HINT obtains significantly better results than InterContiNet and gives SOTA results on several benchmarks.

cs.LG↗

arXiv2023

Physics Informed Neural Networks with strong and weak residuals for advection-dominated diffusion problems

This paper deals with the following important research questions. Is it possible to solve challenging advection-dominated diffusion problems in one and two dimensions using Physics Informed Neural Networks (PINN) and Variational Physics Informed Neural Networks (VPINN)? How does it compare to the higher-order and continuity Finite Element Method (FEM)? How to define the loss functions for PINN and VPINN so they converge to the correct solutions? How to select points or test functions for training of PINN and VPINN? We focus on the one-dimensional advection-dominated diffusion problem and the two-dimensional Eriksson-Johnson model problem. We show that the standard Galerkin method for FEM cannot solve this problem. We discuss the stabilization of the advection-dominated diffusion problem with the Petrov-Galerkin (PG) formulation and present the FEM solution obtained with the PG method. We employ PINN and VPINN methods, defining several strong and weak loss functions. We compare the training and solutions of PINN and VPINN methods with higher-order FEM methods.

math.NA↗