Nikolai Bolik, Lennart Stöpler, Artur Andrzejak

Abstract

Shani et al. (2026) show that LLM representations broadly recover human category boundaries, while failing to reflect fine-grained typicality structure. Their analysis uses cosine similarity over dense model representations. We revisit their approach using overlap over active sparse autoencoder (SAE) latent sets as a more interpretable similarity measure. We first verify that this set-level measure is meaningful: SAE latent sets can recover union-like compositional structure in controlled toy models and induce semantically coherent neighborhoods in natural text. Extending the human-concepts analysis to SAE set similarities, we find that SAE activation sets do not recover human category boundaries or within-category typicality more faithfully than dense embeddings or residual-stream states, but instead track model-internal similarity structure. To probe this gap further, we study active latent sets under well-controlled semantic modifications, revealing a substantial mismatch between human judgements of conceptual change and change in the SAE active set. We interpret this as evidence that, outside idealised settings, SAE features do not compose via simple bag-of-features semantics.

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• arxiv

Eric Benz, Lennart Stöpler, Nikolai Bolik, Artur Andrzejak

Abstract

Recent research has increasingly focused on understanding how Transformers store and process knowledge, as well as how this knowledge can be edited. Research work in this area is often conducted in two phases: first, phenomena are explored on individual samples. Then, when results appear promising, more statistically robust experiments follow. To support the first phase, we propose KnowledgeDebugger, a GUI-based exploration tool for knowledge localization and editing in Transformers. Our tool – inspired by LM-Debugger – offers no-code access to the methods in EasyEdit, a widely used library of state-of-the-art Knowledge Editing approaches. We demonstrate the tool’s effectiveness through case studies of recent findings in this field.

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• arxiv

Min Xue, Nikolai Bolik, Lennart Stöpler, Erik Imgrund, Janik Schmid, Artur Andrzejak

Abstract

Large Language Models (LLMs) have demonstrated outstanding capabilities in various code-related tasks, including code completion, translation, or summarization. However, these pretrained models are static, posing a challenge to incorporate new knowledge into an LLM to correct erroneous behavior. Approaches such as retraining or fine-tuning demand extensive labeled datasets and might be computationally expensive, while prompt engineering fails to change models permanently. Knowledge Editing (KE) techniques offer a more efficient alternative, enabling model updates with minimal data, even just a single example. Nevertheless, existing KE methods often manipulate parameters within the Transformer’s multi-layer perceptrons (MLPs), where neuronal polysemanticity hinders both the precision and interpretability of the edits. To address these limitations, we exploit TransCoder, an MLP-like model component with a wide and sparsely activated hidden feature vector. Specifically, we introduce TransCoder-based Precise Editing (TCPE), a novel method that leverages the sparsity and monosemanticity of the TransCoder’s neurons for highly localized knowledge editing. TCPE exhibits neuron-level mechanistic interpretability characteristics, revealing the correspondence between the edited neurons and the specific code-related knowledge. Furthermore, we present KECode, a new evaluation benchmark for code-to-code translation based on functional equivalence. Using KECode, we conduct a systematic evaluation of representative KE methods in the context of code-to-code translation.

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• OpenReview
• ICLR-Poster

Victoria Motsch, Nikolai Bolik und Sandro Wimberger

Abstract

We study the on-resonance Spin-1/2 Double Kicked Rotor, a periodically driven quantum system that hosts topological phases. Motivated by experimental constraints, we analyze the effects of open and periodic boundary conditions in contrast to the idealized case of infinite momentum space. As a bulk probe for topological invariants, we focus on the Mean Chiral Displacement (MCD) and show that it exhibits a pronounced sensitivity to boundary conditions, which can be traced to the dynamics in momentum space. Under open boundaries, states that would otherwise extend freely become localized at the edges of the finite momentum space, forming quasienergy edge states. While the bulk response measured by the MCD is strongly affected once the evolving wave packet reaches the boundaries, the persistence of these edge states still reflects the bulk-edge correspondence and provides reliable signatures of topological transitions.

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• arxiv
• APS Physical Review A

Nikolai Bolik und Sandro Wimberger

Abstract

Quantum walks have gained significant attention over the past decades, mainly because of their variety of implementations and applications. Atomic quantum walks are typically subject to spontaneous emissions arising from the control fields. We investigate spontaneous emission in an atom-optics kicked-rotor quantum walk. Here, spontaneous emission occurs naturally due to the driving by the kicks, and it is generally viewed as a nuisance in the experiment. We find, however, that spontaneous emission may induce asymmetries in an otherwise symmetric quantum walk. Our results underscore the utility of spontaneous emission and the application of the asymmetric evolution in the walker’s space, i.e., for the construction of a quantum walk ratchet or for Parrondo-like quantum games. This highlights the potential for reinterpreting seemingly adverse effects as beneficial under certain conditions, thus broadening the scope of quantum walks and their applications.

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• APS Physical Review A
• arxiv

Nikolai Bolik, Caspar Groiseau, Jerry H. Clark, Gil S. Summy, Yingmei Liu, and Sandro Wimberger

Abstract

We present a concrete theoretical proposal for detecting topological phase transitions in double kicked atom-optics kicked rotors with internal spin-1/2 degree of freedom. The implementation utilizes a kicked Bose-Einstein condensate evolving in one-dimensional momentum space. To reduce the influence of atom loss and phase decoherence, we aim to keep experimental durations short while maintaining a resonant experimental protocol. Experimental limitations induced by phase noise, quasimomentum distributions, symmetries, and the ac-Stark shift are considered. Our results thus suggest a feasible and optimized procedure for observing topological phase transitions in quantum kicked rotors.

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• APS Physical Review A
• arxiv

Nikolai Bolik, Caspar Groiseau, Jerry H. Clark, Alexander Gresch, Siamak Dadras, Gil S. Summy, Yingmei Liu, and Sandro Wimberger

Abstract

Over the last decade there have been many advances in studies of quantum walks (QWs) including a momentum-space QW recently realized in our spinor Bose-Einstein condensate system. This QW possessed behaviors that generally agreed with theoretical predictions; however, it also showed momentum distributions that were not adequately explained by the theory. We present a theoretical model which proves that the coherent dynamics of the spinor condensate is sufficient to explain the experimental data without invoking the presence of a thermal cloud of atoms as in the original theory. Our numerical findings are supported by an analytical prediction for the momentum distributions in the limit of zero-temperature condensates. This current model provides more complete explanations to the momentum-space QWs that can be applied to study quantum search algorithms and topological phases in Floquet-driven systems..

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• APS Physical Review A
• arxiv

Supplementary Material

The supplementary material includes full derivations and additional numerical testings which are referenced but not explicitly presented in the main article. We present these additional informations for transparancy in our reasoning.

• APS Physical Review A

Abstract

The study of open quantum systems is crucial for understanding physics under realistic conditions given by the interaction of quantum mechanical systems with their environment. This thesis investigates the Dynamics of two distinct open Quantum systems, consisting of ultracold atoms in optical lattices. First, we explore symmetry properties in atom optics kicked rotor quantum walks influenced by spontaneous emissions (SE). We demonstrate that SE induces asymmetries in otherwise symmetric quantum walks. This finding is particularly interesting as it changes the typical perspective on SE, which is generally considered a nuisance. In our study, SE enables the formation of a quantum walk ratchet, illustrating how seemingly adverse effects can be beneficial under specific conditions. Second, we examine the open Bose-Hubbard model, representing a true many-body system interacting not only with its environment but also internally. This introduces significant complexity making the analysis of large interacting systems numerically infeasible. To address These challenges, we discuss the truncated Wigner method and aim to extend this methodology beyond ist typical approximations.
The connection between these two studies lies in their open nature and their common experimental implementation in optical lattices: The atom optics kicked rotor describes non-interacting atoms, where each atom interacts with the environment but not with each other, while the Bose-Hubbard model deals with a true many-particle system, requiring a different analytical approach. This dual investigation enhances our understanding of dissipation in open quantum systems, improving our ability to model and interpret complex quantum phenomena under realistic conditions, such as decoherence, dissipation, and particle loss.

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Abstract

Recently [Phys. Rev. Lett., 121:070402, Aug 2018] a quantum kicked rotor walk has been implemented in momentum space by loading a 87Rb Bose-Einstein condensate into an optical pulsed lattice. The experimental results showed overall good agreement with the theoretical predictions but also differed in the details. A complementary argument to previous explanations will be given, consulting light shift induced effects and dispersive properties of the system for causing the observed discrepancies. Furthermore, from the field of mathematics topological principles have been passed on to physics. For example the quantum hall effect can be understood in terms of Chern numbers as topological invariant. It has been recognized that periodically driven quantum systems have the capacity to resolve the unconventional topological matter. The double kicked quantum rotor with internal spin 1/2 degree of freedom is such a system, displaying a connection between topologically protected edge states and the topologically invariant winding number.

The mean chiral displacement is an experimentally obtainable observable that converges onto the winding number. This offers interesting possibilities for measuring topological phase transition. Recognizing These possibilities, investigations regarding the feasibility will be presented, suggesting a new protocol for an experimental implementation.

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