Robin Staab

LG
h-index64
22papers
526citations
Novelty61%
AI Score61

22 Papers

AIOct 11, 2023
Beyond Memorization: Violating Privacy Via Inference with Large Language Models

Robin Staab, Mark Vero, Mislav Balunović et al.

Current privacy research on large language models (LLMs) primarily focuses on the issue of extracting memorized training data. At the same time, models' inference capabilities have increased drastically. This raises the key question of whether current LLMs could violate individuals' privacy by inferring personal attributes from text given at inference time. In this work, we present the first comprehensive study on the capabilities of pretrained LLMs to infer personal attributes from text. We construct a dataset consisting of real Reddit profiles, and show that current LLMs can infer a wide range of personal attributes (e.g., location, income, sex), achieving up to $85\%$ top-1 and $95\%$ top-3 accuracy at a fraction of the cost ($100\times$) and time ($240\times$) required by humans. As people increasingly interact with LLM-powered chatbots across all aspects of life, we also explore the emerging threat of privacy-invasive chatbots trying to extract personal information through seemingly benign questions. Finally, we show that common mitigations, i.e., text anonymization and model alignment, are currently ineffective at protecting user privacy against LLM inference. Our findings highlight that current LLMs can infer personal data at a previously unattainable scale. In the absence of working defenses, we advocate for a broader discussion around LLM privacy implications beyond memorization, striving for a wider privacy protection.

LGNov 17, 2023
From Principle to Practice: Vertical Data Minimization for Machine Learning

Robin Staab, Nikola Jovanović, Mislav Balunović et al.

Aiming to train and deploy predictive models, organizations collect large amounts of detailed client data, risking the exposure of private information in the event of a breach. To mitigate this, policymakers increasingly demand compliance with the data minimization (DM) principle, restricting data collection to only that data which is relevant and necessary for the task. Despite regulatory pressure, the problem of deploying machine learning models that obey DM has so far received little attention. In this work, we address this challenge in a comprehensive manner. We propose a novel vertical DM (vDM) workflow based on data generalization, which by design ensures that no full-resolution client data is collected during training and deployment of models, benefiting client privacy by reducing the attack surface in case of a breach. We formalize and study the corresponding problem of finding generalizations that both maximize data utility and minimize empirical privacy risk, which we quantify by introducing a diverse set of policy-aligned adversarial scenarios. Finally, we propose a range of baseline vDM algorithms, as well as Privacy-aware Tree (PAT), an especially effective vDM algorithm that outperforms all baselines across several settings. We plan to release our code as a publicly available library, helping advance the standardization of DM for machine learning. Overall, we believe our work can help lay the foundation for further exploration and adoption of DM principles in real-world applications.

CRFeb 6
A Unified Framework for LLM Watermarks

Thibaud Gloaguen, Robin Staab, Nikola Jovanović et al.

LLM watermarks allow tracing AI-generated texts by inserting a detectable signal into their generated content. Recent works have proposed a wide range of watermarking algorithms, each with distinct designs, usually built using a bottom-up approach. Crucially, there is no general and principled formulation for LLM watermarking. In this work, we show that most existing and widely used watermarking schemes can in fact be derived from a principled constrained optimization problem. Our formulation unifies existing watermarking methods and explicitly reveals the constraints that each method optimizes. In particular, it highlights an understudied quality-diversity-power trade-off. At the same time, our framework also provides a principled approach for designing novel watermarking schemes tailored to specific requirements. For instance, it allows us to directly use perplexity as a proxy for quality, and derive new schemes that are optimal with respect to this constraint. Our experimental evaluation validates our framework: watermarking schemes derived from a given constraint consistently maximize detection power with respect to that constraint.

LGFeb 29, 2024Code
Watermark Stealing in Large Language Models

Nikola Jovanović, Robin Staab, Martin Vechev

LLM watermarking has attracted attention as a promising way to detect AI-generated content, with some works suggesting that current schemes may already be fit for deployment. In this work we dispute this claim, identifying watermark stealing (WS) as a fundamental vulnerability of these schemes. We show that querying the API of the watermarked LLM to approximately reverse-engineer a watermark enables practical spoofing attacks, as hypothesized in prior work, but also greatly boosts scrubbing attacks, which was previously unnoticed. We are the first to propose an automated WS algorithm and use it in the first comprehensive study of spoofing and scrubbing in realistic settings. We show that for under $50 an attacker can both spoof and scrub state-of-the-art schemes previously considered safe, with average success rate of over 80%. Our findings challenge common beliefs about LLM watermarking, stressing the need for more robust schemes. We make all our code and additional examples available at https://watermark-stealing.org.

CRFeb 14, 2025Code
Towards Watermarking of Open-Source LLMs

Thibaud Gloaguen, Nikola Jovanović, Robin Staab et al.

While watermarks for closed LLMs have matured and have been included in large-scale deployments, these methods are not applicable to open-source models, which allow users full control over the decoding process. This setting is understudied yet critical, given the rising performance of open-source models. In this work, we lay the foundation for systematic study of open-source LLM watermarking. For the first time, we explicitly formulate key requirements, including durability against common model modifications such as model merging, quantization, or finetuning, and propose a concrete evaluation setup. Given the prevalence of these modifications, durability is crucial for an open-source watermark to be effective. We survey and evaluate existing methods, showing that they are not durable. We also discuss potential ways to improve their durability and highlight remaining challenges. We hope our work enables future progress on this important problem.

LGMay 14
Widening the Gap: Exploiting LLM Quantization via Outlier Injection

Xiaohua Zhan, Kazuki Egashira, Robin Staab et al.

LLM quantization has become essential for memory-efficient deployment. Recent work has shown that quantization schemes can pose critical security risks: an adversary may release a model that appears benign in full precision but exhibits malicious behavior once quantized by users. However, existing quantization-conditioned attacks have been limited to relatively simple quantization methods, where the attacker can estimate weight regions that remain invariant under the target quantization. Notably, prior attacks have consistently failed to compromise more popular and sophisticated schemes, limiting their practical impact. In this work, we introduce the first quantization-conditioned attack that consistently induces malicious behavior that can be triggered by a broad range of advanced quantization techniques, including AWQ, GPTQ, and GGUF I-quants. Our attack exploits a simple property shared by many modern quantization methods: large outliers can cause other weights to be rounded to zero. Consequently, by injecting outliers into specific weight blocks, an adversary can therefore induce a targeted, predictable weight collapse in the model. This effect can be used to craft seemingly benign full-precision models that exhibit a wide range of malicious behaviors after quantization. Through extensive evaluation across three attack scenarios and LLMs, we show that our attack achieves high success rates against a broad range of quantization methods on which prior attacks fail. Our results demonstrate, for the first time, that the security risks of quantization are not restricted to simpler schemes but are broadly relevant across complex, widely-used quantization methods.

LGMay 22, 2025Code
MixAT: Combining Continuous and Discrete Adversarial Training for LLMs

Csaba Dékány, Stefan Balauca, Robin Staab et al.

Despite recent efforts in Large Language Model (LLM) safety and alignment, current adversarial attacks on frontier LLMs can still consistently force harmful generations. Although adversarial training has been widely studied and shown to significantly improve the robustness of traditional machine learning models, its strengths and weaknesses in the context of LLMs are less understood. Specifically, while existing discrete adversarial attacks are effective at producing harmful content, training LLMs with concrete adversarial prompts is often computationally expensive, leading to reliance on continuous relaxations. At the same time, despite their effectiveness and generalization capabilities, training with continuous perturbations does not always capture the full spectrum of vulnerabilities exploited by discrete attacks. In this work, we aim to bridge this gap by introducing MixAT, a novel method that combines stronger discrete and faster continuous attacks during training. We rigorously evaluate MixAT across a wide spectrum of state-of-the-art attacks, proposing the At Least One Attack Success Rate (ALO-ASR) metric to capture the worst-case vulnerability of models. We show MixAT achieves substantially better robustness (ALO-ASR < 20%) compared to prior defenses (ALO-ASR > 50%), while maintaining a runtime comparable to methods based on continuous relaxations. We further analyze MixAT in realistic deployment settings, exploring how chat templates, quantization, low-rank adapters, and temperature affect both adversarial training and evaluation, revealing additional blind spots in current methodologies. Our results demonstrate that MixAT's discrete-continuous defense offers a principled and superior robustness-accuracy tradeoff with minimal computational overhead, highlighting its promise for building safer LLMs. We provide our code and models at https://github.com/insait-institute/MixAT.

CRMay 12
Every Bit, Everywhere, All at Once: A Binomial Multibit LLM Watermark

Thibaud Gloaguen, Robin Staab, Mark Vero et al.

With LLM watermarking already being deployed commercially, practical applications increasingly require multibit watermarks that encode more complex payloads, such as user IDs or timestamps, into the generated text. In this work, we propose a fundamentally new approach for multibit watermarking: introducing binomial encoding to directly encode every bit of the payload at every token position. We complement our approach with a stateful encoder that during generation dynamically redirects encoding pressure toward underencoded bits. Our evaluation against 8 baselines on up to 64-bit payloads shows that our scheme achieves superior message accuracy and robustness, with the gap to baseline methods widening in more relevant settings (i.e., large payloads and low-distortion regimes). At the same time, we challenge prior works' evaluation metrics, highlighting their lack of practical insights, and introduce per-bit confidence scoring as a practically relevant metric for evaluating multibit LLM watermarks.

AIFeb 21, 2024
Large Language Models are Advanced Anonymizers

Robin Staab, Mark Vero, Mislav Balunović et al.

Recent privacy research on large language models (LLMs) has shown that they achieve near-human-level performance at inferring personal data from online texts. With ever-increasing model capabilities, existing text anonymization methods are currently lacking behind regulatory requirements and adversarial threats. In this work, we take two steps to bridge this gap: First, we present a new setting for evaluating anonymization in the face of adversarial LLM inferences, allowing for a natural measurement of anonymization performance while remedying some of the shortcomings of previous metrics. Then, within this setting, we develop a novel LLM-based adversarial anonymization framework leveraging the strong inferential capabilities of LLMs to inform our anonymization procedure. We conduct a comprehensive experimental evaluation of adversarial anonymization across 13 LLMs on real-world and synthetic online texts, comparing it against multiple baselines and industry-grade anonymizers. Our evaluation shows that adversarial anonymization outperforms current commercial anonymizers both in terms of the resulting utility and privacy. We support our findings with a human study (n=50) highlighting a strong and consistent human preference for LLM-anonymized texts.

AIApr 16, 2024
Private Attribute Inference from Images with Vision-Language Models

Batuhan Tömekçe, Mark Vero, Robin Staab et al.

As large language models (LLMs) become ubiquitous in our daily tasks and digital interactions, associated privacy risks are increasingly in focus. While LLM privacy research has primarily focused on the leakage of model training data, it has recently been shown that LLMs can make accurate privacy-infringing inferences from previously unseen texts. With the rise of vision-language models (VLMs), capable of understanding both images and text, a key question is whether this concern transfers to the previously unexplored domain of benign images posted online. To answer this question, we compile an image dataset with human-annotated labels of the image owner's personal attributes. In order to understand the privacy risks posed by VLMs beyond traditional human attribute recognition, our dataset consists of images where the inferable private attributes do not stem from direct depictions of humans. On this dataset, we evaluate 7 state-of-the-art VLMs, finding that they can infer various personal attributes at up to 77.6% accuracy. Concerningly, we observe that accuracy scales with the general capabilities of the models, implying that future models can be misused as stronger inferential adversaries, establishing an imperative for the development of adequate defenses.

CRMay 22, 2025
LLM Fingerprinting via Semantically Conditioned Watermarks

Thibaud Gloaguen, Robin Staab, Nikola Jovanović et al.

Most LLM fingerprinting methods teach the model to respond to a few fixed queries with predefined atypical responses (keys). This memorization often does not survive common deployment steps such as finetuning or quantization, and such keys can be easily detected and filtered from LLM responses, ultimately breaking the fingerprint. To overcome these limitations we introduce LLM fingerprinting via semantically conditioned watermarks, replacing fixed query sets with a broad semantic domain, and replacing brittle atypical keys with a statistical watermarking signal diffused throughout each response. After teaching the model to watermark its responses only to prompts from a predetermined domain e.g., French language, the model owner can use queries from that domain to reliably detect the fingerprint and verify ownership. As we confirm in our thorough experimental evaluation, our fingerprint is both stealthy and robust to all common deployment scenarios.

LGApr 6
Delay, Plateau, or Collapse: Evaluating the Impact of Systematic Verification Error on RLVR

Kazuki Egashira, Mark Vero, Jasper Dekoninck et al.

Reinforcement Learning with Verifiable Rewards (RLVR) has become a powerful approach for improving the reasoning capabilities of large language models (LLMs). While RLVR is designed for tasks with verifiable ground-truth answers, real-world verifiers (e.g., static code checkers) can introduce errors into the reward signal. Prior analyses have largely treated such errors as random and independent across samples, concluding that errors merely slow training with limited effect on final performance. However, practical verifiers tend to exhibit systematic errors. This introduces a risk of models learning unwanted consistent behavior from a structurally incorrect reward signal. In this work, we study the impact of such systematic verification errors on RLVR. Through controlled experiments on arithmetic tasks, we show that systematic false negatives lead to similar effects as random noise. On the other hand, systematic false positives can cause a wide range of behaviors from sub-optimal plateaus to performance collapse. Crucially, these outcomes are not determined by the overall error rate but by the specific pattern of introduced errors, making pre-hoc mitigation difficult. Our results show that, in contrast to prior conclusions, realistic verification errors can critically shape RLVR outcomes and that verifier quality has to be understood beyond its sample-level error rate.

LGSep 29, 2025
Watermarking Diffusion Language Models

Thibaud Gloaguen, Robin Staab, Nikola Jovanović et al.

We introduce the first watermark tailored for diffusion language models (DLMs), an emergent LLM paradigm able to generate tokens in arbitrary order, in contrast to standard autoregressive language models (ARLMs) which generate tokens sequentially. While there has been much work in ARLM watermarking, a key challenge when attempting to apply these schemes directly to the DLM setting is that they rely on previously generated tokens, which are not always available with DLM generation. In this work we address this challenge by: (i) applying the watermark in expectation over the context even when some context tokens are yet to be determined, and (ii) promoting tokens which increase the watermark strength when used as context for other tokens. This is accomplished while keeping the watermark detector unchanged. Our experimental evaluation demonstrates that the DLM watermark leads to a >99% true positive rate with minimal quality impact and achieves similar robustness to existing ARLM watermarks, enabling for the first time reliable DLM watermarking.

LGOct 21, 2025
Pay Attention to the Triggers: Constructing Backdoors That Survive Distillation

Giovanni De Muri, Mark Vero, Robin Staab et al.

LLMs are often used by downstream users as teacher models for knowledge distillation, compressing their capabilities into memory-efficient models. However, as these teacher models may stem from untrusted parties, distillation can raise unexpected security risks. In this paper, we investigate the security implications of knowledge distillation from backdoored teacher models. First, we show that prior backdoors mostly do not transfer onto student models. Our key insight is that this is because existing LLM backdooring methods choose trigger tokens that rarely occur in usual contexts. We argue that this underestimates the security risks of knowledge distillation and introduce a new backdooring technique, T-MTB, that enables the construction and study of transferable backdoors. T-MTB carefully constructs a composite backdoor trigger, made up of several specific tokens that often occur individually in anticipated distillation datasets. As such, the poisoned teacher remains stealthy, while during distillation the individual presence of these tokens provides enough signal for the backdoor to transfer onto the student. Using T-MTB, we demonstrate and extensively study the security risks of transferable backdoors across two attack scenarios, jailbreaking and content modulation, and across four model families of LLMs.

CYOct 14, 2025
Adaptive Generation of Bias-Eliciting Questions for LLMs

Robin Staab, Jasper Dekoninck, Maximilian Baader et al.

Large language models (LLMs) are now widely deployed in user-facing applications, reaching hundreds of millions worldwide. As they become integrated into everyday tasks, growing reliance on their outputs raises significant concerns. In particular, users may unknowingly be exposed to model-inherent biases that systematically disadvantage or stereotype certain groups. However, existing bias benchmarks continue to rely on templated prompts or restrictive multiple-choice questions that are suggestive, simplistic, and fail to capture the complexity of real-world user interactions. In this work, we address this gap by introducing a counterfactual bias evaluation framework that automatically generates realistic, open-ended questions over sensitive attributes such as sex, race, or religion. By iteratively mutating and selecting bias-inducing questions, our approach systematically explores areas where models are most susceptible to biased behavior. Beyond detecting harmful biases, we also capture distinct response dimensions that are increasingly relevant in user interactions, such as asymmetric refusals and explicit acknowledgment of bias. Leveraging our framework, we construct CAB, a human-verified benchmark spanning diverse topics, designed to enable cross-model comparisons. Using CAB, we analyze a range of LLMs across multiple bias dimensions, revealing nuanced insights into how different models manifest bias. For instance, while GPT-5 outperforms other models, it nonetheless exhibits persistent biases in specific scenarios. These findings underscore the need for continual improvements to ensure fair model behavior.

LGOct 9, 2025
Fewer Weights, More Problems: A Practical Attack on LLM Pruning

Kazuki Egashira, Robin Staab, Thibaud Gloaguen et al.

Model pruning, i.e., removing a subset of model weights, has become a prominent approach to reducing the memory footprint of large language models (LLMs) during inference. Notably, popular inference engines, such as vLLM, enable users to conveniently prune downloaded models before they are deployed. While the utility and efficiency of pruning methods have improved significantly, the security implications of pruning remain underexplored. In this work, for the first time, we show that modern LLM pruning methods can be maliciously exploited. In particular, an adversary can construct a model that appears benign yet, once pruned, exhibits malicious behaviors. Our method is based on the idea that the adversary can compute a proxy metric that estimates how likely each parameter is to be pruned. With this information, the adversary can first inject a malicious behavior into those parameters that are unlikely to be pruned. Then, they can repair the model by using parameters that are likely to be pruned, effectively canceling out the injected behavior in the unpruned model. We demonstrate the severity of our attack through extensive evaluation on five models; after any of the pruning in vLLM are applied (Magnitude, Wanda, and SparseGPT), it consistently exhibits strong malicious behaviors in a diverse set of attack scenarios (success rates of up to $95.7\%$ for jailbreak, $98.7\%$ for benign instruction refusal, and $99.5\%$ for targeted content injection). Our results reveal a critical deployment-time security gap and underscore the urgent need for stronger security awareness in model compression.

LGAug 14, 2025
SoK: Data Minimization in Machine Learning

Robin Staab, Nikola Jovanović, Kimberly Mai et al.

Data minimization (DM) describes the principle of collecting only the data strictly necessary for a given task. It is a foundational principle across major data protection regulations like GDPR and CPRA. Violations of this principle have substantial real-world consequences, with regulatory actions resulting in fines reaching hundreds of millions of dollars. Notably, the relevance of data minimization is particularly pronounced in machine learning (ML) applications, which typically rely on large datasets, resulting in an emerging research area known as Data Minimization in Machine Learning (DMML). At the same time, existing work on other ML privacy and security topics often addresses concerns relevant to DMML without explicitly acknowledging the connection. This disconnect leads to confusion among practitioners, complicating their efforts to implement DM principles and interpret the terminology, metrics, and evaluation criteria used across different research communities. To address this gap, our work introduces a comprehensive framework for DMML, including a unified data pipeline, adversaries, and points of minimization. This framework allows us to systematically review the literature on data minimization and \emph{DM-adjacent} methodologies, for the first time presenting a structured overview designed to help practitioners and researchers effectively apply DM principles. Our work facilitates a unified DM-centric understanding and broader adoption of data minimization strategies in AI/ML.

CRMay 24, 2025
Mind the Gap: A Practical Attack on GGUF Quantization

Kazuki Egashira, Robin Staab, Mark Vero et al.

With the increasing size of frontier LLMs, post-training quantization has become the standard for memory-efficient deployment. Recent work has shown that basic rounding-based quantization schemes pose security risks, as they can be exploited to inject malicious behaviors into quantized models that remain hidden in full precision. However, existing attacks cannot be applied to more complex quantization methods, such as the GGUF family used in the popular ollama and llama$.$cpp frameworks. In this work, we address this gap by introducing the first attack on GGUF. Our key insight is that the quantization error -- the difference between the full-precision weights and their (de-)quantized version -- provides sufficient flexibility to construct malicious quantized models that appear benign in full precision. Leveraging this, we develop an attack that trains the target malicious LLM while constraining its weights based on quantization errors. We demonstrate the effectiveness of our attack on three popular LLMs across nine GGUF quantization data types on three diverse attack scenarios: insecure code generation ($Δ$=$88.7\%$), targeted content injection ($Δ$=$85.0\%$), and benign instruction refusal ($Δ$=$30.1\%$). Our attack highlights that (1) the most widely used post-training quantization method is susceptible to adversarial interferences, and (2) the complexity of quantization schemes alone is insufficient as a defense.

LGMay 22, 2025
Watch your steps: Dormant Adversarial Behaviors that Activate upon LLM Finetuning

Thibaud Gloaguen, Mark Vero, Robin Staab et al.

Finetuning open-weight Large Language Models (LLMs) is standard practice for achieving task-specific performance improvements. Until now, finetuning has been regarded as a controlled and secure process in which training on benign datasets leads to predictable behaviors. In this paper, we demonstrate, for the first time, that an adversary can create compromised LLMs that are performant and benign, yet exhibit adversarial behaviors once finetuned by downstream users. To this end, we propose an attack, FAB (Finetuning-activated Adversarial Behaviors), which compromises an LLM via meta-learning techniques that simulate downstream finetuning, explicitly optimizing for the emergence of adversarial behaviors in the finetuned models. At the same time, the compromised LLM is regularized to retain general capabilities and to exhibit no adversarial behaviors prior to finetuning. As a result, when users finetune (e.g., instruction-tuning, distillation, DPO) the seemingly benign model on their own datasets, they unknowingly trigger its dormant adversarial behavior. We experimentally demonstrate the effectiveness of FAB across multiple LLMs and three commonly considered target behaviors: unsolicited advertising, jailbreakability, and over-refusal. We show that FAB-triggers are robust to various finetuning choices made by the user (e.g., dataset, number of steps, scheduler, post-training algorithm). Our findings challenge prevailing assumptions on the security of finetuning, revealing a critical attack vector.

LGJun 11, 2024
A Synthetic Dataset for Personal Attribute Inference

Hanna Yukhymenko, Robin Staab, Mark Vero et al.

Recently, powerful Large Language Models (LLMs) have become easily accessible to hundreds of millions of users world-wide. However, their strong capabilities and vast world knowledge do not come without associated privacy risks. In this work, we focus on the emerging privacy threat LLMs pose -- the ability to accurately infer personal information from online texts. Despite the growing importance of LLM-based author profiling, research in this area has been hampered by a lack of suitable public datasets, largely due to ethical and privacy concerns associated with real personal data. We take two steps to address this problem: (i) we construct a simulation framework for the popular social media platform Reddit using LLM agents seeded with synthetic personal profiles; (ii) using this framework, we generate SynthPAI, a diverse synthetic dataset of over 7800 comments manually labeled for personal attributes. We validate our dataset with a human study showing that humans barely outperform random guessing on the task of distinguishing our synthetic comments from real ones. Further, we verify that our dataset enables meaningful personal attribute inference research by showing across 18 state-of-the-art LLMs that our synthetic comments allow us to draw the same conclusions as real-world data. Combined, our experimental results, dataset and pipeline form a strong basis for future privacy-preserving research geared towards understanding and mitigating inference-based privacy threats that LLMs pose.

LGNov 8, 2021
Bayesian Framework for Gradient Leakage

Mislav Balunović, Dimitar I. Dimitrov, Robin Staab et al.

Federated learning is an established method for training machine learning models without sharing training data. However, recent work has shown that it cannot guarantee data privacy as shared gradients can still leak sensitive information. To formalize the problem of gradient leakage, we propose a theoretical framework that enables, for the first time, analysis of the Bayes optimal adversary phrased as an optimization problem. We demonstrate that existing leakage attacks can be seen as approximations of this optimal adversary with different assumptions on the probability distributions of the input data and gradients. Our experiments confirm the effectiveness of the Bayes optimal adversary when it has knowledge of the underlying distribution. Further, our experimental evaluation shows that several existing heuristic defenses are not effective against stronger attacks, especially early in the training process. Thus, our findings indicate that the construction of more effective defenses and their evaluation remains an open problem.

LGOct 14, 2021
Abstract Interpretation of Fixpoint Iterators with Applications to Neural Networks

Mark Niklas Müller, Marc Fischer, Robin Staab et al.

We present a new abstract interpretation framework for the precise over-approximation of numerical fixpoint iterators. Our key observation is that unlike in standard abstract interpretation (AI), typically used to over-approximate all reachable program states, in this setting, one only needs to abstract the concrete fixpoints, i.e., the final program states. Our framework targets numerical fixpoint iterators with convergence and uniqueness guarantees in the concrete and is based on two major technical contributions: (i) theoretical insights which allow us to compute sound and precise fixpoint abstractions without using joins, and (ii) a new abstract domain, CH-Zonotope, which admits efficient propagation and inclusion checks while retaining high precision. We implement our framework in a tool called CRAFT and evaluate it on a novel fixpoint-based neural network architecture (monDEQ) that is particularly challenging to verify. Our extensive evaluation demonstrates that CRAFT exceeds the state-of-the-art performance in terms of speed (two orders of magnitude), scalability (one order of magnitude), and precision (25% higher certified accuracies).