Training certifiably robust neural networks is an important but challenging task. While many algorithms for (deterministic) certified training have been proposed, they are often evaluated on different training schedules, certification methods, and systematically under-tuned hyperparameters, making it difficult to compare their performance. To address this challenge, we introduce CTBench, a unified library and a high-quality benchmark for certified training that evaluates all algorithms under fair settings and systematically tuned hyperparameters. We show that (1) almost all algorithms in CTBench surpass the corresponding reported performance in literature in the magnitude of algorithmic improvements, thus establishing new state-of-the-art, and (2) the claimed advantage of recent algorithms drops significantly when we enhance the outdated baselines with a fair training schedule, a fair certification method and well-tuned hyperparameters. Based on CTBench, we provide new insights into the current state of certified training, including (1) certified models have less fragmented loss surface, (2) certified models share many mistakes, (3) certified models have more sparse activations, (4) reducing regularization cleverly is crucial for certified training especially for large radii and (5) certified training has the potential to improve out-of-distribution generalization. We are confident that CTBench will serve as a benchmark and testbed for future research in certified training.

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 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.