Finding minimum distortion of adversarial examples and thus certifying robustness in neural networks classifiers is known to be a challenging problem. Nevertheless, recently it has been shown to be possible to give a non-trivial certified lower bound of minimum distortion, and some recent progress has been made towards this direction by exploiting the piece-wise linear nature of ReLU activations. However, a generic robustness certification for \textit{general} activation functions still remains largely unexplored. To address this issue, in this paper we introduce CROWN, a general framework to certify robustness of neural networks with general activation functions. The novelty in our algorithm consists of bounding a given activation function with linear and quadratic functions, hence allowing it to tackle general activation functions including but not limited to the four popular choices: ReLU, tanh, sigmoid and arctan. In addition, we facilitate the search for a tighter certified lower bound by \textit{adaptively} selecting appropriate surrogates for each neuron activation. Experimental results show that CROWN on ReLU networks can notably improve the certified lower bounds compared to the current state-of-the-art algorithm Fast-Lin, while having comparable computational efficiency. Furthermore, CROWN also demonstrates its effectiveness and flexibility on networks with general activation functions, including tanh, sigmoid and arctan.

Finding minimum distortion of adversarial examples and thus certifying robustness in neural networks classifiers is known to be a challenging problem. Nevertheless, recently it has been shown to be possible to give a non-trivial certified lower bound of minimum distortion, and some recent progress has been made towards this direction by exploiting the piece-wise linear nature of ReLU activations. However, a generic robustness certification for \textit{general} activation functions still remains largely unexplored. To address this issue, in this paper we introduce CROWN, a general framework to certify robustness of neural networks with general activation functions. The novelty in our algorithm consists of bounding a given activation function with linear and quadratic functions, hence allowing it to tackle general activation functions including but not limited to the four popular choices: ReLU, tanh, sigmoid and arctan. In addition, we facilitate the search for a tighter certified lower bound by \textit{adaptively} selecting appropriate surrogates for each neuron activation. Experimental results show that CROWN on ReLU networks can notably improve the certified lower bounds compared to the current state-of-the-art algorithm Fast-Lin, while having comparable computational efficiency. Furthermore, CROWN also demonstrates its effectiveness and flexibility on networks with general activation functions, including tanh, sigmoid and arctan.

Muskan Sharma stood up to men who tried to bully her over her clothes - and went on to win hearts and a beauty pageant. The 23-year-old, who was crowned Miss Rishikesh 2025 last week in the northern Indian state of Uttarakhand, told the BBC that even though it was a small local pageant, it made me feel like Miss Universe. Sharma's win has made headlines in India as it came after a viral video that showed her spiritedly arguing with a man who barged into their rehearsals just a day before the 4 October contest. Sharma, who wanted to be a model and participate in a pageant since I was in school, said the intruders came in just as they broke for lunch. We were sitting around, chilling, having a laugh when they walked in, she said.

Transformer-based language models traditionally use uniform (isotropic) layer sizes, yet they ignore the diverse functional roles that different depths can play and their computational capacity needs. Building on Layer-Wise Scaling (LWS) and pruning literature, we introduce three new LWS variants - Framed, Reverse, and Crown - that redistribute FFN widths and attention heads via two or three-point linear interpolation in the pre-training stage. We present the first systematic ablation of LWS and its variants, on a fixed budget of 180M parameters, trained on 5B tokens. All models converge to similar losses and achieve better performance compared to an equal-cost isotropic baseline, without a substantial decrease in training throughput. This work represents an initial step into the design space of layer-wise architectures for pre-training, but future work should scale experiments to orders of magnitude more tokens and parameters to fully assess their potential.

Concept Bottleneck Models (CBMs) and other concept-based interpretable models show great promise for making AI applications more transparent, which is essential in fields like medicine. Despite their success, we demonstrate that CBMs struggle to reliably identify the correct concepts under distribution shifts. T o assess the robustness of CBMs to concept variations, we introduce SUB: a fine-grained image and concept benchmark containing 38,400 synthetic images based on the CUB dataset. T o create SUB, we select a CUB subset of 33 bird classes and 45 concepts to generate images which substitute a specific concept, such as wing color or belly pattern. W e introduce a novel Tied Diffusion Guidance (TDG) method to precisely control generated images, where noise sharing for two parallel denoising processes ensures that both the correct bird class and the correct attribute are generated. This novel benchmark enables rigorous evaluation of CBMs and similar interpretable models, contributing to the development of more robust methods.

The Freeze-Tag Problem (FTP) involves activating a set of initially asleep robots as quickly as possible, starting from a single awake robot. Once activated, a robot can assist in waking up other robots. Each active robot moves at unit speed. The objective is to minimize the makespan, i.e., the time required to activate the last robot. A key performance measure is the wake-up ratio, defined as the maximum time needed to activate any number of robots in any primary positions. This work focuses on the geometric (Euclidean) version of FTP in $\mathbb{R}^d$ under the $\ell_p$ norm, where the initial distance between each asleep robot and the single active robot is at most 1. For $(\mathbb{R}^2, \ell_2)$, we improve the previous upper bound of 4.62 ([7], CCCG 2024) to 4.31. Note that it is known that 3.82 is a lower bound for the wake-up ratio. In $\mathbb{R}^3$, we propose a new strategy that achieves a wake-up ratio of 12 for $(\mathbb{R}^3, \ell_1)$ and 12.76 for $(\mathbb{R}^3, \ell_2)$, improving upon the previous bounds of 13 and $13\sqrt{3}$, respectively, reported in [2].