Following from the discussion in Section 3.1, we want to maximize E [zy (x+)]. B.1 Higher Noise Level In the main paper, we conduct experiments on CIFAR-10 using noise level =0 .25 only. Here, we report our main set of results on CIFAR-10 (Table 3) using higher values. In Table 8, we report results using =0 .5 and in Table 9, we report results using =1 .0. B.2 Using ViT [6] In the main paper, we used Convolutional Neural Network (CNN) based architectures.

Tothis coordinate (1), and necessaryand solutionof (1). We usethemodeltrainedusing MixMatch [5] under 3 cases: (1) l = 100, u =1 , (2) = l = u = 100(reverse) and (3) = 100.

We introduce chefs' random tables (CRTs), a new class of non-trigonometric random features (RFs) to approximate Gaussian and softmax kernels. CRTs are an alternative to standard random kitchen sink (RKS) methods, which inherently rely on the trigonometric maps. We present variants of CRTs where RFs are positive, a key requirement for applications in recent low-rank Transformers. Further variance reduction is possible by leveraging statistics which are simple to compute. One instantiation of CRTs, the optimal positive random features (OPRFs), is to our knowledge the first RF method for unbiased softmax kernel estimation with positive and bounded RFs, resulting in exponentially small tails and much lower variance than its counterparts. As we show, orthogonal random features applied in OPRFs provide additional variance reduction for any dimensionality $d$ (not only asymptotically for sufficiently large $d$, as for RKS). We test CRTs on many tasks ranging from non-parametric classification to training Transformers for text, speech and image data, obtaining new state-of-the-art results for low-rank text Transformers, while providing linear space and time complexity.

Training deep neural network classifiers that are certifiably robust against adversarial attacks is critical to ensuring the security and reliability of AI-controlled systems. Although numerous state-of-the-art certified training methods have been developed, they are computationally expensive and scale poorly with respect to both dataset and network complexity. Widespread usage of certified training is further hindered by the fact that periodic retraining is necessary to incorporate new data and network improvements. In this paper, we propose Certified Robustness Transfer (CRT), a general-purpose framework for reducing the computational overhead of any certifiably robust training method through knowledge transfer. Given a robust teacher, our framework uses a novel training loss to transfer the teacher's robustness to the student. We provide theoretical and empirical validation of CRT. Our experiments on CIFAR-10 show that CRT speeds up certified robustness training by 8 on average across three different architecture generations while achieving comparable robustness to state-of-the-art methods. We also show that CRT can scale to large-scale datasets like ImageNet.

Our work addresses the ambiguity between generalization and memorization in text-to-image diffusion models, focusing on a specific case we term multimodal iconicity. This refers to instances where images and texts evoke culturally shared associations, such as when a title recalls a familiar artwork or film scene. While prior research on memorization and unlearning emphasizes forgetting, we examine what is remembered and how, focusing on the balance between recognizing cultural references and reproducing them. W e introduce an evaluation framework that separates recognition, whether a model identifies a reference, from realization, how it depicts it through replication or reinterpretation, quantified through measures capturing both dimensions. By evaluating five diffusion models across 767 Wikidata-derived cultural references spanning static and dynamic imagery, we show that our framework distinguishes replication from transformation more effectively than existing similarity-based methods. T o assess linguistic sensitivity, we conduct prompt perturbation experiments using synonym substitutions and literal image descriptions, finding that models often reproduce iconic visual structures even when textual cues are altered. Finally, our analysis shows that cultural alignment correlates not only with training data frequency, but also textual uniqueness, reference popularity, and creation date. Our work reveals that the value of diffusion models lies not only in what they reproduce but in how they transform and recontextualize cultural knowledge, advancing evaluation beyond simple text-image matching toward richer contextual understanding.

The Transformer architecture has shown significant success in many language processing and visual tasks. However, the method faces challenges in efficiently scaling to long sequences because the self-attention computation is quadratic with respect to the input length. To overcome this limitation, several approaches scale to longer sequences by breaking long sequences into a series of segments, restricting self-attention to local dependencies between tokens within each segment and using a memory mechanism to manage information flow between segments. However, these approached generally introduce additional compute overhead that restricts them from being used for applications where limited compute memory and power are of great concern (such as edge computing). We propose a novel and efficient Compact Recurrent Transformer (CRT), which combines shallow Transformer models that process short local segments with recurrent neural networks to compress and manage a single persistent memory vector that summarizes long-range global information between segments. We evaluate CRT on WordPTB and WikiText-103 for next-token-prediction tasks, as well as on the Toyota Smarthome video dataset for classification. CRT achieves comparable or superior prediction results to full-length Transformers in the language datasets while using significantly shorter segments (half or quarter size) and substantially reduced FLOPs. Our approach also demonstrates state-of-the-art performance on the Toyota Smarthome video dataset.

We introduce chefs' random tables (CRTs), a new class of non-trigonometric random features (RFs) to approximate Gaussian and softmax kernels. CRTs are an alternative to standard random kitchen sink (RKS) methods, which inherently rely on the trigonometric maps. We present variants of CRTs where RFs are positive, a key requirement for applications in recent low-rank Transformers. Further variance reduction is possible by leveraging statistics which are simple to compute. One instantiation of CRTs, the optimal positive random features (OPRFs), is to our knowledge the first RF method for unbiased softmax kernel estimation with positive and bounded RFs, resulting in exponentially small tails and much lower variance than its counterparts.