Recent reasoning adv through ances in the lar ef ge fecti language ve use of models Chain-of-Thought have significantly (CoT) and impro reinforcement ved textual learning.

Rotary Positional Encodings (RoPE) have emerged as a highly effective technique for one-dimensional sequences in Natural Language Processing spurring recent progress towards generalizing RoPE to higher-dimensional data such as images and videos. The success of RoPE has been thought to be due to its positional equivariance, i.e. its status as a relative positional encoding. In this paper, we mathematically show RoPE to be one of the most general solutions for equivariant positional embedding in one-dimensional data. Moreover, we show Mixed RoPE to be the analogously general solution for M-dimensional data, if we require commutative generators - a property necessary for RoPE's equivariance. However, we question whether strict equivariance plays a large role in RoPE's performance. We propose Spherical RoPE, a method analogous to Mixed RoPE, but assumes non-commutative generators. Empirically, we find Spherical RoPE to have the equivalent or better learning behavior compared to its equivariant analogues. This suggests that relative positional embeddings are not as important as is commonly believed, at least within computer vision. We expect this discovery to facilitate future work in positional encodings for vision that can be faster and generalize better by removing the preconception that they must be relative.

Diffusion-based purification (DBP) has become a cornerstone defense against adversarial examples (AEs), regarded as robust due to its use of diffusion models (DMs) that project AEs onto the natural data manifold. We refute this core claim, theoretically proving that gradient-based attacks effectively target the DM rather than the classifier, causing DBP's outputs to align with adversarial distributions. This prompts a reassessment of DBP's robustness, accrediting it two critical factors: inaccurate gradients and improper evaluation protocols that test only a single random purification of the AE. We show that when accounting for stochasticity and resubmission risk, DBP collapses. To support this, we introduce DiffBreak, the first reliable toolkit for differentiation through DBP, eliminating gradient mismatches that previously further inflated robustness estimates. We also analyze the current defense scheme used for DBP where classification relies on a single purification, pinpointing its inherent invalidity. We provide a statistically grounded majorityvote (MV) alternative that aggregates predictions across multiple purified copies, showing partial but meaningful robustness gain. We then propose a novel adaptation of an optimization method against deepfake watermarking, crafting systemic perturbations that defeat DBP even under MV, challenging DBP's viability.

Discrete state space diffusion models have shown significant advantages in applications involving discrete data, such as text and image generation. It has also been observed that their performance is highly sensitive to the choice of rate matrices, particularly between uniform and absorbing rate matrices. While empirical results suggest that absorbing rate matrices often yield better generation quality compared to uniform rate matrices, existing theoretical works have largely focused on the uniform rate matrices case. Notably, convergence guarantees and error analyses for absorbing diffusion models are still missing. In this work, we provide the first finite-time error bounds and convergence rate analysis for discrete diffusion models using absorbing rate matrices.

The neural activity in the visual processing is influenced by both external stimuli and internal brain states. Ideally, a neural predictive model should account for both of them. Currently, there are no dynamic encoding models that explicitly model a latent state and the entire neuronal response distribution. We address this gap by proposing a probabilistic model that predicts the joint distribution of the neuronal responses from video stimuli and stimulus-independent latent factors. After training and testing our model on mouse V1 neuronal responses, we find that it outperforms video-only models in terms of log-likelihood and achieves improvements in likelihood and correlation when conditioned on responses from other neurons. Furthermore, we find that the learned latent factors strongly correlate with mouse behavior and that they exhibit patterns related to the neurons' position on the visual cortex, although the model was trained without behavior and cortical coordinates. Our findings demonstrate that unsupervised learning of latent factors from population responses can reveal biologically meaningful structure that bridges sensory processing and behavior, without requiring explicit behavioral annotations during training.

The rapid advancement of reasoning capabilities in large language models (LLMs) has led to notable improvements on mathematical benchmarks. However, many of the most commonly used evaluation datasets (e.g., AIME 2024) are widely available online, making it difficult to disentangle genuine reasoning from potential memorization. Furthermore, these benchmarks do not evaluate proof-writing capabilities, which are crucial for many mathematical tasks. To address this, we introduce MATHARENA, a new benchmark based on the following key insight: recurring math competitions provide a stream of high-quality, challenging problems that can be used for real-time evaluation of LLMs. By evaluating models as soon as new problems are released, we effectively eliminate the risk of contamination.

We introduce BikeBench, an engineering design benchmark for evaluating generative models on problems with multiple real-world objectives and constraints. As generative AI's reach continues to grow, evaluating its capability to understand physical laws, human guidelines, and hard constraints grows increasingly important. Engineering product design lies at the intersection of these difficult tasks, providing new challenges for AI capabilities. BikeBench evaluates AI models' capabilities to generate bicycle designs that not only resemble the dataset, but meet specific performance objectives and constraints. To do so, BikeBench quantifies a variety of human-centered and multiphysics performance characteristics, such as aerodynamics, ergonomics, structural mechanics, human-rated usability, and similarity to subjective text or image prompts. Supporting the benchmark are several datasets of simulation results, a dataset of 10,000 human-rated bicycle assessments, and a synthetically generated dataset of 1.6M designs, each with a parametric, CAD/XML, SVG, and PNG representation. BikeBench is uniquely configured to evaluate tabular generative models, large language models (LLMs), design optimization, and hybrid algorithms side-by-side. Our experiments indicate that LLMs and tabular generative models fall short of hybrid GenAI+optimization algorithms in design quality, constraint satisfaction, and similarity scores, suggesting significant room for improvement. We hope that BikeBench, a first-of-its-kind benchmark, will help catalyze progress in generative AI for constrained multi-objective engineering design problems.

The quality of foundation models depends heavily on their training data. Consequently, great efforts have been put into dataset curation. Yet most approaches rely on manual tuning of coarse-grained mixtures of large buckets of data, or filtering by hand-crafted heuristics. An approach that is ultimately more scalable (let alone more satisfying) is to learn which data is actually valuable for training. This type of meta-learning could allow more sophisticated, fine-grained, and effective curation. Our proposed DataRater is an instance of this idea. It estimates the value of training on any particular data point. This is done by meta-learning using'meta-gradients', with the objective of improving training efficiency on held out data. In extensive experiments across a range of model scales and datasets, we find that using our DataRater to filter data is highly effective, resulting in significantly improved compute efficiency.

We initiate the study of multidimensional Bayesian utility maximization, focusing on the unit-demand setting where values are i.i.d.

Paucity of medical data severely limits the generalizability of diagnostic ML models, as the full spectrum of disease variability can not be represented by a small clinical dataset. To address this, diffusion models (DMs) have been considered as a promising avenue for synthetic image generation and augmentation. However, they frequently produce medically inaccurate images, deteriorating the model performance. Expert domain knowledge is critical for synthesizing images that correctly encode clinical information, especially when data is scarce and quality outweighs quantity. Existing approaches for incorporating human feedback, such as reinforcement learning (RL) and Direct Preference Optimization (DPO), rely on robust reward functions or demand labor-intensive expert evaluations. Recent progress in Multimodal Large Language Models (MLLMs) reveals their strong visual reasoning capabilities, making them adept candidates as evaluators. In this work, we propose a novel framework, coined MAGIC (Medically Accurate Generation of Images through AI-Expert Collaboration), that synthesizes clinically accurate skin disease images for data augmentation.