SLAY: Geometry-Aware Spherical Linearized Attention with Yat-Kernel

We propose a new class of linear-time attention mechanisms based on a relaxed and computationally efficient formulation of the recently introduced E-Product, often referred to as the Yat-kernel (Bouhsine, 2025). The resulting interactions are geometry-aware and inspired by inverse-square interactions in physics. Our method, Spherical Linearized Attention with Yat Kernels (SLAY), constrains queries and keys to the unit sphere so that attention depends only on angular alignment. Using Bernstein's theorem, we express the spherical Yat-kernel as a nonnegative mixture of polynomial-exponential product kernels and derive a strictly positive random-feature approximation enabling linear-time O(L) attention. We establish positive definiteness and boundedness on the sphere and show that the estimator yields well-defined, nonnegative attention scores. Empirically, SLAY achieves performance that is nearly indistinguishable from standard softmax attention while retaining linear time and memory scaling, and consistently outperforms prior linear-time attention mechanisms such as Performers and Cosformers. To the best of our knowledge, SLAY represents the closest linear-time approximation to softmax attention reported to date, enabling scalable Transformers without the typical performance trade-offs of attention linearization.

Manifold Random Features

We present a new paradigm for creating random features to approximate bi-variate functions (in particular, kernels) defined on general manifolds. This new mechanism of Manifold Random Features (MRFs) leverages discretization of the manifold and the recently introduced technique of Graph Random Features (GRFs) to learn continuous fields on manifolds. Those fields are used to find continuous approximation mechanisms that otherwise, in general scenarios, cannot be derived analytically. MRFs provide positive and bounded features, a key property for accurate, low-variance approximation. We show deep asymptotic connection between GRFs, defined on discrete graph objects, and continuous random features used for regular kernels. As a by-product of our method, we re-discover recently introduced mechanism of Gaussian kernel approximation applied in particular to improve linear-attention Transformers, considering simple random walks on graphs and by-passing original complex mathematical computations. We complement our algorithm with a rigorous theoretical analysis and verify in thorough experimental studies.

CLAMP: Contrastive Learning for 3D Multi-View Action-Conditioned Robotic Manipulation Pretraining

Leveraging pre-trained 2D image representations in behavior cloning policies has achieved great success and has become a standard approach for robotic manipulation. However, such representations fail to capture the 3D spatial information about objects and scenes that is essential for precise manipulation. In this work, we introduce Contrastive Learning for 3D Multi-View Action-Conditioned Robotic Manipulation Pretraining (CLAMP), a novel 3D pre-training framework that utilizes point clouds and robot actions. From the merged point cloud computed from RGB-D images and camera extrinsics, we re-render multi-view four-channel image observations with depth and 3D coordinates, including dynamic wrist views, to provide clearer views of target objects for high-precision manipulation tasks. The pre-trained encoders learn to associate the 3D geometric and positional information of objects with robot action patterns via contrastive learning on large-scale simulated robot trajectories. During encoder pre-training, we pre-train a Diffusion Policy to initialize the policy weights for fine-tuning, which is essential for improving fine-tuning sample efficiency and performance. After pre-training, we fine-tune the policy on a limited amount of task demonstrations using the learned image and action representations. We demonstrate that this pre-training and fine-tuning design substantially improves learning efficiency and policy performance on unseen tasks. Furthermore, we show that CLAMP outperforms state-of-the-art baselines across six simulated tasks and five real-world tasks.

EUGens: Efficient, Unified, and General Dense Layers

Efficient neural networks are essential for scaling machine learning models to real-time applications and resource-constrained environments. Fully-connected feedforward layers (FFLs) introduce computation and parameter count bottlenecks within neural network architectures. To address this challenge, in this work, we propose a new class of dense layers that generalize standard fully-connected feedforward layers, \textbf{E}fficient, \textbf{U}nified and \textbf{Gen}eral dense layers (EUGens). EUGens leverage random features to approximate standard FFLs and go beyond them by incorporating a direct dependence on the input norms in their computations. The proposed layers unify existing efficient FFL extensions and improve efficiency by reducing inference complexity from quadratic to linear time. They also lead to \textbf{the first} unbiased algorithms approximating FFLs with arbitrary polynomial activation functions. Furthermore, EuGens reduce the parameter count and computational overhead while preserving the expressive power and adaptability of FFLs. We also present a layer-wise knowledge transfer technique that bypasses backpropagation, enabling efficient adaptation of EUGens to pre-trained models. Empirically, we observe that integrating EUGens into Transformers and MLPs yields substantial improvements in inference speed (up to \textbf{27}\%) and memory efficiency (up to \textbf{30}\%) across a range of tasks, including image classification, language model pre-training, and 3D scene reconstruction. Overall, our results highlight the potential of EUGens for the scalable deployment of large-scale neural networks in real-world scenarios.

Computationally-efficient Graph Modeling with Refined Graph Random Features

We propose refined GRFs (GRFs++), a new class of Graph Random Features (GRFs) for efficient and accurate computations involving kernels defined on the nodes of a graph. GRFs++ resolve some of the long-standing limitations of regular GRFs, including difficulty modeling relationships between more distant nodes. They reduce dependence on sampling long graph random walks via a novel walk-stitching technique, concatenating several shorter walks without breaking unbiasedness. By applying these techniques, GRFs++ inherit the approximation quality provided by longer walks but with greater efficiency, trading sequential, inefficient sampling of a long walk for parallel computation of short walks and matrix-matrix multiplication. Furthermore, GRFs++ extend the simplistic GRFs walk termination mechanism (Bernoulli schemes with fixed halting probabilities) to a broader class of strategies, applying general distributions on the walks' lengths. This improves the approximation accuracy of graph kernels, without incurring extra computational cost. We provide empirical evaluations to showcase all our claims and complement our results with theoretical analysis.

Wavelet-Induced Rotary Encodings: RoPE Meets Graphs

We introduce WIRE: Wavelet-Induced Rotary Encodings. WIRE extends Rotary Position Encodings (RoPE), a popular algorithm in LLMs and ViTs, to graph-structured data. We demonstrate that WIRE is more general than RoPE, recovering the latter in the special case of grid graphs. WIRE also enjoys a host of desirable theoretical properties, including equivariance under node ordering permutation, compatibility with linear attention, and (under select assumptions) asymptotic dependence on graph resistive distance. We test WIRE on a range of synthetic and real-world tasks, including identifying monochromatic subgraphs, semantic segmentation of point clouds, and more standard graph benchmarks. We find it to be effective in settings where the underlying graph structure is important.

Gemini Robotics: Bringing AI into the Physical World

Recent advancements in large multimodal models have led to the emergence of remarkable generalist capabilities in digital domains, yet their translation to physical agents such as robots remains a significant challenge. This report introduces a new family of AI models purposefully designed for robotics and built upon the foundation of Gemini 2.0. We present Gemini Robotics, an advanced Vision-Language-Action (VLA) generalist model capable of directly controlling robots. Gemini Robotics executes smooth and reactive movements to tackle a wide range of complex manipulation tasks while also being robust to variations in object types and positions, handling unseen environments as well as following diverse, open vocabulary instructions. We show that with additional fine-tuning, Gemini Robotics can be specialized to new capabilities including solving long-horizon, highly dexterous tasks, learning new short-horizon tasks from as few as 100 demonstrations and adapting to completely novel robot embodiments. This is made possible because Gemini Robotics builds on top of the Gemini Robotics-ER model, the second model we introduce in this work. Gemini Robotics-ER (Embodied Reasoning) extends Gemini's multimodal reasoning capabilities into the physical world, with enhanced spatial and temporal understanding. This enables capabilities relevant to robotics including object detection, pointing, trajectory and grasp prediction, as well as multi-view correspondence and 3D bounding box predictions. We show how this novel combination can support a variety of robotics applications. We also discuss and address important safety considerations related to this new class of robotics foundation models. The Gemini Robotics family marks a substantial step towards developing general-purpose robots that realizes AI's potential in the physical world.

Learning the RoPEs: Better 2D and 3D Position Encodings with STRING

We introduce STRING: Separable Translationally Invariant Position Encodings. STRING extends Rotary Position Encodings, a recently proposed and widely used algorithm in large language models, via a unifying theoretical framework. Importantly, STRING still provides exact translation invariance, including token coordinates of arbitrary dimensionality, whilst maintaining a low computational footprint. These properties are especially important in robotics, where efficient 3D token representation is key. We integrate STRING into Vision Transformers with RGB(-D) inputs (color plus optional depth), showing substantial gains, e.g. in open-vocabulary object detection and for robotics controllers. We complement our experiments with a rigorous mathematical analysis, proving the universality of our methods.

Optimal Time Complexity Algorithms for Computing General Random Walk Graph Kernels on Sparse Graphs

We present the first linear time complexity randomized algorithms for unbiased approximation of the celebrated family of general random walk kernels (RWKs) for sparse graphs. This includes both labelled and unlabelled instances. The previous fastest methods for general RWKs were of cubic time complexity and not applicable to labelled graphs. Our method samples dependent random walks to compute novel graph embeddings in $\mathbb{R}^d$ whose dot product is equal to the true RWK in expectation. It does so without instantiating the direct product graph in memory, meaning we can scale to massive datasets that cannot be stored on a single machine. We derive exponential concentration bounds to prove that our estimator is sharp, and show that the ability to approximate general RWKs (rather than just special cases) unlocks efficient implicit graph kernel learning. Our method is up to $\mathbf{27\times}$ faster than its counterparts for efficient computation on large graphs and scales to graphs $\mathbf{128 \times}$ bigger than largest examples amenable to brute-force computation.

Magnituder Layers for Implicit Neural Representations in 3D

Improving the efficiency and performance of implicit neural representations in 3D, particularly Neural Radiance Fields (NeRF) and Signed Distance Fields (SDF) is crucial for enabling their use in real-time applications. These models, while capable of generating photo-realistic novel views and detailed 3D reconstructions, often suffer from high computational costs and slow inference times. To address this, we introduce a novel neural network layer called the "magnituder", designed to reduce the number of training parameters in these models without sacrificing their expressive power. By integrating magnituders into standard feed-forward layer stacks, we achieve improved inference speed and adaptability. Furthermore, our approach enables a zero-shot performance boost in trained implicit neural representation models through layer-wise knowledge transfer without backpropagation, leading to more efficient scene reconstruction in dynamic environments.