Krzysztof Choromanski

Anthony Brohan, Noah Brown, Justice Carbajal et al. · stanford

We study how vision-language models trained on Internet-scale data can be incorporated directly into end-to-end robotic control to boost generalization and enable emergent semantic reasoning. Our goal is to enable a single end-to-end trained model to both learn to map robot observations to actions and enjoy the benefits of large-scale pretraining on language and vision-language data from the web. To this end, we propose to co-fine-tune state-of-the-art vision-language models on both robotic trajectory data and Internet-scale vision-language tasks, such as visual question answering. In contrast to other approaches, we propose a simple, general recipe to achieve this goal: in order to fit both natural language responses and robotic actions into the same format, we express the actions as text tokens and incorporate them directly into the training set of the model in the same way as natural language tokens. We refer to such category of models as vision-language-action models (VLA) and instantiate an example of such a model, which we call RT-2. Our extensive evaluation (6k evaluation trials) shows that our approach leads to performant robotic policies and enables RT-2 to obtain a range of emergent capabilities from Internet-scale training. This includes significantly improved generalization to novel objects, the ability to interpret commands not present in the robot training data (such as placing an object onto a particular number or icon), and the ability to perform rudimentary reasoning in response to user commands (such as picking up the smallest or largest object, or the one closest to another object). We further show that incorporating chain of thought reasoning allows RT-2 to perform multi-stage semantic reasoning, for example figuring out which object to pick up for use as an improvised hammer (a rock), or which type of drink is best suited for someone who is tired (an energy drink).

Andy Zeng, Maria Attarian, Brian Ichter et al.

Large pretrained (e.g., "foundation") models exhibit distinct capabilities depending on the domain of data they are trained on. While these domains are generic, they may only barely overlap. For example, visual-language models (VLMs) are trained on Internet-scale image captions, but large language models (LMs) are further trained on Internet-scale text with no images (e.g., spreadsheets, SAT questions, code). As a result, these models store different forms of commonsense knowledge across different domains. In this work, we show that this diversity is symbiotic, and can be leveraged through Socratic Models (SMs): a modular framework in which multiple pretrained models may be composed zero-shot i.e., via multimodal-informed prompting, to exchange information with each other and capture new multimodal capabilities, without requiring finetuning. With minimal engineering, SMs are not only competitive with state-of-the-art zero-shot image captioning and video-to-text retrieval, but also enable new applications such as (i) answering free-form questions about egocentric video, (ii) engaging in multimodal assistive dialogue with people (e.g., for cooking recipes) by interfacing with external APIs and databases (e.g., web search), and (iii) robot perception and planning.

Valerii Likhosherstov, Krzysztof Choromanski, Avinava Dubey et al. · cambridge

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.

Isaac Reid, Krzysztof Choromanski, Valerii Likhosherstov et al. · cambridge

We present Simplex Random Features (SimRFs), a new random feature (RF) mechanism for unbiased approximation of the softmax and Gaussian kernels by geometrical correlation of random projection vectors. We prove that SimRFs provide the smallest possible mean square error (MSE) on unbiased estimates of these kernels among the class of weight-independent geometrically-coupled positive random feature (PRF) mechanisms, substantially outperforming the previously most accurate Orthogonal Random Features at no observable extra cost. We present a more computationally expensive SimRFs+ variant, which we prove is asymptotically optimal in the broader family of weight-dependent geometrical coupling schemes (which permit correlations between random vector directions and norms). In extensive empirical studies, we show consistent gains provided by SimRFs in settings including pointwise kernel estimation, nonparametric classification and scalable Transformers.

Krzysztof Choromanski, Arijit Sehanobish, Han Lin et al. · cambridge

We present two new classes of algorithms for efficient field integration on graphs encoding point clouds. The first class, SeparatorFactorization(SF), leverages the bounded genus of point cloud mesh graphs, while the second class, RFDiffusion(RFD), uses popular epsilon-nearest-neighbor graph representations for point clouds. Both can be viewed as providing the functionality of Fast Multipole Methods (FMMs), which have had a tremendous impact on efficient integration, but for non-Euclidean spaces. We focus on geometries induced by distributions of walk lengths between points (e.g., shortest-path distance). We provide an extensive theoretical analysis of our algorithms, obtaining new results in structural graph theory as a byproduct. We also perform exhaustive empirical evaluation, including on-surface interpolation for rigid and deformable objects (particularly for mesh-dynamics modeling), Wasserstein distance computations for point clouds, and the Gromov-Wasserstein variant.

Valerii Likhosherstov, Krzysztof Choromanski, Avinava Dubey et al. · cambridge

The problem of efficient approximation of a linear operator induced by the Gaussian or softmax kernel is often addressed using random features (RFs) which yield an unbiased approximation of the operator's result. Such operators emerge in important applications ranging from kernel methods to efficient Transformers. We propose parameterized, positive, non-trigonometric RFs which approximate Gaussian and softmax-kernels. In contrast to traditional RF approximations, parameters of these new methods can be optimized to reduce the variance of the approximation, and the optimum can be expressed in closed form. We show that our methods lead to variance reduction in practice ($e^{10}$-times smaller variance and beyond) and outperform previous methods in a kernel regression task. Using our proposed mechanism, we also present FAVOR#, a method for self-attention approximation in Transformers. We show that FAVOR# outperforms other random feature methods in speech modelling and natural language processing.

Xuesu Xiao, Tingnan Zhang, Krzysztof Choromanski et al.

Despite decades of research, existing navigation systems still face real-world challenges when deployed in the wild, e.g., in cluttered home environments or in human-occupied public spaces. To address this, we present a new class of implicit control policies combining the benefits of imitation learning with the robust handling of system constraints from Model Predictive Control (MPC). Our approach, called Performer-MPC, uses a learned cost function parameterized by vision context embeddings provided by Performers -- a low-rank implicit-attention Transformer. We jointly train the cost function and construct the controller relying on it, effectively solving end-to-end the corresponding bi-level optimization problem. We show that the resulting policy improves standard MPC performance by leveraging a few expert demonstrations of the desired navigation behavior in different challenging real-world scenarios. Compared with a standard MPC policy, Performer-MPC achieves >40% better goal reached in cluttered environments and >65% better on social metrics when navigating around humans.

David B. D'Ambrosio, Jonathan Abelian, Saminda Abeyruwan et al.

We present a deep-dive into a real-world robotic learning system that, in previous work, was shown to be capable of hundreds of table tennis rallies with a human and has the ability to precisely return the ball to desired targets. This system puts together a highly optimized perception subsystem, a high-speed low-latency robot controller, a simulation paradigm that can prevent damage in the real world and also train policies for zero-shot transfer, and automated real world environment resets that enable autonomous training and evaluation on physical robots. We complement a complete system description, including numerous design decisions that are typically not widely disseminated, with a collection of studies that clarify the importance of mitigating various sources of latency, accounting for training and deployment distribution shifts, robustness of the perception system, sensitivity to policy hyper-parameters, and choice of action space. A video demonstrating the components of the system and details of experimental results can be found at https://youtu.be/uFcnWjB42I0.

Rami Botros, Anmol Gulati, Tara N. Sainath et al.

Conformer models maintain a large number of internal states, the vast majority of which are associated with self-attention layers. With limited memory bandwidth, reading these from memory at each inference step can slow down inference. In this paper, we design an optimized conformer that is small enough to meet on-device restrictions and has fast inference on TPUs. We explore various ideas to improve the execution speed, including replacing lower conformer blocks with convolution-only blocks, strategically downsizing the architecture, and utilizing an RNNAttention-Performer. Our optimized conformer can be readily incorporated into a cascaded-encoder setting, allowing a second-pass decoder to operate on its output and improve the accuracy whenever more resources are available. Altogether, we find that these optimizations can reduce latency by a factor of 6.8x, and come at a reasonable trade-off in quality. With the cascaded second-pass, we show that the recognition accuracy is completely recoverable. Thus, our proposed encoder can double as a strong standalone encoder in on device, and as the first part of a high-performance ASR pipeline.

Krzysztof Choromanski

We introduce in this paper the mechanism of graph random features (GRFs). GRFs can be used to construct unbiased randomized estimators of several important kernels defined on graphs' nodes, in particular the regularized Laplacian kernel. As regular RFs for non-graph kernels, they provide means to scale up kernel methods defined on graphs to larger networks. Importantly, they give substantial computational gains also for smaller graphs, while applied in downstream applications. Consequently, GRFs address the notoriously difficult problem of cubic (in the number of the nodes of the graph) time complexity of graph kernels algorithms. We provide a detailed theoretical analysis of GRFs and an extensive empirical evaluation: from speed tests, through Frobenius relative error analysis to kmeans graph-clustering with graph kernels. We show that the computation of GRFs admits an embarrassingly simple distributed algorithm that can be applied if the graph under consideration needs to be split across several machines. We also introduce a (still unbiased) quasi Monte Carlo variant of GRFs, q-GRFs, relying on the so-called reinforced random walks, that might be used to optimize the variance of GRFs. As a byproduct, we obtain a novel approach to solve certain classes of linear equations with positive and symmetric matrices.

Yunfan Zhao, Qingkai Pan, Krzysztof Choromanski et al.

We present a new class of structured reinforcement learning policy-architectures, Implicit Two-Tower (ITT) policies, where the actions are chosen based on the attention scores of their learnable latent representations with those of the input states. By explicitly disentangling action from state processing in the policy stack, we achieve two main goals: substantial computational gains and better performance. Our architectures are compatible with both: discrete and continuous action spaces. By conducting tests on 15 environments from OpenAI Gym and DeepMind Control Suite, we show that ITT-architectures are particularly suited for blackbox/evolutionary optimization and the corresponding policy training algorithms outperform their vanilla unstructured implicit counterparts as well as commonly used explicit policies. We complement our analysis by showing how techniques such as hashing and lazy tower updates, critically relying on the two-tower structure of ITTs, can be applied to obtain additional computational improvements.

Bingyi Cao, Koert Chen, Kevis-Kokitsi Maninis et al.

Recent progress in vision-language pretraining has enabled significant improvements to many downstream computer vision applications, such as classification, retrieval, segmentation and depth prediction. However, a fundamental capability that these models still struggle with is aligning dense patch representations with text embeddings of corresponding concepts. In this work, we investigate this critical issue and propose novel techniques to enhance this capability in foundational vision-language models. First, we reveal that a patch-level distillation procedure significantly boosts dense patch-text alignment -- surprisingly, the patch-text alignment of the distilled student model strongly surpasses that of the teacher model. This observation inspires us to consider modifications to pretraining recipes, leading us to propose iBOT++, an upgrade to the commonly-used iBOT masked image objective, where unmasked tokens also contribute directly to the loss. This dramatically enhances patch-text alignment of pretrained models. Additionally, to improve vision-language pretraining efficiency and effectiveness, we modify the exponential moving average setup in the learning recipe, and introduce a caption sampling strategy to benefit from synthetic captions at different granularities. Combining these components, we develop TIPSv2, a new family of image-text encoder models suitable for a wide range of downstream applications. Through comprehensive experiments on 9 tasks and 20 datasets, we demonstrate strong performance, generally on par with or better than recent vision encoder models. Code and models are released via our project page at https://gdm-tipsv2.github.io/ .

Alessandro Manenti, Avinava Dubey, Arijit Sehanobish et al.

We propose SWING: Space Walks for Implicit Network Graphs, a new class of algorithms for computations involving Graph Random Features on graphs given by implicit representations (i-graphs), where edge-weights are defined as bi-variate functions of feature vectors in the corresponding nodes. Those classes of graphs include several prominent examples, such as: $ε$-neighborhood graphs, used on regular basis in machine learning. Rather than conducting walks on graphs' nodes, those methods rely on walks in continuous spaces, in which those graphs are embedded. To accurately and efficiently approximate original combinatorial calculations, SWING applies customized Gumbel-softmax sampling mechanism with linearized kernels, obtained via random features coupled with importance sampling techniques. This algorithm is of its own interest. SWING relies on the deep connection between implicitly defined graphs and Fourier analysis, presented in this paper. SWING is accelerator-friendly and does not require input graph materialization. We provide detailed analysis of SWING and complement it with thorough experiments on different classes of i-graphs.

Arijit Sehanobish, Krzysztof Choromanski, Yunfan Zhao et al.

We introduce the concept of scalable neural network kernels (SNNKs), the replacements of regular feedforward layers (FFLs), capable of approximating the latter, but with favorable computational properties. SNNKs effectively disentangle the inputs from the parameters of the neural network in the FFL, only to connect them in the final computation via the dot-product kernel. They are also strictly more expressive, as allowing to model complicated relationships beyond the functions of the dot-products of parameter-input vectors. We also introduce the neural network bundling process that applies SNNKs to compactify deep neural network architectures, resulting in additional compression gains. In its extreme version, it leads to the fully bundled network whose optimal parameters can be expressed via explicit formulae for several loss functions (e.g. mean squared error), opening a possibility to bypass backpropagation. As a by-product of our analysis, we introduce the mechanism of the universal random features (or URFs), applied to instantiate several SNNK variants, and interesting on its own in the context of scalable kernel methods. We provide rigorous theoretical analysis of all these concepts as well as an extensive empirical evaluation, ranging from point-wise kernel estimation to Transformers' fine-tuning with novel adapter layers inspired by SNNKs. Our mechanism provides up to 5x reduction in the number of trainable parameters, while maintaining competitive accuracy.

David Watkins, Peter Allen, Krzysztof Choromanski et al.

We propose the Multiple View Performer (MVP) - a new architecture for 3D shape completion from a series of temporally sequential views. MVP accomplishes this task by using linear-attention Transformers called Performers. Our model allows the current observation of the scene to attend to the previous ones for more accurate infilling. The history of past observations is compressed via the compact associative memory approximating modern continuous Hopfield memory, but crucially of size independent from the history length. We compare our model with several baselines for shape completion over time, demonstrating the generalization gains that MVP provides. To the best of our knowledge, MVP is the first multiple view voxel reconstruction method that does not require registration of multiple depth views and the first causal Transformer based model for 3D shape completion.

Haozhe Shan, Albert Gu, Zhong Meng et al.

Online speech recognition, where the model only accesses context to the left, is an important and challenging use case for ASR systems. In this work, we investigate augmenting neural encoders for online ASR by incorporating structured state-space sequence models (S4), a family of models that provide a parameter-efficient way of accessing arbitrarily long left context. We performed systematic ablation studies to compare variants of S4 models and propose two novel approaches that combine them with convolutions. We found that the most effective design is to stack a small S4 using real-valued recurrent weights with a local convolution, allowing them to work complementarily. Our best model achieves WERs of 4.01%/8.53% on test sets from Librispeech, outperforming Conformers with extensively tuned convolution.

Sang Min Kim, Byeongchan Kim, Arijit Sehanobish et al.

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.

Zahra Shamsi, Isaac Reid, Drew Bryant et al.

We present a machine learning method capable of accurately detecting chromosome abnormalities that cause blood cancers directly from microscope images of the metaphase stage of cell division. The pipeline is built on a series of fine-tuned Vision Transformers. Current state of the art (and standard clinical practice) requires expensive, manual expert analysis, whereas our pipeline takes only 15 seconds per metaphase image. Using a novel pretraining-finetuning strategy to mitigate the challenge of data scarcity, we achieve a high precision-recall score of 94% AUC for the clinically significant del(5q) and t(9;22) anomalies. Our method also unlocks zero-shot detection of rare aberrations based on model latent embeddings. The ability to quickly, accurately, and scalably diagnose genetic abnormalities directly from metaphase images could transform karyotyping practice and improve patient outcomes. We will make code publicly available.

Isaac Reid, Krzysztof Choromanski, Eli Berger et al.

We propose a novel random walk-based algorithm for unbiased estimation of arbitrary functions of a weighted adjacency matrix, coined universal graph random features (u-GRFs). This includes many of the most popular examples of kernels defined on the nodes of a graph. Our algorithm enjoys subquadratic time complexity with respect to the number of nodes, overcoming the notoriously prohibitive cubic scaling of exact graph kernel evaluation. It can also be trivially distributed across machines, permitting learning on much larger networks. At the heart of the algorithm is a modulation function which upweights or downweights the contribution from different random walks depending on their lengths. We show that by parameterising it with a neural network we can obtain u-GRFs that give higher-quality kernel estimates or perform efficient, scalable kernel learning. We provide robust theoretical analysis and support our findings with experiments including pointwise estimation of fixed graph kernels, solving non-homogeneous graph ordinary differential equations, node clustering and kernel regression on triangular meshes.

Isaac Reid, Eli Berger, Krzysztof Choromanski et al.

We present a novel quasi-Monte Carlo mechanism to improve graph-based sampling, coined repelling random walks. By inducing correlations between the trajectories of an interacting ensemble such that their marginal transition probabilities are unmodified, we are able to explore the graph more efficiently, improving the concentration of statistical estimators whilst leaving them unbiased. The mechanism has a trivial drop-in implementation. We showcase the effectiveness of repelling random walks in a range of settings including estimation of graph kernels, the PageRank vector and graphlet concentrations. We provide detailed experimental evaluation and robust theoretical guarantees. To our knowledge, repelling random walks constitute the first rigorously studied quasi-Monte Carlo scheme correlating the directions of walkers on a graph, inviting new research in this exciting nascent domain.

I-Chun Arthur Liu, Krzysztof Choromanski, Sandy Huang et al.

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. The project website and videos can be found at https://clamp3d.github.io/CLAMP/.

Gheorghe Comanici, Eric Bieber, Mike Schaekermann et al. · amazon-science, baidu

In this report, we introduce the Gemini 2.X model family: Gemini 2.5 Pro and Gemini 2.5 Flash, as well as our earlier Gemini 2.0 Flash and Flash-Lite models. Gemini 2.5 Pro is our most capable model yet, achieving SoTA performance on frontier coding and reasoning benchmarks. In addition to its incredible coding and reasoning skills, Gemini 2.5 Pro is a thinking model that excels at multimodal understanding and it is now able to process up to 3 hours of video content. Its unique combination of long context, multimodal and reasoning capabilities can be combined to unlock new agentic workflows. Gemini 2.5 Flash provides excellent reasoning abilities at a fraction of the compute and latency requirements and Gemini 2.0 Flash and Flash-Lite provide high performance at low latency and cost. Taken together, the Gemini 2.X model generation spans the full Pareto frontier of model capability vs cost, allowing users to explore the boundaries of what is possible with complex agentic problem solving.

Byeongchan Kim, Arijit Sehanobish, Avinava Dubey et al.

We present a new class of efficient attention mechanisms applying universal 3D Relative Positional Encoding (RPE) methods given by arbitrary integrable modulation functions $f$. They lead to the new class of 3D-Transformer models, called \textit{RelFlexformers}, flexibly integrating those RPEs, and characterized by the $O(L \log L)$ time complexity of the attention computation for the $L$-length input sequences. RelFlexformers builds on the theory of the Non-Uniform Fourier Transform (NU-FFT), naturally generalizing several existing efficient RPE-attention methods from structured settings with tokens homogeneously embedded in unweighted grids into general non-structured heterogeneous scenarios, where tokens' positions are arbitrarily distributed in the corresponding 3D spaces. As such, RelFlexformers can be applied in particular to model point clouds. Our extensive empirical evaluation on a large portfolio of 3D datasets confirms quality improvements provided by the NU-FFT-driven attention modulation techniques in the RelFlexformers.

Aldo Pacchiano, Jack Parker-Holder, Yunhao Tang et al.

We introduce a new approach for comparing reinforcement learning policies, using Wasserstein distances (WDs) in a newly defined latent behavioral space. We show that by utilizing the dual formulation of the WD, we can learn score functions over policy behaviors that can in turn be used to lead policy optimization towards (or away from) (un)desired behaviors. Combined with smoothed WDs, the dual formulation allows us to devise efficient algorithms that take stochastic gradient descent steps through WD regularizers. We incorporate these regularizers into two novel on-policy algorithms, Behavior-Guided Policy Gradient and Behavior-Guided Evolution Strategies, which we demonstrate can outperform existing methods in a variety of challenging environments. We also provide an open source demo.

Krzysztof Choromanski, Aldo Pacchiano, Jack Parker-Holder et al.

We present a new algorithm ASEBO for optimizing high-dimensional blackbox functions. ASEBO adapts to the geometry of the function and learns optimal sets of sensing directions, which are used to probe it, on-the-fly. It addresses the exploration-exploitation trade-off of blackbox optimization with expensive blackbox queries by continuously learning the bias of the lower-dimensional model used to approximate gradients of smoothings of the function via compressed sensing and contextual bandits methods. To obtain this model, it leverages techniques from the emerging theory of active subspaces in the novel ES blackbox optimization context. As a result, ASEBO learns the dynamically changing intrinsic dimensionality of the gradient space and adapts to the hardness of different stages of the optimization without external supervision. Consequently, it leads to more sample-efficient blackbox optimization than state-of-the-art algorithms. We provide theoretical results and test ASEBO advantages over other methods empirically by evaluating it on the set of reinforcement learning policy optimization tasks as well as functions from the recently open-sourced Nevergrad library.

Krzysztof Choromanski, Derek Long, Ananya Parashar et al.

We present GenusSink, a new class of approximate generalized Sinkhorn algorithms with shortest-path-distance costs for bounded genus (e.g. planar) graphs, providing near-linear time: (1) pre-processing, (2) iteration step, (3) final transport plan matrix querying and near-linear memory. Graphs handled by GenusSink include in particular planar graphs and bounded-genus meshes approximating 3D objects. GenusSink addresses total quadratic time complexity of its brute-force counterpart by leveraging separator-based decomposition of graphs, computational geometry techniques, and new results on fast matrix-vector multiplications with generalized distance matrices, using, in particular, Fourier analysis and low displacement rank theory. It is inspired by recent breakthroughs in graph theory on approximating bounded genus metrics with small treewidth metrics \citep{minor-free-paper}. The graph-centric approach enables us to target optimal transport problem with the corresponding distributions defined on the manifolds approximated by weighted graphs and with cost functions given by geodesic distances. We conduct rigorous theoretical analysis of GenusSink, provide practical implementations, leveraging newly introduced in this paper \textit{separation graph field integrators} (S-GFIs) data structures and present empirical verification. GenusSink provides orders of magnitude more accurate computations than other efficient Sinkhorn algorithms, while still guaranteeing significant computational improvements, as compared to the baseline. As a by-product of the developed methods, we show that GenusSink is \textbf{numerically equivalent} to the brute-force geodesic Sinkhorn algorithm on $n$-vertex graphs with treewidth $O(\log \log (n))$ (e.g. on trees).

Ananya Parashar, Derek Long, Dwaipayan Saha et al.

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.

Isabel Leal, Krzysztof Choromanski, Deepali Jain et al.

We present Self-Adaptive Robust Attention for Robotics Transformers (SARA-RT): a new paradigm for addressing the emerging challenge of scaling up Robotics Transformers (RT) for on-robot deployment. SARA-RT relies on the new method of fine-tuning proposed by us, called up-training. It converts pre-trained or already fine-tuned Transformer-based robotic policies of quadratic time complexity (including massive billion-parameter vision-language-action models or VLAs), into their efficient linear-attention counterparts maintaining high quality. We demonstrate the effectiveness of SARA-RT by speeding up: (a) the class of recently introduced RT-2 models, the first VLA robotic policies pre-trained on internet-scale data, as well as (b) Point Cloud Transformer (PCT) robotic policies operating on large point clouds. We complement our results with the rigorous mathematical analysis providing deeper insight into the phenomenon of SARA.

Connor Schenck, Isaac Reid, Mithun George Jacob et al.

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.

Krzysztof Choromanski, Isaac Reid, Arijit Sehanobish et al.

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.

Gemini Robotics Team, Krzysztof Choromanski, Coline Devin et al.

Generative world models hold significant potential for simulating interactions with visuomotor policies in varied environments. Frontier video models can enable generation of realistic observations and environment interactions in a scalable and general manner. However, the use of video models in robotics has been limited primarily to in-distribution evaluations, i.e., scenarios that are similar to ones used to train the policy or fine-tune the base video model. In this report, we demonstrate that video models can be used for the entire spectrum of policy evaluation use cases in robotics: from assessing nominal performance to out-of-distribution (OOD) generalization, and probing physical and semantic safety. We introduce a generative evaluation system built upon a frontier video foundation model (Veo). The system is optimized to support robot action conditioning and multi-view consistency, while integrating generative image-editing and multi-view completion to synthesize realistic variations of real-world scenes along multiple axes of generalization. We demonstrate that the system preserves the base capabilities of the video model to enable accurate simulation of scenes that have been edited to include novel interaction objects, novel visual backgrounds, and novel distractor objects. This fidelity enables accurately predicting the relative performance of different policies in both nominal and OOD conditions, determining the relative impact of different axes of generalization on policy performance, and performing red teaming of policies to expose behaviors that violate physical or semantic safety constraints. We validate these capabilities through 1600+ real-world evaluations of eight Gemini Robotics policy checkpoints and five tasks for a bimanual manipulator.

Matthew Zhang, Jihao Andreas Lin, Krzysztof Choromanski et al.

We study the application of graph random features (GRFs) - a recently introduced stochastic estimator of graph node kernels - to scalable Gaussian processes on discrete input spaces. We prove that (under mild assumptions) Bayesian inference with GRFs enjoys $O(N^{3/2})$ time complexity with respect to the number of nodes $N$, compared to $O(N^3)$ for exact kernels. Substantial wall-clock speedups and memory savings unlock Bayesian optimisation on graphs with over $10^6$ nodes on a single computer chip, whilst preserving competitive performance.

Jose Miguel Luna, Taha Bouhsine, Krzysztof Choromanski

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.

Krzysztof Choromanski, Avinava Dubey, Arijit Sehanobish et al.

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.

Isaac Reid, Arijit Sehanobish, Cederik Höfs et al.

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.

Sang Min Kim, Byeongchan Kim, Arijit Sehanobish et al. · deepmind

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.

William F. Whitney, Jacob Varley, Deepali Jain et al.

We present High-Density Visual Particle Dynamics (HD-VPD), a learned world model that can emulate the physical dynamics of real scenes by processing massive latent point clouds containing 100K+ particles. To enable efficiency at this scale, we introduce a novel family of Point Cloud Transformers (PCTs) called Interlacers leveraging intertwined linear-attention Performer layers and graph-based neighbour attention layers. We demonstrate the capabilities of HD-VPD by modeling the dynamics of high degree-of-freedom bi-manual robots with two RGB-D cameras. Compared to the previous graph neural network approach, our Interlacer dynamics is twice as fast with the same prediction quality, and can achieve higher quality using 4x as many particles. We illustrate how HD-VPD can evaluate motion plan quality with robotic box pushing and can grasping tasks. See videos and particle dynamics rendered by HD-VPD at https://sites.google.com/view/hd-vpd.

Arijit Sehanobish, Avinava Dubey, Krzysztof Choromanski et al.

Recent efforts to scale Transformer models have demonstrated rapid progress across a wide range of tasks (Wei et al., 2022). However, fine-tuning these models for downstream tasks is expensive due to their large parameter counts. Parameter-efficient fine-tuning (PEFT) approaches have emerged as a viable alternative by allowing us to fine-tune models by updating only a small number of parameters. In this work, we propose a general framework for parameter efficient fine-tuning (PEFT), based on structured unrestricted-rank matrices (SURM) which can serve as a drop-in replacement for popular approaches such as Adapters and LoRA. Unlike other methods like LoRA, SURMs provides more flexibility in finding the right balance between compactness and expressiveness. This is achieved by using low displacement rank matrices (LDRMs), which hasn't been used in this context before. SURMs remain competitive with baselines, often providing significant quality improvements while using a smaller parameter budget. SURMs achieve 5-7% accuracy gains on various image classification tasks while replacing low-rank matrices in LoRA. It also results in up to 12x reduction of the number of parameters in adapters (with virtually no loss in quality) on the GLUE benchmark.

Somnath Basu Roy Chowdhury, Krzysztof Choromanski, Arijit Sehanobish et al.

Machine unlearning is the process of efficiently removing the influence of a training data instance from a trained machine learning model without retraining it from scratch. A popular subclass of unlearning approaches is exact machine unlearning, which focuses on techniques that explicitly guarantee the removal of the influence of a data instance from a model. Exact unlearning approaches use a machine learning model in which individual components are trained on disjoint subsets of the data. During deletion, exact unlearning approaches only retrain the affected components rather than the entire model. While existing approaches reduce retraining costs, it can still be expensive for an organization to retrain a model component as it requires halting a system in production, which leads to service failure and adversely impacts customers. To address these challenges, we introduce an exact unlearning framework -- Sequence-aware Sharded Sliced Training (S3T), which is designed to enhance the deletion capabilities of an exact unlearning system while minimizing the impact on model's performance. At the core of S3T, we utilize a lightweight parameter-efficient fine-tuning approach that enables parameter isolation by sequentially training layers with disjoint data slices. This enables efficient unlearning by simply deactivating the layers affected by data deletion. Furthermore, to reduce the retraining cost and improve model performance, we train the model on multiple data sequences, which allows S3T to handle an increased number of deletion requests. Both theoretically and empirically, we demonstrate that S3T attains superior deletion capabilities and enhanced performance compared to baselines across a wide range of settings.

Krzysztof Choromanski, Arijit Sehanobish, Somnath Basu Roy Chowdhury et al.

We present a new class of fast polylog-linear algorithms based on the theory of structured matrices (in particular low displacement rank) for integrating tensor fields defined on weighted trees. Several applications of the resulting fast tree-field integrators (FTFIs) are presented, including (a) approximation of graph metrics with tree metrics, (b) graph classification, (c) modeling on meshes, and finally (d) Topological Transformers (TTs) (Choromanski et al., 2022) for images. For Topological Transformers, we propose new relative position encoding (RPE) masking mechanisms with as few as three extra learnable parameters per Transformer layer, leading to 1.0-1.5%+ accuracy gains. Importantly, most of FTFIs are exact methods, thus numerically equivalent to their brute-force counterparts. When applied to graphs with thousands of nodes, those exact algorithms provide 5.7-13x speedups. We also provide an extensive theoretical analysis of our methods.

Isaac Reid, Krzysztof Choromanski, Adrian Weller

We present a novel mechanism to improve the accuracy of the recently-introduced class of graph random features (GRFs). Our method induces negative correlations between the lengths of the algorithm's random walks by imposing antithetic termination: a procedure to sample more diverse random walks which may be of independent interest. It has a trivial drop-in implementation. We derive strong theoretical guarantees on the properties of these quasi-Monte Carlo GRFs (q-GRFs), proving that they yield lower-variance estimators of the 2-regularised Laplacian kernel under mild conditions. Remarkably, our results hold for any graph topology. We demonstrate empirical accuracy improvements on a variety of tasks including a new practical application: time-efficient approximation of the graph diffusion process. To our knowledge, q-GRFs constitute the first rigorously studied quasi-Monte Carlo scheme for kernels defined on combinatorial objects, inviting new research on correlations between graph random walks.

Valerii Likhosherstov, Anurag Arnab, Krzysztof Choromanski et al.

Can we train a single transformer model capable of processing multiple modalities and datasets, whilst sharing almost all of its learnable parameters? We present PolyViT, a model trained on image, audio and video which answers this question. By co-training different tasks on a single modality, we are able to improve the accuracy of each individual task and achieve state-of-the-art results on 5 standard video- and audio-classification datasets. Co-training PolyViT on multiple modalities and tasks leads to a model that is even more parameter-efficient, and learns representations that generalize across multiple domains. Moreover, we show that co-training is simple and practical to implement, as we do not need to tune hyperparameters for each combination of datasets, but can simply adapt those from standard, single-task training.

Krzysztof Choromanski, Haoxian Chen, Han Lin et al.

We propose a new class of random feature methods for linearizing softmax and Gaussian kernels called hybrid random features (HRFs) that automatically adapt the quality of kernel estimation to provide most accurate approximation in the defined regions of interest. Special instantiations of HRFs lead to well-known methods such as trigonometric (Rahimi and Recht, 2007) or (recently introduced in the context of linear-attention Transformers) positive random features (Choromanski et al., 2021). By generalizing Bochner's Theorem for softmax/Gaussian kernels and leveraging random features for compositional kernels, the HRF-mechanism provides strong theoretical guarantees - unbiased approximation and strictly smaller worst-case relative errors than its counterparts. We conduct exhaustive empirical evaluation of HRF ranging from pointwise kernel estimation experiments, through tests on data admitting clustering structure to benchmarking implicit-attention Transformers (also for downstream Robotics applications), demonstrating its quality in a wide spectrum of machine learning problems.

Krzysztof Choromanski, Han Lin, Haoxian Chen et al.

In this paper we provide, to the best of our knowledge, the first comprehensive approach for incorporating various masking mechanisms into Transformers architectures in a scalable way. We show that recent results on linear causal attention (Choromanski et al., 2021) and log-linear RPE-attention (Luo et al., 2021) are special cases of this general mechanism. However by casting the problem as a topological (graph-based) modulation of unmasked attention, we obtain several results unknown before, including efficient d-dimensional RPE-masking and graph-kernel masking. We leverage many mathematical techniques ranging from spectral analysis through dynamic programming and random walks to new algorithms for solving Markov processes on graphs. We provide a corresponding empirical evaluation.

Valerii Likhosherstov, Krzysztof Choromanski, Adrian Weller

Transformer networks are able to capture patterns in data coming from many domains (text, images, videos, proteins, etc.) with little or no change to architecture components. We perform a theoretical analysis of the core component responsible for signal propagation between elements, i.e. the self-attention matrix. In practice, this matrix typically exhibits two properties: (1) it is sparse, meaning that each token only attends to a small subset of other tokens; and (2) it changes dynamically depending on the input to the module. With these considerations in mind, we ask the following question: Can a fixed self-attention module approximate arbitrary sparse patterns depending on the input? How small is the hidden size $d$ required for such approximation? We make progress in answering this question and show that the self-attention matrix can provably approximate sparse matrices, where sparsity is in terms of a bounded number of nonzero elements in each row and column. While the parameters of self-attention are fixed, various sparse matrices can be approximated by only modifying the inputs. Our proof is based on the random projection technique and uses the seminal Johnson-Lindenstrauss lemma. Our proof is constructive, enabling us to propose an algorithm for finding adaptive inputs and fixed self-attention parameters in order to approximate a given matrix. In particular, we show that, in order to approximate any sparse matrix up to a given precision defined in terms of preserving matrix element ratios, $d$ grows only logarithmically with the sequence length $L$ (i.e. $d = O(\log L)$).

Valerii Likhosherstov, Xingyou Song, Krzysztof Choromanski et al.

Approximate bi-level optimization (ABLO) consists of (outer-level) optimization problems, involving numerical (inner-level) optimization loops. While ABLO has many applications across deep learning, it suffers from time and memory complexity proportional to the length $r$ of its inner optimization loop. To address this complexity, an earlier first-order method (FOM) was proposed as a heuristic that omits second derivative terms, yielding significant speed gains and requiring only constant memory. Despite FOM's popularity, there is a lack of theoretical understanding of its convergence properties. We contribute by theoretically characterizing FOM's gradient bias under mild assumptions. We further demonstrate a rich family of examples where FOM-based SGD does not converge to a stationary point of the ABLO objective. We address this concern by proposing an unbiased FOM (UFOM) enjoying constant memory complexity as a function of $r$. We characterize the introduced time-variance tradeoff, demonstrate convergence bounds, and find an optimal UFOM for a given ABLO problem. Finally, we propose an efficient adaptive UFOM scheme.

Xingyou Song, Krzysztof Choromanski, Jack Parker-Holder et al.

In this paper, we approach the problem of optimizing blackbox functions over large hybrid search spaces consisting of both combinatorial and continuous parameters. We demonstrate that previous evolutionary algorithms which rely on mutation-based approaches, while flexible over combinatorial spaces, suffer from a curse of dimensionality in high dimensional continuous spaces both theoretically and empirically, which thus limits their scope over hybrid search spaces as well. In order to combat this curse, we propose ES-ENAS, a simple and modular joint optimization procedure combining the class of sample-efficient smoothed gradient techniques, commonly known as Evolutionary Strategies (ES), with combinatorial optimizers in a highly scalable and intuitive way, inspired by the one-shot or supernet paradigm introduced in Efficient Neural Architecture Search (ENAS). By doing so, we achieve significantly more sample efficiency, which we empirically demonstrate over synthetic benchmarks, and are further able to apply ES-ENAS for architecture search over popular RL benchmarks.

Mircea Trofin, Yundi Qian, Eugene Brevdo et al.

Leveraging machine-learning (ML) techniques for compiler optimizations has been widely studied and explored in academia. However, the adoption of ML in general-purpose, industry strength compilers has yet to happen. We propose MLGO, a framework for integrating ML techniques systematically in an industrial compiler -- LLVM. As a case study, we present the details and results of replacing the heuristics-based inlining-for-size optimization in LLVM with machine learned models. To the best of our knowledge, this work is the first full integration of ML in a complex compiler pass in a real-world setting. It is available in the main LLVM repository. We use two different ML algorithms: Policy Gradient and Evolution Strategies, to train the inlining-for-size model, and achieve up to 7\% size reduction, when compared to state of the art LLVM -Oz. The same model, trained on one corpus, generalizes well to a diversity of real-world targets, as well as to the same set of targets after months of active development. This property of the trained models is beneficial to deploy ML techniques in real-world settings.

Valerii Likhosherstov, Krzysztof Choromanski, Jared Davis et al.

The Transformer architecture has revolutionized deep learning on sequential data, becoming ubiquitous in state-of-the-art solutions for a wide variety of applications. Yet vanilla Transformers are notoriously resource-expensive, requiring $O(L^2)$ in serial time and memory as functions of input length $L$. Recent works proposed various linear self-attention mechanisms, scaling only as $O(L)$ for serial computation. We perform a thorough analysis of recent Transformer mechanisms with linear self-attention, Performers, in terms of overall computational complexity. We observe a remarkable computational flexibility: forward and backward propagation can be performed with no approximations using sublinear memory as a function of $L$ (in addition to negligible storage for the input sequence), at a cost of greater time complexity in the parallel setting. In the extreme case, a Performer consumes only $O(1)$ memory during training, and still requires $O(L)$ time. This discovered time-memory tradeoff can be used for training or, due to complete backward-compatibility, for fine-tuning on a low-memory device, e.g. a smartphone or an earlier-generation GPU, thus contributing towards decentralized and democratized deep learning.

Krzysztof Choromanski, Valerii Likhosherstov, David Dohan et al.

We introduce Performers, Transformer architectures which can estimate regular (softmax) full-rank-attention Transformers with provable accuracy, but using only linear (as opposed to quadratic) space and time complexity, without relying on any priors such as sparsity or low-rankness. To approximate softmax attention-kernels, Performers use a novel Fast Attention Via positive Orthogonal Random features approach (FAVOR+), which may be of independent interest for scalable kernel methods. FAVOR+ can be also used to efficiently model kernelizable attention mechanisms beyond softmax. This representational power is crucial to accurately compare softmax with other kernels for the first time on large-scale tasks, beyond the reach of regular Transformers, and investigate optimal attention-kernels. Performers are linear architectures fully compatible with regular Transformers and with strong theoretical guarantees: unbiased or nearly-unbiased estimation of the attention matrix, uniform convergence and low estimation variance. We tested Performers on a rich set of tasks stretching from pixel-prediction through text models to protein sequence modeling. We demonstrate competitive results with other examined efficient sparse and dense attention methods, showcasing effectiveness of the novel attention-learning paradigm leveraged by Performers.