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Arthur Szlam

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Published work

38 published item(s)

preprint2026arXiv

Context Training with Active Information Seeking

Most existing large language models (LLMs) are expensive to adapt after deployment, especially when a task requires newly produced information or niche domain knowledge. Recent work has shown that, by manipulating and optimizing their context, LLMs can be tailored to downstream tasks without updating their weights. However, most existing methods remain closed-loop, relying solely on the model's intrinsic knowledge. In this paper, we equip these context optimizers with Wikipedia search and browser tools for active information seeking. We show that naively adding these tools to a standard sequential context optimization pipeline can actually degrade performance compared to baselines. However, when paired with a search-based training procedure that maintains and prunes multiple candidate contexts, active information seeking delivers consistent and substantial gains. We demonstrate these improvements across diverse domains, including low-resource translation (Flores+), health scenarios (HealthBench), and reasoning-heavy tasks (LiveCodeBench and Humanity's Last Exam). Furthermore, our method proves to be data-efficient, robust across different hyperparameters, and capable of generating effective textual contexts that generalize well across different models.

preprint2026arXiv

Latent Space Communication via K-V Cache Alignment

Solving increasingly complex problems with large language models (LLMs) necessitates a move beyond individual models and towards multi-model systems that can effectively collaborate. While text has traditionally served as the medium for inter-model communication, a richer and more efficient exchange is possible if models can access each other's internal states directly. In this paper, we propose learning a shared representation space that aligns the k-v caches of multiple models, creating a high-bandwidth channel for collaboration without altering the underlying pre-trained parameters. We do so by augmenting each model with adapters to translate its state into and out of this shared space. Via a suite of experiments with Gemma-2 models, we demonstrate that this approach not only enables seamless inter-model communication but also improves individual model performance. We also show that the shared space allows for the direct transfer of learned skills, such as soft prompts, between different models. Our work represents a significant step towards a future where models can fluidly share knowledge and capabilities.

preprint2023arXiv

Infusing Commonsense World Models with Graph Knowledge

While language models have become more capable of producing compelling language, we find there are still gaps in maintaining consistency, especially when describing events in a dynamically changing world. We study the setting of generating narratives in an open world text adventure game, where a graph representation of the underlying game state can be used to train models that consume and output both grounded graph representations and natural language descriptions and actions. We build a large set of tasks by combining crowdsourced and simulated gameplays with a novel dataset of complex actions in order to to construct such models. We find it is possible to improve the consistency of action narration models by training on graph contexts and targets, even if graphs are not present at test time. This is shown both in automatic metrics and human evaluations. We plan to release our code, the new set of tasks, and best performing models.

preprint2023arXiv

Many Episode Learning in a Modular Embodied Agent via End-to-End Interaction

In this work we give a case study of an embodied machine-learning (ML) powered agent that improves itself via interactions with crowd-workers. The agent consists of a set of modules, some of which are learned, and others heuristic. While the agent is not "end-to-end" in the ML sense, end-to-end interaction is a vital part of the agent's learning mechanism. We describe how the design of the agent works together with the design of multiple annotation interfaces to allow crowd-workers to assign credit to module errors from end-to-end interactions, and to label data for individual modules. Over multiple automated human-agent interaction, credit assignment, data annotation, and model re-training and re-deployment, rounds we demonstrate agent improvement.

preprint2022arXiv

BlenderBot 3: a deployed conversational agent that continually learns to responsibly engage

We present BlenderBot 3, a 175B parameter dialogue model capable of open-domain conversation with access to the internet and a long-term memory, and having been trained on a large number of user defined tasks. We release both the model weights and code, and have also deployed the model on a public web page to interact with organic users. This technical report describes how the model was built (architecture, model and training scheme), and details of its deployment, including safety mechanisms. Human evaluations show its superiority to existing open-domain dialogue agents, including its predecessors (Roller et al., 2021; Komeili et al., 2022). Finally, we detail our plan for continual learning using the data collected from deployment, which will also be publicly released. The goal of this research program is thus to enable the community to study ever-improving responsible agents that learn through interaction.

preprint2022arXiv

IGLU 2022: Interactive Grounded Language Understanding in a Collaborative Environment at NeurIPS 2022

Human intelligence has the remarkable ability to adapt to new tasks and environments quickly. Starting from a very young age, humans acquire new skills and learn how to solve new tasks either by imitating the behavior of others or by following provided natural language instructions. To facilitate research in this direction, we propose IGLU: Interactive Grounded Language Understanding in a Collaborative Environment. The primary goal of the competition is to approach the problem of how to develop interactive embodied agents that learn to solve a task while provided with grounded natural language instructions in a collaborative environment. Understanding the complexity of the challenge, we split it into sub-tasks to make it feasible for participants. This research challenge is naturally related, but not limited, to two fields of study that are highly relevant to the NeurIPS community: Natural Language Understanding and Generation (NLU/G) and Reinforcement Learning (RL). Therefore, the suggested challenge can bring two communities together to approach one of the crucial challenges in AI. Another critical aspect of the challenge is the dedication to perform a human-in-the-loop evaluation as a final evaluation for the agents developed by contestants.

preprint2022arXiv

Interactive Grounded Language Understanding in a Collaborative Environment: IGLU 2021

Human intelligence has the remarkable ability to quickly adapt to new tasks and environments. Starting from a very young age, humans acquire new skills and learn how to solve new tasks either by imitating the behavior of others or by following provided natural language instructions. To facilitate research in this direction, we propose \emph{IGLU: Interactive Grounded Language Understanding in a Collaborative Environment}. The primary goal of the competition is to approach the problem of how to build interactive agents that learn to solve a task while provided with grounded natural language instructions in a collaborative environment. Understanding the complexity of the challenge, we split it into sub-tasks to make it feasible for participants.

preprint2022arXiv

Language Models that Seek for Knowledge: Modular Search & Generation for Dialogue and Prompt Completion

Language models (LMs) have recently been shown to generate more factual responses by employing modularity (Zhou et al., 2021) in combination with retrieval (Adolphs et al., 2021). We extend the recent approach of Adolphs et al. (2021) to include internet search as a module. Our SeeKeR (Search engine->Knowledge->Response) method thus applies a single LM to three modular tasks in succession: search, generating knowledge, and generating a final response. We show that, when using SeeKeR as a dialogue model, it outperforms the state-of-the-art model BlenderBot 2 (Chen et al., 2021) on open-domain knowledge-grounded conversations for the same number of parameters, in terms of consistency, knowledge and per-turn engagingness. SeeKeR applied to topical prompt completions as a standard language model outperforms GPT2 (Radford et al., 2019) and GPT3 (Brown et al., 2020) in terms of factuality and topicality, despite GPT3 being a vastly larger model. Our code and models are made publicly available.

preprint2022arXiv

Reducing conversational agents' overconfidence through linguistic calibration

While improving neural dialogue agents' factual accuracy is the object of much research, another important aspect of communication, less studied in the setting of neural dialogue, is transparency about ignorance. In this work, we analyze to what extent state-of-the-art chit-chat models are linguistically calibrated in the sense that their verbalized expression of doubt (or confidence) matches the likelihood that the model's responses are factually incorrect (or correct). We find that these models are poorly calibrated, yet we show that likelihood of correctness can accurately be predicted. By incorporating such metacognitive features into the training of a controllable generation model, we obtain a dialogue agent with greatly improved linguistic calibration. While improving neural dialogue agents' factual accuracy is the object of much research, another important aspect of communication, less studied in the setting of neural dialogue, is transparency about ignorance. In this work, we analyze to what extent state-of-the-art chit-chat models are linguistically calibrated in the sense that their verbalized expression of doubt (or confidence) matches the likelihood that the model's responses are factually incorrect (or correct). We find that these models are poorly calibrated, yet we show that likelihood of correctness can accurately be predicted. By incorporating such metacognitive features into the training of a controllable generation model, we obtain a dialogue agent with greatly improved linguistic calibration.

preprint2021arXiv

droidlet: modular, heterogenous, multi-modal agents

In recent years, there have been significant advances in building end-to-end Machine Learning (ML) systems that learn at scale. But most of these systems are: (a) isolated (perception, speech, or language only); (b) trained on static datasets. On the other hand, in the field of robotics, large-scale learning has always been difficult. Supervision is hard to gather and real world physical interactions are expensive. In this work we introduce and open-source droidlet, a modular, heterogeneous agent architecture and platform. It allows us to exploit both large-scale static datasets in perception and language and sophisticated heuristics often used in robotics; and provides tools for interactive annotation. Furthermore, it brings together perception, language and action onto one platform, providing a path towards agents that learn from the richness of real world interactions.

preprint2020arXiv

Deploying Lifelong Open-Domain Dialogue Learning

Much of NLP research has focused on crowdsourced static datasets and the supervised learning paradigm of training once and then evaluating test performance. As argued in de Vries et al. (2020), crowdsourced data has the issues of lack of naturalness and relevance to real-world use cases, while the static dataset paradigm does not allow for a model to learn from its experiences of using language (Silver et al., 2013). In contrast, one might hope for machine learning systems that become more useful as they interact with people. In this work, we build and deploy a role-playing game, whereby human players converse with learning agents situated in an open-domain fantasy world. We show that by training models on the conversations they have with humans in the game the models progressively improve, as measured by automatic metrics and online engagement scores. This learning is shown to be more efficient than crowdsourced data when applied to conversations with real users, as well as being far cheaper to collect.

preprint2020arXiv

Empirically Verifying Hypotheses Using Reinforcement Learning

This paper formulates hypothesis verification as an RL problem. Specifically, we aim to build an agent that, given a hypothesis about the dynamics of the world, can take actions to generate observations which can help predict whether the hypothesis is true or false. Existing RL algorithms fail to solve this task, even for simple environments. In order to train the agents, we exploit the underlying structure of many hypotheses, factorizing them as {pre-condition, action sequence, post-condition} triplets. By leveraging this structure we show that RL agents are able to succeed at the task. Furthermore, subsequent fine-tuning of the policies allows the agent to correctly verify hypotheses not amenable to the above factorization.

preprint2020arXiv

Fast Adaptation via Policy-Dynamics Value Functions

Standard RL algorithms assume fixed environment dynamics and require a significant amount of interaction to adapt to new environments. We introduce Policy-Dynamics Value Functions (PD-VF), a novel approach for rapidly adapting to dynamics different from those previously seen in training. PD-VF explicitly estimates the cumulative reward in a space of policies and environments. An ensemble of conventional RL policies is used to gather experience on training environments, from which embeddings of both policies and environments can be learned. Then, a value function conditioned on both embeddings is trained. At test time, a few actions are sufficient to infer the environment embedding, enabling a policy to be selected by maximizing the learned value function (which requires no additional environment interaction). We show that our method can rapidly adapt to new dynamics on a set of MuJoCo domains. Code available at https://github.com/rraileanu/policy-dynamics-value-functions.

preprint2020arXiv

I love your chain mail! Making knights smile in a fantasy game world: Open-domain goal-oriented dialogue agents

Dialogue research tends to distinguish between chit-chat and goal-oriented tasks. While the former is arguably more naturalistic and has a wider use of language, the latter has clearer metrics and a straightforward learning signal. Humans effortlessly combine the two, for example engaging in chit-chat with the goal of exchanging information or eliciting a specific response. Here, we bridge the divide between these two domains in the setting of a rich multi-player text-based fantasy environment where agents and humans engage in both actions and dialogue. Specifically, we train a goal-oriented model with reinforcement learning against an imitation-learned ``chit-chat'' model with two approaches: the policy either learns to pick a topic or learns to pick an utterance given the top-K utterances from the chit-chat model. We show that both models outperform an inverse model baseline and can converse naturally with their dialogue partner in order to achieve goals.

preprint2020arXiv

Learning to Visually Navigate in Photorealistic Environments Without any Supervision

Learning to navigate in a realistic setting where an agent must rely solely on visual inputs is a challenging task, in part because the lack of position information makes it difficult to provide supervision during training. In this paper, we introduce a novel approach for learning to navigate from image inputs without external supervision or reward. Our approach consists of three stages: learning a good representation of first-person views, then learning to explore using memory, and finally learning to navigate by setting its own goals. The model is trained with intrinsic rewards only so that it can be applied to any environment with image observations. We show the benefits of our approach by training an agent to navigate challenging photo-realistic environments from the Gibson dataset with RGB inputs only.

preprint2020arXiv

Open-Domain Conversational Agents: Current Progress, Open Problems, and Future Directions

We present our view of what is necessary to build an engaging open-domain conversational agent: covering the qualities of such an agent, the pieces of the puzzle that have been built so far, and the gaping holes we have not filled yet. We present a biased view, focusing on work done by our own group, while citing related work in each area. In particular, we discuss in detail the properties of continual learning, providing engaging content, and being well-behaved -- and how to measure success in providing them. We end with a discussion of our experience and learnings, and our recommendations to the community.

preprint2020arXiv

Residual Energy-Based Models for Text Generation

Text generation is ubiquitous in many NLP tasks, from summarization, to dialogue and machine translation. The dominant parametric approach is based on locally normalized models which predict one word at a time. While these work remarkably well, they are plagued by exposure bias due to the greedy nature of the generation process. In this work, we investigate un-normalized energy-based models (EBMs) which operate not at the token but at the sequence level. In order to make training tractable, we first work in the residual of a pretrained locally normalized language model and second we train using noise contrastive estimation. Furthermore, since the EBM works at the sequence level, we can leverage pretrained bi-directional contextual representations, such as BERT and RoBERTa. Our experiments on two large language modeling datasets show that residual EBMs yield lower perplexity compared to locally normalized baselines. Moreover, generation via importance sampling is very efficient and of higher quality than the baseline models according to human evaluation.

preprint2016arXiv

Convolutional networks and learning invariant to homogeneous multiplicative scalings

The conventional classification schemes -- notably multinomial logistic regression -- used in conjunction with convolutional networks (convnets) are classical in statistics, designed without consideration for the usual coupling with convnets, stochastic gradient descent, and backpropagation. In the specific application to supervised learning for convnets, a simple scale-invariant classification stage turns out to be more robust than multinomial logistic regression, appears to result in slightly lower errors on several standard test sets, has similar computational costs, and features precise control over the actual rate of learning. "Scale-invariant" means that multiplying the input values by any nonzero scalar leaves the output unchanged.

preprint2016arXiv

Evaluating Prerequisite Qualities for Learning End-to-End Dialog Systems

A long-term goal of machine learning is to build intelligent conversational agents. One recent popular approach is to train end-to-end models on a large amount of real dialog transcripts between humans (Sordoni et al., 2015; Vinyals & Le, 2015; Shang et al., 2015). However, this approach leaves many questions unanswered as an understanding of the precise successes and shortcomings of each model is hard to assess. A contrasting recent proposal are the bAbI tasks (Weston et al., 2015b) which are synthetic data that measure the ability of learning machines at various reasoning tasks over toy language. Unfortunately, those tests are very small and hence may encourage methods that do not scale. In this work, we propose a suite of new tasks of a much larger scale that attempt to bridge the gap between the two regimes. Choosing the domain of movies, we provide tasks that test the ability of models to answer factual questions (utilizing OMDB), provide personalization (utilizing MovieLens), carry short conversations about the two, and finally to perform on natural dialogs from Reddit. We provide a dataset covering 75k movie entities and with 3.5M training examples. We present results of various models on these tasks, and evaluate their performance.

preprint2016arXiv

Learning Multiagent Communication with Backpropagation

Many tasks in AI require the collaboration of multiple agents. Typically, the communication protocol between agents is manually specified and not altered during training. In this paper we explore a simple neural model, called CommNet, that uses continuous communication for fully cooperative tasks. The model consists of multiple agents and the communication between them is learned alongside their policy. We apply this model to a diverse set of tasks, demonstrating the ability of the agents to learn to communicate amongst themselves, yielding improved performance over non-communicative agents and baselines. In some cases, it is possible to interpret the language devised by the agents, revealing simple but effective strategies for solving the task at hand.

preprint2016arXiv

MazeBase: A Sandbox for Learning from Games

This paper introduces MazeBase: an environment for simple 2D games, designed as a sandbox for machine learning approaches to reasoning and planning. Within it, we create 10 simple games embodying a range of algorithmic tasks (e.g. if-then statements or set negation). A variety of neural models (fully connected, convolutional network, memory network) are deployed via reinforcement learning on these games, with and without a procedurally generated curriculum. Despite the tasks' simplicity, the performance of the models is far from optimal, suggesting directions for future development. We also demonstrate the versatility of MazeBase by using it to emulate small combat scenarios from StarCraft. Models trained on the MazeBase version can be directly applied to StarCraft, where they consistently beat the in-game AI.

preprint2016arXiv

Video (language) modeling: a baseline for generative models of natural videos

We propose a strong baseline model for unsupervised feature learning using video data. By learning to predict missing frames or extrapolate future frames from an input video sequence, the model discovers both spatial and temporal correlations which are useful to represent complex deformations and motion patterns. The models we propose are largely borrowed from the language modeling literature, and adapted to the vision domain by quantizing the space of image patches into a large dictionary. We demonstrate the approach on both a filling and a generation task. For the first time, we show that, after training on natural videos, such a model can predict non-trivial motions over short video sequences.

preprint2015arXiv

A mathematical motivation for complex-valued convolutional networks

A complex-valued convolutional network (convnet) implements the repeated application of the following composition of three operations, recursively applying the composition to an input vector of nonnegative real numbers: (1) convolution with complex-valued vectors followed by (2) taking the absolute value of every entry of the resulting vectors followed by (3) local averaging. For processing real-valued random vectors, complex-valued convnets can be viewed as "data-driven multiscale windowed power spectra," "data-driven multiscale windowed absolute spectra," "data-driven multiwavelet absolute values," or (in their most general configuration) "data-driven nonlinear multiwavelet packets." Indeed, complex-valued convnets can calculate multiscale windowed spectra when the convnet filters are windowed complex-valued exponentials. Standard real-valued convnets, using rectified linear units (ReLUs), sigmoidal (for example, logistic or tanh) nonlinearities, max. pooling, etc., do not obviously exhibit the same exact correspondence with data-driven wavelets (whereas for complex-valued convnets, the correspondence is much more than just a vague analogy). Courtesy of the exact correspondence, the remarkably rich and rigorous body of mathematical analysis for wavelets applies directly to (complex-valued) convnets.

preprint2015arXiv

Deep Generative Image Models using a Laplacian Pyramid of Adversarial Networks

In this paper we introduce a generative parametric model capable of producing high quality samples of natural images. Our approach uses a cascade of convolutional networks within a Laplacian pyramid framework to generate images in a coarse-to-fine fashion. At each level of the pyramid, a separate generative convnet model is trained using the Generative Adversarial Nets (GAN) approach (Goodfellow et al.). Samples drawn from our model are of significantly higher quality than alternate approaches. In a quantitative assessment by human evaluators, our CIFAR10 samples were mistaken for real images around 40% of the time, compared to 10% for samples drawn from a GAN baseline model. We also show samples from models trained on the higher resolution images of the LSUN scene dataset.

preprint2015arXiv

End-To-End Memory Networks

We introduce a neural network with a recurrent attention model over a possibly large external memory. The architecture is a form of Memory Network (Weston et al., 2015) but unlike the model in that work, it is trained end-to-end, and hence requires significantly less supervision during training, making it more generally applicable in realistic settings. It can also be seen as an extension of RNNsearch to the case where multiple computational steps (hops) are performed per output symbol. The flexibility of the model allows us to apply it to tasks as diverse as (synthetic) question answering and to language modeling. For the former our approach is competitive with Memory Networks, but with less supervision. For the latter, on the Penn TreeBank and Text8 datasets our approach demonstrates comparable performance to RNNs and LSTMs. In both cases we show that the key concept of multiple computational hops yields improved results.

preprint2015arXiv

Simple Baseline for Visual Question Answering

We describe a very simple bag-of-words baseline for visual question answering. This baseline concatenates the word features from the question and CNN features from the image to predict the answer. When evaluated on the challenging VQA dataset [2], it shows comparable performance to many recent approaches using recurrent neural networks. To explore the strength and weakness of the trained model, we also provide an interactive web demo and open-source code. .

preprint2014arXiv

An implementation of a randomized algorithm for principal component analysis

Recent years have witnessed intense development of randomized methods for low-rank approximation. These methods target principal component analysis (PCA) and the calculation of truncated singular value decompositions (SVD). The present paper presents an essentially black-box, fool-proof implementation for Mathworks' MATLAB, a popular software platform for numerical computation. As illustrated via several tests, the randomized algorithms for low-rank approximation outperform or at least match the classical techniques (such as Lanczos iterations) in basically all respects: accuracy, computational efficiency (both speed and memory usage), ease-of-use, parallelizability, and reliability. However, the classical procedures remain the methods of choice for estimating spectral norms, and are far superior for calculating the least singular values and corresponding singular vectors (or singular subspaces).

preprint2014arXiv

An Incremental Reseeding Strategy for Clustering

In this work we propose a simple and easily parallelizable algorithm for multiway graph partitioning. The algorithm alternates between three basic components: diffusing seed vertices over the graph, thresholding the diffused seeds, and then randomly reseeding the thresholded clusters. We demonstrate experimentally that the proper combination of these ingredients leads to an algorithm that achieves state-of-the-art performance in terms of cluster purity on standard benchmarks datasets. Moreover, the algorithm runs an order of magnitude faster than the other algorithms that achieve comparable results in terms of accuracy. We also describe a coarsen, cluster and refine approach similar to GRACLUS and METIS that removes an additional order of magnitude from the runtime of our algorithm while still maintaining competitive accuracy.

preprint2014arXiv

Signal Recovery from Pooling Representations

In this work we compute lower Lipschitz bounds of $\ell_p$ pooling operators for $p=1, 2, \infty$ as well as $\ell_p$ pooling operators preceded by half-rectification layers. These give sufficient conditions for the design of invertible neural network layers. Numerical experiments on MNIST and image patches confirm that pooling layers can be inverted with phase recovery algorithms. Moreover, the regularity of the inverse pooling, controlled by the lower Lipschitz constant, is empirically verified with a nearest neighbor regression.

preprint2014arXiv

Spectral Networks and Locally Connected Networks on Graphs

Convolutional Neural Networks are extremely efficient architectures in image and audio recognition tasks, thanks to their ability to exploit the local translational invariance of signal classes over their domain. In this paper we consider possible generalizations of CNNs to signals defined on more general domains without the action of a translation group. In particular, we propose two constructions, one based upon a hierarchical clustering of the domain, and another based on the spectrum of the graph Laplacian. We show through experiments that for low-dimensional graphs it is possible to learn convolutional layers with a number of parameters independent of the input size, resulting in efficient deep architectures.

preprint2013arXiv

Learning Stable Group Invariant Representations with Convolutional Networks

Transformation groups, such as translations or rotations, effectively express part of the variability observed in many recognition problems. The group structure enables the construction of invariant signal representations with appealing mathematical properties, where convolutions, together with pooling operators, bring stability to additive and geometric perturbations of the input. Whereas physical transformation groups are ubiquitous in image and audio applications, they do not account for all the variability of complex signal classes. We show that the invariance properties built by deep convolutional networks can be cast as a form of stable group invariance. The network wiring architecture determines the invariance group, while the trainable filter coefficients characterize the group action. We give explanatory examples which illustrate how the network architecture controls the resulting invariance group. We also explore the principle by which additional convolutional layers induce a group factorization enabling more abstract, powerful invariant representations.

preprint2013arXiv

Unsupervised Feature Learning by Deep Sparse Coding

In this paper, we propose a new unsupervised feature learning framework, namely Deep Sparse Coding (DeepSC), that extends sparse coding to a multi-layer architecture for visual object recognition tasks. The main innovation of the framework is that it connects the sparse-encoders from different layers by a sparse-to-dense module. The sparse-to-dense module is a composition of a local spatial pooling step and a low-dimensional embedding process, which takes advantage of the spatial smoothness information in the image. As a result, the new method is able to learn several levels of sparse representation of the image which capture features at a variety of abstraction levels and simultaneously preserve the spatial smoothness between the neighboring image patches. Combining the feature representations from multiple layers, DeepSC achieves the state-of-the-art performance on multiple object recognition tasks.

preprint2012arXiv

Fast approximations to structured sparse coding and applications to object classification

We describe a method for fast approximation of sparse coding. The input space is subdivided by a binary decision tree, and we simultaneously learn a dictionary and assignment of allowed dictionary elements for each leaf of the tree. We store a lookup table with the assignments and the pseudoinverses for each node, allowing for very fast inference. We give an algorithm for learning the tree, the dictionary and the dictionary element assignment, and In the process of describing this algorithm, we discuss the more general problem of learning the groups in group structured sparse modelling. We show that our method creates good sparse representations by using it in the object recognition framework of \cite{lazebnik06,yang-cvpr-09}. Implementing our own fast version of the SIFT descriptor the whole system runs at 20 frames per second on $321 \times 481$ sized images on a laptop with a quad-core cpu, while sacrificing very little accuracy on the Caltech 101 and 15 scenes benchmarks.

preprint2012arXiv

Hybrid Linear Modeling via Local Best-fit Flats

We present a simple and fast geometric method for modeling data by a union of affine subspaces. The method begins by forming a collection of local best-fit affine subspaces, i.e., subspaces approximating the data in local neighborhoods. The correct sizes of the local neighborhoods are determined automatically by the Jones' $β_2$ numbers (we prove under certain geometric conditions that our method finds the optimal local neighborhoods). The collection of subspaces is further processed by a greedy selection procedure or a spectral method to generate the final model. We discuss applications to tracking-based motion segmentation and clustering of faces under different illuminating conditions. We give extensive experimental evidence demonstrating the state of the art accuracy and speed of the suggested algorithms on these problems and also on synthetic hybrid linear data as well as the MNIST handwritten digits data; and we demonstrate how to use our algorithms for fast determination of the number of affine subspaces.

preprint2010arXiv

Randomized hybrid linear modeling by local best-fit flats

The hybrid linear modeling problem is to identify a set of d-dimensional affine sets in a D-dimensional Euclidean space. It arises, for example, in object tracking and structure from motion. The hybrid linear model can be considered as the second simplest (behind linear) manifold model of data. In this paper we will present a very simple geometric method for hybrid linear modeling based on selecting a set of local best fit flats that minimize a global l1 error measure. The size of the local neighborhoods is determined automatically by the Jones' l2 beta numbers; it is proven under certain geometric conditions that good local neighborhoods exist and are found by our method. We also demonstrate how to use this algorithm for fast determination of the number of affine subspaces. We give extensive experimental evidence demonstrating the state of the art accuracy and speed of the algorithm on synthetic and real hybrid linear data.

preprint2009arXiv

Median K-flats for hybrid linear modeling with many outliers

We describe the Median K-Flats (MKF) algorithm, a simple online method for hybrid linear modeling, i.e., for approximating data by a mixture of flats. This algorithm simultaneously partitions the data into clusters while finding their corresponding best approximating l1 d-flats, so that the cumulative l1 error is minimized. The current implementation restricts d-flats to be d-dimensional linear subspaces. It requires a negligible amount of storage, and its complexity, when modeling data consisting of N points in D-dimensional Euclidean space with K d-dimensional linear subspaces, is of order O(n K d D+n d^2 D), where n is the number of iterations required for convergence (empirically on the order of 10^4). Since it is an online algorithm, data can be supplied to it incrementally and it can incrementally produce the corresponding output. The performance of the algorithm is carefully evaluated using synthetic and real data.