Hanie Sedghi

Jiri Hron, Laura Culp, Gamaleldin Elsayed et al. · anthropic, deepmind

While many capabilities of language models (LMs) improve with increased training budget, the influence of scale on hallucinations is not yet fully understood. Hallucinations come in many forms, and there is no universally accepted definition. We thus focus on studying only those hallucinations where a correct answer appears verbatim in the training set. To fully control the training data content, we construct a knowledge graph (KG)-based dataset, and use it to train a set of increasingly large LMs. We find that for a fixed dataset, larger and longer-trained LMs hallucinate less. However, hallucinating on $\leq5$% of the training data requires an order of magnitude larger model, and thus an order of magnitude more compute, than Hoffmann et al. (2022) reported was optimal. Given this costliness, we study how hallucination detectors depend on scale. While we see detector size improves performance on fixed LM's outputs, we find an inverse relationship between the scale of the LM and the detectability of its hallucinations.

C. Daniel Freeman, Laura Culp, Aaron Parisi et al. · anthropic, deepmind

We introduce and study the problem of adversarial arithmetic, which provides a simple yet challenging testbed for language model alignment. This problem is comprised of arithmetic questions posed in natural language, with an arbitrary adversarial string inserted before the question is complete. Even in the simple setting of 1-digit addition problems, it is easy to find adversarial prompts that make all tested models (including PaLM2, GPT4, Claude2) misbehave, and even to steer models to a particular wrong answer. We additionally provide a simple algorithm for finding successful attacks by querying those same models, which we name "prompt inversion rejection sampling" (PIRS). We finally show that models can be partially hardened against these attacks via reinforcement learning and via agentic constitutional loops. However, we were not able to make a language model fully robust against adversarial arithmetic attacks.

Hattie Zhou, Azade Nova, Hugo Larochelle et al.

Large language models (LLMs) have shown increasing in-context learning capabilities through scaling up model and data size. Despite this progress, LLMs are still unable to solve algorithmic reasoning problems. While providing a rationale with the final answer has led to further improvements in multi-step reasoning problems, Anil et al. 2022 showed that even simple algorithmic reasoning tasks such as parity are far from solved. In this work, we identify and study four key stages for successfully teaching algorithmic reasoning to LLMs: (1) formulating algorithms as skills, (2) teaching multiple skills simultaneously (skill accumulation), (3) teaching how to combine skills (skill composition) and (4) teaching how to use skills as tools. We show that it is possible to teach algorithmic reasoning to LLMs via in-context learning, which we refer to as algorithmic prompting. We evaluate our approach on a variety of arithmetic and quantitative reasoning tasks, and demonstrate significant boosts in performance over existing prompting techniques. In particular, for long parity, addition, multiplication and subtraction, we achieve an error reduction of approximately 10x, 9x, 5x and 2x respectively compared to the best available baselines.

Pratyush Maini, Michael C. Mozer, Hanie Sedghi et al.

Recent efforts at explaining the interplay of memorization and generalization in deep overparametrized networks have posited that neural networks $\textit{memorize}$ "hard" examples in the final few layers of the model. Memorization refers to the ability to correctly predict on $\textit{atypical}$ examples of the training set. In this work, we show that rather than being confined to individual layers, memorization is a phenomenon confined to a small set of neurons in various layers of the model. First, via three experimental sources of converging evidence, we find that most layers are redundant for the memorization of examples and the layers that contribute to example memorization are, in general, not the final layers. The three sources are $\textit{gradient accounting}$ (measuring the contribution to the gradient norms from memorized and clean examples), $\textit{layer rewinding}$ (replacing specific model weights of a converged model with previous training checkpoints), and $\textit{retraining}$ (training rewound layers only on clean examples). Second, we ask a more generic question: can memorization be localized $\textit{anywhere}$ in a model? We discover that memorization is often confined to a small number of neurons or channels (around 5) of the model. Based on these insights we propose a new form of dropout -- $\textit{example-tied dropout}$ that enables us to direct the memorization of examples to an apriori determined set of neurons. By dropping out these neurons, we are able to reduce the accuracy on memorized examples from $100\%\to3\%$, while also reducing the generalization gap.

Keller Jordan, Hanie Sedghi, Olga Saukh et al.

In this paper we look into the conjecture of Entezari et al. (2021) which states that if the permutation invariance of neural networks is taken into account, then there is likely no loss barrier to the linear interpolation between SGD solutions. First, we observe that neuron alignment methods alone are insufficient to establish low-barrier linear connectivity between SGD solutions due to a phenomenon we call variance collapse: interpolated deep networks suffer a collapse in the variance of their activations, causing poor performance. Next, we propose REPAIR (REnormalizing Permuted Activations for Interpolation Repair) which mitigates variance collapse by rescaling the preactivations of such interpolated networks. We explore the interaction between our method and the choice of normalization layer, network width, and depth, and demonstrate that using REPAIR on top of neuron alignment methods leads to 60%-100% relative barrier reduction across a wide variety of architecture families and tasks. In particular, we report a 74% barrier reduction for ResNet50 on ImageNet and 90% barrier reduction for ResNet18 on CIFAR10.

Rahim Entezari, Mitchell Wortsman, Olga Saukh et al.

The transfer learning paradigm of model pre-training and subsequent fine-tuning produces high-accuracy models. While most studies recommend scaling the pre-training size to benefit most from transfer learning, a question remains: what data and method should be used for pre-training? We investigate the impact of pre-training data distribution on the few-shot and full fine-tuning performance using 3 pre-training methods (supervised, contrastive language-image and image-image), 7 pre-training datasets, and 9 downstream datasets. Through extensive controlled experiments, we find that the choice of the pre-training data source is essential for the few-shot transfer, but its role decreases as more data is made available for fine-tuning. Additionally, we explore the role of data curation and examine the trade-offs between label noise and the size of the pre-training dataset. We find that using 2000X more pre-training data from LAION can match the performance of supervised ImageNet pre-training. Furthermore, we investigate the effect of pre-training methods, comparing language-image contrastive vs. image-image contrastive, and find that the latter leads to better downstream accuracy

Lukas Timpl, Rahim Entezari, Hanie Sedghi et al.

This paper examines the impact of static sparsity on the robustness of a trained network to weight perturbations, data corruption, and adversarial examples. We show that, up to a certain sparsity achieved by increasing network width and depth while keeping the network capacity fixed, sparsified networks consistently match and often outperform their initially dense versions. Robustness and accuracy decline simultaneously for very high sparsity due to loose connectivity between network layers. Our findings show that a rapid robustness drop caused by network compression observed in the literature is due to a reduced network capacity rather than sparsity.

Mahsa Forouzesh, Hanie Sedghi, Patrick Thiran

Deep neural networks may easily memorize noisy labels present in real-world data, which degrades their ability to generalize. It is therefore important to track and evaluate the robustness of models against noisy label memorization. We propose a metric, called susceptibility, to gauge such memorization for neural networks. Susceptibility is simple and easy to compute during training. Moreover, it does not require access to ground-truth labels and it only uses unlabeled data. We empirically show the effectiveness of our metric in tracking memorization on various architectures and datasets and provide theoretical insights into the design of the susceptibility metric. Finally, we show through extensive experiments on datasets with synthetic and real-world label noise that one can utilize susceptibility and the overall training accuracy to distinguish models that maintain a low memorization on the training set and generalize well to unseen clean data.

Amr Khalifa, Michael C. Mozer, Hanie Sedghi et al.

Recent works demonstrate that early layers in a neural network contain useful information for prediction. Inspired by this, we show that extending temperature scaling across all layers improves both calibration and accuracy. We call this procedure "layer-stack temperature scaling" (LATES). Informally, LATES grants each layer a weighted vote during inference. We evaluate it on five popular convolutional neural network architectures both in- and out-of-distribution and observe a consistent improvement over temperature scaling in terms of accuracy, calibration, and AUC. All conclusions are supported by comprehensive statistical analyses. Since LATES neither retrains the architecture nor introduces many more parameters, its advantages can be reaped without requiring additional data beyond what is used in temperature scaling. Finally, we show that combining LATES with Monte Carlo Dropout matches state-of-the-art results on CIFAR10/100.

Bernd Bohnet, Pierre-Alexandre Kamienny, Hanie Sedghi et al.

We demonstrate an approach for LLMs to critique their \emph{own} answers with the goal of enhancing their performance that leads to significant improvements over established planning benchmarks. Despite the findings of earlier research that has cast doubt on the effectiveness of LLMs leveraging self critique methods, we show significant performance gains on planning datasets in the Blocksworld domain through intrinsic self-critique, without external source such as a verifier. We also demonstrate similar improvements on Logistics and Mini-grid datasets, exceeding strong baseline accuracies. We employ a few-shot learning technique and progressively extend it to a many-shot approach as our base method and demonstrate that it is possible to gain substantial improvement on top of this already competitive approach by employing an iterative process for correction and refinement. We illustrate how self-critique can significantly boost planning performance. Our empirical results present new state-of-the-art on the class of models considered, namely LLM model checkpoints from October 2024. Our primary focus lies on the method itself, demonstrating intrinsic self-improvement capabilities that are applicable regardless of the specific model version, and we believe that applying our method to more complex search techniques and more capable models will lead to even better performance.

Gemini Team, Petko Georgiev, Ving Ian Lei et al. · deepmind, mila

In this report, we introduce the Gemini 1.5 family of models, representing the next generation of highly compute-efficient multimodal models capable of recalling and reasoning over fine-grained information from millions of tokens of context, including multiple long documents and hours of video and audio. The family includes two new models: (1) an updated Gemini 1.5 Pro, which exceeds the February version on the great majority of capabilities and benchmarks; (2) Gemini 1.5 Flash, a more lightweight variant designed for efficiency with minimal regression in quality. Gemini 1.5 models achieve near-perfect recall on long-context retrieval tasks across modalities, improve the state-of-the-art in long-document QA, long-video QA and long-context ASR, and match or surpass Gemini 1.0 Ultra's state-of-the-art performance across a broad set of benchmarks. Studying the limits of Gemini 1.5's long-context ability, we find continued improvement in next-token prediction and near-perfect retrieval (>99%) up to at least 10M tokens, a generational leap over existing models such as Claude 3.0 (200k) and GPT-4 Turbo (128k). Finally, we highlight real-world use cases, such as Gemini 1.5 collaborating with professionals on completing their tasks achieving 26 to 75% time savings across 10 different job categories, as well as surprising new capabilities of large language models at the frontier; when given a grammar manual for Kalamang, a language with fewer than 200 speakers worldwide, the model learns to translate English to Kalamang at a similar level to a person who learned from the same content.

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.

Avi Singh, John D. Co-Reyes, Rishabh Agarwal et al. · anthropic, deepmind

Fine-tuning language models~(LMs) on human-generated data remains a prevalent practice. However, the performance of such models is often limited by the quantity and diversity of high-quality human data. In this paper, we explore whether we can go beyond human data on tasks where we have access to scalar feedback, for example, on math problems where one can verify correctness. To do so, we investigate a simple self-training method based on expectation-maximization, which we call ReST$^{EM}$, where we (1) generate samples from the model and filter them using binary feedback, (2) fine-tune the model on these samples, and (3) repeat this process a few times. Testing on advanced MATH reasoning and APPS coding benchmarks using PaLM-2 models, we find that ReST$^{EM}$ scales favorably with model size and significantly surpasses fine-tuning only on human data. Overall, our findings suggest self-training with feedback can substantially reduce dependence on human-generated data.

Saurabh Garg, Sivaraman Balakrishnan, Zachary C. Lipton et al.

Real-world machine learning deployments are characterized by mismatches between the source (training) and target (test) distributions that may cause performance drops. In this work, we investigate methods for predicting the target domain accuracy using only labeled source data and unlabeled target data. We propose Average Thresholded Confidence (ATC), a practical method that learns a threshold on the model's confidence, predicting accuracy as the fraction of unlabeled examples for which model confidence exceeds that threshold. ATC outperforms previous methods across several model architectures, types of distribution shifts (e.g., due to synthetic corruptions, dataset reproduction, or novel subpopulations), and datasets (Wilds, ImageNet, Breeds, CIFAR, and MNIST). In our experiments, ATC estimates target performance $2$-$4\times$ more accurately than prior methods. We also explore the theoretical foundations of the problem, proving that, in general, identifying the accuracy is just as hard as identifying the optimal predictor and thus, the efficacy of any method rests upon (perhaps unstated) assumptions on the nature of the shift. Finally, analyzing our method on some toy distributions, we provide insights concerning when it works. Code is available at https://github.com/saurabhgarg1996/ATC_code/.

Xinran Zhao, Hanie Sedghi, Bernd Bohnet et al.

Planning is essential for artificial intelligence systems to look ahead and proactively determine a course of actions to reach objectives in the virtual and real world. Recent work on large language models (LLMs) sheds light on their planning capability in various tasks. However, it remains unclear what signals in the context influence the model performance. In this work, we explore how to improve the model planning capability through in-context learning (ICL), specifically, what signals can help select the exemplars. Through extensive experiments, we observe that commonly used problem similarity may result in false positives with drastically different plans, which can mislead the model. In response, we propose to sample and filter exemplars leveraging plan side action sequence similarity (AS). We propose GRASE-DC: a two-stage pipeline that first re-samples high AS exemplars and then curates the selected exemplars with dynamic clustering on AS to achieve a balance of relevance and diversity. Our experimental result confirms that GRASE-DC achieves significant performance improvement on various planning tasks (up to ~11-40 point absolute accuracy improvement with 27.3% fewer exemplars needed on average). With GRASE-DC* + VAL, where we iteratively apply GRASE-DC with a validator, we are able to even boost the performance by 18.9% more. Extensive analysis validates the consistent performance improvement of GRASE-DC with various backbone LLMs and on both classical planning and natural language planning benchmarks. GRASE-DC can further boost the planning accuracy by ~24 absolute points on harder problems using simpler problems as exemplars over a random baseline. This demonstrates its ability to generalize to out-of-distribution problems.

Bernd Bohnet, Azade Nova, Aaron T Parisi et al.

Classical and natural language planning tasks remain a difficult domain for modern large language models (LLMs). In this work, we lay the foundations for improving planning capabilities of LLMs. First, we construct a comprehensive benchmark suite encompassing both classical planning benchmarks and natural language scenarios. This suite includes algorithms to methodically generate instances of tasks with varying levels of difficulty, allowing for rigorous and systematic evaluation of LLM performance. Next, we investigate the use of many-shot in-context learning to enhance LLM planning, exploring the relationship between increased context length and improved planning performance. In addition, we demonstrate the positive impact of fine-tuning LLMs on optimal planning paths. We also probe the efficacy of chain-of-thought reasoning methods to improve LLM planning performance. Moreover, we probe the performance of the proposed methods in out-of-distribution scenarios, assessing the ability to generalize to novel and unseen planning challenges. Finally, we investigate model's failure modes and reveal insights that hold true across different benchmarks.

Rahim Entezari, Hanie Sedghi, Olga Saukh et al.

In this paper, we conjecture that if the permutation invariance of neural networks is taken into account, SGD solutions will likely have no barrier in the linear interpolation between them. Although it is a bold conjecture, we show how extensive empirical attempts fall short of refuting it. We further provide a preliminary theoretical result to support our conjecture. Our conjecture has implications for lottery ticket hypothesis, distributed training, and ensemble methods.

Samira Abnar, Mostafa Dehghani, Behnam Neyshabur et al.

Recent developments in large-scale machine learning suggest that by scaling up data, model size and training time properly, one might observe that improvements in pre-training would transfer favorably to most downstream tasks. In this work, we systematically study this phenomena and establish that, as we increase the upstream accuracy, the performance of downstream tasks saturates. In particular, we investigate more than 4800 experiments on Vision Transformers, MLP-Mixers and ResNets with number of parameters ranging from ten million to ten billion, trained on the largest scale of available image data (JFT, ImageNet21K) and evaluated on more than 20 downstream image recognition tasks. We propose a model for downstream performance that reflects the saturation phenomena and captures the nonlinear relationship in performance of upstream and downstream tasks. Delving deeper to understand the reasons that give rise to these phenomena, we show that the saturation behavior we observe is closely related to the way that representations evolve through the layers of the models. We showcase an even more extreme scenario where performance on upstream and downstream are at odds with each other. That is, to have a better downstream performance, we need to hurt upstream accuracy.

Samira Abnar, Rianne van den Berg, Golnaz Ghiasi et al.

We focus on the problem of domain adaptation when the goal is shifting the model towards the target distribution, rather than learning domain invariant representations. It has been shown that under the following two assumptions: (a) access to samples from intermediate distributions, and (b) samples being annotated with the amount of change from the source distribution, self-training can be successfully applied on gradually shifted samples to adapt the model toward the target distribution. We hypothesize having (a) is enough to enable iterative self-training to slowly adapt the model to the target distribution, by making use of an implicit curriculum. In the case where (a) does not hold, we observe that iterative self-training falls short. We propose GIFT, a method that creates virtual samples from intermediate distributions by interpolating representations of examples from source and target domains. We evaluate an iterative-self-training method on datasets with natural distribution shifts, and show that when applied on top of other domain adaptation methods, it improves the performance of the model on the target dataset. We run an analysis on a synthetic dataset to show that in the presence of (a) iterative-self-training naturally forms a curriculum of samples. Furthermore, we show that when (a) does not hold, GIFT performs better than iterative self-training.

Preetum Nakkiran, Behnam Neyshabur, Hanie Sedghi

We propose a new framework for reasoning about generalization in deep learning. The core idea is to couple the Real World, where optimizers take stochastic gradient steps on the empirical loss, to an Ideal World, where optimizers take steps on the population loss. This leads to an alternate decomposition of test error into: (1) the Ideal World test error plus (2) the gap between the two worlds. If the gap (2) is universally small, this reduces the problem of generalization in offline learning to the problem of optimization in online learning. We then give empirical evidence that this gap between worlds can be small in realistic deep learning settings, in particular supervised image classification. For example, CNNs generalize better than MLPs on image distributions in the Real World, but this is "because" they optimize faster on the population loss in the Ideal World. This suggests our framework is a useful tool for understanding generalization in deep learning, and lays a foundation for future research in the area.

Behnam Neyshabur, Hanie Sedghi, Chiyuan Zhang

One desired capability for machines is the ability to transfer their knowledge of one domain to another where data is (usually) scarce. Despite ample adaptation of transfer learning in various deep learning applications, we yet do not understand what enables a successful transfer and which part of the network is responsible for that. In this paper, we provide new tools and analyses to address these fundamental questions. Through a series of analyses on transferring to block-shuffled images, we separate the effect of feature reuse from learning low-level statistics of data and show that some benefit of transfer learning comes from the latter. We present that when training from pre-trained weights, the model stays in the same basin in the loss landscape and different instances of such model are similar in feature space and close in parameter space.

Niladri S. Chatterji, Behnam Neyshabur, Hanie Sedghi

We study the phenomenon that some modules of deep neural networks (DNNs) are more critical than others. Meaning that rewinding their parameter values back to initialization, while keeping other modules fixed at the trained parameters, results in a large drop in the network's performance. Our analysis reveals interesting properties of the loss landscape which leads us to propose a complexity measure, called module criticality, based on the shape of the valleys that connects the initial and final values of the module parameters. We formulate how generalization relates to the module criticality, and show that this measure is able to explain the superior generalization performance of some architectures over others, whereas earlier measures fail to do so.

Philip M. Long, Hanie Sedghi

We prove bounds on the generalization error of convolutional networks. The bounds are in terms of the training loss, the number of parameters, the Lipschitz constant of the loss and the distance from the weights to the initial weights. They are independent of the number of pixels in the input, and the height and width of hidden feature maps. We present experiments using CIFAR-10 with varying hyperparameters of a deep convolutional network, comparing our bounds with practical generalization gaps.

Alexander Ratner, Dan Alistarh, Gustavo Alonso et al.

Machine learning (ML) techniques are enjoying rapidly increasing adoption. However, designing and implementing the systems that support ML models in real-world deployments remains a significant obstacle, in large part due to the radically different development and deployment profile of modern ML methods, and the range of practical concerns that come with broader adoption. We propose to foster a new systems machine learning research community at the intersection of the traditional systems and ML communities, focused on topics such as hardware systems for ML, software systems for ML, and ML optimized for metrics beyond predictive accuracy. To do this, we describe a new conference, MLSys, that explicitly targets research at the intersection of systems and machine learning with a program committee split evenly between experts in systems and ML, and an explicit focus on topics at the intersection of the two.

Philip M. Long, Hanie Sedghi

We analyze the joint probability distribution on the lengths of the vectors of hidden variables in different layers of a fully connected deep network, when the weights and biases are chosen randomly according to Gaussian distributions, and the input is in $\{ -1, 1\}^N$. We show that, if the activation function $φ$ satisfies a minimal set of assumptions, satisfied by all activation functions that we know that are used in practice, then, as the width of the network gets large, the `length process' converges in probability to a length map that is determined as a simple function of the variances of the random weights and biases, and the activation function $φ$. We also show that this convergence may fail for $φ$ that violate our assumptions.

Hanie Sedghi, Vineet Gupta, Philip M. Long

We characterize the singular values of the linear transformation associated with a standard 2D multi-channel convolutional layer, enabling their efficient computation. This characterization also leads to an algorithm for projecting a convolutional layer onto an operator-norm ball. We show that this is an effective regularizer; for example, it improves the test error of a deep residual network using batch normalization on CIFAR-10 from 6.2\% to 5.3\%.

Hanie Sedghi, Ashish Sabharwal

Given a knowledge base or KB containing (noisy) facts about common nouns or generics, such as "all trees produce oxygen" or "some animals live in forests", we consider the problem of inferring additional such facts at a precision similar to that of the starting KB. Such KBs capture general knowledge about the world, and are crucial for various applications such as question answering. Different from commonly studied named entity KBs such as Freebase, generics KBs involve quantification, have more complex underlying regularities, tend to be more incomplete, and violate the commonly used locally closed world assumption (LCWA). We show that existing KB completion methods struggle with this new task, and present the first approach that is successful. Our results demonstrate that external information, such as relation schemas and entity taxonomies, if used appropriately, can be a surprisingly powerful tool in this setting. First, our simple yet effective knowledge guided tensor factorization approach achieves state-of-the-art results on two generics KBs (80% precise) for science, doubling their size at 74%-86% precision. Second, our novel taxonomy guided, submodular, active learning method for collecting annotations about rare entities (e.g., oriole, a bird) is 6x more effective at inferring further new facts about them than multiple active learning baselines.

Hanie Sedghi, Anima Anandkumar

We consider the problem of training input-output recurrent neural networks (RNN) for sequence labeling tasks. We propose a novel spectral approach for learning the network parameters. It is based on decomposition of the cross-moment tensor between the output and a non-linear transformation of the input, based on score functions. We guarantee consistent learning with polynomial sample and computational complexity under transparent conditions such as non-degeneracy of model parameters, polynomial activations for the neurons, and a Markovian evolution of the input sequence. We also extend our results to Bidirectional RNN which uses both previous and future information to output the label at each time point, and is employed in many NLP tasks such as POS tagging.

Majid Janzamin, Hanie Sedghi, Anima Anandkumar

Training neural networks is a challenging non-convex optimization problem, and backpropagation or gradient descent can get stuck in spurious local optima. We propose a novel algorithm based on tensor decomposition for guaranteed training of two-layer neural networks. We provide risk bounds for our proposed method, with a polynomial sample complexity in the relevant parameters, such as input dimension and number of neurons. While learning arbitrary target functions is NP-hard, we provide transparent conditions on the function and the input for learnability. Our training method is based on tensor decomposition, which provably converges to the global optimum, under a set of mild non-degeneracy conditions. It consists of simple embarrassingly parallel linear and multi-linear operations, and is competitive with standard stochastic gradient descent (SGD), in terms of computational complexity. Thus, we propose a computationally efficient method with guaranteed risk bounds for training neural networks with one hidden layer.

Anima Anandkumar, Hanie Sedghi

Community detection in graphs has been extensively studied both in theory and in applications. However, detecting communities in hypergraphs is more challenging. In this paper, we propose a tensor decomposition approach for guaranteed learning of communities in a special class of hypergraphs modeling social tagging systems or folksonomies. A folksonomy is a tripartite 3-uniform hypergraph consisting of (user, tag, resource) hyperedges. We posit a probabilistic mixed membership community model, and prove that the tensor method consistently learns the communities under efficient sample complexity and separation requirements.

Majid Janzamin, Hanie Sedghi, Anima Anandkumar

Feature learning forms the cornerstone for tackling challenging learning problems in domains such as speech, computer vision and natural language processing. In this paper, we consider a novel class of matrix and tensor-valued features, which can be pre-trained using unlabeled samples. We present efficient algorithms for extracting discriminative information, given these pre-trained features and labeled samples for any related task. Our class of features are based on higher-order score functions, which capture local variations in the probability density function of the input. We establish a theoretical framework to characterize the nature of discriminative information that can be extracted from score-function features, when used in conjunction with labeled samples. We employ efficient spectral decomposition algorithms (on matrices and tensors) for extracting discriminative components. The advantage of employing tensor-valued features is that we can extract richer discriminative information in the form of an overcomplete representations. Thus, we present a novel framework for employing generative models of the input for discriminative learning.

Hanie Sedghi, Majid Janzamin, Anima Anandkumar

We consider the problem of learning mixtures of generalized linear models (GLM) which arise in classification and regression problems. Typical learning approaches such as expectation maximization (EM) or variational Bayes can get stuck in spurious local optima. In contrast, we present a tensor decomposition method which is guaranteed to correctly recover the parameters. The key insight is to employ certain feature transformations of the input, which depend on the input generative model. Specifically, we employ score function tensors of the input and compute their cross-correlation with the response variable. We establish that the decomposition of this tensor consistently recovers the parameters, under mild non-degeneracy conditions. We demonstrate that the computational and sample complexity of our method is a low order polynomial of the input and the latent dimensions.

Majid Janzamin, Hanie Sedghi, Anima Anandkumar

Feature learning forms the cornerstone for tackling challenging learning problems in domains such as speech, computer vision and natural language processing. In this paper, we consider a novel class of matrix and tensor-valued features, which can be pre-trained using unlabeled samples. We present efficient algorithms for extracting discriminative information, given these pre-trained features and labeled samples for any related task. Our class of features are based on higher-order score functions, which capture local variations in the probability density function of the input. We establish a theoretical framework to characterize the nature of discriminative information that can be extracted from score-function features, when used in conjunction with labeled samples. We employ efficient spectral decomposition algorithms (on matrices and tensors) for extracting discriminative components. The advantage of employing tensor-valued features is that we can extract richer discriminative information in the form of an overcomplete representations. Thus, we present a novel framework for employing generative models of the input for discriminative learning.

Hanie Sedghi, Anima Anandkumar

We provide novel guaranteed approaches for training feedforward neural networks with sparse connectivity. We leverage on the techniques developed previously for learning linear networks and show that they can also be effectively adopted to learn non-linear networks. We operate on the moments involving label and the score function of the input, and show that their factorization provably yields the weight matrix of the first layer of a deep network under mild conditions. In practice, the output of our method can be employed as effective initializers for gradient descent.

Hanie Sedghi, Edmond Jonckheere

Robust control and maintenance of the grid relies on accurate data. Both PMUs and state estimators are prone to false data injection attacks. Thus, it is crucial to have a mechanism for fast and accurate detection of an agent maliciously tampering with the data---for both preventing attacks that may lead to blackouts, and for routine monitoring and control tasks of current and future grids. We propose a decentralized false data injection detection scheme based on Markov graph of the bus phase angles. We utilize the Conditional Covariance Test (CCT) to learn the structure of the grid. Using the DC power flow model, we show that under normal circumstances, and because of walk-summability of the grid graph, the Markov graph of the voltage angles can be determined by the power grid graph. Therefore, a discrepancy between calculated Markov graph and learned structure should trigger the alarm. Local grid topology is available online from the protection system and we exploit it to check for mismatch. Should a mismatch be detected, we use correlation anomaly score to detect the set of attacked nodes. Our method can detect the most recent stealthy deception attack on the power grid that assumes knowledge of bus-branch model of the system and is capable of deceiving the state estimator, damaging power network observatory, control, monitoring, demand response and pricing schemes. Specifically, under the stealthy deception attack, the Markov graph of phase angles changes. In addition to detect a state of attack, our method can detect the set of attacked nodes. To the best of our knowledge, our remedy is the first to comprehensively detect this sophisticated attack and it does not need additional hardware. Moreover, our detection scheme is successful no matter the size of the attacked subset. Simulation of various power networks confirms our claims.

Hanie Sedghi, Anima Anandkumar, Edmond Jonckheere

We propose an efficient ADMM method with guarantees for high-dimensional problems. We provide explicit bounds for the sparse optimization problem and the noisy matrix decomposition problem. For sparse optimization, we establish that the modified ADMM method has an optimal convergence rate of $\mathcal{O}(s\log d/T)$, where $s$ is the sparsity level, $d$ is the data dimension and $T$ is the number of steps. This matches with the minimax lower bounds for sparse estimation. For matrix decomposition into sparse and low rank components, we provide the first guarantees for any online method, and prove a convergence rate of $\tilde{\mathcal{O}}((s+r)β^2(p) /T) + \mathcal{O}(1/p)$ for a $p\times p$ matrix, where $s$ is the sparsity level, $r$ is the rank and $Θ(\sqrt{p})\leq β(p)\leq Θ(p)$. Our guarantees match the minimax lower bound with respect to $s,r$ and $T$. In addition, we match the minimax lower bound with respect to the matrix dimension $p$, i.e. $β(p)=Θ(\sqrt{p})$, for many important statistical models including the independent noise model, the linear Bayesian network and the latent Gaussian graphical model under some conditions. Our ADMM method is based on epoch-based annealing and consists of inexpensive steps which involve projections on to simple norm balls. Experiments show that for both sparse optimization and matrix decomposition problems, our algorithm outperforms the state-of-the-art methods. In particular, we reach higher accuracy with same time complexity.