Puneet K. Dokania

Ameya Prabhu, Hasan Abed Al Kader Hammoud, Puneet Dokania et al.

Continual Learning (CL) aims to sequentially train models on streams of incoming data that vary in distribution by preserving previous knowledge while adapting to new data. Current CL literature focuses on restricted access to previously seen data, while imposing no constraints on the computational budget for training. This is unreasonable for applications in-the-wild, where systems are primarily constrained by computational and time budgets, not storage. We revisit this problem with a large-scale benchmark and analyze the performance of traditional CL approaches in a compute-constrained setting, where effective memory samples used in training can be implicitly restricted as a consequence of limited computation. We conduct experiments evaluating various CL sampling strategies, distillation losses, and partial fine-tuning on two large-scale datasets, namely ImageNet2K and Continual Google Landmarks V2 in data incremental, class incremental, and time incremental settings. Through extensive experiments amounting to a total of over 1500 GPU-hours, we find that, under compute-constrained setting, traditional CL approaches, with no exception, fail to outperform a simple minimal baseline that samples uniformly from memory. Our conclusions are consistent in a different number of stream time steps, e.g., 20 to 200, and under several computational budgets. This suggests that most existing CL methods are particularly too computationally expensive for realistic budgeted deployment. Code for this project is available at: https://github.com/drimpossible/BudgetCL.

Guillermo Ortiz-Jiménez, Pau de Jorge, Amartya Sanyal et al. · oxford

Adversarial training (AT) is the de facto method for building robust neural networks, but it can be computationally expensive. To mitigate this, fast single-step attacks can be used, but this may lead to catastrophic overfitting (CO). This phenomenon appears when networks gain non-trivial robustness during the first stages of AT, but then reach a breaking point where they become vulnerable in just a few iterations. The mechanisms that lead to this failure mode are still poorly understood. In this work, we study the onset of CO in single-step AT methods through controlled modifications of typical datasets of natural images. In particular, we show that CO can be induced at much smaller $ε$ values than it was observed before just by injecting images with seemingly innocuous features. These features aid non-robust classification but are not enough to achieve robustness on their own. Through extensive experiments we analyze this novel phenomenon and discover that the presence of these easy features induces a learning shortcut that leads to CO. Our findings provide new insights into the mechanisms of CO and improve our understanding of the dynamics of AT. The code to reproduce our experiments can be found at https://github.com/gortizji/co_features.

Tom Joy, Francesco Pinto, Ser-Nam Lim et al.

It is now well known that neural networks can be wrong with high confidence in their predictions, leading to poor calibration. The most common post-hoc approach to compensate for this is to perform temperature scaling, which adjusts the confidences of the predictions on any input by scaling the logits by a fixed value. Whilst this approach typically improves the average calibration across the whole test dataset, this improvement typically reduces the individual confidences of the predictions irrespective of whether the classification of a given input is correct or incorrect. With this insight, we base our method on the observation that different samples contribute to the calibration error by varying amounts, with some needing to increase their confidence and others needing to decrease it. Therefore, for each input, we propose to predict a different temperature value, allowing us to adjust the mismatch between confidence and accuracy at a finer granularity. Furthermore, we observe improved results on OOD detection and can also extract a notion of hardness for the data-points. Our method is applied post-hoc, consequently using very little computation time and with a negligible memory footprint and is applied to off-the-shelf pre-trained classifiers. We test our method on the ResNet50 and WideResNet28-10 architectures using the CIFAR10/100 and Tiny-ImageNet datasets, showing that producing per-data-point temperatures is beneficial also for the expected calibration error across the whole test set. Code is available at: https://github.com/thwjoy/adats.

Samyak Jain, Ekdeep Singh Lubana, Kemal Oksuz et al. · oxford

Safety fine-tuning helps align Large Language Models (LLMs) with human preferences for their safe deployment. To better understand the underlying factors that make models safe via safety fine-tuning, we design a synthetic data generation framework that captures salient aspects of an unsafe input by modeling the interaction between the task the model is asked to perform (e.g., "design") versus the specific concepts the task is asked to be performed upon (e.g., a "cycle" vs. a "bomb"). Using this, we investigate three well-known safety fine-tuning methods -- supervised safety fine-tuning, direct preference optimization, and unlearning -- and provide significant evidence demonstrating that these methods minimally transform MLP weights to specifically align unsafe inputs into its weights' null space. This yields a clustering of inputs based on whether the model deems them safe or not. Correspondingly, when an adversarial input (e.g., a jailbreak) is provided, its activations are closer to safer samples, leading to the model processing such an input as if it were safe. We validate our findings, wherever possible, on real-world models -- specifically, Llama-2 7B and Llama-3 8B.

Francisco Eiras, Kemal Oksuz, Adel Bibi et al.

Referring Image Segmentation (RIS) - the problem of identifying objects in images through natural language sentences - is a challenging task currently mostly solved through supervised learning. However, while collecting referred annotation masks is a time-consuming process, the few existing weakly-supervised and zero-shot approaches fall significantly short in performance compared to fully-supervised learning ones. To bridge the performance gap without mask annotations, we propose a novel weakly-supervised framework that tackles RIS by decomposing it into three steps: obtaining instance masks for the object mentioned in the referencing instruction (segment), using zero-shot learning to select a potentially correct mask for the given instruction (select), and bootstrapping a model which allows for fixing the mistakes of zero-shot selection (correct). In our experiments, using only the first two steps (zero-shot segment and select) outperforms other zero-shot baselines by as much as 16.5%, while our full method improves upon this much stronger baseline and sets the new state-of-the-art for weakly-supervised RIS, reducing the gap between the weakly-supervised and fully-supervised methods in some cases from around 33% to as little as 7%. Code is available at https://github.com/fgirbal/segment-select-correct.

Kemal Oksuz, Tom Joy, Puneet K. Dokania

The current approach for testing the robustness of object detectors suffers from serious deficiencies such as improper methods of performing out-of-distribution detection and using calibration metrics which do not consider both localisation and classification quality. In this work, we address these issues, and introduce the Self-Aware Object Detection (SAOD) task, a unified testing framework which respects and adheres to the challenges that object detectors face in safety-critical environments such as autonomous driving. Specifically, the SAOD task requires an object detector to be: robust to domain shift; obtain reliable uncertainty estimates for the entire scene; and provide calibrated confidence scores for the detections. We extensively use our framework, which introduces novel metrics and large scale test datasets, to test numerous object detectors in two different use-cases, allowing us to highlight critical insights into their robustness performance. Finally, we introduce a simple baseline for the SAOD task, enabling researchers to benchmark future proposed methods and move towards robust object detectors which are fit for purpose. Code is available at https://github.com/fiveai/saod

Jishnu Mukhoti, Yarin Gal, Philip H. S. Torr et al.

Pre-trained foundation models, due to their enormous capacity and exposure to vast amounts of data during pre-training, are known to have learned plenty of real-world concepts. An important step in making these pre-trained models effective on downstream tasks is to fine-tune them on related datasets. While various fine-tuning methods have been devised and have been shown to be highly effective, we observe that a fine-tuned model's ability to recognize concepts on tasks $\textit{different}$ from the downstream one is reduced significantly compared to its pre-trained counterpart. This is an undesirable effect of fine-tuning as a substantial amount of resources was used to learn these pre-trained concepts in the first place. We call this phenomenon ''concept forgetting'' and via experiments show that most end-to-end fine-tuning approaches suffer heavily from this side effect. To this end, we propose a simple fix to this problem by designing a new fine-tuning method called $\textit{LDIFS}$ (short for $\ell_2$ distance in feature space) that, while learning new concepts related to the downstream task, allows a model to preserve its pre-trained knowledge as well. Through extensive experiments on 10 fine-tuning tasks we show that $\textit{LDIFS}$ significantly reduces concept forgetting. Additionally, we show that LDIFS is highly effective in performing continual fine-tuning on a sequence of tasks as well, in comparison with both fine-tuning as well as continual learning baselines.

Francesco Pinto, Philip H. S. Torr, Puneet K. Dokania

Following the surge of popularity of Transformers in Computer Vision, several studies have attempted to determine whether they could be more robust to distribution shifts and provide better uncertainty estimates than Convolutional Neural Networks (CNNs). The almost unanimous conclusion is that they are, and it is often conjectured more or less explicitly that the reason of this supposed superiority is to be attributed to the self-attention mechanism. In this paper we perform extensive empirical analyses showing that recent state-of-the-art CNNs (particularly, ConvNeXt) can be as robust and reliable or even sometimes more than the current state-of-the-art Transformers. However, there is no clear winner. Therefore, although it is tempting to state the definitive superiority of one family of architectures over another, they seem to enjoy similar extraordinary performances on a variety of tasks while also suffering from similar vulnerabilities such as texture, background, and simplicity biases.

Francesco Pinto, Harry Yang, Ser-Nam Lim et al.

We show that the effectiveness of the well celebrated Mixup [Zhang et al., 2018] can be further improved if instead of using it as the sole learning objective, it is utilized as an additional regularizer to the standard cross-entropy loss. This simple change not only provides much improved accuracy but also significantly improves the quality of the predictive uncertainty estimation of Mixup in most cases under various forms of covariate shifts and out-of-distribution detection experiments. In fact, we observe that Mixup yields much degraded performance on detecting out-of-distribution samples possibly, as we show empirically, because of its tendency to learn models that exhibit high-entropy throughout; making it difficult to differentiate in-distribution samples from out-distribution ones. To show the efficacy of our approach (RegMixup), we provide thorough analyses and experiments on vision datasets (ImageNet & CIFAR-10/100) and compare it with a suite of recent approaches for reliable uncertainty estimation.

Edward Ayers, Jonathan Sadeghi, John Redford et al.

There is a longstanding interest in capturing the error behaviour of object detectors by finding images where their performance is likely to be unsatisfactory. In real-world applications such as autonomous driving, it is also crucial to characterise potential failures beyond simple requirements of detection performance. For example, a missed detection of a pedestrian close to an ego vehicle will generally require closer inspection than a missed detection of a car in the distance. The problem of predicting such potential failures at test time has largely been overlooked in the literature and conventional approaches based on detection uncertainty fall short in that they are agnostic to such fine-grained characterisation of errors. In this work, we propose to reformulate the problem of finding "hard" images as a query-based hard image retrieval task, where queries are specific definitions of "hardness", and offer a simple and intuitive method that can solve this task for a large family of queries. Our method is entirely post-hoc, does not require ground-truth annotations, is independent of the choice of a detector, and relies on an efficient Monte Carlo estimation that uses a simple stochastic model in place of the ground-truth. We show experimentally that it can be applied successfully to a wide variety of queries for which it can reliably identify hard images for a given detector without any labelled data. We provide results on ranking and classification tasks using the widely used RetinaNet, Faster-RCNN, Mask-RCNN, and Cascade Mask-RCNN object detectors. The code for this project is available at https://github.com/fiveai/hardest.

Kemal Oksuz, Alexandru Buburuzan, Anthony Knittel et al.

The emergence of multi-modal foundation models has markedly transformed the technology for autonomous driving, shifting away from conventional and mostly hand-crafted design choices towards unified, foundation-model-based approaches, capable of directly inferring motion trajectories from raw sensory inputs. This new class of methods can also incorporate natural language as an additional modality, with Vision-Language-Action (VLA) models serving as a representative example. In this review, we provide a comprehensive examination of such methods through a unifying taxonomy to critically evaluate their architectural design choices, methodological strengths, and their inherent capabilities and limitations. Our survey covers 37 recently proposed approaches that span the landscape of trajectory planning with foundation models. Furthermore, we assess these approaches with respect to the openness of their source code and datasets, offering valuable information to practitioners and researchers. We provide an accompanying webpage that catalogues the methods based on our taxonomy, available at: https://github.com/fiveai/FMs-for-driving-trajectories

Jishnu Mukhoti, Tsung-Yu Lin, Bor-Chun Chen et al.

In image classification, a lot of development has happened in detecting out-of-distribution (OoD) data. However, most OoD detection methods are evaluated on a standard set of datasets, arbitrarily different from training data. There is no clear definition of what forms a ``good" OoD dataset. Furthermore, the state-of-the-art OoD detection methods already achieve near perfect results on these standard benchmarks. In this paper, we define 2 categories of OoD data using the subtly different concepts of perceptual/visual and semantic similarity to in-distribution (iD) data. We define Near OoD samples as perceptually similar but semantically different from iD samples, and Shifted samples as points which are visually different but semantically akin to iD data. We then propose a GAN based framework for generating OoD samples from each of these 2 categories, given an iD dataset. Through extensive experiments on MNIST, CIFAR-10/100 and ImageNet, we show that a) state-of-the-art OoD detection methods which perform exceedingly well on conventional benchmarks are significantly less robust to our proposed benchmark. Moreover, b) models performing well on our setup also perform well on conventional real-world OoD detection benchmarks and vice versa, thereby indicating that one might not even need a separate OoD set, to reliably evaluate performance in OoD detection.

Kemal Oksuz, Selim Kuzucu, Tom Joy et al.

Combining the strengths of many existing predictors to obtain a Mixture of Experts which is superior to its individual components is an effective way to improve the performance without having to develop new architectures or train a model from scratch. However, surprisingly, we find that naïvely combining expert object detectors in a similar way to Deep Ensembles, can often lead to degraded performance. We identify that the primary cause of this issue is that the predictions of the experts do not match their performance, a term referred to as miscalibration. Consequently, the most confident detector dominates the final predictions, preventing the mixture from leveraging all the predictions from the experts appropriately. To address this, when constructing the Mixture of Experts, we propose to combine their predictions in a manner which reflects the individual performance of the experts; an objective we achieve by first calibrating the predictions before filtering and refining them. We term this approach the Mixture of Calibrated Experts and demonstrate its effectiveness through extensive experiments on 5 different detection tasks using a variety of detectors, showing that it: (i) improves object detectors on COCO and instance segmentation methods on LVIS by up to $\sim 2.5$ AP; (ii) reaches state-of-the-art on COCO test-dev with $65.1$ AP and on DOTA with $82.62$ $\mathrm{AP_{50}}$; (iii) outperforms single models consistently on recent detection tasks such as Open Vocabulary Object Detection.

Pau de Jorge, Riccardo Volpi, Puneet K. Dokania et al.

When deploying a semantic segmentation model into the real world, it will inevitably encounter semantic classes that were not seen during training. To ensure a safe deployment of such systems, it is crucial to accurately evaluate and improve their anomaly segmentation capabilities. However, acquiring and labelling semantic segmentation data is expensive and unanticipated conditions are long-tail and potentially hazardous. Indeed, existing anomaly segmentation datasets capture a limited number of anomalies, lack realism or have strong domain shifts. In this paper, we propose the Placing Objects in Context (POC) pipeline to realistically add any object into any image via diffusion models. POC can be used to easily extend any dataset with an arbitrary number of objects. In our experiments, we present different anomaly segmentation datasets based on POC-generated data and show that POC can improve the performance of recent state-of-the-art anomaly fine-tuning methods across several standardized benchmarks. POC is also effective for learning new classes. For example, we utilize it to augment Cityscapes samples by incorporating a subset of Pascal classes and demonstrate that models trained on such data achieve comparable performance to the Pascal-trained baseline. This corroborates the low synth2real gap of models trained on POC-generated images. Code: https://github.com/naver/poc

Ameya Prabhu, Shiven Sinha, Ponnurangam Kumaraguru et al.

Continual learning has primarily focused on the issue of catastrophic forgetting and the associated stability-plasticity tradeoffs. However, little attention has been paid to the efficacy of continually learned representations, as representations are learned alongside classifiers throughout the learning process. Our primary contribution is empirically demonstrating that existing online continually trained deep networks produce inferior representations compared to a simple pre-defined random transforms. Our approach projects raw pixels using a fixed random transform, approximating an RBF-Kernel initialized before any data is seen. We then train a simple linear classifier on top without storing any exemplars, processing one sample at a time in an online continual learning setting. This method, called RanDumb, significantly outperforms state-of-the-art continually learned representations across all standard online continual learning benchmarks. Our study reveals the significant limitations of representation learning, particularly in low-exemplar and online continual learning scenarios. Extending our investigation to popular exemplar-free scenarios with pretrained models, we find that training only a linear classifier on top of pretrained representations surpasses most continual fine-tuning and prompt-tuning strategies. Overall, our investigation challenges the prevailing assumptions about effective representation learning in online continual learning. Our code is available at://github.com/drimpossible/RanDumb.

Magnus Sesodia, Alina Petrova, John Armour et al.

Legal systems worldwide continue to struggle with overwhelming caseloads, limited judicial resources, and growing complexities in legal proceedings. Artificial intelligence (AI) offers a promising solution, with Legal Judgment Prediction (LJP) -- the practice of predicting a court's decision from the case facts -- emerging as a key research area. However, existing datasets often formulate the task of LJP unrealistically, not reflecting its true difficulty. They also lack high-quality annotation essential for legal reasoning and explainability. To address these shortcomings, we introduce AnnoCaseLaw, a first-of-its-kind dataset of 471 meticulously annotated U.S. Appeals Court negligence cases. Each case is enriched with comprehensive, expert-labeled annotations that highlight key components of judicial decision making, along with relevant legal concepts. Our dataset lays the groundwork for more human-aligned, explainable LJP models. We define three legally relevant tasks: (1) judgment prediction; (2) concept identification; and (3) automated case annotation, and establish a performance baseline using industry-leading large language models (LLMs). Our results demonstrate that LJP remains a formidable task, with application of legal precedent proving particularly difficult. Code and data are available at https://github.com/anonymouspolar1/annocaselaw.

Ameya Prabhu, Zhipeng Cai, Puneet Dokania et al.

Traditional online continual learning (OCL) research has primarily focused on mitigating catastrophic forgetting with fixed and limited storage allocation throughout an agent's lifetime. However, a broad range of real-world applications are primarily constrained by computational costs rather than storage limitations. In this paper, we target such applications, investigating the online continual learning problem under relaxed storage constraints and limited computational budgets. We contribute a simple algorithm, which updates a kNN classifier continually along with a fixed, pretrained feature extractor. We selected this algorithm due to its exceptional suitability for online continual learning. It can adapt to rapidly changing streams, has zero stability gap, operates within tiny computational budgets, has low storage requirements by only storing features, and has a consistency property: It never forgets previously seen data. These attributes yield significant improvements, allowing our proposed algorithm to outperform existing methods by over 20% in accuracy on two large-scale OCL datasets: Continual LOCalization (CLOC) with 39M images and 712 classes and Continual Google Landmarks V2 (CGLM) with 580K images and 10,788 classes, even when existing methods retain all previously seen images. Furthermore, we achieve this superior performance with considerably reduced computational and storage expenses. We provide code to reproduce our results at github.com/drimpossible/ACM.

Pau de Jorge, Adel Bibi, Riccardo Volpi et al.

Recently, Wong et al. showed that adversarial training with single-step FGSM leads to a characteristic failure mode named Catastrophic Overfitting (CO), in which a model becomes suddenly vulnerable to multi-step attacks. Experimentally they showed that simply adding a random perturbation prior to FGSM (RS-FGSM) could prevent CO. However, Andriushchenko and Flammarion observed that RS-FGSM still leads to CO for larger perturbations, and proposed a computationally expensive regularizer (GradAlign) to avoid it. In this work, we methodically revisit the role of noise and clipping in single-step adversarial training. Contrary to previous intuitions, we find that using a stronger noise around the clean sample combined with \textit{not clipping} is highly effective in avoiding CO for large perturbation radii. We then propose Noise-FGSM (N-FGSM) that, while providing the benefits of single-step adversarial training, does not suffer from CO. Empirical analyses on a large suite of experiments show that N-FGSM is able to match or surpass the performance of previous state-of-the-art GradAlign, while achieving 3x speed-up. Code can be found in https://github.com/pdejorge/N-FGSM

Francisco Eiras, Motasem Alfarra, M. Pawan Kumar et al.

Randomized smoothing has recently emerged as an effective tool that enables certification of deep neural network classifiers at scale. All prior art on randomized smoothing has focused on isotropic $\ell_p$ certification, which has the advantage of yielding certificates that can be easily compared among isotropic methods via $\ell_p$-norm radius. However, isotropic certification limits the region that can be certified around an input to worst-case adversaries, i.e., it cannot reason about other "close", potentially large, constant prediction safe regions. To alleviate this issue, (i) we theoretically extend the isotropic randomized smoothing $\ell_1$ and $\ell_2$ certificates to their generalized anisotropic counterparts following a simplified analysis. Moreover, (ii) we propose evaluation metrics allowing for the comparison of general certificates - a certificate is superior to another if it certifies a superset region - with the quantification of each certificate through the volume of the certified region. We introduce ANCER, a framework for obtaining anisotropic certificates for a given test set sample via volume maximization. We achieve it by generalizing memory-based certification of data-dependent classifiers. Our empirical results demonstrate that ANCER achieves state-of-the-art $\ell_1$ and $\ell_2$ certified accuracy on CIFAR-10 and ImageNet in the data-dependence setting, while certifying larger regions in terms of volume, highlighting the benefits of moving away from isotropic analysis. Our code is available in https://github.com/MotasemAlfarra/ANCER.

Pau de Jorge, Amartya Sanyal, Harkirat S. Behl et al.

Recent studies have shown that skeletonization (pruning parameters) of networks \textit{at initialization} provides all the practical benefits of sparsity both at inference and training time, while only marginally degrading their performance. However, we observe that beyond a certain level of sparsity (approx $95\%$), these approaches fail to preserve the network performance, and to our surprise, in many cases perform even worse than trivial random pruning. To this end, we propose an objective to find a skeletonized network with maximum {\em foresight connection sensitivity} (FORCE) whereby the trainability, in terms of connection sensitivity, of a pruned network is taken into consideration. We then propose two approximate procedures to maximize our objective (1) Iterative SNIP: allows parameters that were unimportant at earlier stages of skeletonization to become important at later stages; and (2) FORCE: iterative process that allows exploration by allowing already pruned parameters to resurrect at later stages of skeletonization. Empirical analyses on a large suite of experiments show that our approach, while providing at least as good a performance as other recent approaches on moderate pruning levels, provides remarkably improved performance on higher pruning levels (could remove up to $99.5\%$ parameters while keeping the networks trainable). Code can be found in https://github.com/naver/force.

Christian Schroeder de Witt, Bradley Gram-Hansen, Nantas Nardelli et al.

The COVID-19 pandemic has highlighted the importance of in-silico epidemiological modelling in predicting the dynamics of infectious diseases to inform health policy and decision makers about suitable prevention and containment strategies. Work in this setting involves solving challenging inference and control problems in individual-based models of ever increasing complexity. Here we discuss recent breakthroughs in machine learning, specifically in simulation-based inference, and explore its potential as a novel venue for model calibration to support the design and evaluation of public health interventions. To further stimulate research, we are developing software interfaces that turn two cornerstone COVID-19 and malaria epidemiology models COVID-sim, (https://github.com/mrc-ide/covid-sim/) and OpenMalaria (https://github.com/SwissTPH/openmalaria) into probabilistic programs, enabling efficient interpretable Bayesian inference within those simulators.

Jishnu Mukhoti, Viveka Kulharia, Amartya Sanyal et al.

Miscalibration - a mismatch between a model's confidence and its correctness - of Deep Neural Networks (DNNs) makes their predictions hard to rely on. Ideally, we want networks to be accurate, calibrated and confident. We show that, as opposed to the standard cross-entropy loss, focal loss [Lin et. al., 2017] allows us to learn models that are already very well calibrated. When combined with temperature scaling, whilst preserving accuracy, it yields state-of-the-art calibrated models. We provide a thorough analysis of the factors causing miscalibration, and use the insights we glean from this to justify the empirically excellent performance of focal loss. To facilitate the use of focal loss in practice, we also provide a principled approach to automatically select the hyperparameter involved in the loss function. We perform extensive experiments on a variety of computer vision and NLP datasets, and with a wide variety of network architectures, and show that our approach achieves state-of-the-art calibration without compromising on accuracy in almost all cases. Code is available at https://github.com/torrvision/focal_calibration.

Thalaiyasingam Ajanthan, Kartik Gupta, Philip H. S. Torr et al.

Quantizing large Neural Networks (NN) while maintaining the performance is highly desirable for resource-limited devices due to reduced memory and time complexity. It is usually formulated as a constrained optimization problem and optimized via a modified version of gradient descent. In this work, by interpreting the continuous parameters (unconstrained) as the dual of the quantized ones, we introduce a Mirror Descent (MD) framework for NN quantization. Specifically, we provide conditions on the projections (i.e., mapping from continuous to quantized ones) which would enable us to derive valid mirror maps and in turn the respective MD updates. Furthermore, we present a numerically stable implementation of MD that requires storing an additional set of auxiliary variables (unconstrained), and show that it is strikingly analogous to the Straight Through Estimator (STE) based method which is typically viewed as a "trick" to avoid vanishing gradients issue. Our experiments on CIFAR-10/100, TinyImageNet, and ImageNet classification datasets with VGG-16, ResNet-18, and MobileNetV2 architectures show that our MD variants obtain quantized networks with state-of-the-art performance. Code is available at https://github.com/kartikgupta-at-anu/md-bnn.

Xingyi Yang, Constantin Venhoff, Ashkan Khakzar et al.

Neurons in large language models often exhibit \emph{polysemanticity}, simultaneously encoding multiple unrelated concepts and obscuring interpretability. Instead of relying on post-hoc methods, we present \textbf{MoE-X}, a Mixture-of-Experts (MoE) language model designed to be \emph{intrinsically} interpretable. Our approach is motivated by the observation that, in language models, wider networks with sparse activations are more likely to capture interpretable factors. However, directly training such large sparse networks is computationally prohibitive. MoE architectures offer a scalable alternative by activating only a subset of experts for any given input, inherently aligning with interpretability objectives. In MoE-X, we establish this connection by rewriting the MoE layer as an equivalent sparse, large MLP. This approach enables efficient scaling of the hidden size while maintaining sparsity. To further enhance interpretability, we enforce sparse activation within each expert and redesign the routing mechanism to prioritize experts with the highest activation sparsity. These designs ensure that only the most salient features are routed and processed by the experts. We evaluate MoE-X on chess and natural language tasks, showing that it achieves performance comparable to dense models while significantly improving interpretability. MoE-X achieves a perplexity better than GPT-2, with interpretability surpassing even sparse autoencoder (SAE)-based approaches.

Alexandru Buburuzan, Anuj Sharma, John Redford et al.

Safety-critical applications, such as autonomous driving, require extensive multimodal data for rigorous testing. Methods based on synthetic data are gaining prominence due to the cost and complexity of gathering real-world data but require a high degree of realism and controllability in order to be useful. This paper introduces MObI, a novel framework for Multimodal Object Inpainting that leverages a diffusion model to create realistic and controllable object inpaintings across perceptual modalities, demonstrated for both camera and lidar simultaneously. Using a single reference RGB image, MObI enables objects to be seamlessly inserted into existing multimodal scenes at a 3D location specified by a bounding box, while maintaining semantic consistency and multimodal coherence. Unlike traditional inpainting methods that rely solely on edit masks, our 3D bounding box conditioning gives objects accurate spatial positioning and realistic scaling. As a result, our approach can be used to insert novel objects flexibly into multimodal scenes, providing significant advantages for testing perception models.

Liheng Ma, Chen Lin, Derek Lim et al.

Transformers for graph data are increasingly widely studied and successful in numerous learning tasks. Graph inductive biases are crucial for Graph Transformers, and previous works incorporate them using message-passing modules and/or positional encodings. However, Graph Transformers that use message-passing inherit known issues of message-passing, and differ significantly from Transformers used in other domains, thus making transfer of research advances more difficult. On the other hand, Graph Transformers without message-passing often perform poorly on smaller datasets, where inductive biases are more crucial. To bridge this gap, we propose the Graph Inductive bias Transformer (GRIT) -- a new Graph Transformer that incorporates graph inductive biases without using message passing. GRIT is based on several architectural changes that are each theoretically and empirically justified, including: learned relative positional encodings initialized with random walk probabilities, a flexible attention mechanism that updates node and node-pair representations, and injection of degree information in each layer. We prove that GRIT is expressive -- it can express shortest path distances and various graph propagation matrices. GRIT achieves state-of-the-art empirical performance across a variety of graph datasets, thus showing the power that Graph Transformers without message-passing can deliver.

Jonathan Sadeghi, Blaine Rogers, James Gunn et al.

There has been increasing interest in characterising the error behaviour of systems which contain deep learning models before deploying them into any safety-critical scenario. However, characterising such behaviour usually requires large-scale testing of the model that can be extremely computationally expensive for complex real-world tasks. For example, tasks involving compute intensive object detectors as one of their components. In this work, we propose an approach that enables efficient large-scale testing using simplified low-fidelity simulators and without the computational cost of executing expensive deep learning models. Our approach relies on designing an efficient surrogate model corresponding to the compute intensive components of the task under test. We demonstrate the efficacy of our methodology by evaluating the performance of an autonomous driving task in the Carla simulator with reduced computational expense by training efficient surrogate models for PIXOR and CenterPoint LiDAR detectors, whilst demonstrating that the accuracy of the simulation is maintained.

Botos Csaba, Xiaojuan Qi, Arslan Chaudhry et al.

Domain shift is a well known problem where a model trained on a particular domain (source) does not perform well when exposed to samples from a different domain (target). Unsupervised methods that can adapt to domain shift are highly desirable as they allow effective utilization of the source data without requiring additional annotated training data from the target. Practically, obtaining sufficient amount of annotated data from the target domain can be both infeasible and extremely expensive. In this work, we address the domain shift problem for the object detection task. Our approach relies on gradually removing the domain shift between the source and the target domains. The key ingredients to our approach are -- (a) mapping the source to the target domain on pixel-level; (b) training a teacher network on the mapped source and the unannotated target domain using adversarial feature alignment; and (c) finally training a student network using the pseudo-labels obtained from the teacher. Experimentally, when tested on challenging scenarios involving domain shift, we consistently obtain significantly large performance gains over various recent state of the art approaches.

Shyamgopal Karthik, Ameya Prabhu, Puneet K. Dokania et al.

There has been increasing interest in building deep hierarchy-aware classifiers that aim to quantify and reduce the severity of mistakes, and not just reduce the number of errors. The idea is to exploit the label hierarchy (e.g., the WordNet ontology) and consider graph distances as a proxy for mistake severity. Surprisingly, on examining mistake-severity distributions of the top-1 prediction, we find that current state-of-the-art hierarchy-aware deep classifiers do not always show practical improvement over the standard cross-entropy baseline in making better mistakes. The reason for the reduction in average mistake-severity can be attributed to the increase in low-severity mistakes, which may also explain the noticeable drop in their accuracy. To this end, we use the classical Conditional Risk Minimization (CRM) framework for hierarchy-aware classification. Given a cost matrix and a reliable estimate of likelihoods (obtained from a trained network), CRM simply amends mistakes at inference time; it needs no extra hyperparameters and requires adding just a few lines of code to the standard cross-entropy baseline. It significantly outperforms the state-of-the-art and consistently obtains large reductions in the average hierarchical distance of top-$k$ predictions across datasets, with very little loss in accuracy. CRM, because of its simplicity, can be used with any off-the-shelf trained model that provides reliable likelihood estimates.

Jishnu Mukhoti, Puneet K. Dokania, Philip H. S. Torr et al.

We study batch normalisation in the context of variational inference methods in Bayesian neural networks, such as mean-field or MC Dropout. We show that batch-normalisation does not affect the optimum of the evidence lower bound (ELBO). Furthermore, we study the Monte Carlo Batch Normalisation (MCBN) algorithm, proposed as an approximate inference technique parallel to MC Dropout, and show that for larger batch sizes, MCBN fails to capture epistemic uncertainty. Finally, we provide insights into what is required to fix this failure, namely having to view the mini-batch size as a variational parameter in MCBN. We comment on the asymptotics of the ELBO with respect to this variational parameter, showing that as dataset size increases towards infinity, the batch-size must increase towards infinity as well for MCBN to be a valid approximate inference technique.

Arslan Chaudhry, Naeemullah Khan, Puneet K. Dokania et al.

In continual learning (CL), a learner is faced with a sequence of tasks, arriving one after the other, and the goal is to remember all the tasks once the continual learning experience is finished. The prior art in CL uses episodic memory, parameter regularization or extensible network structures to reduce interference among tasks, but in the end, all the approaches learn different tasks in a joint vector space. We believe this invariably leads to interference among different tasks. We propose to learn tasks in different (low-rank) vector subspaces that are kept orthogonal to each other in order to minimize interference. Further, to keep the gradients of different tasks coming from these subspaces orthogonal to each other, we learn isometric mappings by posing network training as an optimization problem over the Stiefel manifold. To the best of our understanding, we report, for the first time, strong results over experience-replay baseline with and without memory on standard classification benchmarks in continual learning. The code is made publicly available.

Thomas Tanay, Aivar Sootla, Matteo Maggioni et al.

Recurrent models are a popular choice for video enhancement tasks such as video denoising or super-resolution. In this work, we focus on their stability as dynamical systems and show that they tend to fail catastrophically at inference time on long video sequences. To address this issue, we (1) introduce a diagnostic tool which produces input sequences optimized to trigger instabilities and that can be interpreted as visualizations of temporal receptive fields, and (2) propose two approaches to enforce the stability of a model during training: constraining the spectral norm or constraining the stable rank of its convolutional layers. We then introduce Stable Rank Normalization for Convolutional layers (SRN-C), a new algorithm that enforces these constraints. Our experimental results suggest that SRN-C successfully enforces stability in recurrent video processing models without a significant performance loss.

Amartya Sanyal, Puneet K Dokania, Varun Kanade et al.

We investigate two causes for adversarial vulnerability in deep neural networks: bad data and (poorly) trained models. When trained with SGD, deep neural networks essentially achieve zero training error, even in the presence of label noise, while also exhibiting good generalization on natural test data, something referred to as benign overfitting [2, 10]. However, these models are vulnerable to adversarial attacks. We identify label noise as one of the causes for adversarial vulnerability, and provide theoretical and empirical evidence in support of this. Surprisingly, we find several instances of label noise in datasets such as MNIST and CIFAR, and that robustly trained models incur training error on some of these, i.e. they don't fit the noise. However, removing noisy labels alone does not suffice to achieve adversarial robustness. Standard training procedures bias neural networks towards learning "simple" classification boundaries, which may be less robust than more complex ones. We observe that adversarial training does produce more complex decision boundaries. We conjecture that in part the need for complex decision boundaries arises from sub-optimal representation learning. By means of simple toy examples, we show theoretically how the choice of representation can drastically affect adversarial robustness.

Daniela Massiceti, Viveka Kulharia, Puneet K. Dokania et al.

Evaluating Visual Dialogue, the task of answering a sequence of questions relating to a visual input, remains an open research challenge. The current evaluation scheme of the VisDial dataset computes the ranks of ground-truth answers in predefined candidate sets, which Massiceti et al. (2018) show can be susceptible to the exploitation of dataset biases. This scheme also does little to account for the different ways of expressing the same answer--an aspect of language that has been well studied in NLP. We propose a revised evaluation scheme for the VisDial dataset leveraging metrics from the NLP literature to measure consensus between answers generated by the model and a set of relevant answers. We construct these relevant answer sets using a simple and effective semi-supervised method based on correlation, which allows us to automatically extend and scale sparse relevance annotations from humans to the entire dataset. We release these sets and code for the revised evaluation scheme as DenseVisDial, and intend them to be an improvement to the dataset in the face of its existing constraints and design choices.

Arslan Chaudhry, Albert Gordo, Puneet K. Dokania et al.

In continual learning, the learner faces a stream of data whose distribution changes over time. Modern neural networks are known to suffer under this setting, as they quickly forget previously acquired knowledge. To address such catastrophic forgetting, many continual learning methods implement different types of experience replay, re-learning on past data stored in a small buffer known as episodic memory. In this work, we complement experience replay with a new objective that we call anchoring, where the learner uses bilevel optimization to update its knowledge on the current task, while keeping intact the predictions on some anchor points of past tasks. These anchor points are learned using gradient-based optimization to maximize forgetting, which is approximated by fine-tuning the currently trained model on the episodic memory of past tasks. Experiments on several supervised learning benchmarks for continual learning demonstrate that our approach improves the standard experience replay in terms of both accuracy and forgetting metrics and for various sizes of episodic memories.

Arnab Ghosh, Richard Zhang, Puneet K. Dokania et al.

We propose an interactive GAN-based sketch-to-image translation method that helps novice users create images of simple objects. As the user starts to draw a sketch of a desired object type, the network interactively recommends plausible completions, and shows a corresponding synthesized image to the user. This enables a feedback loop, where the user can edit their sketch based on the network's recommendations, visualizing both the completed shape and final rendered image while they draw. In order to use a single trained model across a wide array of object classes, we introduce a gating-based approach for class conditioning, which allows us to generate distinct classes without feature mixing, from a single generator network. Video available at our website: https://arnabgho.github.io/iSketchNFill/.

Amartya Sanyal, Philip H. S. Torr, Puneet K. Dokania

Exciting new work on the generalization bounds for neural networks (NN) given by Neyshabur et al. , Bartlett et al. closely depend on two parameter-depenedent quantities: the Lipschitz constant upper-bound and the stable rank (a softer version of the rank operator). This leads to an interesting question of whether controlling these quantities might improve the generalization behaviour of NNs. To this end, we propose stable rank normalization (SRN), a novel, optimal, and computationally efficient weight-normalization scheme which minimizes the stable rank of a linear operator. Surprisingly we find that SRN, inspite of being non-convex problem, can be shown to have a unique optimal solution. Moreover, we show that SRN allows control of the data-dependent empirical Lipschitz constant, which in contrast to the Lipschitz upper-bound, reflects the true behaviour of a model on a given dataset. We provide thorough analyses to show that SRN, when applied to the linear layers of a NN for classification, provides striking improvements-11.3% on the generalization gap compared to the standard NN along with significant reduction in memorization. When applied to the discriminator of GANs (called SRN-GAN) it improves Inception, FID, and Neural divergence scores on the CIFAR 10/100 and CelebA datasets, while learning mappings with low empirical Lipschitz constants.

Arslan Chaudhry, Marcus Rohrbach, Mohamed Elhoseiny et al.

In continual learning (CL), an agent learns from a stream of tasks leveraging prior experience to transfer knowledge to future tasks. It is an ideal framework to decrease the amount of supervision in the existing learning algorithms. But for a successful knowledge transfer, the learner needs to remember how to perform previous tasks. One way to endow the learner the ability to perform tasks seen in the past is to store a small memory, dubbed episodic memory, that stores few examples from previous tasks and then to replay these examples when training for future tasks. In this work, we empirically analyze the effectiveness of a very small episodic memory in a CL setup where each training example is only seen once. Surprisingly, across four rather different supervised learning benchmarks adapted to CL, a very simple baseline, that jointly trains on both examples from the current task as well as examples stored in the episodic memory, significantly outperforms specifically designed CL approaches with and without episodic memory. Interestingly, we find that repetitive training on even tiny memories of past tasks does not harm generalization, on the contrary, it improves it, with gains between 7\% and 17\% when the memory is populated with a single example per class.

Daniela Massiceti, Puneet K. Dokania, N. Siddharth et al.

We characterise some of the quirks and shortcomings in the exploration of Visual Dialogue - a sequential question-answering task where the questions and corresponding answers are related through given visual stimuli. To do so, we develop an embarrassingly simple method based on Canonical Correlation Analysis (CCA) that, on the standard dataset, achieves near state-of-the-art performance on mean rank (MR). In direct contrast to current complex and over-parametrised architectures that are both compute and time intensive, our method ignores the visual stimuli, ignores the sequencing of dialogue, does not need gradients, uses off-the-shelf feature extractors, has at least an order of magnitude fewer parameters, and learns in practically no time. We argue that these results are indicative of issues in current approaches to Visual Dialogue and conduct analyses to highlight implicit dataset biases and effects of over-constrained evaluation metrics. Our code is publicly available.

Thalaiyasingam Ajanthan, Puneet K. Dokania, Richard Hartley et al.

Compressing large Neural Networks (NN) by quantizing the parameters, while maintaining the performance is highly desirable due to reduced memory and time complexity. In this work, we cast NN quantization as a discrete labelling problem, and by examining relaxations, we design an efficient iterative optimization procedure that involves stochastic gradient descent followed by a projection. We prove that our simple projected gradient descent approach is, in fact, equivalent to a proximal version of the well-known mean-field method. These findings would allow the decades-old and theoretically grounded research on MRF optimization to be used to design better network quantization schemes. Our experiments on standard classification datasets (MNIST, CIFAR10/100, TinyImageNet) with convolutional and residual architectures show that our algorithm obtains fully-quantized networks with accuracies very close to the floating-point reference networks.

Amartya Sanyal, Varun Kanade, Philip H. S. Torr et al.

We investigate the effect of the dimensionality of the representations learned in Deep Neural Networks (DNNs) on their robustness to input perturbations, both adversarial and random. To achieve low dimensionality of learned representations, we propose an easy-to-use, end-to-end trainable, low-rank regularizer (LR) that can be applied to any intermediate layer representation of a DNN. This regularizer forces the feature representations to (mostly) lie in a low-dimensional linear subspace. We perform a wide range of experiments that demonstrate that the LR indeed induces low rank on the representations, while providing modest improvements to accuracy as an added benefit. Furthermore, the learned features make the trained model significantly more robust to input perturbations such as Gaussian and adversarial noise (even without adversarial training). Lastly, the low-dimensionality means that the learned features are highly compressible; thus discriminative features of the data can be stored using very little memory. Our experiments indicate that models trained using the LR learn robust classifiers by discovering subspaces that avoid non-robust features. Algorithmically, the LR is scalable, generic, and straightforward to implement into existing deep learning frameworks.

Daniela Massiceti, N. Siddharth, Puneet K. Dokania et al.

We present FlipDial, a generative model for visual dialogue that simultaneously plays the role of both participants in a visually-grounded dialogue. Given context in the form of an image and an associated caption summarising the contents of the image, FlipDial learns both to answer questions and put forward questions, capable of generating entire sequences of dialogue (question-answer pairs) which are diverse and relevant to the image. To do this, FlipDial relies on a simple but surprisingly powerful idea: it uses convolutional neural networks (CNNs) to encode entire dialogues directly, implicitly capturing dialogue context, and conditional VAEs to learn the generative model. FlipDial outperforms the state-of-the-art model in the sequential answering task (one-way visual dialogue) on the VisDial dataset by 5 points in Mean Rank using the generated answers. We are the first to extend this paradigm to full two-way visual dialogue, where our model is capable of generating both questions and answers in sequence based on a visual input, for which we propose a set of novel evaluation measures and metrics.

Arslan Chaudhry, Puneet K. Dokania, Thalaiyasingam Ajanthan et al.

Incremental learning (IL) has received a lot of attention recently, however, the literature lacks a precise problem definition, proper evaluation settings, and metrics tailored specifically for the IL problem. One of the main objectives of this work is to fill these gaps so as to provide a common ground for better understanding of IL. The main challenge for an IL algorithm is to update the classifier whilst preserving existing knowledge. We observe that, in addition to forgetting, a known issue while preserving knowledge, IL also suffers from a problem we call intransigence, inability of a model to update its knowledge. We introduce two metrics to quantify forgetting and intransigence that allow us to understand, analyse, and gain better insights into the behaviour of IL algorithms. We present RWalk, a generalization of EWC++ (our efficient version of EWC [Kirkpatrick2016EWC]) and Path Integral [Zenke2017Continual] with a theoretically grounded KL-divergence based perspective. We provide a thorough analysis of various IL algorithms on MNIST and CIFAR-100 datasets. In these experiments, RWalk obtains superior results in terms of accuracy, and also provides a better trade-off between forgetting and intransigence.

Enzo Ferrante, Puneet K Dokania, Rafael Marini et al.

We propose a novel weakly supervised discriminative algorithm for learning context specific registration metrics as a linear combination of conventional similarity measures. Conventional metrics have been extensively used over the past two decades and therefore both their strengths and limitations are known. The challenge is to find the optimal relative weighting (or parameters) of different metrics forming the similarity measure of the registration algorithm. Hand-tuning these parameters would result in sub optimal solutions and quickly become infeasible as the number of metrics increases. Furthermore, such hand-crafted combination can only happen at global scale (entire volume) and therefore will not be able to account for the different tissue properties. We propose a learning algorithm for estimating these parameters locally, conditioned to the data semantic classes. The objective function of our formulation is a special case of non-convex function, difference of convex function, which we optimize using the concave convex procedure. As a proof of concept, we show the impact of our approach on three challenging datasets for different anatomical structures and modalities.

Arslan Chaudhry, Puneet K. Dokania, Philip H. S. Torr

We propose an approach to discover class-specific pixels for the weakly-supervised semantic segmentation task. We show that properly combining saliency and attention maps allows us to obtain reliable cues capable of significantly boosting the performance. First, we propose a simple yet powerful hierarchical approach to discover the class-agnostic salient regions, obtained using a salient object detector, which otherwise would be ignored. Second, we use fully convolutional attention maps to reliably localize the class-specific regions in a given image. We combine these two cues to discover class-specific pixels which are then used as an approximate ground truth for training a CNN. While solving the weakly supervised semantic segmentation task, we ensure that the image-level classification task is also solved in order to enforce the CNN to assign at least one pixel to each object present in the image. Experimentally, on the PASCAL VOC12 val and test sets, we obtain the mIoU of 60.8% and 61.9%, achieving the performance gains of 5.1% and 5.2% compared to the published state-of-the-art results. The code is made publicly available.

Arnab Ghosh, Viveka Kulharia, Vinay Namboodiri et al.

We propose MAD-GAN, an intuitive generalization to the Generative Adversarial Networks (GANs) and its conditional variants to address the well known problem of mode collapse. First, MAD-GAN is a multi-agent GAN architecture incorporating multiple generators and one discriminator. Second, to enforce that different generators capture diverse high probability modes, the discriminator of MAD-GAN is designed such that along with finding the real and fake samples, it is also required to identify the generator that generated the given fake sample. Intuitively, to succeed in this task, the discriminator must learn to push different generators towards different identifiable modes. We perform extensive experiments on synthetic and real datasets and compare MAD-GAN with different variants of GAN. We show high quality diverse sample generations for challenging tasks such as image-to-image translation and face generation. In addition, we also show that MAD-GAN is able to disentangle different modalities when trained using highly challenging diverse-class dataset (e.g. dataset with images of forests, icebergs, and bedrooms). In the end, we show its efficacy on the unsupervised feature representation task. In Appendix, we introduce a similarity based competing objective (MAD-GAN-Sim) which encourages different generators to generate diverse samples based on a user defined similarity metric. We show its performance on the image-to-image translation, and also show its effectiveness on the unsupervised feature representation task.

Qinbin Hou, Puneet Kumar Dokania, Daniela Massiceti et al.

We consider the task of learning a classifier for semantic segmentation using weak supervision in the form of image labels which specify the object classes present in the image. Our method uses deep convolutional neural networks (CNNs) and adopts an Expectation-Maximization (EM) based approach. We focus on the following three aspects of EM: (i) initialization; (ii) latent posterior estimation (E-step) and (iii) the parameter update (M-step). We show that saliency and attention maps, our bottom-up and top-down cues respectively, of simple images provide very good cues to learn an initialization for the EM-based algorithm. Intuitively, we show that before trying to learn to segment complex images, it is much easier and highly effective to first learn to segment a set of simple images and then move towards the complex ones. Next, in order to update the parameters, we propose minimizing the combination of the standard softmax loss and the KL divergence between the true latent posterior and the likelihood given by the CNN. We argue that this combination is more robust to wrong predictions made by the expectation step of the EM method. We support this argument with empirical and visual results. Extensive experiments and discussions show that: (i) our method is very simple and intuitive; (ii) requires only image-level labels; and (iii) consistently outperforms other weakly-supervised state-of-the-art methods with a very high margin on the PASCAL VOC 2012 dataset.

Anton Osokin, Jean-Baptiste Alayrac, Isabella Lukasewitz et al.

In this paper, we propose several improvements on the block-coordinate Frank-Wolfe (BCFW) algorithm from Lacoste-Julien et al. (2013) recently used to optimize the structured support vector machine (SSVM) objective in the context of structured prediction, though it has wider applications. The key intuition behind our improvements is that the estimates of block gaps maintained by BCFW reveal the block suboptimality that can be used as an adaptive criterion. First, we sample objects at each iteration of BCFW in an adaptive non-uniform way via gapbased sampling. Second, we incorporate pairwise and away-step variants of Frank-Wolfe into the block-coordinate setting. Third, we cache oracle calls with a cache-hit criterion based on the block gaps. Fourth, we provide the first method to compute an approximate regularization path for SSVM. Finally, we provide an exhaustive empirical evaluation of all our methods on four structured prediction datasets.

Puneet K. Dokania, M. Pawan Kumar

We propose a new family of discrete energy minimization problems, which we call parsimonious labeling. Specifically, our energy functional consists of unary potentials and high-order clique potentials. While the unary potentials are arbitrary, the clique potentials are proportional to the {\em diversity} of set of the unique labels assigned to the clique. Intuitively, our energy functional encourages the labeling to be parsimonious, that is, use as few labels as possible. This in turn allows us to capture useful cues for important computer vision applications such as stereo correspondence and image denoising. Furthermore, we propose an efficient graph-cuts based algorithm for the parsimonious labeling problem that provides strong theoretical guarantees on the quality of the solution. Our algorithm consists of three steps. First, we approximate a given diversity using a mixture of a novel hierarchical $P^n$ Potts model. Second, we use a divide-and-conquer approach for each mixture component, where each subproblem is solved using an effficient $α$-expansion algorithm. This provides us with a small number of putative labelings, one for each mixture component. Third, we choose the best putative labeling in terms of the energy value. Using both sythetic and standard real datasets, we show that our algorithm significantly outperforms other graph-cuts based approaches.