We establish an efficient approximation algorithm for the partition functions of a class of quantum spin systems at low temperature, which can be viewed as stable quantum perturbations of classical spin systems. Our algorithm is based on combining the contour representation of quantum spin systems of this type due to Borgs, Koteck\'y, and Ueltschi with the algorithmic framework developed by Helmuth, Perkins, and Regts, and Borgs et al.
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We present a novel formulation of structural design optimization problems specifically tailored to be solved by quantum annealing (QA). Structural design optimization aims to find the best, i.e., material-efficient yet high-performance, configuration of a structure. To this end, computational optimization strategies can be employed, where a recently evolving strategy based on quantum mechanical effects is QA. This approach requires the optimization problem to be present, e.g., as a quadratic unconstrained binary optimization (QUBO) model. Thus, we develop a novel formulation of the optimization problem. The latter typically involves an analysis model for the component. Here, we use energy minimization principles that govern the behavior of structures under applied loads. This allows us to state the optimization problem as one overall minimization problem. Next, we map this to a QUBO problem that can be immediately solved by QA. We validate the proposed approach using a size optimization problem of a compound rod under self-weight loading. To this end, we develop strategies to account for the limitations of currently available hardware and find that the presented formulation is suitable for solving structural design optimization problems through QA and, for small-scale problems, already works on today's hardware.
Mixed linear regression (MLR) is a powerful model for characterizing nonlinear relationships by utilizing a mixture of linear regression sub-models. The identification of MLR is a fundamental problem, where most of the existing results focus on offline algorithms, rely on independent and identically distributed (i.i.d) data assumptions, and provide local convergence results only. This paper investigates the online identification and data clustering problems for two basic classes of MLRs, by introducing two corresponding new online identification algorithms based on the expectation-maximization (EM) principle. It is shown that both algorithms will converge globally without resorting to the traditional i.i.d data assumptions. The main challenge in our investigation lies in the fact that the gradient of the maximum likelihood function does not have a unique zero, and a key step in our analysis is to establish the stability of the corresponding differential equation in order to apply the celebrated Ljung's ODE method. It is also shown that the within-cluster error and the probability that the new data is categorized into the correct cluster are asymptotically the same as those in the case of known parameters. Finally, numerical simulations are provided to verify the effectiveness of our online algorithms.
Previously, non-autoregressive models were widely perceived as being superior in generation efficiency but inferior in generation quality due to the difficulties of modeling multiple target modalities. To enhance the multi-modality modeling ability, we propose the diffusion glancing transformer, which employs a modality diffusion process and residual glancing sampling. The modality diffusion process is a discrete process that interpolates the multi-modal distribution along the decoding steps, and the residual glancing sampling approach guides the model to continuously learn the remaining modalities across the layers. Experimental results on various machine translation and text generation benchmarks demonstrate that DIFFGLAT achieves better generation accuracy while maintaining fast decoding speed compared with both autoregressive and non-autoregressive models.
Mechanistic interpretability aims to understand model behaviors in terms of specific, interpretable features, often hypothesized to manifest as low-dimensional subspaces of activations. Specifically, recent studies have explored subspace interventions (such as activation patching) as a way to simultaneously manipulate model behavior and attribute the features behind it to given subspaces. In this work, we demonstrate that these two aims diverge, potentially leading to an illusory sense of interpretability. Counterintuitively, even if a subspace intervention makes the model's output behave as if the value of a feature was changed, this effect may be achieved by activating a dormant parallel pathway leveraging another subspace that is causally disconnected from model outputs. We demonstrate this phenomenon in a distilled mathematical example, in two real-world domains (the indirect object identification task and factual recall), and present evidence for its prevalence in practice. In the context of factual recall, we further show a link to rank-1 fact editing, providing a mechanistic explanation for previous work observing an inconsistency between fact editing performance and fact localization. However, this does not imply that activation patching of subspaces is intrinsically unfit for interpretability. To contextualize our findings, we also show what a success case looks like in a task (indirect object identification) where prior manual circuit analysis informs an understanding of the location of a feature. We explore the additional evidence needed to argue that a patched subspace is faithful.
Most existing debiasing methods for multimodal models, including causal intervention and inference methods, utilize approximate heuristics to represent the biases, such as shallow features from early stages of training or unimodal features for multimodal tasks like VQA, etc., which may not be accurate. In this paper, we study bias arising from confounders in a causal graph for multimodal data and examine a novel approach that leverages causally-motivated information minimization to learn the confounder representations. Robust predictive features contain diverse information that helps a model generalize to out-of-distribution data. Hence, minimizing the information content of features obtained from a pretrained biased model helps learn the simplest predictive features that capture the underlying data distribution. We treat these features as confounder representations and use them via methods motivated by causal theory to remove bias from models. We find that the learned confounder representations indeed capture dataset biases, and the proposed debiasing methods improve out-of-distribution (OOD) performance on multiple multimodal datasets without sacrificing in-distribution performance. Additionally, we introduce a novel metric to quantify the sufficiency of spurious features in models' predictions that further demonstrates the effectiveness of our proposed methods. Our code is available at: //github.com/Vaidehi99/CausalInfoMin
Differentially private algorithms protect individuals in data analysis scenarios by ensuring that there is only a weak correlation between the existence of the user in the data and the result of the analysis. Dynamic graph algorithms maintain the solution to a problem (e.g., a matching) on an evolving input, i.e., a graph where nodes or edges are inserted or deleted over time. They output the value of the solution after each update operation, i.e., continuously. We study (event-level and user-level) differentially private algorithms for graph problems under continual observation, i.e., differentially private dynamic graph algorithms. We present event-level private algorithms for partially dynamic counting-based problems such as triangle count that improve the additive error by a polynomial factor (in the length $T$ of the update sequence) on the state of the art, resulting in the first algorithms with additive error polylogarithmic in $T$. We also give $\varepsilon$-differentially private and partially dynamic algorithms for minimum spanning tree, minimum cut, densest subgraph, and maximum matching. The additive error of our improved MST algorithm is $O(W \log^{3/2}T / \varepsilon)$, where $W$ is the maximum weight of any edge, which, as we show, is tight up to a $(\sqrt{\log T} / \varepsilon)$-factor. For the other problems, we present a partially-dynamic algorithm with multiplicative error $(1+\beta)$ for any constant $\beta > 0$ and additive error $O(W \log(nW) \log(T) / (\varepsilon \beta) )$. Finally, we show that the additive error for a broad class of dynamic graph algorithms with user-level privacy must be linear in the value of the output solution's range.
The existence of representative datasets is a prerequisite of many successful artificial intelligence and machine learning models. However, the subsequent application of these models often involves scenarios that are inadequately represented in the data used for training. The reasons for this are manifold and range from time and cost constraints to ethical considerations. As a consequence, the reliable use of these models, especially in safety-critical applications, is a huge challenge. Leveraging additional, already existing sources of knowledge is key to overcome the limitations of purely data-driven approaches, and eventually to increase the generalization capability of these models. Furthermore, predictions that conform with knowledge are crucial for making trustworthy and safe decisions even in underrepresented scenarios. This work provides an overview of existing techniques and methods in the literature that combine data-based models with existing knowledge. The identified approaches are structured according to the categories integration, extraction and conformity. Special attention is given to applications in the field of autonomous driving.
As soon as abstract mathematical computations were adapted to computation on digital computers, the problem of efficient representation, manipulation, and communication of the numerical values in those computations arose. Strongly related to the problem of numerical representation is the problem of quantization: in what manner should a set of continuous real-valued numbers be distributed over a fixed discrete set of numbers to minimize the number of bits required and also to maximize the accuracy of the attendant computations? This perennial problem of quantization is particularly relevant whenever memory and/or computational resources are severely restricted, and it has come to the forefront in recent years due to the remarkable performance of Neural Network models in computer vision, natural language processing, and related areas. Moving from floating-point representations to low-precision fixed integer values represented in four bits or less holds the potential to reduce the memory footprint and latency by a factor of 16x; and, in fact, reductions of 4x to 8x are often realized in practice in these applications. Thus, it is not surprising that quantization has emerged recently as an important and very active sub-area of research in the efficient implementation of computations associated with Neural Networks. In this article, we survey approaches to the problem of quantizing the numerical values in deep Neural Network computations, covering the advantages/disadvantages of current methods. With this survey and its organization, we hope to have presented a useful snapshot of the current research in quantization for Neural Networks and to have given an intelligent organization to ease the evaluation of future research in this area.
We introduce a generic framework that reduces the computational cost of object detection while retaining accuracy for scenarios where objects with varied sizes appear in high resolution images. Detection progresses in a coarse-to-fine manner, first on a down-sampled version of the image and then on a sequence of higher resolution regions identified as likely to improve the detection accuracy. Built upon reinforcement learning, our approach consists of a model (R-net) that uses coarse detection results to predict the potential accuracy gain for analyzing a region at a higher resolution and another model (Q-net) that sequentially selects regions to zoom in. Experiments on the Caltech Pedestrians dataset show that our approach reduces the number of processed pixels by over 50% without a drop in detection accuracy. The merits of our approach become more significant on a high resolution test set collected from YFCC100M dataset, where our approach maintains high detection performance while reducing the number of processed pixels by about 70% and the detection time by over 50%.
Detecting carried objects is one of the requirements for developing systems to reason about activities involving people and objects. We present an approach to detect carried objects from a single video frame with a novel method that incorporates features from multiple scales. Initially, a foreground mask in a video frame is segmented into multi-scale superpixels. Then the human-like regions in the segmented area are identified by matching a set of extracted features from superpixels against learned features in a codebook. A carried object probability map is generated using the complement of the matching probabilities of superpixels to human-like regions and background information. A group of superpixels with high carried object probability and strong edge support is then merged to obtain the shape of the carried object. We applied our method to two challenging datasets, and results show that our method is competitive with or better than the state-of-the-art.
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