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Despite the promising progress in multi-modal tasks, current large multi-modal models (LMM) are prone to hallucinating inconsistent descriptions with respect to the associated image and human instructions. This paper addresses this issue by introducing the first large and diverse visual instruction tuning dataset, named Large-scale Robust Visual (LRV)-Instruction. Our dataset consists of 120k visual instructions generated by GPT4, covering 16 vision-and-language tasks with open-ended instructions and answers. Unlike existing studies that primarily focus on positive instruction samples, we design LRV-Instruction to include both positive and negative instructions for more robust visual instruction tuning. Our negative instructions are designed at two semantic levels: (i) Nonexistent Element Manipulation and (ii) Existent Element Manipulation. To efficiently measure the hallucination generated by LMMs, we propose GPT4-Assisted Visual Instruction Evaluation (GAVIE), a novel approach to evaluate visual instruction tuning without the need for human-annotated groundtruth answers and can adapt to diverse instruction formats. We conduct comprehensive experiments to investigate the hallucination of LMMs. Our results demonstrate that existing LMMs exhibit significant hallucination when presented with our negative instructions, particularly with Existent Element Manipulation instructions. Moreover, by finetuning MiniGPT4 on LRV-Instruction, we successfully mitigate hallucination while improving performance on public datasets using less training data compared to state-of-the-art methods. Additionally, we observed that a balanced ratio of positive and negative instances in the training data leads to a more robust model. Updates of our project are available at //fuxiaoliu.github.io/LRV/.

Distribution-dependent stochastic dynamical systems arise widely in engineering and science. We consider a class of such systems which model the limit behaviors of interacting particles moving in a vector field with random fluctuations. We aim to examine the most likely transition path between equilibrium stable states of the vector field. In the small noise regime, the action functional does not involve the solution of the skeleton equation which describes the unperturbed deterministic flow of the vector field shifted by the interaction at zero distance. As a result, we are led to study the most likely transition path for a stochastic differential equation without distribution dependency. This enables the computation of the most likely transition path for these distribution-dependent stochastic dynamical systems by the adaptive minimum action method and we illustrate our approach in two examples.

We develop models to classify desirable reasoning revisions in argumentative writing. We explore two approaches -- multi-task learning and transfer learning -- to take advantage of auxiliary sources of revision data for similar tasks. Results of intrinsic and extrinsic evaluations show that both approaches can indeed improve classifier performance over baselines. While multi-task learning shows that training on different sources of data at the same time may improve performance, transfer-learning better represents the relationship between the data.

Markov processes are widely used mathematical models for describing dynamic systems in various fields. However, accurately simulating large-scale systems at long time scales is computationally expensive due to the short time steps required for accurate integration. In this paper, we introduce an inference process that maps complex systems into a simplified representational space and models large jumps in time. To achieve this, we propose Time-lagged Information Bottleneck (T-IB), a principled objective rooted in information theory, which aims to capture relevant temporal features while discarding high-frequency information to simplify the simulation task and minimize the inference error. Our experiments demonstrate that T-IB learns information-optimal representations for accurately modeling the statistical properties and dynamics of the original process at a selected time lag, outperforming existing time-lagged dimensionality reduction methods.

We present two effective methods for solving high-dimensional partial differential equations (PDE) based on randomized neural networks. Motivated by the universal approximation property of this type of networks, both methods extend the extreme learning machine (ELM) approach from low to high dimensions. With the first method the unknown solution field in $d$ dimensions is represented by a randomized feed-forward neural network, in which the hidden-layer parameters are randomly assigned and fixed while the output-layer parameters are trained. The PDE and the boundary/initial conditions, as well as the continuity conditions (for the local variant of the method), are enforced on a set of random interior/boundary collocation points. The resultant linear or nonlinear algebraic system, through its least squares solution, provides the trained values for the network parameters. With the second method the high-dimensional PDE problem is reformulated through a constrained expression based on an Approximate variant of the Theory of Functional Connections (A-TFC), which avoids the exponential growth in the number of terms of TFC as the dimension increases. The free field function in the A-TFC constrained expression is represented by a randomized neural network and is trained by a procedure analogous to the first method. We present ample numerical simulations for a number of high-dimensional linear/nonlinear stationary/dynamic PDEs to demonstrate their performance. These methods can produce accurate solutions to high-dimensional PDEs, in particular with their errors reaching levels not far from the machine accuracy for relatively lower dimensions. Compared with the physics-informed neural network (PINN) method, the current method is both cost-effective and more accurate for high-dimensional PDEs.

Until high-fidelity quantum computers with a large number of qubits become widely available, classical simulation remains a vital tool for algorithm design, tuning, and validation. We present a simulator for the Quantum Approximate Optimization Algorithm (QAOA). Our simulator is designed with the goal of reducing the computational cost of QAOA parameter optimization and supports both CPU and GPU execution. Our central observation is that the computational cost of both simulating the QAOA state and computing the QAOA objective to be optimized can be reduced by precomputing the diagonal Hamiltonian encoding the problem. We reduce the time for a typical QAOA parameter optimization by eleven times for $n = 26$ qubits compared to a state-of-the-art GPU quantum circuit simulator based on cuQuantum. Our simulator is available on GitHub: //github.com/jpmorganchase/QOKit

There has been a growing interest in parallel strategies for solving trajectory optimization problems. One key step in many algorithmic approaches to trajectory optimization is the solution of moderately-large and sparse linear systems. Iterative methods are particularly well-suited for parallel solves of such systems. However, fast and stable convergence of iterative methods is reliant on the application of a high-quality preconditioner that reduces the spread and increase the clustering of the eigenvalues of the target matrix. To improve the performance of these approaches, we present a new parallel-friendly symmetric stair preconditioner. We prove that our preconditioner has advantageous theoretical properties when used in conjunction with iterative methods for trajectory optimization such as a more clustered eigenvalue spectrum. Numerical experiments with typical trajectory optimization problems reveal that as compared to the best alternative parallel preconditioner from the literature, our symmetric stair preconditioner provides up to a 34% reduction in condition number and up to a 25% reduction in the number of resulting linear system solver iterations.

Solving linear inverse problems plays a crucial role in numerous applications. Algorithm unfolding based, model-aware data-driven approaches have gained significant attention for effectively addressing these problems. Learned iterative soft-thresholding algorithm (LISTA) and alternating direction method of multipliers compressive sensing network (ADMM-CSNet) are two widely used such approaches, based on ISTA and ADMM algorithms, respectively. In this work, we study optimization guarantees, i.e., achieving near-zero training loss with the increase in the number of learning epochs, for finite-layer unfolded networks such as LISTA and ADMM-CSNet with smooth soft-thresholding in an over-parameterized (OP) regime. We achieve this by leveraging a modified version of the Polyak-Lojasiewicz, denoted PL$^*$, condition. Satisfying the PL$^*$ condition within a specific region of the loss landscape ensures the existence of a global minimum and exponential convergence from initialization using gradient descent based methods. Hence, we provide conditions, in terms of the network width and the number of training samples, on these unfolded networks for the PL$^*$ condition to hold. We achieve this by deriving the Hessian spectral norm of these networks. Additionally, we show that the threshold on the number of training samples increases with the increase in the network width. Furthermore, we compare the threshold on training samples of unfolded networks with that of a standard fully-connected feed-forward network (FFNN) with smooth soft-thresholding non-linearity. We prove that unfolded networks have a higher threshold value than FFNN. Consequently, one can expect a better expected error for unfolded networks than FFNN.

CholeskyQR2 and shifted CholeskyQR3 are two state-of-the-art algorithms for computing tall-and-skinny QR factorizations since they attain high performance on current computer architectures. However, to guarantee stability, for some applications, CholeskyQR2 faces a prohibitive restriction on the condition number of the underlying matrix to factorize. Shifted CholeskyQR3 is stable but has $50\%$ more computational and communication costs than CholeskyQR2. In this paper, a randomized QR algorithm called Randomized Householder-Cholesky (\texttt{rand\_cholQR}) is proposed and analyzed. Using one or two random sketch matrices, it is proved that with high probability, its orthogonality error is bounded by a constant of the order of unit roundoff for any numerically full-rank matrix, and hence it is as stable as shifted CholeskyQR3. An evaluation of the performance of \texttt{rand\_cholQR} on a NVIDIA A100 GPU demonstrates that for tall-and-skinny matrices, \texttt{rand\_cholQR} with multiple sketch matrices is nearly as fast as, or in some cases faster than, CholeskyQR2. Hence, compared to CholeskyQR2, \texttt{rand\_cholQR} is more stable with almost no extra computational or memory cost, and therefore a superior algorithm both in theory and practice.

Deep Learning (DL) is vulnerable to out-of-distribution and adversarial examples resulting in incorrect outputs. To make DL more robust, several posthoc anomaly detection techniques to detect (and discard) these anomalous samples have been proposed in the recent past. This survey tries to provide a structured and comprehensive overview of the research on anomaly detection for DL based applications. We provide a taxonomy for existing techniques based on their underlying assumptions and adopted approaches. We discuss various techniques in each of the categories and provide the relative strengths and weaknesses of the approaches. Our goal in this survey is to provide an easier yet better understanding of the techniques belonging to different categories in which research has been done on this topic. Finally, we highlight the unsolved research challenges while applying anomaly detection techniques in DL systems and present some high-impact future research directions.