Frequency-Guided Posterior Sampling for Diffusion-Based Image Restoration

Image restoration aims to recover high-quality images from degraded observations. When the degradation process is known, the recovery problem can be formulated as an inverse problem, and in a Bayesian context, the goal is to sample a clean reconstruction given the degraded observation. Recently, modern pretrained diffusion models have been used for image restoration by modifying their sampling procedure to account for the degradation process. However, these methods often rely on certain approximations that can lead to significant errors and compromised sample quality. In this paper, we provide the first rigorous analysis of this approximation error for linear inverse problems under distributional assumptions on the space of natural images, demonstrating cases where previous works can fail dramatically. Motivated by our theoretical insights, we propose a simple modification to existing diffusion-based restoration methods. Our approach introduces a time-varying low-pass filter in the frequency domain of the measurements, progressively incorporating higher frequencies during the restoration process. We develop an adaptive curriculum for this frequency schedule based on the underlying data distribution. Our method significantly improves performance on challenging image restoration tasks including motion deblurring and image dehazing.

PaCE: Parsimonious Concept Engineering for Large Language Models

Large Language Models (LLMs) are being used for a wide variety of tasks. While they are capable of generating human-like responses, they can also produce undesirable output including potentially harmful information, racist or sexist language, and hallucinations. Alignment methods are designed to reduce such undesirable output, via techniques such as fine-tuning, prompt engineering, and representation engineering. However, existing methods face several challenges: some require costly fine-tuning for every alignment task; some do not adequately remove undesirable concepts, failing alignment; some remove benign concepts, lowering the linguistic capabilities of LLMs. To address these issues, we propose Parsimonious Concept Engineering (PaCE), a novel activation engineering framework for alignment. First, to sufficiently model the concepts, we construct a large-scale concept dictionary in the activation space, in which each atom corresponds to a semantic concept. Then, given any alignment task, we instruct a concept partitioner to efficiently annotate the concepts as benign or undesirable. Finally, at inference time, we decompose the LLM activations along the concept dictionary via sparse coding, to accurately represent the activation as a linear combination of the benign and undesirable components. By removing the latter ones from the activation, we reorient the behavior of LLMs towards alignment goals. We conduct experiments on tasks such as response detoxification, faithfulness enhancement, and sentiment revising, and show that PaCE achieves state-of-the-art alignment performance while maintaining linguistic capabilities.

A Linearly Convergent GAN Inversion-based Algorithm for Reverse Engineering of Deceptions

An important aspect of developing reliable deep learning systems is devising strategies that make these systems robust to adversarial attacks. There is a long line of work that focuses on developing defenses against these attacks, but recently, researchers have began to study ways to reverse engineer the attack process. This allows us to not only defend against several attack models, but also classify the threat model. However, there is still a lack of theoretical guarantees for the reverse engineering process. Current approaches that give any guarantees are based on the assumption that the data lies in a union of linear subspaces, which is not a valid assumption for more complex datasets. In this paper, we build on prior work and propose a novel framework for reverse engineering of deceptions which supposes that the clean data lies in the range of a GAN. To classify the signal and attack, we jointly solve a GAN inversion problem and a block-sparse recovery problem. For the first time in the literature, we provide deterministic linear convergence guarantees for this problem. We also empirically demonstrate the merits of the proposed approach on several nonlinear datasets as compared to state-of-the-art methods.

Reverse Engineering $\ell_p$ attacks: A block-sparse optimization approach with recovery guarantees

Deep neural network-based classifiers have been shown to be vulnerable to imperceptible perturbations to their input, such as $\ell_p$-bounded norm adversarial attacks. This has motivated the development of many defense methods, which are then broken by new attacks, and so on. This paper focuses on a different but related problem of reverse engineering adversarial attacks. Specifically, given an attacked signal, we study conditions under which one can determine the type of attack ($\ell_1$, $\ell_2$ or $\ell_\infty$) and recover the clean signal. We pose this problem as a block-sparse recovery problem, where both the signal and the attack are assumed to lie in a union of subspaces that includes one subspace per class and one subspace per attack type. We derive geometric conditions on the subspaces under which any attacked signal can be decomposed as the sum of a clean signal plus an attack. In addition, by determining the subspaces that contain the signal and the attack, we can also classify the signal and determine the attack type. Experiments on digit and face classification demonstrate the effectiveness of the proposed approach.

Combinatorial Optimization by Graph Pointer Networks and Hierarchical Reinforcement Learning

In this work, we introduce Graph Pointer Networks (GPNs) trained using reinforcement learning (RL) for tackling the traveling salesman problem (TSP). GPNs build upon Pointer Networks by introducing a graph embedding layer on the input, which captures relationships between nodes. Furthermore, to approximate solutions to constrained combinatorial optimization problems such as the TSP with time windows, we train hierarchical GPNs (HGPNs) using RL, which learns a hierarchical policy to find an optimal city permutation under constraints. Each layer of the hierarchy is designed with a separate reward function, resulting in stable training. Our results demonstrate that GPNs trained on small-scale TSP50/100 problems generalize well to larger-scale TSP500/1000 problems, with shorter tour lengths and faster computational times. We verify that for constrained TSP problems such as the TSP with time windows, the feasible solutions found via hierarchical RL training outperform previous baselines. In the spirit of reproducible research we make our data, models, and code publicly available.

Accurate Protein Structure Prediction by Embeddings and Deep Learning Representations

Proteins are the major building blocks of life, and actuators of almost all chemical and biophysical events in living organisms. Their native structures in turn enable their biological functions which have a fundamental role in drug design. This motivates predicting the structure of a protein from its sequence of amino acids, a fundamental problem in computational biology. In this work, we demonstrate state-of-the-art protein structure prediction (PSP) results using embeddings and deep learning models for prediction of backbone atom distance matrices and torsion angles. We recover 3D coordinates of backbone atoms and reconstruct full atom protein by optimization. We create a new gold standard dataset of proteins which is comprehensive and easy to use. Our dataset consists of amino acid sequences, Q8 secondary structures, position specific scoring matrices, multiple sequence alignment co-evolutionary features, backbone atom distance matrices, torsion angles, and 3D coordinates. We evaluate the quality of our structure prediction by RMSD on the latest Critical Assessment of Techniques for Protein Structure Prediction (CASP) test data and demonstrate competitive results with the winning teams and AlphaFold in CASP13 and supersede the results of the winning teams in CASP12. We make our data, models, and code publicly available.