Criteria and Bias of Parameterized Linear Regression under Edge of Stability Regime

Classical optimization theory requires a small step-size for gradient-based methods to converge. Nevertheless, recent findings challenge the traditional idea by empirically demonstrating Gradient Descent (GD) converges even when the step-size $\eta$ exceeds the threshold of $2/L$, where $L$ is the global smooth constant. This is usually known as the Edge of Stability (EoS) phenomenon. A widely held belief suggests that an objective function with subquadratic growth plays an important role in incurring EoS. In this paper, we provide a more comprehensive answer by considering the task of finding linear interpolator $\beta \in R^{d}$ for regression with loss function $l(\cdot)$, where $\beta$ admits parameterization as $\beta = w^2_{+} - w^2_{-}$. Contrary to the previous work that suggests a subquadratic $l$ is necessary for EoS, our novel finding reveals that EoS occurs even when $l$ is quadratic under proper conditions. This argument is made rigorous by both empirical and theoretical evidence, demonstrating the GD trajectory converges to a linear interpolator in a non-asymptotic way. Moreover, the model under quadratic $l$, also known as a depth-$2$ diagonal linear network, remains largely unexplored under the EoS regime. Our analysis then sheds some new light on the implicit bias of diagonal linear networks when a larger step-size is employed, enriching the understanding of EoS on more practical models.

Procurement Auctions via Approximately Optimal Submodular Optimization

We study procurement auctions, where an auctioneer seeks to acquire services from strategic sellers with private costs. The quality of services is measured by a submodular function known to the auctioneer. Our goal is to design computationally efficient procurement auctions that (approximately) maximize the difference between the quality of the acquired services and the total cost of the sellers, while ensuring incentive compatibility (IC), individual rationality (IR) for sellers, and non-negative surplus (NAS) for the auctioneer. Our contributions are twofold: (i) we provide an improved analysis of existing algorithms for non-positive submodular function maximization, and (ii) we design efficient frameworks that transform submodular optimization algorithms into mechanisms that are IC, IR, NAS, and approximation-preserving. These frameworks apply to both the offline setting, where all sellers' bids and services are available simultaneously, and the online setting, where sellers arrive in an adversarial order, requiring the auctioneer to make irrevocable decisions. We also explore whether state-of-the-art submodular optimization algorithms can be converted into descending auctions in adversarial settings, where the schedule of descending prices is determined by an adversary. We show that a submodular optimization algorithm satisfying bi-criteria $(1/2, 1)$-approximation in welfare can be effectively adapted to a descending auction. Additionally, we establish a connection between descending auctions and online submodular optimization. Finally, we demonstrate the practical applications of our frameworks by instantiating them with state-of-the-art submodular optimization algorithms and empirically comparing their welfare performance on publicly available datasets with thousands of sellers.

A Flow-based Truncated Denoising Diffusion Model for Super-resolution Magnetic Resonance Spectroscopic Imaging

Magnetic Resonance Spectroscopic Imaging (MRSI) is a non-invasive imaging technique for studying metabolism and has become a crucial tool for understanding neurological diseases, cancers and diabetes. High spatial resolution MRSI is needed to characterize lesions, but in practice MRSI is acquired at low resolution due to time and sensitivity restrictions caused by the low metabolite concentrations. Therefore, there is an imperative need for a post-processing approach to generate high-resolution MRSI from low-resolution data that can be acquired fast and with high sensitivity. Deep learning-based super-resolution methods provided promising results for improving the spatial resolution of MRSI, but they still have limited capability to generate accurate and high-quality images. Recently, diffusion models have demonstrated superior learning capability than other generative models in various tasks, but sampling from diffusion models requires iterating through a large number of diffusion steps, which is time-consuming. This work introduces a Flow-based Truncated Denoising Diffusion Model (FTDDM) for super-resolution MRSI, which shortens the diffusion process by truncating the diffusion chain, and the truncated steps are estimated using a normalizing flow-based network. The network is conditioned on upscaling factors to enable multi-scale super-resolution. To train and evaluate the deep learning models, we developed a 1H-MRSI dataset acquired from 25 high-grade glioma patients. We demonstrate that FTDDM outperforms existing generative models while speeding up the sampling process by over 9-fold compared to the baseline diffusion model. Neuroradiologists' evaluations confirmed the clinical advantages of our method, which also supports uncertainty estimation and sharpness adjustment, extending its potential clinical applications.

TSDS: Data Selection for Task-Specific Model Finetuning

Finetuning foundation models for specific tasks is an emerging paradigm in modern machine learning. The efficacy of task-specific finetuning largely depends on the selection of appropriate training data. We present TSDS (Task-Specific Data Selection), a framework to select data for task-specific model finetuning, guided by a small but representative set of examples from the target task. To do so, we formulate data selection for task-specific finetuning as an optimization problem with a distribution alignment loss based on optimal transport to capture the discrepancy between the selected data and the target distribution. In addition, we add a regularizer to encourage the diversity of the selected data and incorporate kernel density estimation into the regularizer to reduce the negative effects of near-duplicates among the candidate data. We connect our optimization problem to nearest neighbor search and design efficient algorithms to compute the optimal solution based on approximate nearest neighbor search techniques. We evaluate our method on data selection for both continued pretraining and instruction tuning of language models. We show that instruction tuning using data selected by our method with a 1% selection ratio often outperforms using the full dataset and beats the baseline selection methods by 1.5 points in F1 score on average.

Cognitive Overload Attack:Prompt Injection for Long Context

Large Language Models (LLMs) have demonstrated remarkable capabilities in performing tasks across various domains without needing explicit retraining. This capability, known as In-Context Learning (ICL), while impressive, exposes LLMs to a variety of adversarial prompts and jailbreaks that manipulate safety-trained LLMs into generating undesired or harmful output. In this paper, we propose a novel interpretation of ICL in LLMs through the lens of cognitive neuroscience, by drawing parallels between learning in human cognition with ICL. We applied the principles of Cognitive Load Theory in LLMs and empirically validate that similar to human cognition, LLMs also suffer from cognitive overload a state where the demand on cognitive processing exceeds the available capacity of the model, leading to potential errors. Furthermore, we demonstrated how an attacker can exploit ICL to jailbreak LLMs through deliberately designed prompts that induce cognitive overload on LLMs, thereby compromising the safety mechanisms of LLMs. We empirically validate this threat model by crafting various cognitive overload prompts and show that advanced models such as GPT-4, Claude-3.5 Sonnet, Claude-3 OPUS, Llama-3-70B-Instruct, Gemini-1.0-Pro, and Gemini-1.5-Pro can be successfully jailbroken, with attack success rates of up to 99.99%. Our findings highlight critical vulnerabilities in LLMs and underscore the urgency of developing robust safeguards. We propose integrating insights from cognitive load theory into the design and evaluation of LLMs to better anticipate and mitigate the risks of adversarial attacks. By expanding our experiments to encompass a broader range of models and by highlighting vulnerabilities in LLMs' ICL, we aim to ensure the development of safer and more reliable AI systems.

Data Selection for Task-Specific Model Finetuning

Finetuning foundation models for specific tasks is an emerging paradigm in modern machine learning. The efficacy of task-specific finetuning largely depends on the selection of appropriate training data. We present a framework to select data for task-specific model finetuning, guided by a small but representative set of examples from the target task. To do so, we formulate data selection for task-specific finetuning as an optimization problem with a distribution alignment loss based on optimal transport to capture the discrepancy between the selected data and the target distribution. In addition, we add a regularizer to encourage the diversity of the selected data and incorporate kernel density estimation into the regularizer to reduce the negative effects of near-duplicates among the candidate data. We connect our optimization problem to nearest neighbor search and design efficient algorithms to compute the optimal solution based on approximate nearest neighbor search techniques. We evaluate our method on data selection for both continued pretraining and instruction tuning of language models. We show that instruction tuning using data selected by our method with a 1% selection ratio often outperforms using the full dataset and beats the baseline selection methods by 1.5 points in F1 score on average.

Intelligence at the Edge of Chaos

We explore the emergence of intelligent behavior in artificial systems by investigating how the complexity of rule-based systems influences the capabilities of models trained to predict these rules. Our study focuses on elementary cellular automata (ECA), simple yet powerful one-dimensional systems that generate behaviors ranging from trivial to highly complex. By training distinct Large Language Models (LLMs) on different ECAs, we evaluated the relationship between the complexity of the rules' behavior and the intelligence exhibited by the LLMs, as reflected in their performance on downstream tasks. Our findings reveal that rules with higher complexity lead to models exhibiting greater intelligence, as demonstrated by their performance on reasoning and chess move prediction tasks. Both uniform and periodic systems, and often also highly chaotic systems, resulted in poorer downstream performance, highlighting a sweet spot of complexity conducive to intelligence. We conjecture that intelligence arises from the ability to predict complexity and that creating intelligence may require only exposure to complexity.

Injecting Undetectable Backdoors in Deep Learning and Language Models

As ML models become increasingly complex and integral to high-stakes domains such as finance and healthcare, they also become more susceptible to sophisticated adversarial attacks. We investigate the threat posed by undetectable backdoors in models developed by insidious external expert firms. When such backdoors exist, they allow the designer of the model to sell information to the users on how to carefully perturb the least significant bits of their input to change the classification outcome to a favorable one. We develop a general strategy to plant a backdoor to neural networks while ensuring that even if the model's weights and architecture are accessible, the existence of the backdoor is still undetectable. To achieve this, we utilize techniques from cryptography such as cryptographic signatures and indistinguishability obfuscation. We further introduce the notion of undetectable backdoors to language models and extend our neural network backdoor attacks to such models based on the existence of steganographic functions.

On the Computational Landscape of Replicable Learning

We study computational aspects of algorithmic replicability, a notion of stability introduced by Impagliazzo, Lei, Pitassi, and Sorrell [2022]. Motivated by a recent line of work that established strong statistical connections between replicability and other notions of learnability such as online learning, private learning, and SQ learning, we aim to understand better the computational connections between replicability and these learning paradigms. Our first result shows that there is a concept class that is efficiently replicably PAC learnable, but, under standard cryptographic assumptions, no efficient online learner exists for this class. Subsequently, we design an efficient replicable learner for PAC learning parities when the marginal distribution is far from uniform, making progress on a question posed by Impagliazzo et al. [2022]. To obtain this result, we design a replicable lifting framework inspired by Blanc, Lange, Malik, and Tan [2023] that transforms in a black-box manner efficient replicable PAC learners under the uniform marginal distribution over the Boolean hypercube to replicable PAC learners under any marginal distribution, with sample and time complexity that depends on a certain measure of the complexity of the distribution. Finally, we show that any pure DP learner can be transformed to a replicable one in time polynomial in the accuracy, confidence parameters and exponential in the representation dimension of the underlying hypothesis class.

Replicable Learning of Large-Margin Halfspaces

We provide efficient replicable algorithms for the problem of learning large-margin halfspaces. Our results improve upon the algorithms provided by Impagliazzo, Lei, Pitassi, and Sorrell [STOC, 2022]. We design the first dimension-independent replicable algorithms for this task which runs in polynomial time, is proper, and has strictly improved sample complexity compared to the one achieved by Impagliazzo et al. [2022] with respect to all the relevant parameters. Moreover, our first algorithm has sample complexity that is optimal with respect to the accuracy parameter $\epsilon$. We also design an SGD-based replicable algorithm that, in some parameters' regimes, achieves better sample and time complexity than our first algorithm. Departing from the requirement of polynomial time algorithms, using the DP-to-Replicability reduction of Bun, Gaboardi, Hopkins, Impagliazzo, Lei, Pitassi, Sorrell, and Sivakumar [STOC, 2023], we show how to obtain a replicable algorithm for large-margin halfspaces with improved sample complexity with respect to the margin parameter $\tau$, but running time doubly exponential in $1/\tau^2$ and worse sample complexity dependence on $\epsilon$ than one of our previous algorithms. We then design an improved algorithm with better sample complexity than all three of our previous algorithms and running time exponential in $1/\tau^{2}$.