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Deep Learning · Theory

Micah Goldblum, Marc Finzi, Keefer Rowan, Andrew Wilson

No free lunch theorems for supervised learning state that no learner can solve all problems or that all learners achieve exactly the same accuracy on average over a uniform distribution on learning problems. Accordingly, these theorems are often referenced in support of the notion that individual problems require specially tailored inductive biases. While virtually all uniformly sampled datasets have high complexity, real-world problems disproportionately generate low-complexity data, and we argue that neural network models share this same preference, formalized using Kolmogorov complexity. Notably, we show that architectures designed for a particular domain, such as computer vision, can compress datasets on a variety of seemingly unrelated domains. Our experiments show that pre-trained and even randomly initialized language models prefer to generate low-complexity sequences. Whereas no free lunch theorems seemingly indicate that individual problems require specialized learners, we explain how tasks that often require human intervention such as picking an appropriately sized model when labeled data is scarce or plentiful can be automated into a single learning algorithm. These observations justify the trend in deep learning of unifying seemingly disparate problems with an increasingly small set of machine learning models.

Deep Learning · Generative Models and Autoencoders

Nate Gillman, Michael Freeman, Daksh Aggarwal, Chia-Hong HSU, Calvin Luo, Yonglong Tian, Chen Sun

As synthetic data becomes higher quality and proliferates on the internet, machine learning models are increasingly trained on a mix of human- and machine-generated data. Despite the successful stories of using synthetic data for representation learning, using synthetic data for generative model training creates ``self-consuming loops'' which may lead to training instability or even collapse, unless certain conditions are met. Our paper aims to stabilize self-consuming generative model training. Our theoretical results demonstrate that by introducing an idealized correction function, which maps a data point to be more likely under the true data distribution, self-consuming loops can be made *exponentially* more stable. We then propose self-correction functions, which rely on expert knowledge (e.g. the laws of physics programmed in a simulator), and aim to approximate the idealized corrector automatically and at scale. We empirically validate the effectiveness of self-correcting self-consuming loops on the challenging human motion synthesis task, and observe that it successfully avoids model collapse, even when the ratio of synthetic data to real data is as high as 100%.

Miscellaneous Aspects of Machine Learning · Unsupervised and Semi-supervised Learning

Avrajit Ghosh, Xitong Zhang, Kenneth Sun, Qing Qu, Saiprasad Ravishankar, Rongrong Wang

We introduce Optimal Eye Surgeon (OES), a framework for pruning and training deep image generator networks. Typically, untrained deep convolutional networks, which include image sampling operations, serve as effective image priors. However, they tend to overfit to noise in image restoration tasks due to being overparameterized. OES addresses this by adaptively pruning networks at random initialization to a level of underparameterization. This process effectively captures low-frequency image components even without training, by just masking. When trained to fit noisy image, these pruned subnetworks, which we term Sparse-DIP, resist overfitting to noise. This benefit arises from underparameterization and the regularization effect of masking, constraining them in the manifold of image priors. We demonstrate that subnetworks pruned through OES surpass other leading pruning methods, such as the Lottery Ticket Hypothesis, which is known to be suboptimal for image recovery tasks. Our extensive experiments demonstrate the transferability of OES-masks and the characteristics of sparse-subnetworks for image generation. Code is available at https://github.com/Avra98/Optimal-Eye-Surgeon.

Theory · Learning Theory

Avishek Ghosh, Arya Mazumdar

Mixed linear regression is a well-studied problem in parametric statistics and machine learning. Given a set of samples, tuples of covariates and labels, the task of mixed linear regression is to find a small list of linear relationships that best fit the samples. Usually it is assumed that the label is generated stochastically by randomly selecting one of two or more linear functions, applying this chosen function to the covariates, and potentially introducing noise to the result. In that situation, the objective is to estimate the ground-truth linear functions up to some parameter error. The popular expectation maximization (EM) and alternating minimization (AM) algorithms have been previously analyzed for this. In this paper, we consider the more general problem of agnostic learning of mixed linear regression from samples, without such generative models. In particular, we show that the AM and EM algorithms, under standard conditions of separability and good initialization, lead to agnostic learning in mixed linear regression by converging to the population loss minimizers, for suitably defined loss functions. In some sense, this shows the strength of AM and EM algorithms that converges to ``optimal solutions'' even in the absence of realizable generative models.

Theory · Game Theory

Mukesh Ghimire, Lei Zhang, Zhe Xu, Yi Ren

We study zero-sum differential games with state constraints and one-sided information, where the informed player (Player 1) has a categorical payoff type unknown to the uninformed player (Player 2). The goal of Player 1 is to minimize his payoff without violating the constraints, while that of Player 2 is to violate the state constraints if possible, or to maximize the payoff otherwise. One example of the game is a man-to-man matchup in football. Without state constraints, Cardaliaguet (2007) showed that the value of such a game exists and is convex to the common belief of players. Our theoretical contribution is an extension of this result to games with state constraints and the derivation of the primal and dual subdynamic principles necessary for computing behavioral strategies. Different from existing works that are concerned about the scalability of no-regret learning in games with discrete dynamics, our study reveals the underlying structure of strategies for belief manipulation resulting from information asymmetry and state constraints. This structure will be necessary for scalable learning on games with continuous actions and long time windows. We use a simplified football game to demonstrate the utility of this work, where we reveal player positions and belief states in which the attacker should (or should not) play specific random deceptive moves to take advantage of information asymmetry, and compute how the defender should respond.

Social Aspects · Privacy-preserving Statistics and Machine Learning

Badih Ghazi, Pritish Kamath, Ravi Kumar, Pasin Manurangsi, Adam Sealfon

In this work, we give a new technique for analyzing individualized privacy accounting via the following simple observation: if an algorithm is one-sided add-DP, then its subsampled variant satisfies two-sided DP. From this, we obtain several improved algorithms for private combinatorial optimization problems, including decomposable submodular maximization and set cover. Our error guarantees are asymptotically tight and our algorithm satisfies pure-DP while previously known algorithms (Gupta et al., 2010; Chaturvedi et al., 2021) are approximate-DP. We also show an application of our technique beyond combinatorial optimization by giving a pure-DP algorithm for the shifting heavy hitter problem in a stream; previously, only an approximate-DP algorithm was known (Kaplan et al., 2021; Cohen & Lyu, 2023).

Social Aspects · Accountability, Transparency and Interpretability

Asma Ghandeharioun, ‪Avi Caciularu‬‏, Adam Pearce, Lucas Dixon, Mor Geva

Understanding the internal representations of large language models (LLMs) can help explain models' behavior and verify their alignment with human values. Given the capabilities of LLMs in generating human-understandable text, we propose leveraging the model itself to explain its internal representations in natural language. We introduce a framework called Patchscopes and show how it can be used to answer a wide range of questions about an LLM's computation. We show that many prior interpretability methods based on projecting representations into the vocabulary space and intervening on the LLM computation can be viewed as instances of this framework. Moreover, several of their shortcomings such as failure in inspecting early layers or lack of expressivity can be mitigated by Patchscopes. Beyond unifying prior inspection techniques, Patchscopes also opens up *new* possibilities such as using a more capable model to explain the representations of a smaller model, and multihop reasoning error correction.

Applications · Everything Else

Zijie Geng, Jie Wang, Ziyan Liu, Siyuan Xu, Zhentao Tang, Mingxuan Yuan, Jianye Hao, Yongdong Zhang, Feng Wu

Macro placement is a crucial step in modern chip design, and reinforcement learning (RL) has recently emerged as a promising technique for improving the placement quality. However, existing RL-based techniques are hindered by their low sample efficiency, requiring numerous online rollouts or substantial offline expert data to achieve bootstrap, which are often impractical in industrial scenarios. To address this challenge, we propose a novel sample-efficient framework, namely **EfficientPlace**, for fast macro placement. EfficientPlace integrates a global tree search algorithm to strategically direct the optimization process, as well as a RL agent for local policy learning to advance the tree search. Experiments on commonly used benchmarks demonstrate that EfficientPlace achieves remarkable placement quality within a short timeframe, outperforming recent state-of-the-art approaches.

Theory · Online Learning and Bandits

Gianmarco Genalti, Marco Mussi, Nicola Gatti, Marcello Restelli, Matteo Castiglioni, Alberto Maria Metelli

In this paper, we propose a novel generalization of rested and restless bandits where the evolution of the arms' expected rewards is governed by a graph defined over the arms. An edge connecting a pair of arms $(i,j)$ represents the fact that a pull of arm $i$ *triggers* the evolution of arm $j$, and vice versa. Interestingly, rested and restless bandits are both special cases of our model for some suitable (degenerate) graphs. Still, the model can represent way more general and interesting scenarios. We first tackle the problem of computing the optimal policy when no specific structure is assumed on the graph, showing that it is NP-hard. Then, we focus on a specific structure forcing the graph to be composed of a set of fully connected subgraphs (i.e., cliques), and we prove that the optimal policy can be easily computed in closed form. Then, we move to the learning problem presenting regret minimization algorithms for deterministic and stochastic cases. Our regret bounds highlight the complexity of the learning problem by incorporating instance-dependent terms that encode specific properties of the underlying graph structure. Moreover, we illustrate how the knowledge of the underlying graph is not necessary for achieving the no-regret property.

Miscellaneous Aspects of Machine Learning · Supervised Learning

Andreas René Geist, Jonas Frey, Mikel Zhobro, Anna Levina, Georg Martius

Many settings in machine learning require the selection of a rotation representation. However, choosing a suitable representation from the many available options is challenging. This paper acts as a survey and guide through rotation representations. We walk through their properties that harm or benefit deep learning with gradient-based optimization. By consolidating insights from rotation-based learning, we provide a comprehensive overview of learning functions with rotation representations. We provide guidance on selecting representations based on whether rotations are in the model’s input or output and whether the data primarily comprises small angles.

Social Aspects · Accountability, Transparency and Interpretability

Robert Geirhos, Roland S. Zimmermann, Blair Bilodeau, Wieland Brendel, Been Kim

How do neural networks extract patterns from pixels? Feature visualizations attempt to answer this important question by visualizing highly activating patterns through optimization. Today, visualization methods form the foundation of our knowledge about the internal workings of neural networks, as a type of mechanistic interpretability. Here we ask: How reliable are feature visualizations? We start our investigation by developing network circuits that trick feature visualizations into showing arbitrary patterns that are completely disconnected from normal network behavior on natural input. We then provide evidence for a similar phenomenon occurring in standard, unmanipulated networks: feature visualizations are processed very differently from standard input, casting doubt on their ability to "explain" how neural networks process natural images. This can be used as a sanity check for feature visualizations. We underpin our empirical findings by theory proving that the set of functions that can be reliably understood by feature visualization is extremely small and does not include general black-box neural networks. Therefore, a promising way forward could be the development of networks that enforce certain structures in order to ensure more reliable feature visualizations.

Theory · Game Theory

Zhenxing Ge, Zheng Xu, Tianyu Ding, Linjian Meng, Bo An, Wenbin Li, Yang Gao

Opponent exploitation is an important task for players to exploit the weaknesses of others in games. Existing approaches mainly focus on balancing between exploitation and exploitability but are often vulnerable to modeling errors and deceptive adversaries. To address this problem, our paper offers a novel perspective on the safety of opponent exploitation, named Adaptation Safety. This concept leverages the insight that strategies, even those not explicitly aimed at opponent exploitation, may inherently be exploitable due to computational complexities, rendering traditional safety overly rigorous. In contrast, adaptation safety requires that the strategy should not be more exploitable than it would be in scenarios where opponent exploitation is not considered. Building on such adaptation safety, we further propose an Opponent eXploitation Search (OX-Search) framework by incorporating real-time search techniques for efficient online opponent exploitation. Moreover, we provide theoretical analyses to show the adaptation safety and robust exploitation of OX-Search, even with inaccurate opponent models. Empirical evaluations in popular poker games demonstrate OX-Search's superiority in both exploitability and exploitation compared to previous methods.

Deep Learning · Theory

Bruno Gavranović, Paul Lessard, Andrew Dudzik, Tamara von Glehn, João Madeira Araujo, Petar Veličković

We present our position on the elusive quest for a general-purpose framework for specifying and studying deep learning architectures. Our opinion is that the key attempts made so far lack a coherent bridge between specifying constraints which models must satisfy and specifying their implementations. Focusing on building a such a bridge, we propose to apply category theory---precisely, the universal algebra of monads valued in a 2-category of parametric maps---as a single theory elegantly subsuming both of these flavours of neural network design. To defend our position, we show how this theory recovers constraints induced by geometric deep learning, as well as implementations of many architectures drawn from the diverse landscape of neural networks, such as RNNs. We also illustrate how the theory naturally encodes many standard constructs in computer science and automata theory.

Applications · Language, Speech and Dialog

Joshua Gardner, Simon Durand, Daniel Stoller, Rachel Bittner

Music has a unique and complex structure which is challenging for both expert humans and existing AI systems to understand, and presents unique challenges relative to other forms of audio. We present LLark, an instruction-tuned multimodal model for *music* understanding. We detail our process for dataset creation, which involves augmenting the annotations of diverse open-source music datasets and converting them to a unified instruction-tuning format. We propose a multimodal architecture for LLark, integrating a pretrained generative model for music with a pretrained language model. In evaluations on three types of tasks (music understanding, captioning, reasoning), we show that LLark matches or outperforms existing baselines in music understanding, and that humans show a high degree of agreement with its responses in captioning and reasoning tasks. LLark is trained entirely from open-source music data and models, and we make our training code available along with the release of this paper. Additional results and audio examples are at https://bit.ly/llark, and our source code is available at https://github.com/spotify-research/llark.

Theory · Online Learning and Bandits

Dan Garber, Ben Kretzu

We consider the setting of online convex optimization with adversarial time-varying constraints in which actions must be feasible w.r.t. a fixed constraint set, and are also required on average to approximately satisfy additional time-varying constraints. Motivated by scenarios in which the fixed feasible set (hard constraint) is difficult to project on, we consider projection-free algorithms that access this set only through a linear optimization oracle (LOO). We present an algorithm that, on a sequence of length $T$ and using overall $T$ calls to the LOO, guarantees $\tilde{O}(T^{3/4})$ regret w.r.t. the losses and $O(T^{7/8})$ constraints violation (ignoring all quantities except for $T$). In particular, these bounds hold w.r.t. any interval of the sequence. This algorithm however also requires access to an oracle for minimizing a strongly convex nonsmooth function over a Euclidean ball. We present a more efficient algorithm that does not require the latter optimization oracle but only first-order access to the time-varying constraints, and achieves similar bounds w.r.t. the entire sequence. We extend the latter to the setting of bandit feedback and obtain similar bounds (as a function of $T$) in expectation.

Miscellaneous Aspects of Machine Learning · Causality

Chenyin Gao, ZHIMING ZHANG, Shu Yang

This study introduces an innovative method for analyzing the impact of various interventions on customer churn, using the potential outcomes framework. We present a new causal model, the tensorized latent factor block hazard model, which incorporates tensor completion methods for a principled causal analysis of customer churn. A crucial element of our approach is the formulation of a 1-bit tensor completion for the parameter tensor. This captures hidden customer characteristics and temporal elements from churn records, effectively addressing the binary nature of churn data and its time-monotonic trends. Our model also uniquely categorizes interventions by their similar impacts, enhancing the precision and practicality of implementing customer retention strategies. For computational efficiency, we apply a projected gradient descent algorithm combined with spectral clustering. We lay down the theoretical groundwork for our model, including its non-asymptotic properties. The efficacy and superiority of our model are further validated through comprehensive experiments on both simulated and real-world applications.

Applications · Robotics

JUNYU GAO, Xuan Yao, Changsheng Xu

The ability to accurately comprehend natural language instructions and navigate to the target location is essential for an embodied agent. Such agents are typically required to execute user instructions in an online manner, leading us to explore the use of unlabeled test samples for effective online model adaptation. However, for online Vision-and-Language Navigation (VLN), due to the intrinsic nature of inter-sample online instruction execution and intra-sample multi-step action decision, frequent updates can result in drastic changes in model parameters, while occasional updates can make the model ill-equipped to handle dynamically changing environments. Therefore, we propose a Fast-Slow Test-Time Adaptation (FSTTA) approach for online VLN by performing joint decomposition-accumulation analysis for both gradients and parameters in a unified framework. Extensive experiments show that our method obtains impressive performance gains on four popular benchmarks. Code is available at https://github.com/Feliciaxyao/ICML2024-FSTTA.

Ziqi Gao, Qichao Wang, Aochuan Chen, Zijing Liu, Bingzhe Wu, Liang Chen, Jia Li

Low-rank adaptation (LoRA) has recently gained much interest in fine-tuning foundation models. It effectively reduces the number of trainable parameters by incorporating low-rank matrices $A$ and $B$ to represent the weight change, i.e., $\Delta W=BA$. Despite LoRA's progress, it faces storage challenges when handling extensive customization adaptations or larger base models. In this work, we aim to further compress trainable parameters by enjoying the powerful expressiveness of the Fourier transform. Specifically, we introduce FourierFT, which treats $\Delta W$ as a matrix in the spatial domain and learns only a small fraction of its spectral coefficients. With the trained spectral coefficients, we implement the inverse discrete Fourier transform to recover $\Delta W$. Empirically, our FourierFT method shows comparable or better performance with fewer parameters than LoRA on various tasks, including natural language understanding, natural language generation, instruction tuning, and image classification. For example, when performing instruction tuning on the LLaMA2-7B model, FourierFT surpasses LoRA with only 0.064M trainable parameters, compared to LoRA's 33.5M. Our code is released at [this link](https://github.com/Chaos96/fourierft).

Theory · Online Learning and Bandits

Wenzhi Gao, Chunlin Sun, Chenyu Xue, Yinyu Ye

Online linear programming plays an important role in both revenue management and resource allocation, and recent research has focused on developing efficient first-order online learning algorithms. Despite the empirical success of first-order methods, they typically achieve regret no better than $\mathcal{O}(\sqrt{T})$, which is suboptimal compared to the $\mathcal{O}(\log T)$ result guaranteed by the state-of-the-art linear programming (LP)-based online algorithms. This paper establishes several important facts about online linear programming, which unveils the challenge for first-order online algorithms to achieve beyond $\mathcal{O}(\sqrt{T})$ regret. To address this challenge, we introduce a new algorithmic framework which decouples learning from decision-making. For the first time, we show that first-order methods can achieve regret $\mathcal{O}(T^{1/3})$ with this new framework.

Reinforcement Learning

Feng Gao, Liangzhi Shi, Shenao Zhang, Zhaoran Wang, Yi Wu

Recent advancements in differentiable simulators highlight the potential of policy optimization using simulation gradients. Yet, these approaches are largely contingent on the continuity and smoothness of the simulation, which precludes the use of certain simulation engines, such as Mujoco. To tackle this challenge, we introduce the adaptive analytic gradient. This method views the Q function as a surrogate for future returns, consistent with the Bellman equation. By analyzing the variance of batched gradients, our method can autonomously opt for a more resilient Q function to compute the gradient when encountering rough simulation transitions. We also put forth the Adaptive-Gradient Policy Optimization (AGPO) algorithm, which leverages our proposed method for policy learning. On the theoretical side, we demonstrate AGPO's convergence, emphasizing its stable performance under non-smooth dynamics due to low variance. On the empirical side, our results show that AGPO effectively mitigates the challenges posed by non-smoothness in policy learning through differentiable simulation.