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Learning Theory

Massimiliano Datres, Gian Leonardi, Alessio Figalli, David Sutter

We introduce a novel capacity measure 2sED for statistical models based on the effective dimension. The new quantity provably bounds the generalization error under mild assumptions on the model. Furthermore, simulations on standard data sets and popular model architectures show that 2sED correlates well with the training error. For Markovian models, we show how to efficiently approximate 2sED from below through a layerwise iterative approach, which allows us to tackle deep learning models with a large number of parameters. Simulation results suggest that the approximation is good for different prominent models and data sets.

Reinforcement Learning · Batch Offline

Allen Nie, Yash Chandak, Christina Yuan, Anirudhan Badrinath, Yannis Flet-Berliac, Emma Brunskill

Offline policy evaluation (OPE) allows us to evaluate and estimate a new sequential decision-making policy's performance by leveraging historical interaction data collected from other policies. Evaluating a new policy online without a confident estimate of its performance can lead to costly, unsafe, or hazardous outcomes, especially in education and healthcare. Several OPE estimators have been proposed in the last decade, many of which have hyperparameters and require training. Unfortunately, choosing the best OPE algorithm for each task and domain is still unclear. In this paper, we propose a new algorithm that adaptively blends a set of OPE estimators given a dataset without relying on an explicit selection using a statistical procedure. We prove that our estimator is consistent and satisfies several desirable properties for policy evaluation. Additionally, we demonstrate that when compared to alternative approaches, our estimator can be used to select higher-performing policies in healthcare and robotics. Our work contributes to improving ease of use for a general-purpose, estimator-agnostic, off-policy evaluation framework for offline RL.

Optimization · Zero-order and Black-box Optimization

Shukuan Wang, Ke Xue, Song Lei, Xiaobin Huang, Chao Qian

Bayesian optimization (BO) is a popular method for computationally expensive black-box optimization. However, traditional BO methods need to solve new problems from scratch, leading to slow convergence. Recent studies try to extend BO to a transfer learning setup to speed up the optimization, where search space transfer is one of the most promising approaches and has shown impressive performance on many tasks. However, existing search space transfer methods either lack an adaptive mechanism or are not flexible enough, making it difficult to efficiently identify promising search space during the optimization process. In this paper, we propose a search space transfer learning method based on Monte Carlo tree search (MCTS), called MCTS-transfer, to iteratively divide, select, and optimize in a learned subspace. MCTS-transfer can not only provide a well-performing search space for warm-start but also adaptively identify and leverage the information of similar source tasks to reconstruct the search space during the optimization process. Experiments on synthetic functions, real-world problems, Design-Bench and hyper-parameter optimization show that MCTS-transfer can demonstrate superior performance compared to other search space transfer methods under different settings. Our code is available at \url{https://github.com/lamda-bbo/mcts-transfer}.

Generative Models · New Approaches

Abhinav Jain, Swarat Chaudhuri, Thomas Reps, Christopher Jermaine

Parameter-Efficient Fine-Tuning (PEFT) has become the standard for customising Foundation Models (FMs) to user-specific downstream tasks. However, typical PEFT methods require storing multiple task-specific adapters, creating scalability issues as these adapters must be housed and run at the FM server. Traditional prompt tuning offers a potential solution by customising them through task-specific input prefixes, but it under-performs compared to other PEFT methods like LoRA. To address this gap, we propose Low-Rank Prompt Adaptation (LoPA), a prompt-tuning-based approach that performs on par with state-of-the-art PEFT methods and full fine-tuning while being more parameter-efficient and not requiring a server-based adapter. LoPA generates soft prompts by balancing between sharing task-specific information across instances and customization for each instance. It uses a low-rank decomposition of the soft-prompt component encoded for each instance to achieve parameter efficiency. We provide a comprehensive evaluation on multiple natural language understanding and code generation and understanding tasks across a wide range of foundation models with varying sizes.

Generative Models · Reasoning

Shangzi Xue, Zhenya Huang, Jiayu Liu, Xin Lin, Yuting Ning, Binbin Jin, Xin Li, Qi Liu

In this paper, we introduce DeAR (_Decompose-Analyze-Rethink_), a framework that iteratively builds a reasoning tree to tackle intricate problems within a single large language model (LLM). Unlike approaches that extend or search for rationales, DeAR is featured by 1) adopting a tree-based question decomposition manner to plan the organization of rationales, which mimics the logical planning inherentin human cognition; 2) globally updating the rationales at each reasoning step through natural language feedback. Specifically, the _Decompose_ stage decomposes the question into simpler sub-questions, storing them as new nodes; the _Analyze_ stage generates and self-checks rationales for sub-questions at each node evel; and the _Rethink_ stage updates parent-node rationales based on feedback from their child nodes. By generating and updating the reasoning process from a more global perspective, DeAR constructs more adaptive and accurate logical structures for complex problems, facilitating timely error correction compared to rationale-extension and search-based approaches such as Tree-of-Thoughts (ToT) and Graph-of-Thoughts (GoT). We conduct extensive experiments on three reasoning benchmarks, including ScienceQA, StrategyQA, and GSM8K, which cover a variety of reasoning tasks, demonstrating that our approach significantly reduces logical errors and enhances performance across various LLMs. Furthermore, we validate that DeAR is an efficient method that achieves a superior trade-off between accuracy and reasoning time compared to ToT and GoT.

Generative Models · Diffusion models

Yunshu Wu, Yingtao Luo, Xianghao Kong, Vagelis Papalexakis, Greg Ver Steeg

Diffusion models learn to denoise data and the trained denoiser is then used to generate new samples from the data distribution. In this paper, we revisit the diffusion sampling process and identify a fundamental cause of sample quality degradation: the denoiser is poorly estimated in regions that are far Outside Of the training Distribution (OOD), and the sampling process inevitably evaluates in these OOD regions.This can become problematic for all sampling methods, especially when we move to parallel sampling which requires us to initialize and update the entire sample trajectory of dynamics in parallel, leading to many OOD evaluations. To address this problem, we introduce a new self-supervised training objective that differentiates the levels of noise added to a sample, leading to improved OOD denoising performance. The approach is based on our observation that diffusion models implicitly define a log-likelihood ratio that distinguishes distributions with different amounts of noise, and this expression depends on denoiser performance outside the standard training distribution.We show by diverse experiments that the proposed contrastive diffusion training is effective for both sequential and parallel settings, and it improves the performance and speed of parallel samplers significantly. Code for our paper can be found at https://github.com/yunshuwu/ContrastiveDiffusionLoss

Generative Models · New Approaches

Lujun Li, Peijie Dong, Zhenheng Tang, Xiang Liu, Qiang Wang, Wenhan Luo, Wei Xue, Qifeng Liu, Xiaowen Chu, Yike Guo

In this paper, we present DSA, the first automated framework for discovering sparsity allocation schemes for layer-wise pruning in Large Language Models (LLMs). LLMs have become increasingly powerful, but their large parameter counts make them computationally expensive. Existing pruning methods for compressing LLMs primarily focus on evaluating redundancies and removing element-wise weights. However, these methods fail to allocate adaptive layer-wise sparsities, leading to performance degradation in challenging tasks. We observe that per-layer importance statistics can serve as allocation indications, but their effectiveness depends on the allocation function between layers. To address this issue, we develop an expression discovery framework to explore potential allocation strategies. Our allocation functions involve two steps: reducing element-wise metrics to per-layer importance scores, and modelling layer importance to sparsity ratios. To search for the most effective allocation function, we construct a search space consisting of pre-process, reduction, transform, and post-process operations. We leverage an evolutionary algorithm to perform crossover and mutation on superior candidates within the population, guided by performance evaluation. Finally, we seamlessly integrate our discovered functions into various uniform methods, resulting in significant performance improvements. We conduct extensive experiments on multiple challenging tasks such as arithmetic, knowledge reasoning, and multimodal benchmarks spanning GSM8K, MMLU, SQA, and VQA, demonstrating that our DSA method achieves significant performance gains on the LLaMA-1|2|3, Mistral, and OPT models. Notably, the LLaMA-1|2|3 model pruned by our DSA reaches 4.73\%|6.18\%|10.65\% gain over the state-of-the-art techniques (e.g., Wanda and SparseGPT).

Multimodal Models

Weiguo Pian, Yiyang Nan, Shijian Deng, Shentong Mo, Yunhui Guo, Yapeng Tian

In this paper, we introduce a novel continual audio-visual sound separation task, aiming to continuously separate sound sources for new classes while preserving performance on previously learned classes, with the aid of visual guidance. This problem is crucial for practical visually guided auditory perception as it can significantly enhance the adaptability and robustness of audio-visual sound separation models, making them more applicable for real-world scenarios where encountering new sound sources is commonplace. The task is inherently challenging as our models must not only effectively utilize information from both modalities in current tasks but also preserve their cross-modal association in old tasks to mitigate catastrophic forgetting during audio-visual continual learning. To address these challenges, we propose a novel approach named ContAV-Sep ($\textbf{Cont}$inual $\textbf{A}$udio-$\textbf{V}$isual Sound $\textbf{Sep}$aration). ContAV-Sep presents a novel Cross-modal Similarity Distillation Constraint (CrossSDC) to uphold the cross-modal semantic similarity through incremental tasks and retain previously acquired knowledge of semantic similarity in old models, mitigating the risk of catastrophic forgetting. The CrossSDC can seamlessly integrate into the training process of different audio-visual sound separation frameworks. Experiments demonstrate that ContAV-Sep can effectively mitigate catastrophic forgetting and achieve significantly better performance compared to other continual learning baselines for audio-visual sound separation. Code is available at: https://github.com/weiguoPian/ContAV-Sep_NeurIPS2024.

Learning Theory

Yi-Shan Wu, Yijie Zhang, Badr-Eddine Cherief-Abdellatif, Yevgeny Seldin

PAC-Bayesian analysis is a frequentist framework for incorporating prior knowledge into learning. It was inspired by Bayesian learning, which allows sequential data processing and naturally turns posteriors from one processing step into priors for the next. However, despite two and a half decades of research, the ability to update priors sequentially without losing confidence information along the way remained elusive for PAC-Bayes. While PAC-Bayes allows construction of data-informed priors, the final confidence intervals depend only on the number of points that were not used for the construction of the prior, whereas confidence information in the prior, which is related to the number of points used to construct the prior, is lost. This limits the possibility and benefit of sequential prior updates, because the final bounds depend only on the size of the final batch.We present a novel and, in retrospect, surprisingly simple and powerful PAC-Bayesian procedure that allows sequential prior updates with no information loss. The procedure is based on a novel decomposition of the expected loss of randomized classifiers. The decomposition rewrites the loss of the posterior as an excess loss relative to a downscaled loss of the prior plus the downscaled loss of the prior, which is bounded recursively. As a side result, we also present a generalization of the split-kl and PAC-Bayes-split-kl inequalities to discrete random variables, which we use for bounding the excess losses, and which can be of independent interest. In empirical evaluation the new procedure significantly outperforms state-of-the-art.

Generative Models

Nick Huang, Aaron Gokaslan, Volodymyr Kuleshov, James Tompkin

There is a widely-spread claim that GANs are difficult to train, and GAN architectures in the literature are littered with empirical tricks. We provide evidence against this claim and build a modern GAN baseline in a more principled manner. First, we derive a well-behaved regularized relativistic GAN loss that addresses issues of mode dropping and non-convergence that were previously tackled via a bag of ad-hoc tricks. We analyze our loss mathematically and prove that it admits local convergence guarantees, unlike most existing relativistic losses. Second, this loss allows us to discard all ad-hoc tricks and replace outdated backbones used in common GANs with modern architectures. Using StyleGAN2 as an example, we present a roadmap of simplification and modernization that results in a new minimalist baseline---R3GAN. Despite being simple, our approach surpasses StyleGAN2 on FFHQ, ImageNet, CIFAR, and Stacked MNIST datasets, and compares favorably against state-of-the-art GANs and diffusion models. Code: https://www.github.com/brownvc/R3GAN

Miscellaneous Aspects of Machine Learning · Transfer, Multitask and Meta-learning

Tyler Ingebrand, Adam Thorpe, Ufuk Topcu

Autonomous systems often encounter environments and scenarios beyond the scope of their training data, which underscores a critical challenge: the need to generalize and adapt to unseen scenarios in real time. This challenge necessitates new mathematical and algorithmic tools that enable adaptation and zero-shot transfer. To this end, we leverage the theory of function encoders, which enables zero-shot transfer by combining the flexibility of neural networks with the mathematical principles of Hilbert spaces. Using this theory, we first present a method for learning a space of dynamics spanned by a set of neural ODE basis functions. After training, the proposed approach can rapidly identify dynamics in the learned space using an efficient inner product calculation. Critically, this calculation requires no gradient calculations or retraining during the online phase. This method enables zero-shot transfer for autonomous systems at runtime and opens the door for a new class of adaptable control algorithms. We demonstrate state-of-the-art system modeling accuracy for two MuJoCo robot environments and show that the learned models can be used for more efficient MPC control of a quadrotor.

Interpretability

Xinyue Luo, Jin Cheng, Yu Chen

Lossless compression of large-scale scientific floating-point data is critical yet challenging due to the presence of high-order information and noise that arises from model truncation and discretization errors. Existing entropy coding techniques fail to effectively leverage the mechanisms underlying the data generation process. This paper introduces MeLLoC(Mechanism Learning for Lossless Compression), a novel approach that combines high-order mechanism learning with classical encoding to enhance lossless compression for scientific data. The key idea is to treat the data as discrete samples from an underlying physical field described by differential equations and solve an inverse problem to identify the governing equation coefficients exhibiting more compressible numeric representations. Periodic extension techniques are employed to accelerate the decompression. Through extensive experiments on various scientific datasets, MeLLoC consistently outperforms state-of-the-art lossless compressors while offering compelling trade-offs between compression ratios and computational costs. This work opens up new avenues for exploiting domain knowledge and high-order information to improve data compression in scientific computing.

Xinyu Zhou, Jinglun Li, Lingyi Hong, Kaixun Jiang, Pinxue Guo, Weifeng Ge, Wenqiang Zhang

Previous visual object tracking methods employ image-feature regression models or coordinate autoregression models for bounding box prediction. Image-feature regression methods heavily depend on matching results and do not utilize positional prior, while the autoregressive approach can only be trained using bounding boxes available in the training set, potentially resulting in suboptimal performance during testing with unseen data. Inspired by the diffusion model, denoising learning enhances the model’s robustness to unseen data. Therefore, We introduce noise to bounding boxes, generating noisy boxes for training, thus enhancing model robustness on testing data. We propose a new paradigm to formulate the visual object tracking problem as a denoising learning process. However, tracking algorithms are usually asked to run in real-time, directly applying the diffusion model to object tracking would severely impair tracking speed. Therefore, we decompose the denoising learning process into every denoising block within a model, not by running the model multiple times, and thus we summarize the proposed paradigm as an in-model latent denoising learning process. Specifically, we propose a denoising Vision Transformer (ViT), which is composed of multiple denoising blocks. In the denoising block, template and search embeddings are projected into every denoising block as conditions. A denoising block is responsible for removing the noise in a predicted bounding box, and multiple stacked denoising blocks cooperate to accomplish the whole denoising process. Subsequently, weutilize image features and trajectory information to refine the denoised bounding box. Besides, we also utilize trajectory memory and visual memory to improve tracking stability. Experimental results validate the effectiveness of our approach, achieving competitive performance on several challenging datasets. The proposed in-model latent denoising tracker achieve real-time speed, rendering denoising learning applicable in the visual object tracking community.

Generative Models · Reasoning

Shangzi Xue, Zhenya Huang, Jiayu Liu, Xin Lin, Yuting Ning, Binbin Jin, Xin Li, Qi Liu

In this paper, we introduce DeAR (_Decompose-Analyze-Rethink_), a framework that iteratively builds a reasoning tree to tackle intricate problems within a single large language model (LLM). Unlike approaches that extend or search for rationales, DeAR is featured by 1) adopting a tree-based question decomposition manner to plan the organization of rationales, which mimics the logical planning inherentin human cognition; 2) globally updating the rationales at each reasoning step through natural language feedback. Specifically, the _Decompose_ stage decomposes the question into simpler sub-questions, storing them as new nodes; the _Analyze_ stage generates and self-checks rationales for sub-questions at each node evel; and the _Rethink_ stage updates parent-node rationales based on feedback from their child nodes. By generating and updating the reasoning process from a more global perspective, DeAR constructs more adaptive and accurate logical structures for complex problems, facilitating timely error correction compared to rationale-extension and search-based approaches such as Tree-of-Thoughts (ToT) and Graph-of-Thoughts (GoT). We conduct extensive experiments on three reasoning benchmarks, including ScienceQA, StrategyQA, and GSM8K, which cover a variety of reasoning tasks, demonstrating that our approach significantly reduces logical errors and enhances performance across various LLMs. Furthermore, we validate that DeAR is an efficient method that achieves a superior trade-off between accuracy and reasoning time compared to ToT and GoT.

Computer Vision

Xizhou Zhu, Xue Yang, Zhaokai Wang, Hao Li, Wenhan Dou, Junqi Ge, Lewei Lu, Yu Qiao, Jifeng Dai

Image pyramids are commonly used in modern computer vision tasks to obtain multi-scale features for precise understanding of images. However, image pyramids process multiple resolutions of images using the same large-scale model, which requires significant computational cost. To overcome this issue, we propose a novel network architecture known as the Parameter-Inverted Image Pyramid Networks (PIIP). Our core idea is to use models with different parameter sizes to process different resolution levels of the image pyramid, thereby balancing computational efficiency and performance. Specifically, the input to PIIP is a set of multi-scale images, where higher resolution images are processed by smaller networks. We further propose a feature interaction mechanism to allow features of different resolutions to complement each other and effectively integrate information from different spatial scales. Extensive experiments demonstrate that the PIIP achieves superior performance in tasks such as object detection, segmentation, and image classification, compared to traditional image pyramid methods and single-branch networks, while reducing computational cost. Notably, when applying our method on a large-scale vision foundation model InternViT-6B, we improve its performance by 1\%-2\% on detection and segmentation with only 40\%-60\% of the original computation. These results validate the effectiveness of the PIIP approach and provide a new technical direction for future vision computing tasks.

Generative Models · New Approaches

Avelina Hadji-Kyriacou, Ognjen Arandjelovic

Pre-trained Language Models (LMs) exhibit strong zero-shot and in-context learning capabilities; however, their behaviors are often difficult to control. By utilizing Reinforcement Learning from Human Feedback (RLHF), it is possible to fine-tune unsupervised LMs to follow instructions and produce outputs that reflect human preferences. Despite its benefits, RLHF has been shown to potentially harm a language model's reasoning capabilities and introduce artifacts such as hallucinations where the model may fabricate facts. To address this issue we introduce Direct Preference Heads (DPH), a fine-tuning framework that enables LMs to learn human preference signals through an auxiliary reward head without directly affecting the output distribution of the language modeling head. We perform a theoretical analysis of our objective function and find strong ties to Conservative Direct Preference Optimization (cDPO). Finally we evaluate our models on GLUE, RACE, and the GPT4All evaluation suite and demonstrate that our method produces models which achieve higher scores than those fine-tuned with Supervised Fine-Tuning (SFT) or Direct Preference Optimization (DPO) alone.

Theory · Statistics

Junghyun Lee, Se-Young Yun, Kwang-Sung Jun

We present a unified likelihood ratio-based confidence sequence (CS) for *any* (self-concordant) generalized linear model (GLM) that is guaranteed to be convex and numerically tight. We show that this is on par or improves upon known CSs for various GLMs, including Gaussian, Bernoulli, and Poisson. In particular, for the first time, our CS for Bernoulli has a $\mathrm{poly}(S)$-free radius where $S$ is the norm of the unknown parameter. Our first technical novelty is its derivation, which utilizes a time-uniform PAC-Bayesian bound with a uniform prior/posterior, despite the latter being a rather unpopular choice for deriving CSs. As a direct application of our new CS, we propose a simple and natural optimistic algorithm called **OFUGLB**, applicable to *any* generalized linear bandits (**GLB**; Filippi et al. (2010)). Our analysis shows that the celebrated optimistic approach simultaneously attains state-of-the-art regrets for various self-concordant (not necessarily bounded) **GLB**s, and even $\mathrm{poly}(S)$-free for bounded **GLB**s, including logistic bandits. The regret analysis, our second technical novelty, follows from combining our new CS with a new proof technique that completely avoids the previously widely used self-concordant control lemma (Faury et al., 2020, Lemma 9). Numerically, **OFUGLB** outperforms or is at par with prior algorithms for logistic bandits.

Learning Theory

Jake Soloff, Rina Barber, Rebecca Willett

We propose a new framework for algorithmic stability in the context of multiclass classification. In practice, classification algorithms often operate by first assigning a continuous score (for instance, an estimated probability) to each possible label, then taking the maximizer---i.e., selecting the class that has the highest score. A drawback of this type of approach is that it is inherently unstable, meaning that it is very sensitive to slight perturbations of the training data, since taking the maximizer is discontinuous. Motivated by this challenge, we propose a pipeline for constructing stable classifiers from data, using bagging (i.e., resampling and averaging) to produce stable continuous scores, and then using a stable relaxation of argmax, which we call the "inflated argmax", to convert these scores to a set of candidate labels. The resulting stability guarantee places no distributional assumptions on the data, does not depend on the number of classes or dimensionality of the covariates, and holds for any base classifier. Using a common benchmark data set, we demonstrate that the inflated argmax provides necessary protection against unstable classifiers, without loss of accuracy.

Generative Models

Jingwei Zhao, Gus Xia, Ziyu Wang, Ye Wang

In the realm of music AI, arranging rich and structured multi-track accompaniments from a simple lead sheet presents significant challenges. Such challenges include maintaining track cohesion, ensuring long-term coherence, and optimizing computational efficiency. In this paper, we introduce a novel system that leverages prior modelling over disentangled style factors to address these challenges. Our method presents a two-stage process: initially, a piano arrangement is derived from the lead sheet by retrieving piano texture styles; subsequently, a multi-track orchestration is generated by infusing orchestral function styles into the piano arrangement. Our key design is the use of vector quantization and a unique multi-stream Transformer to model the long-term flow of the orchestration style, which enables flexible, controllable, and structured music generation. Experiments show that by factorizing the arrangement task into interpretable sub-stages, our approach enhances generative capacity while improving efficiency. Additionally, our system supports a variety of music genres and provides style control at different composition hierarchies. We further show that our system achieves superior coherence, structure, and overall arrangement quality compared to existing baselines.

Trustworthy Machine Learning

Edwige Cyffers, Muni Sreenivas Pydi, Jamal Atif, Olivier Cappé

Performative learning addresses the increasingly pervasive situations in which algorithmic decisions may induce changes in the data distribution as a consequence of their public deployment. We propose a novel view in which these performative effects are modelled as push forward measures. This general framework encompasses existing models and enables novel performative gradient estimation methods, leading to more efficient and scalable learning strategies. For distribution shifts, unlike previous models which require full specification of the data distribution, we only assume knowledge of the shift operator that represents the performative changes. This approach can also be integrated into various change-of-variable-based models, such as VAEs or normalizing flows. Focusing on classification with a linear-in-parameters performative effect, we prove the convexity of the performative risk under a new set of assumptions. Notably, we do not limit the strength of performative effects but rather their direction, requiring only that classification becomes harder when deploying more accurate models. In this case, we also establish a connection with adversarially robust classification by reformulating the performative risk as a min-max variational problem. Finally, we illustrate our approach on synthetic and real datasets.