NeurIPS 2024 Papers

Spectral methods are widely used to estimate eigenvectors of a low-rank signal matrix subject to noise. These methods use the leading eigenspace of an observed matrix to estimate this low-rank signal. Typically, the entrywise estimation error of these methods depends on the coherence of the low-rank signal matrix with respect to the standard basis. In this work, we present a novel method for eigenvector estimation that avoids this dependence on coherence. Assuming a rank-one signal matrix, under mild technical conditions, the entrywise estimation error of our method provably has no dependence on the coherence under Gaussian noise (i.e., in the spiked Wigner model), and achieves the optimal estimation rate up to logarithmic factors. Simulations demonstrate that our method performs well under non-Gaussian noise and that an extension of our method to the case of a rank-$r$ signal matrix has little to no dependence on the coherence. In addition, we derive new metric entropy bounds for rank-$r$ singular subspaces under $\ell_{2,\infty}$ distance, which may be of independent interest. We use these new bounds to improve the best known lower bound for rank-$r$ eigenspace estimation under $\ell_{2,\infty}$ distance.

Neural Radiance Fields (NeRFs) have shown remarkable performances in producing novel-view images from high-quality scene images. However, hand-held low-light photography challenges NeRFs as the captured images may simultaneously suffer from low visibility, noise, and camera shakes. While existing NeRF methods may handle either low light or motion, directly combining them or incorporating additional image-based enhancement methods does not work as these degradation factors are highly coupled. We observe that noise in low-light images is always sharp regardless of camera shakes, which implies an implicit order of these degradation factors within the image formation process. This inspires us to explore such an order to decouple and remove these degradation factors while training the NeRF. To this end, we propose in this paper a novel model, named LuSh-NeRF, which can reconstruct a clean and sharp NeRF from a group of hand-held low-light images. The key idea of LuSh-NeRF is to sequentially model noise and blur in the images via multi-view feature consistency and frequency information of NeRF, respectively. Specifically, LuSh-NeRF includes a novel Scene-Noise Decomposition (SND) module for decoupling the noise from the scene representation and a novel Camera Trajectory Prediction (CTP) module for the estimation of camera motions based on low-frequency scene information. To facilitate training and evaluations, we construct a new dataset containing both synthetic and real images. Experiments show that LuSh-NeRF outperforms existing approaches. Our code and dataset can be found here: https://github.com/quzefan/LuSh-NeRF.

While ensembling deep neural networks has shown promise in improving generalization performance, scaling current ensemble methods for large models remains challenging. Given that recent progress in deep learning is largely driven by the scale, exemplified by the widespread adoption of large-scale neural network architectures, scalability emerges an increasingly critical issue for machine learning algorithms in the era of large-scale models. In this work, we first showcase the potential of low precision ensembling, where ensemble members are derived from a single model within low precision number systems in a training-free manner. Our empirical analysis demonstrates the effectiveness of our proposed low precision ensembling method compared to existing ensemble approaches.

A central aim in computational neuroscience is to relate the activity of large populations of neurons to an underlying dynamical system. Models of these neural dynamics should ideally be both interpretable and fit the observed data well. Low-rank recurrent neural networks (RNNs) exhibit such interpretability by having tractable dynamics. However, it is unclear how to best fit low-rank RNNs to data consisting of noisy observations of an underlying stochastic system. Here, we propose to fit stochastic low-rank RNNs with variational sequential Monte Carlo methods. We validate our method on several datasets consisting of both continuous and spiking neural data, where we obtain lower dimensional latent dynamics than current state of the art methods. Additionally, for low-rank models with piecewise linear nonlinearities, we show how to efficiently identify all fixed points in polynomial rather than exponential cost in the number of units, making analysis of the inferred dynamics tractable for large RNNs. Our method both elucidates the dynamical systems underlying experimental recordings and provides a generative model whose trajectories match observed variability.

A common strategy for Parameter-Efficient Fine-Tuning (PEFT) of pre-trained Vision Transformers (ViTs) involves adapting the model to downstream tasks by learning a low-rank adaptation matrix. This matrix is decomposed into a product of down-projection and up-projection matrices, with the bottleneck dimensionality being crucial for reducing the number of learnable parameters, as exemplified by prevalent methods like LoRA and Adapter. However, these low-rank strategies typically employ a fixed bottleneck dimensionality, which limits their flexibility in handling layer-wise variations. To address this limitation, we propose a novel PEFT approach inspired by Singular Value Decomposition (SVD) for representing the adaptation matrix. SVD decomposes a matrix into the product of a left unitary matrix, a diagonal matrix of scaling values, and a right unitary matrix. We utilize Householder transformations to construct orthogonal matrices that efficiently mimic the unitary matrices, requiring only a vector. The diagonal values are learned in a layer-wise manner, allowing them to flexibly capture the unique properties of each layer. This approach enables the generation of adaptation matrices with varying ranks across different layers, providing greater flexibility in adapting pre-trained models. Experiments on standard downstream vision tasks demonstrate that our method achieves promising fine-tuning performance.

Parameter-efficient fine-tuning (PEFT) is an effective method for adapting pre-trained vision models to downstream tasks by tuning a small subset of parameters. Among PEFT methods, sparse tuning achieves superior performance by only adjusting the weights most relevant to downstream tasks, rather than densely tuning the whole weight matrix. However, this performance improvement has been accompanied by increases in memory usage, which stems from two factors, i.e., the storage of the whole weight matrix as learnable parameters in the optimizer and the additional storage of tunable weight indexes. In this paper, we propose a method named SNELL (Sparse tuning with kerNELized LoRA) for sparse tuning with low memory usage. To achieve low memory usage, SNELL decomposes the tunable matrix for sparsification into two learnable low-rank matrices, saving from the costly storage of the whole original matrix. A competition-based sparsification mechanism is further proposed to avoid the storage of tunable weight indexes. To maintain the effectiveness of sparse tuning with low-rank matrices, we extend the low-rank decomposition by applying nonlinear kernel functions to the whole-matrix merging. Consequently, we gain an increase in the rank of the merged matrix, enhancing the ability of SNELL in adapting the pre-trained models to downstream tasks. Extensive experiments on multiple downstream tasks show that SNELL achieves state-of-the-art performance with low memory usage, endowing PEFT with sparse tuning to large-scale models. Codes are available at https://github.com/ssfgunner/SNELL.

Unsupervised Domain Adaptation has been an efficient approach to transferring the semantic segmentation model across data distributions. Meanwhile, the recent Open-vocabulary Semantic Scene understanding based on large-scale vision language models is effective in open-set settings because it can learn diverse concepts and categories. However, these prior methods fail to generalize across different camera views due to the lack of cross-view geometric modeling. At present, there are limited studies analyzing cross-view learning. To address this problem, we introduce a novel Unsupervised Cross-view Adaptation Learning approach to modeling the geometric structural change across views in Semantic Scene Understanding. First, we introduce a novel Cross-view Geometric Constraint on Unpaired Data to model structural changes in images and segmentation masks across cameras. Second, we present a new Geodesic Flow-based Correlation Metric to efficiently measure the geometric structural changes across camera views. Third, we introduce a novel view-condition prompting mechanism to enhance the view-information modeling of the open-vocabulary segmentation network in cross-view adaptation learning. The experiments on different cross-view adaptation benchmarks have shown the effectiveness of our approach in cross-view modeling, demonstrating that we achieve State-of-the-Art (SOTA) performance compared to prior unsupervised domain adaptation and open-vocabulary semantic segmentation methods.

Generative modelling paradigms based on denoising diffusion processes have emerged as a leading candidate for conditional sampling in inverse problems. In many real-world applications, we often have access to large, expensively trained unconditional diffusion models, which we aim to exploit for improving conditional sampling. Most recent approaches are motivated heuristically and lack a unifying framework, obscuring connections between them. Further, they often suffer from issues such as being very sensitive to hyperparameters, being expensive to train or needing access to weights hidden behind a closed API. In this work, we unify conditional training and sampling using the mathematically well-understood Doob's h-transform. This new perspective allows us to unify many existing methods under a common umbrella. Under this framework, we propose DEFT (Doob's h-transform Efficient FineTuning), a new approach for conditional generation that simply fine-tunes a very small network to quickly learn the conditional $h$-transform, while keeping the larger unconditional network unchanged. DEFT is much faster than existing baselines while achieving state-of-the-art performance across a variety of linear and non-linear benchmarks. On image reconstruction tasks, we achieve speedups of up to 1.6$\times$, while having the best perceptual quality on natural images and reconstruction performance on medical images. Further, we also provide initial experiments on protein motif scaffolding and outperform reconstruction guidance methods.

Low-bit quantization has become widespread for compressing image super-resolution (SR) models for edge deployment, which allows advanced SR models to enjoy compact low-bit parameters and efficient integer/bitwise constructions for storage compression and inference acceleration, respectively. However, it is notorious that low-bit quantization degrades the accuracy of SR models compared to their full-precision (FP) counterparts. Despite several efforts to alleviate the degradation, the transformer-based SR model still suffers severe degradation due to its distinctive activation distribution. In this work, we present a dual-stage low-bit post-training quantization (PTQ) method for image super-resolution, namely 2DQuant, which achieves efficient and accurate SR under low-bit quantization. The proposed method first investigates the weight and activation and finds that the distribution is characterized by coexisting symmetry and asymmetry, long tails. Specifically, we propose Distribution-Oriented Bound Initialization (DOBI), using different searching strategies to search a coarse bound for quantizers. To obtain refined quantizer parameters, we further propose Distillation Quantization Calibration (DQC), which employs a distillation approach to make the quantized model learn from its FP counterpart. Through extensive experiments on different bits and scaling factors, the performance of DOBI can reach the state-of-the-art (SOTA) while after stage two, our method surpasses existing PTQ in both metrics and visual effects. 2DQuant gains an increase in PSNR as high as 4.52dB on Set5 (x2) compared with SOTA when quantized to 2-bit and enjoys a 3.60x compression ratio and 5.08x speedup ratio. The code and models are available at https://github.com/Kai-Liu001/2DQuant.

Standardized benchmarks drive progress in machine learning. However, with repeated testing, the risk of overfitting grows as algorithms over-exploit benchmark idiosyncrasies. In our work, we seek to mitigate this challenge by compiling \textit{ever-expanding} large-scale benchmarks called \textit{Lifelong Benchmarks}. As exemplars of our approach, we create \textit{Lifelong-CIFAR10} and \textit{Lifelong-ImageNet}, containing (for now) 1.69M and 1.98M test samples, respectively. While reducing overfitting, lifelong benchmarks introduce a key challenge: the high cost of evaluating a growing number of models across an ever-expanding sample set. To address this challenge, we also introduce an efficient evaluation framework: \textit{Sort \& Search (S\&S)}, which reuses previously evaluated models by leveraging dynamic programming algorithms to selectively rank and sub-select test samples, enabling cost-effective lifelong benchmarking. Extensive empirical evaluations across $\sim$31,000 models demonstrate that \textit{S\&S} achieves highly-efficient approximate accuracy measurement, reducing compute cost from 180 GPU days to 5 GPU hours ($\sim$1000x reduction) on a single A100 GPU, with low approximation error. As such, lifelong benchmarks offer a robust, practical solution to the ``benchmark exhaustion'' problem.

Matrix factorization models have been extensively studied as a valuable test-bed for understanding the implicit biases of overparameterized models. Although both low nuclear norm and low rank regularization have been studied for these models, a unified understanding of when, how, and why they achieve different implicit regularization effects remains elusive. In this work, we systematically investigate the implicit regularization of matrix factorization for solving matrix completion problems. We empirically discover that the connectivity of observed data plays a key role in the implicit bias, with a transition from low nuclear norm to low rank as data shifts from disconnected to connected with increased observations. We identify a hierarchy of intrinsic invariant manifolds in the loss landscape that guide the training trajectory to evolve from low-rank to higher-rank solutions. Based on this finding, we theoretically characterize the training trajectory as following the hierarchical invariant manifold traversal process, generalizing the characterization of Li et al.(2020) to include the disconnected case. Furthermore, we establish conditions that guarantee minimum nuclear norm, closely aligning with our experimental findings, and we provide a dynamics characterization condition for ensuring minimum rank. Our work reveals the intricate interplay between data connectivity, training dynamics, and implicit regularization in matrix factorization models.

Data point selection (DPS) is becoming a critical topic in deep learning due to the ease of acquiring uncurated training data compared to the difficulty of obtaining curated or processed data. Existing approaches to DPS are predominantly based on a bi-level optimisation (BLO) formulation, which is demanding in terms of memory and computation, and exhibits some theoretical defects regarding minibatches. Thus, we propose a novel Bayesian approach to DPS. We view the DPS problem as posterior inference in a novel Bayesian model where the posterior distributions of the instance-wise weights and the main neural network parameters are inferred under a reasonable prior and likelihood model. We employ stochastic gradient Langevin MCMC sampling to learn the main network and instance-wise weights jointly, ensuring convergence even with minibatches. Our update equation is comparable to the widely used SGD and much more efficient than existing BLO-based methods. Through controlled experiments in both the vision and language domains, we present the proof-of-concept. Additionally, we demonstrate that our method scales effectively to large language models and facilitates automated per-task optimization for instruction fine-tuning datasets.

Minimum Bayes Risk (MBR) decoding is a powerful decoding strategy widely used for text generation tasks but its quadratic computational complexity limits its practical application. This paper presents a novel approach for approximating MBR decoding using matrix completion techniques, focusing on a machine translation task. We formulate MBR decoding as a matrix completion problem, where the utility metric scores between candidate hypotheses and reference translations form a low-rank matrix. First we empirically show that the scores matrices indeed have a low-rank structure. Then we exploit this by only computing a random subset of the scores and efficiently recover the missing entries in the matrix by applying the Alternating Least Squares (ALS) algorithm, thereby enabling fast approximation of the MBR decoding process. Our experimental results on machine translation tasks demonstrate that the proposed method requires 1/16 utility metric computations compared to the vanilla MBR decoding while achieving equal translation quality measured by COMET on the WMT22 dataset (en<>de, en<>ru). We also benchmark our method against other approximation methods and we show significant gains in quality.

The increasing size of neural networks has led to a growing demand for methods of efficient finetuning. Recently, an orthogonal finetuning paradigm was introduced that uses orthogonal matrices for adapting the weights of a pretrained model. In this paper, we introduce a new class of structured matrices, which unifies and generalizes structured classes from previous works. We examine properties of this class and build a structured orthogonal parametrization upon it. We then use this parametrization to modify the orthogonal finetuning framework, improving parameter efficiency. We empirically validate our method on different domains, including adapting of text-to-image diffusion models and downstream task finetuning in language modeling. Additionally, we adapt our construction for orthogonal convolutions and conduct experiments with 1-Lipschitz neural networks.

Zero-shot reinforcement learning (RL) promises to provide agents that can perform _any_ task in an environment after an offline, reward-free pre-training phase. Methods leveraging successor measures and successor features have shown strong performance in this setting, but require access to large heterogenous datasets for pre-training which cannot be expected for most real problems. Here, we explore how the performance of zero-shot RL methods degrades when trained on small homogeneous datasets, and propose fixes inspired by _conservatism_, a well-established feature of performant single-task offline RL algorithms. We evaluate our proposals across various datasets, domains and tasks, and show that conservative zero-shot RL algorithms outperform their non-conservative counterparts on low quality datasets, and perform no worse on high quality datasets. Somewhat surprisingly, our proposals also outperform baselines that get to see the task during training. Our code is available via the project page https://enjeeneer.io/projects/zero-shot-rl/.

We study the problem of learning mixtures of Gaussians with approximate differential privacy. We prove that roughly $kd^2 + k^{1.5} d^{1.75} + k^2 d$ samples suffice to learn a mixture of $k$ arbitrary $d$-dimensional Gaussians up to low total variation distance, with differential privacy. Our work improves over the previous best result (which required roughly $k^2 d^4$ samples) and is provably optimal when $d$ is much larger than $k^2$. Moreover, we give the first optimal bound for privately learning mixtures of $k$ univariate (i.e., $1$-dimensional) Gaussians. Importantly, we show that the sample complexity for learning mixtures of univariate Gaussians is linear in the number of components $k$, whereas the previous best sample complexity was quadratic in $k$. Our algorithms utilize various techniques, including the inverse sensitivity mechanism, sample compression for distributions, and methods for bounding volumes of sumsets.

Low Rank Adaptation (LoRA) has gained massive attention in the recent generative AI research. One of the main advantages of LoRA is its ability to be fused with pretrained models, adding no overhead during inference. However, from a mobile deployment standpoint, we can either avoid inference overhead in the fused mode but lose the ability to switch adapters rapidly, or suffer significant (up to 30% higher) inference latency while enabling rapid switching in the unfused mode. LoRA also exhibits concept-loss when multiple adapters are used concurrently. In this paper, we propose Sparse High Rank Adapters (SHiRA), a new paradigm which incurs no inference overhead, enables rapid switching, and significantly reduces concept-loss. Specifically, SHiRA can be trained by directly tuning only 1-2% of the base model weights while leaving others unchanged. This results in a highly sparse adapter which can be switched directly in the fused mode. We further provide theoretical and empirical insights on how high sparsity in SHiRA can aid multi-adapter fusion by reducing concept loss. Our extensive experiments on LVMs and LLMs demonstrate that finetuning only a small fraction of the parameters in the base model significantly outperforms LoRA while enabling both rapid switching and multi-adapter fusion. Finally, we provide a latency- and memory-efficient SHiRA implementation based on Parameter-Efficient Finetuning (PEFT) Library which trains at nearly the same speed as LoRA while consuming up to 16% lower peak GPU memory, thus making SHiRA easy to adopt for practical use cases. To demonstrate rapid switching benefits during inference, we show that loading SHiRA on a base model can be 5x-16x faster than LoRA fusion on a CPU.

We consider regret minimization in low-rank MDPs with fixed transition and adversarial losses. Previous work has investigated this problem under either full-information loss feedback with unknown transitions (Zhao et al., 2024), or bandit loss feedback with known transitions (Foster et al., 2022). First, we improve the $poly(d, A, H)T^{5/6}$ regret bound of Zhao et al. (2024) to $poly(d, A, H)T^{2/3}$ for the full-information unknown transition setting, where $d$ is the rank of the transitions, $A$ is the number of actions, $H$ is the horizon length, and $T$ is the number of episodes. Next, we initiate the study on the setting with bandit loss feedback and unknown transitions. Assuming that the loss has a linear structure, we propose both model-based and model-free algorithms achieving $poly(d, A, H)T^{2/3}$ regret, though they are computationally inefficient. We also propose oracle-efficient model-free algorithms with $poly(d, A, H)T^{4/5}$ regret. We show that the linear structure is necessary for the bandit case—without structure on the reward function, the regret has to scale polynomially with the number of states. This is contrary to the full-information case (Zhao et al., 2024), where the regret can be independent of the number of states even for unstructured reward functions.

To parameter-efficiently fine-tune (PEFT) large language models (LLMs), the low-rank adaptation (LoRA) method approximates the model changes $\Delta W \in \mathbb{R}^{m \times n}$ through the product of two matrices $A \in \mathbb{R}^{m \times r}$ and $B \in \mathbb{R}^{r \times n}$, where $r \ll \min(m, n)$, $A$ is initialized with Gaussian noise, and $B$ with zeros. LoRA **freezes the original model $W$** and **updates the "Noise \& Zero" adapter**, which may lead to slow convergence. To overcome this limitation, we introduce **P**r**i**ncipal **S**ingular values and **S**ingular vectors **A**daptation (PiSSA). PiSSA shares the same architecture as LoRA, but initializes the adaptor matrices $A$ and $B$ with the principal components of the original matrix $W$, and put the remaining components into a residual matrix $W^{res} \in \mathbb{R}^{m \times n}$ which is frozen during fine-tuning. Compared to LoRA, PiSSA **updates the principal components** while **freezing the "residual" parts**, allowing faster convergence and enhanced performance. Comparative experiments of PiSSA and LoRA across 11 different models, ranging from 184M to 70B, encompassing 5 NLG and 8 NLU tasks, reveal that PiSSA consistently outperforms LoRA under identical experimental setups. On the GSM8K benchmark, Gemma-7B fine-tuned with PiSSA achieves an accuracy of 77.7\%, surpassing LoRA's 74.53\% by 3.25\%. Due to the same architecture, PiSSA is also compatible with quantization to further reduce the memory requirement of fine-tuning. Compared to QLoRA, QPiSSA (PiSSA with 4-bit quantization) exhibits smaller quantization errors in the initial stages. Fine-tuning LLaMA-3-70B on GSM8K, QPiSSA attains an accuracy of 86.05\%, exceeding the performances of QLoRA at 81.73\%. Leveraging a fast SVD technique, PiSSA can be initialized in only a few seconds, presenting a negligible cost for transitioning from LoRA to PiSSA.