NeurIPS 2023 Papers

Despite the demonstrated empirical efficacy of prompt tuning to adapt a pretrained language model for a new task, the theoretical underpinnings of the difference between "tuning parameters before the input" against "the tuning of model weights" are limited. We thus take one of the first steps to understand the role of soft-prompt tuning for transformer-based architectures. By considering a general purpose architecture, we analyze prompt tuning from the lens of both: universal approximation and limitations with finite-depth fixed-weight pretrained transformers for continuous-valued functions. Our universality result guarantees the existence of a strong transformer with a prompt to approximate any sequence-to-sequence function in the set of Lipschitz functions. The limitations of prompt tuning for limited-depth transformers are first proved by constructing a set of datasets, that cannot be memorized by a prompt of any length for a given single encoder layer. We also provide a lower bound on the required number of tunable prompt parameters and compare the result with the number of parameters required for a low-rank update (based on LoRA) for a single-layer setting. We finally extend our analysis to multi-layer settings by providing sufficient conditions under which the transformer can at best learn datasets from invertible functions only. Our theoretical claims are also corroborated by empirical results.

Adapting models deployed to test distributions can mitigate the performance degradation caused by distribution shifts. However, privacy concerns may render model parameters inaccessible. One promising approach involves utilizing zeroth-order optimization (ZOO) to train a data adaptor to adapt the test data to fit the deployed models. Nevertheless, the data adaptor trained with ZOO typically brings restricted improvements due to the potential corruption of data features caused by the data adaptor. To address this issue, we revisit ZOO in the context of test-time data adaptation. We find that the issue directly stems from the unreliable estimation of the gradients used to optimize the data adaptor, which is inherently due to the unreliable nature of the pseudo-labels assigned to the test data. Based on this observation, we propose pseudo-label-robust data adaptation (SODA) to improve the performance of data adaptation. Specifically, SODA leverages high-confidence predicted labels as reliable labels to optimize the data adaptor with ZOO for label prediction. For data with low-confidence predictions, SODA encourages the adaptor to preserve data information to mitigate data corruption. Empirical results indicate that SODA can significantly enhance the performance of deployed models in the presence of distribution shifts without requiring access to model parameters.

Knowledge distillation is commonly used to compress an ensemble of models into a single model. In this work we study the problem of progressive ensemble distillation: Given a large, pretrained teacher model , we seek to decompose the model into an ensemble of smaller, low-inference cost student models . The resulting ensemble allows for flexibly tuning accuracy vs. inference cost, which can be useful for a multitude of applications in efficient inference. Our method, B-DISTIL, uses a boosting procedure that allows function composition based aggregation rules to construct expressive ensembles with similar performance as using much smaller student models. We demonstrate the effectiveness of B-DISTIL by decomposing pretrained models across a variety of image, speech, and sensor datasets. Our method comes with strong theoretical guarantees in terms of convergence as well as generalization.

Neurons in early sensory areas rapidly adapt to changing sensory statistics, both by normalizing the variance of their individual responses and by reducing correlations between their responses. Together, these transformations may be viewed as an adaptive form of statistical whitening. Existing mechanistic models of adaptive whitening exclusively use either synaptic plasticity or gain modulation as the biological substrate for adaptation; however, on their own, each of these models has significant limitations. In this work, we unify these approaches in a normative multi-timescale mechanistic model that adaptively whitens its responses with complementary computational roles for synaptic plasticity and gain modulation. Gains are modified on a fast timescale to adapt to the current statistical context, whereas synapses are modified on a slow timescale to match structural properties of the input statistics that are invariant across contexts. Our model is derived from a novel multi-timescale whitening objective that factorizes the inverse whitening matrix into basis vectors, which correspond to synaptic weights, and a diagonal matrix, which corresponds to neuronal gains. We test our model on synthetic and natural datasets and find that the synapses learn optimal configurations over long timescales that enable adaptive whitening on short timescales using gain modulation.

Model reparametrization, which follows the change-of-variable rule of calculus, is a popular way to improve the training of neural nets. But it can also be problematic since it can induce inconsistencies in, e.g., Hessian-based flatness measures, optimization trajectories, and modes of probability densities. This complicates downstream analyses: e.g. one cannot definitively relate flatness with generalization since arbitrary reparametrization changes their relationship. In this work, we study the invariance of neural nets under reparametrization from the perspective of Riemannian geometry. From this point of view, invariance is an inherent property of any neural net if one explicitly represents the metric and uses the correct associated transformation rules. This is important since although the metric is always present, it is often implicitly assumed as identity, and thus dropped from the notation, then lost under reparametrization. We discuss implications for measuring the flatness of minima, optimization, and for probability-density maximization. Finally, we explore some interesting directions where invariance is useful.

Combinatorial Optimization underpins many real-world applications and yet, designing performant algorithms to solve these complex, typically NP-hard, problems remains a significant research challenge. Reinforcement Learning (RL) provides a versatile framework for designing heuristics across a broad spectrum of problem domains. However, despite notable progress, RL has not yet supplanted industrial solvers as the go-to solution. Current approaches emphasize pre-training heuristics that construct solutions, but often rely on search procedures with limited variance, such as stochastically sampling numerous solutions from a single policy, or employing computationally expensive fine-tuning of the policy on individual problem instances. Building on the intuition that performant search at inference time should be anticipated during pre-training, we propose COMPASS, a novel RL approach that parameterizes a distribution of diverse and specialized policies conditioned on a continuous latent space. We evaluate COMPASS across three canonical problems - Travelling Salesman, Capacitated Vehicle Routing, and Job-Shop Scheduling - and demonstrate that our search strategy (i) outperforms state-of-the-art approaches in 9 out of 11 standard benchmarking tasks and (ii) generalizes better, surpassing all other approaches on a set of 18 procedurally transformed instance distributions.

Selecting a suitable pretraining dataset is crucial for both general-domain (e.g., GPT-3) and domain-specific (e.g., Codex) language models (LMs). We formalize this problem as selecting a subset of a large raw unlabeled dataset to match a desired target distribution given unlabeled target samples. Due to the scale and dimensionality of the raw text data, existing methods use simple heuristics or require human experts to manually curate data. Instead, we extend the classic importance resampling approach used in low-dimensions for LM data selection. We propose Data Selection with Importance Resampling (DSIR), an efficient and scalable framework that estimates importance weights in a reduced feature space for tractability and selects data with importance resampling according to these weights. We instantiate the DSIR framework with hashed n-gram features for efficiency, enabling the selection of 100M documents from the full Pile dataset in 4.5 hours. To measure whether hashed n-gram features preserve the aspects of the data that are relevant to the target, we define KL reduction, a data metric that measures the proximity between the selected pretraining data and the target on some feature space. Across 8 data selection methods (including expert selection), KL reduction on hashed n-gram features highly correlates with average downstream accuracy (r=0.82). When selecting data for continued pretraining on a specific domain, DSIR performs comparably to expert curation across 8 target distributions. When pretraining general-domain models (target is Wikipedia and books), DSIR improves over random selection and heuristic filtering baselines by 2--2.5% on the GLUE benchmark.

Traditional multi-armed bandit (MAB) frameworks, predominantly examined under stochastic or adversarial settings, often overlook the temporal dynamics inherent in many real-world applications such as recommendation systems and online advertising. This paper introduces a novel non-stationary MAB framework that captures the temporal structure of these real-world dynamics through an auto-regressive (AR) reward structure. We propose an algorithm that integrates two key mechanisms: (i) an alternation mechanism adept at leveraging temporal dependencies to dynamically balance exploration and exploitation, and (ii) a restarting mechanism designed to discard out-of-date information. Our algorithm achieves a regret upper bound that nearly matches the lower bound, with regret measured against a robust dynamic benchmark. Finally, via a real-world case study on tourism demand prediction, we demonstrate both the efficacy of our algorithm and the broader applicability of our techniques to more complex, rapidly evolving time series.

Recently, growing interest has been aroused in extending the multimodal capability of large language models (LLMs), e.g., vision-language (VL) learning, which is regarded as the next milestone of artificial general intelligence. However, existing solutions are prohibitively expensive, which not only need to optimize excessive parameters, but also require another large-scale pre-training before VL instruction tuning. In this paper, we propose a novel and affordable solution for the effective VL adaption of LLMs, called Mixture-of-Modality Adaptation (MMA). Instead of using large neural networks to connect the image encoder and LLM, MMA adopts lightweight modules, i.e., adapters, to bridge the gap between LLMs and VL tasks, which also enables the joint optimization of the image and language models. Meanwhile, MMA is also equipped with a routing algorithm to help LLMs achieve an automatic shift between single- and multi-modal instructions without compromising their ability of natural language understanding. To validate MMA, we apply it to a recent LLM called LLaMA and term this formed large vision-language instructed model as LaVIN. To validate MMA and LaVIN, we conduct extensive experiments under two setups, namely multimodal science question answering and multimodal dialogue. The experimental results not only demonstrate the competitive performance and the superior training efficiency of LaVIN than existing multimodal LLMs, but also confirm its great potential as a general-purpose chatbot. More importantly, the actual expenditure of LaVIN is extremely cheap, e.g., only 1.4 training hours with 3.8M trainable parameters, greatly confirming the effectiveness of MMA. Our code is anonymously released at: https://anonymous.4open.science/r/LaVIN--1067.

We introduce new methods for 1) accelerating and 2) stabilizing training for large language-vision models. 1) For acceleration, we introduce SwitchBack, a linear layer for int8 quantized training which provides a speed-up of 13-25% while matching the performance of bfloat16 training within 0.1 percentage points for the 1B parameter CLIP ViT-Huge---the largest int8 training to date. Our main focus is int8 as GPU support for float8 is rare, though we also analyze float8 training through simulation. While SwitchBack proves effective for float8, we show that standard techniques are also successful if the network is trained and initialized so that large feature magnitudes are discouraged, which we accomplish via layer-scale initialized with zeros. 2) For stability, we analyze loss spikes and find they consistently occur 1-8 iterations after the squared gradients become under-estimated by their AdamW second moment estimator. As a result, we recommend an AdamW-Adafactor hybrid which avoids loss spikes when training a CLIP ViT-Huge model and outperforms gradient clipping at the scales we test.

Denoising diffusion generative models are capable of generating high-quality data, but suffers from the computation-costly generation process, due to a iterative noise estimation using full-precision networks. As an intuitive solution, quantization can significantly reduce the computational and memory consumption by low-bit parameters and operations. However, low-bit noise estimation networks in diffusion models (DMs) remain unexplored yet and perform much worse than the full-precision counterparts as observed in our experimental studies. In this paper, we first identify that the bottlenecks of low-bit quantized DMs come from a large distribution oscillation on activations and accumulated quantization error caused by the multi-step denoising process. To address these issues, we first develop a Timestep-aware Quantization (TaQ) method and a Noise-estimating Mimicking (NeM) scheme for low-bit quantized DMs (Q-DM) to effectively eliminate such oscillation and accumulated error respectively, leading to well-performed low-bit DMs. In this way, we propose an efficient Q-DM to calculate low-bit DMs by considering both training and inference process in the same framework. We evaluate our methods on popular DDPM and DDIM models. Extensive experimental results show that our method achieves a much better performance than the prior arts. For example, the 4-bit Q-DM theoretically accelerates the 1000-step DDPM by 7.8x and achieves a FID score of 5.17, on the unconditional CIFAR-10 dataset.

Matrices are exceptionally useful in various fields of study as they provide a convenient framework to organize and manipulate data in a structured manner. However, modern matrices can involve billions of elements, making their storage and processing quite demanding in terms of computational resources and memory usage. Although prohibitively large, such matrices are often approximately low rank. We propose an algorithm that exploits this structure to obtain a low rank decomposition of any matrix $\mathbf{A}$ as $\mathbf{A} \approx \mathbf{L}\mathbf{R}$, where $\mathbf{L}$ and $\mathbf{R}$ are the low rank factors. The total number of elements in $\mathbf{L}$ and $\mathbf{R}$ can be significantly less than that in $\mathbf{A}$. Furthermore, the entries of $\mathbf{L}$ and $\mathbf{R}$ are quantized to low precision formats -- compressing $\mathbf{A}$ by giving us a low rank and low precision factorization. Our algorithm first computes an approximate basis of the range space of $\mathbf{A}$ by randomly sketching its columns, followed by a quantization of the vectors constituting this basis. It then computes approximate projections of the columns of $\mathbf{A}$ onto this quantized basis. We derive upper bounds on the approximation error of our algorithm, and analyze the impact of target rank and quantization bit-budget. The tradeoff between compression ratio and approximation accuracy allows for flexibility in choosing these parameters based on specific application requirements. We empirically demonstrate the efficacy of our algorithm in image compression, nearest neighbor classification of image and text embeddings, and compressing the layers of LlaMa-$7$b. Our results illustrate that we can achieve compression ratios as aggressive as one bit per matrix coordinate, all while surpassing or maintaining the performance of traditional compression techniques.

Neural radiance field (NeRF) shows powerful performance in novel view synthesis and 3D geometry reconstruction, but it suffers from critical performance degradation when the number of known viewpoints is drastically reduced. Existing works attempt to overcome this problem by employing external priors, but their success is limited to certain types of scenes or datasets. Employing monocular depth estimation (MDE) networks, pretrained on large-scale RGB-D datasets, with powerful generalization capability may be a key to solving this problem: however, using MDE in conjunction with NeRF comes with a new set of challenges due to various ambiguity problems exhibited by monocular depths. In this light, we propose a novel framework, dubbed DäRF, that achieves robust NeRF reconstruction with a handful of real-world images by combining the strengths of NeRF and monocular depth estimation through online complementary training. Our framework imposes the MDE network's powerful geometry prior to NeRF representation at both seen and unseen viewpoints to enhance its robustness and coherence. In addition, we overcome the ambiguity problems of monocular depths through patch-wise scale-shift fitting and geometry distillation, which adapts the MDE network to produce depths aligned accurately with NeRF geometry. Experiments show our framework achieves state-of-the-art results both quantitatively and qualitatively, demonstrating consistent and reliable performance in both indoor and outdoor real-world datasets.

Multi-channel learning has gained significant attention in recent applications, where neural networks with t-product layers (t-NNs) have shown promising performance through novel feature mapping in the transformed domain. However, despite the practical success of t-NNs, the theoretical analysis of their generalization remains unexplored. We address this gap by deriving upper bounds on the generalization error of t-NNs in both standard and adversarial settings. Notably, it reveals that t-NNs compressed with exact transformed low-rank parameterization can achieve tighter adversarial generalization bounds compared to non-compressed models. While exact transformed low-rank weights are rare in practice, the analysis demonstrates that through adversarial training with gradient flow, highly over-parameterized t-NNs with the ReLU activation can be implicitly regularized towards a transformed low-rank parameterization under certain conditions. Moreover, this paper establishes sharp adversarial generalization bounds for t-NNs with approximately transformed low-rank weights. Our analysis highlights the potential of transformed low-rank parameterization in enhancing the robust generalization of t-NNs, offering valuable insights for further research and development.

Low-rank matrix factorization (LRMF) is a canonical problem in non-convex optimization, the objective function to be minimized is non-convex and even non-smooth, which makes the global convergence guarantee of gradient-based algorithm quite challenging. Recent work made a breakthrough on proving that standard gradient descent converges to the $\varepsilon$-global minima after $O( \frac{d \kappa^2}{\tau^2} {\rm ln} \frac{d \sigma_d}{\tau} + \frac{d \kappa^2}{\tau^2} {\rm ln} \frac{\sigma_d}{\varepsilon})$ iterations from small initialization with a very small learning rate (both are related to the small constant $\tau$). While the dependence of the convergence on the \textit{condition number} $\kappa$ and \textit{small learning rate} makes it not practical especially for ill-conditioned LRMF problem. In this paper, we show that precondition helps in accelerating the convergence and prove that the scaled gradient descent (ScaledGD) and its variant, alternating scaled gradient descent (AltScaledGD) converge to an $\varepsilon$-global minima after $O( {\rm ln} \frac{d}{\delta} + {\rm ln} \frac{d}{\varepsilon})$ iterations from general random initialization. Meanwhile, for small initialization as in gradient descent, both ScaledGD and AltScaledGD converge to $\varepsilon$-global minima after only $O({\rm ln} \frac{d}{\varepsilon})$ iterations. Furthermore, we prove that as a proximity to the alternating minimization, AltScaledGD converges faster than ScaledGD, its global convergence does not rely on small learning rate and small initialization, which certificates the advantages of AltScaledGD in LRMF.

We study lower bounds on adaptive sensing algorithms for recovering low rank matrices using linear measurements. Given an $n \times n$ matrix $A$, a general linear measurement $S(A)$, for an $n \times n$ matrix $S$, is just the inner product of $S$ and $A$, each treated as $n^2$-dimensional vectors. By performing as few linear measurements as possible on a rank-$r$ matrix $A$, we hope to construct a matrix $\hat{A}$ that satisfies $|A - \hat{A}|\_F^2 \le c |A|\_F^2$, for a small constant $c$. Here $|A|\_F$ denotes the Frobenius norm $(\sum_{i,j} A_{i,j}^2)^{1/2}$. It is commonly assumed that when measuring $A$ with $S$, the response is corrupted with an independent Gaussian random variable of mean $0$ and variance $\sigma^2$. Candès and Plan (IEEE Trans. Inform. Theory 2011) study non-adaptive algorithms for low rank matrix recovery using random linear measurements. They use the restricted isometry property (RIP) of Random Gaussian Matrices to give tractable algorithms to estimate $A$ from the measurements. At the edge of the noise level where recovery is information-theoretically feasible, it is known that their non-adaptive algorithms need to perform $\Omega(n^2)$ measurements, which amounts to reading the entire matrix. An important question is whether adaptivity helps in decreasing the overall number of measurements. While for the related problem of sparse recovery, adaptive algorithms have been extensively studied, as far as we are aware adaptive algorithms and lower bounds on them seem largely unexplored for matrix recovery. We show that any adaptive algorithm that uses $k$ linear measurements in each round and outputs an approximation as in (1) with probability $\ge 9/10$ must run for $t = \Omega(\log(n^2/k)/\log\log n)$ rounds. Our lower bound shows that any adaptive algorithm which uses $n^{2-\beta}$ ($\beta > 0$ is arbitrary constant) linear measurements in each round must run for $\Omega(\log n/\log\log n)$ rounds. Our techniques also readily extend to obtain lower bounds on adaptive algorithms for tensor recovery. Our hard distribution also allows us to give a measurement-vs-rounds trade-off for many sensing problems in numerical linear algebra, such as spectral norm low rank approximation, Frobenius norm low rank approximation, singular vector approximation, and more.

The nonconvex formulation of the matrix completion problem has received significant attention in recent years due to its affordable complexity compared to the convex formulation. Gradient Descent (GD) is a simple yet efficient baseline algorithm for solving nonconvex optimization problems. The success of GD has been witnessed in many different problems in both theory and practice when it is combined with random initialization. However, previous works on matrix completion require either careful initialization or regularizers to prove the convergence of GD. In this paper, we study the rank-1 symmetric matrix completion and prove that GD converges to the ground truth when small random initialization is used. We show that in a logarithmic number of iterations, the trajectory enters the region where local convergence occurs. We provide an upper bound on the initialization size that is sufficient to guarantee the convergence, and show that a larger initialization can be used as more samples are available. We observe that the implicit regularization effect of GD plays a critical role in the analysis, and for the entire trajectory, it prevents each entry from becoming much larger than the others.

We identify incremental learning dynamics in transformers, where the difference between trained and initial weights progressively increases in rank. We rigorously prove this occurs under the simplifying assumptions of diagonal weight matrices and small initialization. Our experiments support the theory and also show that phenomenon can occur in practice without the simplifying assumptions.

Generalizing policies across different domains with dynamics mismatch poses a significant challenge in reinforcement learning. For example, a robot learns the policy in a simulator, but when it is deployed in the real world, the dynamics of the environment may be different. Given the source and target domain with dynamics mismatch, we consider the online dynamics adaptation problem, in which case the agent can access sufficient source domain data while online interactions with the target domain are limited. Existing research has attempted to solve the problem from the dynamics discrepancy perspective. In this work, we reveal the limitations of these methods and explore the problem from the value difference perspective via a novel insight on the value consistency across domains. Specifically, we present the Value-Guided Data Filtering (VGDF) algorithm, which selectively shares transitions from the source domain based on the proximity of paired value targets across the two domains. Empirical results on various environments with kinematic and morphology shifts demonstrate that our method achieves superior performance compared to prior approaches.