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

Enneng Yang, Zhenyi Wang, Li Shen, Shiwei Liu, Guibing Guo, Xingwei Wang, Dacheng Tao

Multi-task learning (MTL) aims to empower a model to tackle multiple tasks simultaneously. A recent development known as task arithmetic has revealed that several models, each fine-tuned for distinct tasks, can be directly merged into a single model to execute MTL without necessitating a retraining process using the initial training data. Nevertheless, this direct addition of models often leads to a significant deterioration in the overall performance of the merged model. This decline occurs due to potential conflicts and intricate correlations among the multiple tasks. Consequently, the challenge emerges of how to merge pre-trained models more effectively without using their original training data. This paper introduces an innovative technique called Adaptive Model Merging (AdaMerging). This approach aims to autonomously learn the coefficients for model merging, either in a task-wise or layer-wise manner, without relying on the original training data. Specifically, our AdaMerging method operates as an automatic, unsupervised task arithmetic scheme. It leverages entropy minimization on unlabeled test samples from the multi-task setup as a surrogate objective function to iteratively refine the merging coefficients of the multiple models. Our experimental findings across eight tasks demonstrate the efficacy of the AdaMerging scheme we put forth. Compared to the current state-of-the-art (SOTA) task arithmetic merging scheme, AdaMerging showcases a remarkable 11\% improvement in performance. Notably, AdaMerging also exhibits superior generalization capabilities when applied to unseen downstream tasks. Furthermore, it displays a significantly enhanced robustness to data distribution shifts that may occur during the testing phase.

Optimization · Optimization and Learning under Uncertainty

Zhou Lu, Qiuyi (Richard) Zhang, Xinyi Chen, Fred Zhang, David Woodruff, Elad Hazan

Fast changing states or volatile environments pose a significant challenge to online optimization, which needs to perform rapid adaptation under limited observation. In this paper, we give query and regret optimal bandit algorithms under the strict notion of strongly adaptive regret, which measures the maximum regret over any contiguous interval $I$. Due to its worst-case nature, there is an almost-linear $\Omega(|I|^{1-\epsilon})$ regret lower bound, when only one query per round is allowed [Daniely el al, ICML 2015]. Surprisingly, with just two queries per round, we give Strongly Adaptive Bandit Learner (StABL) that achieves $\widetilde{O}(\sqrt{n|I|})$ adaptive regret for multi-armed bandits with $n$ arms. The bound is tight and cannot be improved in general. Our algorithm leverages a multiplicative update scheme of varying stepsizes and a carefully chosen observation distribution to control the variance. Furthermore, we extend our results and provide optimal algorithms in the bandit convex optimization setting. Finally, we empirically demonstrate the superior performance of our algorithms under volatile environments and for downstream tasks, such as algorithm selection for hyperparameter optimization.

Hansheng Xue, Vijini Mallawaarachchi, Lexing Xie, Vaibhav Rajan

Metagenomics studies genomic material derived from mixed microbial communities in diverse environments, holding considerable significance for both human health and environmental sustainability. Metagenomic binning refers to the clustering of genomic subsequences obtained from high-throughput DNA sequencing into distinct bins, each representing a constituent organism within the community. Mainstream binning methods primarily rely on sequence features such as composition and abundance, making them unable to effectively handle sequences shorter than 1,000 bp and inherent noise within sequences. Several binning tools have emerged, aiming to enhance binning outcomes by using the assembly graph generated by assemblers, which encodes valuable overlapping information among genomic sequences. However, existing assembly graph-based binners mainly focus on simplified contig-level assembly graphs that are recreated from assembler’s original graphs, unitig-level assembly graphs. The simplification reduces the resolution of the connectivity information in original graphs. In this paper, we design a novel binning tool named UnitigBin, which leverages representation learning on unitig-level assembly graphs while adhering to heterophilious constraints imposed by single-copy marker genes, ensuring that constrained contigs cannot be grouped together. Extensive experiments conducted on synthetic and real datasets demonstrate that UnitigBin significantly surpasses state-of-the-art binning tools.

Reinforcement Learning · Deep RL

Vint Lee, Pieter Abbeel, Youngwoon Lee

Model-based reinforcement learning (MBRL) has gained much attention for its ability to learn complex behaviors in a sample-efficient way: planning actions by generating imaginary trajectories with predicted rewards. Despite its success, we found that surprisingly, reward prediction is often a bottleneck of MBRL, especially for sparse rewards that are challenging (or even ambiguous) to predict. Motivated by the intuition that humans can learn from rough reward estimates, we propose a simple yet effective reward smoothing approach, DreamSmooth, which learns to predict a temporally-smoothed reward, instead of the exact reward at the given timestep. We empirically show that DreamSmooth achieves state-of-the-art performance on long-horizon sparse-reward tasks both in sample efficiency and final performance without losing performance on common benchmarks, such as Deepmind Control Suite and Atari benchmarks.

Applications · Neuroscience, Cognitive Science

Aaron Spieler, Nasim Rahaman, Georg Martius, Bernhard Schoelkopf, Anna Levina

Biological cortical neurons are remarkably sophisticated computational devices, temporally integrating their vast synaptic input over an intricate dendritic tree, subject to complex, nonlinearly interacting internal biological processes. A recent study proposed to characterize this complexity by fitting accurate surrogate models to replicate the input-output relationship of a detailed biophysical cortical pyramidal neuron model and discovered it needed temporal convolutional networks (TCN) with millions of parameters. Requiring these many parameters, however, could stem from a misalignment between the inductive biases of the TCN and cortical neuron's computations.In light of this, and to explore the computational implications of leaky memory units and nonlinear dendritic processing, we introduce the Expressive Leaky Memory (ELM) neuron model, a biologically inspired phenomenological model of a cortical neuron.Remarkably, by exploiting such slowly decaying memory-like hidden states and two-layered nonlinear integration of synaptic input, our ELM neuron can accurately match the aforementioned input-output relationship with under ten thousand trainable parameters.To further assess the computational ramifications of our neuron design, we evaluate it on various tasks with demanding temporal structures, including the Long Range Arena (LRA) datasets, as well as a novel neuromorphic dataset based on the Spiking Heidelberg Digits dataset (SHD-Adding). Leveraging a larger number of memory units with sufficiently long timescales, and correspondingly sophisticated synaptic integration, the ELM neuron displays substantial long-range processing capabilities, reliably outperforming the classic Transformer or Chrono-LSTM architectures on LRA, and even solving the Pathfinder-X task with over 70\% accuracy (16k context length). These findings raise further questions about the computational sophistication of individual cortical neurons and their role in extracting complex long-range temporal dependencies.

Deep Learning · Everything Else

Qin ZHANG, Linghan Xu, Jun Fang, Qingming Tang, Yingnian Wu, Joseph Tighe, Yifan Xing

Existing losses used in deep metric learning (DML) for image retrieval often lead to highly non-uniform intra-class and inter-class representation structures across test classes and data distributions. When combined with the common practice of using a fixed threshold to declare a match, this gives rise to significant performance variations in terms of false accept rate (FAR) and false reject rate (FRR) across test classes and data distributions. We define this issue in DML as threshold inconsistency. In real-world applications, such inconsistency often complicates the threshold selection process when deploying large-scale image retrieval systems. To measure this inconsistency, we propose a novel variance-based metric called Operating-Point-Inconsistency-Score (OPIS) that quantifies the variance in the operating characteristics across classes. Using the OPIS metric, we find that achieving high accuracy levels in a DML model does not automatically guarantee threshold consistency. In fact, our investigation reveals a Pareto frontier in the high-accuracy regime, where existing methods to improve accuracy often lead to degradation in threshold consistency. To address this trade-off, we introduce the Threshold-Consistent Margin (TCM) loss, a simple yet effective regularization technique that promotes uniformity in representation structures across classes by selectively penalizing hard sample pairs. Large-scale experiments demonstrate TCM's effectiveness in enhancing threshold consistency while preserving accuracy, simplifying the threshold selection process in practical DML settings.

Guibin Zhang, Kun Wang, Wei Huang, Yanwei Yue, Yang Wang, Roger Zimmermann, Aojun Zhou, Dawei Cheng, Jin Zeng, Yuxuan Liang

Graph Neural Networks (GNNs) have emerged as the leading deep learning models for graph-based representation learning. However, the training and inference of GNNs on large graphs remain resource-intensive, impeding their utility in real-world scenarios and curtailing their applicability in deeper and more sophisticated GNN architectures. To address this issue, the Graph Lottery Ticket (GLT) hypothesis assumes that GNN with random initialization harbors a pair of core subgraph and sparse subnetwork, which can yield comparable performance and higher efficiency to that of the original dense network and complete graph. Despite that GLT offers a new paradigm for GNN training and inference, existing GLT algorithms heavily rely on trial-and-error pruning rate tuning and scheduling, and adhere to an irreversible pruning paradigm that lacks elasticity. Worse still, current methods suffer scalability issues when applied to deep GNNs, as they maintain the same topology structure across all layers. These challenges hinder the integration of GLT into deeper and larger-scale GNN contexts. To bridge this critical gap, this paper introduces an $\textbf{A}$daptive, $\textbf{D}$ynamic, and $\textbf{A}$utomated framework for identifying $\textbf{G}$raph $\textbf{L}$ottery $\textbf{T}$ickets ($\textbf{AdaGLT}$). Our proposed method derives its key advantages and addresses the above limitations through the following three aspects: 1) tailoring layer-adaptive sparse structures for various datasets and GNNs, thus endowing it with the capability to facilitate deeper GNNs; 2) integrating the pruning and training processes, thereby achieving a dynamic workflow encompassing both pruning and restoration; 3) automatically capturing graph lottery tickets across diverse sparsity levels, obviating the necessity for extensive pruning parameter tuning. More importantly, we rigorously provide theoretical proofs to guarantee $\textbf{AdaGLT}$ to mitigate over-smoothing issues and obtain improved sparse structures in deep GNN scenarios. Extensive experiments demonstrate that $\textbf{AdaGLT}$ outperforms state-of-the-art competitors across multiple graph datasets of various scales and types, particularly in scenarios involving deep GNNs.

Optimization · Learning for Optimization

Jiacheng Chen, Zeyuan Ma, Hongshu Guo, Yining Ma, Jie Zhang, Yue-Jiao Gong

Recent Meta-learning for Black-Box Optimization (MetaBBO) methods harness neural networks to meta-learn configurations of traditional black-box optimizers. Despite their success, they are inevitably restricted by the limitations of predefined hand-crafted optimizers. In this paper, we present SYMBOL, a novel framework that promotes the automated discovery of black-box optimizers through symbolic equation learning. Specifically, we propose a Symbolic Equation Generator (SEG) that allows closed-form optimization rules to be dynamically generated for specific tasks and optimization steps. Within SYMBOL, we then develop three distinct strategies based on reinforcement learning, so as to meta-learn the SEG efficiently. Extensive experiments reveal that the optimizers generated by SYMBOL not only surpass the state-of-the-art BBO and MetaBBO baselines, but also exhibit exceptional zero-shot generalization abilities across entirely unseen tasks with different problem dimensions, population sizes, and optimization horizons. Furthermore, we conduct in-depth analyses of our SYMBOL framework and the optimization rules that it generates, underscoring its desirable flexibility and interpretability.

Miscellaneous Aspects of Machine Learning · Causality

Yuhang Liu, Zhen Zhang, Dong Gong, Mingming Gong, Biwei Huang, Anton Hengel, Kun Zhang, Qinfeng Shi

Causal representation learning aims to unveil latent high-level causal representations from observed low-level data. One of its primary tasks is to provide reliable assurance of identifying these latent causal models, known as \textit{identifiability}. A recent breakthrough explores identifiability by leveraging the change of causal influences among latent causal variables across multiple environments \citep{liu2022identifying}. However, this progress rests on the assumption that the causal relationships among latent causal variables adhere strictly to linear Gaussian models. In this paper, we extend the scope of latent causal models to involve nonlinear causal relationships, represented by polynomial models, and general noise distributions conforming to the exponential family. Additionally, we investigate the necessity of imposing changes on all causal parameters and present partial identifiability results when part of them remains unchanged. Further, we propose a novel empirical estimation method, grounded in our theoretical finding, that enables learning consistent latent causal representations. Our experimental results, obtained from both synthetic and real-world data, validate our theoretical contributions concerning identifiability and consistency.

Applications · Chemistry and Drug Discovery

Urszula Julia Komorowska, Simon Mathis, Kieran Didi, Francisco Vargas, Pietro Lio, Mateja Jamnik

Current protein generative models are able to design novel backbones with desired shapes or functional motifs. However, despite the importance of a protein’s dynamical properties for its function, conditioning on dynamical properties remains elusive. We present a new approach to protein generative modeling by leveraging Normal Mode Analysis that enables us to capture dynamical properties too. We introduce a method for conditioning the diffusion probabilistic models on protein dynamics, specifically on the lowest non-trivial normal mode of oscillation. Our method, similar to the classifier guidance conditioning, formulates the sampling process as being driven by conditional and unconditional terms. However, unlike previous works, we approximate the conditional term with a simple analytical function rather than an external neural network, thus making the eigenvector calculations approachable. We present the corresponding SDE theory as a formal justification of our approach. We extend our framework to conditioning on structure and dynamics at the same time, enabling scaffolding of the dynamical motifs. We demonstrate the empirical effectiveness of our method by turning the open-source unconditional protein diffusion model Genie into the conditional model with no retraining. Generated proteins exhibit the desired dynamical and structural properties while still being biologically plausible. Our work represents a first step towards incorporating dynamical behaviour in protein design and may open the door to designing more flexible and functional proteins in the future.

Deep Learning · Robustness

Ziqiang Li, Hong Sun, Pengfei Xia, Heng Li, Beihao Xia, Yi Wu, Bin Li

Recent deep neural networks (DNNs) have came to rely on vast amounts of training data, providing an opportunity for malicious attackers to exploit and contaminate the data to carry out backdoor attacks. However, existing backdoor attack methods make unrealistic assumptions, assuming that all training data comes from a single source and that attackers have full access to the training data. In this paper, we introduce a more realistic attack scenario where victims collect data from multiple sources, and attackers cannot access the complete training data. We refer to this scenario as $\textbf{data-constrained backdoor attacks}$. In such cases, previous attack methods suffer from severe efficiency degradation due to the $\textbf{entanglement}$ between benign and poisoning features during the backdoor injection process. To tackle this problem, we introduce three CLIP-based technologies from two distinct streams: $\textit{Clean Feature Suppression}$ and $\textit{Poisoning Feature Augmentation}$. The results demonstrate remarkable improvements, with some settings achieving over $\textbf{100}$% improvement compared to existing attacks in data-constrained scenarios.

Applications · Computer Vision

Jiale Zhang, Yulun Zhang, Jinjin Gu, Jiahua Dong, Linghe Kong, Xiaokang Yang

In this paper, we present a hybrid X-shaped vision Transformer, named Xformer, which performs notably on image denoising tasks. We explore strengthening the global representation of tokens from different scopes. In detail, we adopt two types of Transformer blocks. The spatial-wise Transformer block performs fine-grained local patches interactions across tokens defined by spatial dimension. The channel-wise Transformer block performs direct global context interactions across tokens defined by channel dimension. Based on the concurrent network structure, we design two branches to conduct these two interaction fashions. Within each branch, we employ an encoder-decoder architecture to capture multi-scale features. Besides, we propose the Bidirectional Connection Unit (BCU) to couple the learned representations from these two branches while providing enhanced information fusion. The joint designs make our Xformer powerful to conduct global information modeling in both spatial and channel dimensions. Extensive experiments show that Xformer, under the comparable model complexity, achieves state-of-the-art performance on the synthetic and real-world image denoising tasks. We also provide code and models at https://github.com/gladzhang/Xformer.

Reinforcement Learning · Deep RL

Guozheng Ma, Lu Li, Sen Zhang, Zixuan Liu, Zhen Wang, Yixin Chen, Li Shen, Xueqian Wang, Dacheng Tao

Plasticity, the ability of a neural network to evolve with new data, is crucial for high-performance and sample-efficient visual reinforcement learning (VRL). Although methods like resetting and regularization can potentially mitigate plasticity loss, the influences of various components within the VRL framework on the agent's plasticity are still poorly understood. In this work, we conduct a systematic empirical exploration focusing on three primary underexplored facets and derive the following insightful conclusions: (1) data augmentation is essential in maintaining plasticity; (2) the critic's plasticity loss serves as the principal bottleneck impeding efficient training; and (3) without timely intervention to recover critic's plasticity in the early stages, its loss becomes catastrophic. These insights suggest a novel strategy to address the high replay ratio (RR) dilemma, where exacerbated plasticity loss hinders the potential improvements of sample efficiency brought by increased reuse frequency. Rather than setting a static RR for the entire training process, we propose Adaptive RR, which dynamically adjusts the RR based on the critic’s plasticity level. Extensive evaluations indicate that Adaptive RR not only avoids catastrophic plasticity loss in the early stages but also benefits from more frequent reuse in later phases, resulting in superior sample efficiency.

Reinforcement Learning · Multi-agent

Yat Long (Richie) Lo, Biswa Sengupta, Jakob Foerster, Mikhail Noukhovitch

Communication is a powerful tool for coordination in multi-agent RL. But inducing an effective, common language is a difficult challenge, particularly in the decentralized setting. In this work, we introduce an alternative perspective where communicative messages sent between agents are considered as different incomplete views of the environment state. By examining the relationship between messages sent and received, we propose to learn to communicate using contrastive learning to maximize the mutual information between messages of a given trajectory. In communication-essential environments, our method outperforms previous work in both performance and learning speed. Using qualitative metrics and representation probing, we show that our method induces more symmetric communication and captures global state information from the environment. Overall, we show the power of contrastive learning and the importance of leveraging messages as encodings for effective communication.

Deep Learning · Everything Else

Yusuke Sekikawa, Shingo Yashima

Wide networks usually yield better accuracy than their narrower counterpart at the expense of the massive $\texttt{mult}$ cost.To break this tradeoff, we advocate a novel concept of $\textit{Structured Activation Sparsification}$, dubbed SAS, which boosts accuracy without increasing computation by utilizing the projected sparsity in activation maps with a specific structure. Concretely, the projected sparse activation is allowed to have N nonzero value among M consecutive activations.Owing to the local structure in sparsity, the wide $\texttt{matmul}$ between a dense weight and the sparse activation is executed as an equivalent narrow $\texttt{matmul}$ between a dense weight and dense activation, which is compatible with NVIDIA's $\textit{SparseTensorCore}$ developed for the N:M structured sparse weight.In extensive experiments, we demonstrate that increasing sparsity monotonically improves accuracy (up to 7% on CIFAR10) without increasing the $\texttt{mult}$ count.Furthermore, we show that structured sparsification of $\textit{activation}$ scales better than that of $\textit{weight}$ given the same computational budget.

Applications · Time Series

Jiecheng Lu, Xu Han, Shihao Yang

Long-term time series forecasting (LTSF) is important for various domains but is confronted by challenges in handling the complex temporal-contextual relationships. As multivariate input models underperforming some recent univariate counterparts, we posit that the issue lies in the inefficiency of existing multivariate LTSF Transformers to model series-wise relationships: the characteristic differences between series are often captured incorrectly. To address this, we introduce ARM: a multivariate temporal-contextual adaptive learning method, which is an enhanced architecture specifically designed for multivariate LTSF modelling. ARM employs Adaptive Univariate Effect Learning (**A**UEL), Random Dropping (**R**D) training strategy, and Multi-kernel Local Smoothing (**M**KLS), to better handle individual series temporal patterns and correctly learn inter-series dependencies. ARM demonstrates superior performance on multiple benchmarks without significantly increasing computational costs compared to vanilla Transformer, thereby advancing the state-of-the-art in LTSF. ARM is also generally applicable to other LTSF architecture beyond vanilla Transformer.

Reinforcement Learning · Batch/Offline

Prajjwal Bhargava, Rohan Chitnis, Alborz Geramifard, Shagun Sodhani, Amy Zhang

Offline reinforcement learning (RL) allows agents to learn effective, return-maximizing policies from a static dataset. Three popular algorithms for offline RL are Conservative Q-Learning (CQL), Behavior Cloning (BC), and Decision Transformer (DT), from the class of Q-Learning, Imitation Learning, and Sequence Modeling respectively. A key open question is: which algorithm is preferred under what conditions? We study this question empirically by exploring the performance of these algorithms across the commonly used D4RL and Robomimic benchmarks. We design targeted experiments to understand their behavior concerning data suboptimality, task complexity, and stochasticity. Our key findings are: (1) DT requires more data than CQL to learn competitive policies but is more robust; (2) DT is a substantially better choice than both CQL and BC in sparse-reward and low-quality data settings; (3) DT and BC are preferable as task horizon increases, or when data is obtained from human demonstrators; and (4) CQL excels in situations characterized by the combination of high stochasticity and low data quality. We also investigate architectural choices and scaling trends for DT on \textsc{atari} and D4RL and make design/scaling recommendations. We find that scaling the amount of data for DT by 5x gives a 2.5x average score improvement on Atari.

Deep Learning · Large Language Models

Zhijing Jin, Jiarui Liu, Zhiheng LYU, spencer poff, Mrinmaya Sachan, Rada Mihalcea, Mona Diab, Bernhard Schoelkopf

Causal inference is one of the hallmarks of human intelligence. While the field of CausalNLP has attracted much interest in the recent years, existing causal inference datasets in NLP primarily rely on discovering causality from empirical knowledge (e.g., commonsense knowledge). In this work, we propose the first benchmark dataset to test the pure causal inference skills of large language models (LLMs). Specifically, we formulate a novel task Corr2Cause, which takes a set of correlational statements and determines the causal relationship between the variables. We curate a large-scale dataset of more than 200K samples, on which we evaluate seventeen existing LLMs. Through our experiments, we identify a key shortcoming of LLMs in terms of their causal inference skills, and show that these models achieve almost close to random performance on the task. This shortcoming is somewhat mitigated when we try to re-purpose LLMs for this skill via finetuning, but we find that these models still fail to generalize – they can only perform causal inference in in-distribution settings when variable names and textual expressions used in the queries are similar to those in the training set, but fail in out-of-distribution settings generated by perturbing these queries. Corr2Cause is a challenging task for LLMs, and can be helpful in guiding future research on improving LLMs’ pure reasoning skills and generalizability. Our data is at https://huggingface.co/datasets/causalnlp/corr2cause. Our code is at https://github.com/causalNLP/corr2cause.

Reinforcement Learning · Deep RL

Zifan Wu, Bo Tang, Qian Lin, Chao Yu, Shangqin Mao, Qianlong Xie, Xingxing Wang, Dong Wang

Primal-dual safe RL methods commonly perform iterations between the primal update of the policy and the dual update of the Lagrange Multiplier. Such a training paradigm is highly susceptible to the error in cumulative cost estimation since this estimation serves as the key bond connecting the primal and dual update processes. We show that this problem causes significant underestimation of cost when using off-policy methods, leading to the failure to satisfy the safety constraint. To address this issue, we propose conservative policy optimization, which learns a policy in a constraint-satisfying area by considering the uncertainty in cost estimation. This improves constraint satisfaction but also potentially hinders reward maximization. We then introduce local policy convexification to help eliminate such suboptimality by gradually reducing the estimation uncertainty. We provide theoretical interpretations of the joint coupling effect of these two ingredients and further verify them by extensive experiments. Results on benchmark tasks show that our method not only achieves an asymptotic performance comparable to state-of-the-art on-policy methods while using much fewer samples, but also significantly reduces constraint violation during training. Our code is available at https://github.com/ZifanWu/CAL.

Applications · Computer Vision

Junoh Lee, Hyunjun Jung, Jinhwi Park, Inhwan Bae, Hae-Gon Jeon

Estimating neural radiance fields (NeRFs) is able to generate novel views of a scene from known imagery. Recent approaches have afforded dramatic progress on small bounded regions of the scene. For an unbounded scene where cameras point in any direction and contents exist at any distance, certain mapping functions are used to represent it within a bounded space, yet they either work in object-centric scenes or focus on objects close to the camera. The goal of this paper is to understand how to design a proper mapping function that considers per-scene optimization, which remains unexplored. We first present a geometric understanding of existing mapping functions that express the relation between the bounded and unbounded scenes. Here, we exploit a stereographic projection method to explain failures of the mapping functions, where input ray samples are too sparse to account for scene geometry in unbounded regions. To overcome the failures, we propose a novel mapping function based on a $p$-norm distance, allowing to adaptively sample the rays by adjusting the $p$-value according to scene geometry, even in unbounded regions. To take the advantage of our mapping function, we also introduce a new ray parameterization to properly allocate ray samples in the geometry of unbounded regions. Through the incorporation of both the novel mapping function and the ray parameterization within existing NeRF frameworks, our method achieves state-of-the-art novel view synthesis results on a variety of challenging datasets.