A Consistency-Aware Spot-Guided Transformer for Versatile and Hierarchical Point Cloud Registration

Point cloud registration;Rigid transformation estimation;Feature matching;Correspondence;Deep learning

Summary: We propose a novel consistency-aware spot-guided Transformer for versatile and hierarchical point cloud registration, achieving state-of-the-art accuracy, efficiency, and robustness on both outdoor and indoor benchmarks.

Abstract: Deep learning-based feature matching has shown great superiority for point cloud registration in the absence of pose priors. Although coarse-to-fine matching approaches are prevalent, the coarse matching of existing methods is typically sparse and loose without consideration of geometric consistency, which makes the subsequent fine matching rely on ineffective optimal transport and hypothesis-and-selection methods for consistency. Therefore, these methods are neither efficient nor scalable for real-time applications such as odometry in robotics. To address these issues, we design a consistency-aware spot-guided Transformer (CAST), which incorporates a spot-guided cross-attention module to avoid interfering with irrelevant areas, and a consistency-aware self-attention module to enhance matching capabilities with geometrically consistent correspondences. Furthermore, a lightweight fine matching module for both sparse keypoints and dense features can estimate the transformation accurately. Extensive experiments on both outdoor LiDAR point cloud datasets and indoor RGBD point cloud datasets demonstrate that our method achieves state-of-the-art accuracy, efficiency, and robustness.


Flow Snapshot Neurons in Action: Deep Neural Networks Generalize to Biological Motion Perception

biological motion perception;generalization;video action recognition

Summary: We propose an AI model for video action recognition, which can generalize to biological motion perception tasks.

Abstract: Biological motion perception (BMP) refers to humans' ability to perceive and recognize the actions of living beings solely from their motion patterns, sometimes as minimal as those depicted on point-light displays. While humans excel at these tasks \textit{without any prior training}, current AI models struggle with poor generalization performance. To close this research gap, we propose the Motion Perceiver (MP). MP solely relies on patch-level optical flows from video clips as inputs. During training, it learns prototypical flow snapshots through a competitive binding mechanism and integrates invariant motion representations to predict action labels for the given video. During inference, we evaluate the generalization ability of all AI models and humans on 62,656 video stimuli spanning 24 BMP conditions using point-light displays in neuroscience. Remarkably, MP outperforms all existing AI models with a maximum improvement of 29% in top-1 action recognition accuracy on these conditions. Moreover, we benchmark all AI models in point-light displays of two standard video datasets in computer vision. MP also demonstrates superior performance in these cases. More interestingly, via psychophysics experiments, we found that MP recognizes biological movements in a way that aligns with human behaviors. Our data and code are available at https://github.com/ZhangLab-DeepNeuroCogLab/MotionPerceiver.


Self-Labeling the Job Shop Scheduling Problem

Self-Labeling;Generative Model;Job Shop Scheduling;Traveling Salesman Problem

Summary: We propose a novel self-labeling improvement method for combinatorial problems that enables the training of state-of-the-art generative models without requiring optimality information or defining Markov Decision Processes.

Abstract: This work proposes a self-supervised training strategy designed for combinatorial problems. An obstacle in applying supervised paradigms to such problems is the need for costly target solutions often produced with exact solvers. Inspired by semi- and self-supervised learning, we show that generative models can be trained by sampling multiple solutions and using the best one according to the problem objective as a pseudo-label. In this way, we iteratively improve the model generation capability by relying only on its self-supervision, eliminating the need for optimality information. We validate this Self-Labeling Improvement Method (SLIM) on the Job Shop Scheduling (JSP), a complex combinatorial problem that is receiving much attention from the neural combinatorial community. We propose a generative model based on the well-known Pointer Network and train it with SLIM. Experiments on popular benchmarks demonstrate the potential of this approach as the resulting models outperform constructive heuristics and state-of-the-art learning proposals for the JSP. Lastly, we prove the robustness of SLIM to various parameters and its generality by applying it to the Traveling Salesman Problem.


Soft Superpixel Neighborhood Attention

attention module;superpixels;image denoising;deep learning

Summary: This paper proposes a novel deep learning attention module, named soft superpixel neighborhood attention (SNA), to reweight a local attention map according to the deformable boundaries of real-world images.

Abstract: Images contain objects with deformable boundaries, such as the contours of a human face, yet attention operators act on square windows. This mixes features from perceptually unrelated regions, which can degrade the quality of a denoiser. One can exclude pixels using an estimate of perceptual groupings, such as superpixels, but the naive use of superpixels can be theoretically and empirically worse than standard attention. Using superpixel probabilities rather than superpixel assignments, this paper proposes soft superpixel neighborhood attention (SNA), which interpolates between the existing neighborhood attention and the naive superpixel neighborhood attention. This paper presents theoretical results showing SNA is the optimal denoiser under a latent superpixel model. SNA outperforms alternative local attention modules on image denoising, and we compare the superpixels learned from denoising with those learned with supervision.


Splatter a Video: Video Gaussian Representation for Versatile Processing

Summary: A method to represent casual videos using 3D Gaussians without estimating camera pose

Abstract: Video representation is a long-standing problem that is crucial for various downstream tasks, such as tracking, depth prediction, segmentation, view synthesis, and editing. However, current methods either struggle to model complex motions due to the absence of 3D structure or rely on implicit 3D representations that are ill-suited for manipulation tasks. To address these challenges, we introduce a novel explicit 3D representation—video Gaussian representation—that embeds a video into 3D Gaussians. Our proposed representation models video appearance in a 3D canonical space using explicit Gaussians as proxies and associates each Gaussian with 3D motions for video motion. This approach offers a more intrinsic and explicit representation than layered atlas or volumetric pixel matrices. To obtain such a representation, we distill 2D priors, such as optical flow and depth, from foundation models to regularize learning in this ill-posed setting. Extensive applications demonstrate the versatility of our new video representation. It has been proven effective in numerous video processing tasks, including tracking, consistent video depth and feature refinement, motion and appearance editing, and stereoscopic video generation.


Estimating Heterogeneous Treatment Effects by Combining Weak Instruments and Observational Data

Causal inference;heterogeneous treatment effects;weak instrumental variables;unobserved confounding;data combination

Summary: We propose a method to estimate heterogeneous treatment effects by combining weak instrumental variables with observational data, enabling reliable treatment effect estimation in the presence of confounding bias.

Abstract: Accurately predicting conditional average treatment effects (CATEs) is crucial in personalized medicine and digital platform analytics. Since the treatments of interest often cannot be directly randomized, observational data is leveraged to learn CATEs, but this approach can incur significant bias from unobserved confounding. One strategy to overcome these limitations is to leverage instrumental variables (IVs) as latent quasi-experiments, such as randomized intent-to-treat assignments or randomized product recommendations. This approach, on the other hand, can suffer from low compliance, i.e., IV weakness. Some subgroups may even exhibit zero compliance, meaning we cannot instrument for their CATEs at all. In this paper, we develop a novel approach to combine IV and observational data to enable reliable CATE estimation in the presence of unobserved confounding in the observational data and low compliance in the IV data, including no compliance for some subgroups. We propose a two-stage framework that first learns \textit{biased} CATEs from the observational data, and then applies a compliance-weighted correction using IV data, effectively leveraging IV strength variability across covariates. We characterize the convergence rates of our method and validate its effectiveness through a simulation study. Additionally, we demonstrate its utility with real data by analyzing the heterogeneous effects of 401(k) plan participation on wealth.


Efficient $\Phi$-Regret Minimization with Low-Degree Swap Deviations in Extensive-Form Games

swap regret;extensive-form games;low-degree deviations

Summary: We develop algorithms to efficiently minimize swap regret with respect to the set of low-degree deviations in extensive-form games.

Abstract:
Recent breakthrough results by Dagan, Daskalakis, Fishelson and Golowich [2023] and Peng and Rubinstein [2023] established an efficient algorithm attaining at most
ϵ
swap regret over extensive-form strategy spaces of dimension
N
in
N
O
~
(
1
/
ϵ
)
rounds. On the other extreme, Farina and Pipis [2023] developed an efficient algorithm for minimizing the weaker notion of linear-swap regret in
poly
(
N
)
/
ϵ
2
rounds. In this paper, we develop efficient parameterized algorithms for regimes between these two extremes. We introduce the set of
k
-mediator deviations, which generalize the untimed communication deviations recently introduced by Zhang, Farina and Sandholm [2024] to the case of having multiple mediators, and we develop algorithms for minimizing the regret with respect to this set of deviations in
N
O
(
k
)
/
ϵ
2
rounds. Moreover, by relating
k
-mediator deviations to low-degree polynomials, we show that regret minimization against degree-
k
polynomial swap deviations is achievable in
N
O
(
k
d
)
3
/
ϵ
2
rounds, where
d
is the depth of the game, assuming a constant branching factor. For a fixed degree
k
, this is polynomial for Bayesian games and quasipolynomial more broadly when
d
=
polylog
N
---the usual balancedness assumption on the game tree. The first key ingredient in our approach is a relaxation of the usual notion of a fixed point required in the framework of Gordon, Greenwald and Marks [2008]. Namely, for a given deviation
ϕ
, we show that it suffices to compute what we refer to as a fixed point in expectation; that is, a distribution
π
such that
E
x
∼
π
[
ϕ
(
x
)
−
x
]
≈
0
. Unlike the problem of computing an actual (approximate) fixed point
x
≈
ϕ
(
x
)
, which we show is \PPAD-hard, there is a simple and efficient algorithm for finding a solution that satisfies our relaxed notion. As a byproduct, we provide, to our knowledge, the fastest algorithm for computing
ϵ
-correlated equilibria in normal-form games in the medium-precision regime, obviating the need to solve a linear system in every round. Our second main contribution is a characterization of the set of low-degree deviations, made possible through a connection to low-depth decisions trees from Boolean analysis.


Exploring Structured Semantic Priors Underlying Diffusion Score for Test-time Adaptation

test-time adaptation;diffusion models;generative models;classification;segmentation

Summary: We introduce DUSA, an effective method with improved efficiency for test-time adaptation that exploits structured semantic priors from pre-trained score-based diffusion models for enhancing pre-trained discriminative models.

Abstract: Capitalizing on the complementary advantages of generative and discriminative models has always been a compelling vision in machine learning, backed by a growing body of research. This work discloses the hidden semantic structure within score-based generative models, unveiling their potential as effective discriminative priors. Inspired by our theoretical findings, we propose DUSA to exploit the structured semantic priors underlying diffusion score to facilitate the test-time adaptation of image classifiers or dense predictors. Notably, DUSA extracts knowledge from a single timestep of denoising diffusion, lifting the curse of Monte Carlo-based likelihood estimation over timesteps. We demonstrate the efficacy of our DUSA in adapting a wide variety of competitive pre-trained discriminative models on diverse test-time scenarios. Additionally, a thorough ablation study is conducted to dissect the pivotal elements in DUSA. Code is publicly available at https://github.com/BIT-DA/DUSA.


Convolutions and More as Einsum: A Tensor Network Perspective with Advances for Second-Order Methods

Summary: We introduce einsum implementations of many operations related to convolution that speed up the computation of second-order methods like KFAC

Abstract: Despite their simple intuition, convolutions are more tedious to analyze than dense layers, which complicates the transfer of theoretical and algorithmic ideas to convolutions. We simplify convolutions by viewing them as tensor networks (TNs) that allow reasoning about the underlying tensor multiplications by drawing diagrams, manipulating them to perform function transformations like differentiation, and efficiently evaluating them with einsum. To demonstrate their simplicity and expressiveness, we derive diagrams of various autodiff operations and popular curvature approximations with full hyper-parameter support, batching, channel groups, and generalization to any convolution dimension. Further, we provide convolution-specific transformations based on the connectivity pattern which allow to simplify diagrams before evaluation. Finally, we probe performance. Our TN implementation accelerates a recently-proposed KFAC variant up to 4.5 x while removing the standard implementation's memory overhead, and enables new hardware-efficient tensor dropout for approximate backpropagation.


StepbaQ: Stepping backward as Correction for Quantized Diffusion Models

Summary: This work introduces a novel perspective that considers quantization error as a stepback in the denoising process; through a sampling step correction mechanism it improves the performance of quantized diffusion models.

Abstract: Quantization of diffusion models has attracted considerable attention due to its potential to enable various applications on resource-constrained mobile devices. However, given the cumulative nature of quantization errors in quantized diffusion models, overall performance may still decline even with efforts to minimize quantization error at each sampling step. Recent studies have proposed several methods to address accumulated quantization error, yet these solutions often suffer from limited applicability due to their underlying assumptions or only partially resolve the issue due to an incomplete understanding. In this work, we introduce a novel perspective by conceptualizing quantization error as a "stepback" in the denoising process. We investigate how the accumulation of quantization error can distort the sampling trajectory, resulting in a notable decrease in model performance. To address this challenge, we introduce StepbaQ, a method that calibrates the sampling trajectory and counteracts the adverse effects of accumulated quantization error through a sampling step correction mechanism. Notably, StepbaQ relies solely on statistics of quantization error derived from a small calibration dataset, highlighting its strong applicability. Our experimental results demonstrate that StepbaQ can serve as a plug-and-play technique to enhance the performance of diffusion models quantized by off-the-shelf tools without modifying the quantization settings. For example, StepbaQ significantly improves the performance of the quantized SD v1.5 model by 7.30 in terms of FID on SDprompts dataset under the common W8A8 setting, and it enhances the performance of the quantized SDXL-Turbo model by 17.31 in terms of FID on SDprompts dataset under the challenging W4A8 setting.


Private Geometric Median

Differential Privacy;Differentially Private Convex Optimization;Geometric Median

Summary: In this paper, we develop private algorithms for computing the geometric median of a dataset with an adaptive error guarantee.

Abstract: In this paper, we study differentially private (DP) algorithms for computing the geometric median (GM) of a dataset: Given $n$ points, $x_1,\dots,x_n$ in $\mathbb{R}^d$, the goal is to find a point $\theta$ that minimizes the sum of the Euclidean distances to these points, i.e., $\sum_{i=1}^{n} \lVert|\theta - x_i\rVert_2$. Off-the-shelf methods, such as DP-GD, require strong a priori knowledge locating the data within a ball of radius $R$, and the excess risk of the algorithm depends linearly on $R$. In this paper, we ask: can we design an efficient and private algorithm with an excess error guarantee that scales with the (unknown) radius containing the majority of the datapoints? Our main contribution is a pair of polynomial-time DP algorithms for the task of private GM with an excess error guarantee that scales with the effective diameter of the datapoints. Additionally, we propose an inefficient algorithm based on the inverse smooth sensitivity mechanism, which satisfies the more restrictive notion of pure DP. We complement our results with a lower bound and demonstrate the optimality of our polynomial-time algorithms in terms of sample complexity.


Improving Deep Reinforcement Learning by Reducing the Chain Effect of Value and Policy Churn

Reinforcement Learning;Deep Learning;Regularization and Optimization

Summary: Improving deep reinforcement learning by reducing undesired changes to out of batch data.

Abstract: Deep neural networks provide Reinforcement Learning (RL) powerful function approximators to address large-scale decision-making problems. However, these approximators introduce challenges due to the non-stationary nature of RL training. One source of the challenges in RL is that output predictions can churn, leading to uncontrolled changes after each batch update for states not included in the batch. Although such a churn phenomenon exists in each step of network training, it remains under-explored on how churn occurs and impacts RL. In this work, we start by characterizing churn in a view of Generalized Policy Iteration with function approximation, and we discover a chain effect of churn that leads to a cycle where the churns in value estimation and policy improvement compound and bias the learning dynamics throughout the iteration. Further, we concretize the study and focus on the learning issues caused by the chain effect in different settings, including greedy action deviation in value-based methods, trust region violation in proximal policy optimization, and dual bias of policy value in actor-critic methods. We then propose a method to reduce the chain effect across different settings, called Churn Approximated ReductIoN (CHAIN), which can be easily plugged into most existing DRL algorithms. Our experiments demonstrate the effectiveness of our method in both reducing churn and improving learning performance across online and offline, value-based and policy-based RL settings.


Credit Attribution and Stable Compression

Credit Attribution;Algorithmic Stability;Stable Sample Compression

Summary:
We study credit attribution by machine learning algorithms via new relaxations of Differential Privacy that specifically weaken the stability guarantees for a designated subset of
k
 datapoints.

Abstract:
Credit attribution is crucial across various fields. In academic research, proper citation acknowledges prior work and establishes original contributions. Similarly, in generative models, such as those trained on existing artworks or music, it is important to ensure that any generated content influenced by these works appropriately credits the original creators.
We study credit attribution by machine learning algorithms. We propose new definitions--relaxations of Differential Privacy--that weaken the stability guarantees for a designated subset of
k
datapoints. These
k
datapoints can be used non-stably with permission from their owners, potentially in exchange for compensation. Meanwhile, the remaining datapoints are guaranteed to have no significant influence on the algorithm's output.
Our framework extends well-studied notions of stability, including Differential Privacy (
k
=
0
), differentially private learning with public data (where the
k
public datapoints are fixed in advance), and stable sample compression (where the
k
datapoints are selected adaptively by the algorithm). We examine the expressive power of these stability notions within the PAC learning framework, provide a comprehensive characterization of learnability for algorithms adhering to these principles, and propose directions and questions for future research.


Generative Forests

Summary: A new class of tree-based generative models and a training algorithm with fast, boosting compliant induction and models that can be used for data generation, missing data imputation and density estimation.

Abstract: We focus on generative AI for a type of data that still represent one of the most prevalent form of data: tabular data. We introduce a new powerful class of forest-based models fit for such tasks and a simple training algorithm with strong convergence guarantees in a boosting model that parallels that of the original weak / strong supervised learning setting. This algorithm can be implemented by a few tweaks to the most popular induction scheme for decision tree induction (i.e. supervised learning) with two classes. Experiments on the quality of generated data display substantial improvements compared to the state of the art. The losses our algorithm minimize and the structure of our models make them practical for related tasks that require fast estimation of a density given a generative model and an observation (even partially specified): such tasks include missing data imputation and density estimation. Additional experiments on these tasks reveal that our models can be notably good contenders to diverse state of the art methods, relying on models as diverse as (or mixing elements of) trees, neural nets, kernels or graphical models.


Distributional regression: CRPS-error bounds for model fitting, model selection and convex aggregation

distributional regression; error bounds; concentration inequality; continuous rank probability score; empirical risk minimization

Summary: We provide concentration inequalities for the CRPS-error in distributional regression when empirical risk minimization is used for model fitting, model selection or convex aggregation.

Abstract: Distributional regression aims at estimating the conditional distribution of a target variable given explanatory co-variates. It is a crucial tool for forecasting when a precise uncertainty quantification is required. A popular methodology consists in fitting a parametric model via empirical risk minimization where the risk is measured by the Continuous Rank Probability Score (CRPS). For independent and identically distributed observations, we provide a concentration result for the estimation error and an upper bound for its expectation. Furthermore, we consider model selection performed by minimization of the validation error and provide a concentration bound for the regret. A similar result is proved for convex aggregation of models. Finally, we show that our results may be applied to various models such as EMOS, distributional regression networks, distributional nearest neighbours or distributional random forests and we illustrate our findings on two data sets (QSAR aquatic toxicity and Airfoil self-noise).


Learning Truncated Causal History Model for Video Restoration

video restoration;low-level computer vision;motion understanding

Summary: We present a new video restoration framework to learn and model the history of the video frames.

Abstract: One key challenge to video restoration is to model the transition dynamics of video frames governed by motion. In this work, we propose Turtle to learn the truncated causal history model for efficient and high-performing video restoration. Unlike traditional methods that process a range of contextual frames in parallel, Turtle enhances efficiency by storing and summarizing a truncated history of the input frame latent representation into an evolving historical state. This is achieved through a sophisticated similarity-based retrieval mechanism that implicitly accounts for inter-frame motion and alignment. The causal design in Turtle enables recurrence in inference through state-memorized historical features while allowing parallel training by sampling truncated video clips. We report new state-of-the-art results on a multitude of video restoration benchmark tasks, including video desnowing, nighttime video deraining, video raindrops and rain streak removal, video super-resolution, real-world and synthetic video deblurring, and blind video denoising while reducing the computational cost compared to existing best contextual methods on all these tasks.


On Statistical Rates and Provably Efficient Criteria of Latent Diffusion Transformers (DiTs)

DiT;Score Matching;Diffusion Transformer;Efficiency;Universal Approximation;Convergence Analysis;Diffusion Generative Model;DDPM

Summary: We study the statistical and computational limits of Diffusion Transformers (DiTs).

Abstract: We investigate the statistical and computational limits of latent Diffusion Transformers (DiTs) under the low-dimensional linear latent space assumption. Statistically, we study the universal approximation and sample complexity of the DiTs score function, as well as the distribution recovery property of the initial data. Specifically, under mild data assumptions, we derive an approximation error bound for the score network of latent DiTs, which is sub-linear in the latent space dimension. Additionally, we derive the corresponding sample complexity bound and show that the data distribution generated from the estimated score function converges toward a proximate area of the original one. Computationally, we characterize the hardness of both forward inference and backward computation of latent DiTs, assuming the Strong Exponential Time Hypothesis (SETH). For forward inference, we identify efficient criteria for all possible latent DiTs inference algorithms and showcase our theory by pushing the efficiency toward almost-linear time inference. For backward computation, we leverage the low-rank structure within the gradient computation of DiTs training for possible algorithmic speedup. Specifically, we show that such speedup achieves almost-linear time latent DiTs training by casting the DiTs gradient as a series of chained low-rank approximations with bounded error. Under the low-dimensional assumption, we show that the statistical rates and the computational efficiency are all dominated by the dimension of the subspace, suggesting that latent DiTs have the potential to bypass the challenges associated with the high dimensionality of initial data.


Abstract Reward Processes: Leveraging State Abstraction for Consistent Off-Policy Evaluation

Off-Policy Evaluation;State Abstraction;Importance Sampling

Summary: Perform model-based OPE, but instead of trying to estimate a perfect model of the MDP, estimate an abstract model, customized to a policy, that preserves the performance of that policy and can be learnt from off-policy data.

Abstract: Evaluating policies using off-policy data is crucial for applying reinforcement learning to real-world problems such as healthcare and autonomous driving. Previous methods for off-policy evaluation (OPE) generally suffer from high variance or irreducible bias, leading to unacceptably high prediction errors. In this work, we introduce STAR, a framework for OPE that encompasses a broad range of estimators -- which include existing OPE methods as special cases -- that achieve lower mean squared prediction errors. STAR leverages state abstraction to distill complex, potentially continuous problems into compact, discrete models which we call abstract reward processes (ARPs). Predictions from ARPs estimated from off-policy data are provably consistent (asymptotically correct). Rather than proposing a specific estimator, we present a new framework for OPE and empirically demonstrate that estimators within STAR outperform existing methods. The best STAR estimator outperforms baselines in all twelve cases studied, and even the median STAR estimator surpasses the baselines in seven out of the twelve cases.


BELM: Bidirectional Explicit Linear Multi-step Sampler for Exact Inversion in Diffusion Models

diffusion model; exact inversion; ODE sampler

Summary: We propose a novel generic eacxt inversion samplers of diffusion models and derive the variant with optimal accuracy .

Abstract: The inversion of diffusion model sampling, which aims to find the corresponding initial noise of a sample, plays a critical role in various tasks. Recently, several heuristic exact inversion samplers have been proposed to address the inexact inversion issue in a training-free manner. However, the theoretical properties of these heuristic samplers remain unknown and they often exhibit mediocre sampling quality. In this paper, we introduce a generic formulation, \emph{Bidirectional Explicit Linear Multi-step} (BELM) samplers, of the exact inversion samplers, which includes all previously proposed heuristic exact inversion samplers as special cases. The BELM formulation is derived from the variable-stepsize-variable-formula linear multi-step method via integrating a bidirectional explicit constraint. We highlight this bidirectional explicit constraint is the key of mathematically exact inversion. We systematically investigate the Local Truncation Error (LTE) within the BELM framework and show that the existing heuristic designs of exact inversion samplers yield sub-optimal LTE. Consequently, we propose the Optimal BELM (O-BELM) sampler through the LTE minimization approach. We conduct additional analysis to substantiate the theoretical stability and global convergence property of the proposed optimal sampler. Comprehensive experiments demonstrate our O-BELM sampler establishes the exact inversion property while achieving high-quality sampling. Additional experiments in image editing and image interpolation highlight the extensive potential of applying O-BELM in varying applications.


Discretely beyond $1/e$: Guided Combinatorial Algortihms for Submodular Maximization

combinatorial algorithms;deterministic algorithms;submodular optimization

Summary: First combinatorial algorithms for submodular maximization with ratio better than 1/e ≈ 0.367

Abstract:
For constrained, not necessarily monotone submodular maximization, all known approximation algorithms with ratio greater than
1
/
e
require continuous ideas, such as queries to the multilinear extension of a submodular function and its gradient, which are typically expensive to simulate with the original set function. For combinatorial algorithms, the best known approximation ratios for both size and matroid constraint are obtained by a simple randomized greedy algorithm of Buchbinder et al. [9]:
1
/
e
≈
0.367
for size constraint and
0.281
for the matroid constraint in
O
(
k
n
)
queries, where
k
is the rank of the matroid. In this work, we develop the first combinatorial algorithms to break the
1
/
e
barrier: we obtain approximation ratio of
0.385
in
O
(
k
n
)
queries to the submodular set function for size constraint, and
0.305
for a general matroid constraint. These are achieved by guiding the randomized greedy algorithm with a fast local search algorithm. Further, we develop deterministic versions of these algorithms, maintaining the same ratio and asymptotic time complexity. Finally, we develop a deterministic, nearly linear time algorithm with ratio
0.377
.


IF-Font: Ideographic Description Sequence-Following Font Generation

Font Generation;Vector Quantization;Ideographic Description Sequence;Multimodal

Summary: IF-Font uses Ideographic Description Sequence as the semantic condition instead of the content image, outperforming all state-of-the-art methods in the few-shot font generation task.

Abstract: Few-shot font generation (FFG) aims to learn the target style from a limited number of reference glyphs and generate the remaining glyphs in the target font. Previous works focus on disentangling the content and style features of glyphs, combining the content features of the source glyph with the style features of the reference glyph to generate new glyphs. However, the disentanglement is challenging due to the complexity of glyphs, often resulting in glyphs that are influenced by the style of the source glyph and prone to artifacts. We propose IF-Font, a novel paradigm which incorporates Ideographic Description Sequence (IDS) instead of the source glyph to control the semantics of generated glyphs. To achieve this, we quantize the reference glyphs into tokens, and model the token distribution of target glyphs using corresponding IDS and reference tokens. The proposed method excels in synthesizing glyphs with neat and correct strokes, and enables the creation of new glyphs based on provided IDS. Extensive experiments demonstrate that our method greatly outperforms state-of-the-art methods in both one-shot and few-shot settings, particularly when the target styles differ significantly from the training font styles. The code is available at https://github.com/Stareven233/IF-Font.


CycleNet: Enhancing Time Series Forecasting through Modeling Periodic Patterns

Time Series Forecasting;Time Series Analysis;Machine Learning

Summary: This paper pioneers the exploration of explicitly modeling periodic patterns in time-series data to enhance the accuracy of long-term time series forecasting (LTSF) tasks.

Abstract: The stable periodic patterns present in time series data serve as the foundation for conducting long-horizon forecasts. In this paper, we pioneer the exploration of explicitly modeling this periodicity to enhance the performance of models in long-term time series forecasting (LTSF) tasks. Specifically, we introduce the Residual Cycle Forecasting (RCF) technique, which utilizes learnable recurrent cycles to model the inherent periodic patterns within sequences, and then performs predictions on the residual components of the modeled cycles. Combining RCF with a Linear layer or a shallow MLP forms the simple yet powerful method proposed in this paper, called CycleNet. CycleNet achieves state-of-the-art prediction accuracy in multiple domains including electricity, weather, and energy, while offering significant efficiency advantages by reducing over 90% of the required parameter quantity. Furthermore, as a novel plug-and-play technique, the RCF can also significantly improve the prediction accuracy of existing models, including PatchTST and iTransformer. The source code is available at: https://github.com/ACAT-SCUT/CycleNet.


InversionView: A General-Purpose Method for Reading Information from Neural Activations

Summary: We develop a method that reads out information from neural activations.

Abstract: The inner workings of neural networks can be better understood if we can fully decipher the information encoded in neural activations. In this paper, we argue that this information is embodied by the subset of inputs that give rise to similar activations. We propose InversionView, which allows us to practically inspect this subset by sampling from a trained decoder model conditioned on activations. This helps uncover the information content of activation vectors, and facilitates understanding of the algorithms implemented by transformer models. We present four case studies where we investigate models ranging from small transformers to GPT-2. In these studies, we show that InversionView can reveal clear information contained in activations, including basic information about tokens appearing in the context, as well as more complex information, such as the count of certain tokens, their relative positions, and abstract knowledge about the subject. We also provide causally verified circuits to confirm the decoded information.


Oja's Algorithm for Streaming Sparse PCA

Streaming PCA;Oja's Algorithm;Sparse PCA;Support Recovery;Entrywise Bounds

Summary: We give a O(d) space, O(nd) time algorithm for Streaming Sparse PCA via a novel analysis of Oja's Algorithm followed by thresholding

Abstract:
Oja's algorithm for Streaming Principal Component Analysis (PCA) for
n
data-points in a
d
dimensional space achieves the same sin-squared error
O
(
r
eff
/
n
)
as the offline algorithm in
O
(
d
)
space and
O
(
n
d
)
time and a single pass through the datapoints. Here
r
eff
is the effective rank (ratio of the trace and the principal eigenvalue of the population covariance matrix
Σ
). Under this computational budget, we consider the problem of sparse PCA, where the principal eigenvector of
Σ
is
s
-sparse, and
r
eff
can be large. In this setting, to our knowledge, there are no known single-pass algorithms that achieve the minimax error bound in
O
(
d
)
space and
O
(
n
d
)
time without either requiring strong initialization conditions or assuming further structure (e.g., spiked) of the covariance matrix. We show that a simple single-pass procedure that thresholds the output of Oja's algorithm (the Oja vector) can achieve the minimax error bound under some regularity conditions in
O
(
d
)
space and
O
(
n
d
)
time.
We present a nontrivial and novel analysis of the entries of the unnormalized Oja vector, which involves the projection of a product of independent random matrices on a random initial vector. This is completely different from previous analyses of Oja's algorithm and matrix products, which have been done when the
r
eff
is bounded.


DeiSAM: Segment Anything with Deictic Prompting

neuro-symbolic reasoning;object segmentation;deictic representation;large language models;differentiable logic programming

Summary: Segment objects from complex textual prompts using neuro-symbolic reasoning with large-scale neural networks.

Abstract: Large-scale, pre-trained neural networks have demonstrated strong capabilities in various tasks, including zero-shot image segmentation. To identify concrete objects in complex scenes, humans instinctively rely on deictic descriptions in natural language, i.e., referring to something depending on the context such as "The object that is on the desk and behind the cup.". However, deep learning approaches cannot reliably interpret such deictic representations due to their lack of reasoning capabilities in complex scenarios. To remedy this issue, we propose DeiSAM — a combination of large pre-trained neural networks with differentiable logic reasoners — for deictic promptable segmentation. Given a complex, textual segmentation description, DeiSAM leverages Large Language Models (LLMs) to generate first-order logic rules and performs differentiable forward reasoning on generated scene graphs. Subsequently, DeiSAM segments objects by matching them to the logically inferred image regions. As part of our evaluation, we propose the Deictic Visual Genome (DeiVG) dataset, containing paired visual input and complex, deictic textual prompts. Our empirical results demonstrate that DeiSAM is a substantial improvement over purely data-driven baselines for deictic promptable segmentation.


Community Detection Guarantees using Embeddings Learned by Node2Vec

Summary: We show theoretical guarantees for community detection using node2vec embeddings of networks.

Abstract: Embedding the nodes of a large network into an Euclidean space is a common objective in modern machine learning, with a variety of tools available. These embeddings can then be used as features for tasks such as community detection/node clustering or link prediction, where they achieve state of the art performance. With the exception of spectral clustering methods, there is little theoretical understanding for commonly used approaches to learning embeddings. In this work we examine the theoretical properties of the embeddings learned by node2vec. Our main result shows that the use of k-means clustering on the embedding vectors produced by node2vec gives weakly consistent community recovery for the nodes in (degree corrected) stochastic block models. We also discuss the use of these embeddings for node and link prediction tasks. We demonstrate this result empirically for both real and simulated networks, and examine how this relates to other embedding tools for network data.


Unrolled denoising networks provably learn to perform optimal Bayesian inference

algorithm unrolling;approximate message passing (AMP);inverse problems;denoising

Summary: We show that an algorithmically inspired architecture similar to reverse diffusion denoising can provably learn Bayes optimal inference with gradient descent, and we show the score-matching objective is learnable in one-dimension along the way.

Abstract:
Much of Bayesian inference centers around the design of estimators for inverse problems which are optimal assuming the data comes from a known prior. But what do these optimality guarantees mean if the prior is unknown? In recent years, algorithm unrolling has emerged as deep learning's answer to this age-old question: design a neural network whose layers can in principle simulate iterations of inference algorithms and train on data generated by the unknown prior. Despite its empirical success, however, it has remained unclear whether this method can provably recover the performance of its optimal, prior-aware counterparts.
In this work, we prove the first rigorous learning guarantees for neural networks based on unrolling approximate message passing (AMP). For compressed sensing, we prove that when trained on data drawn from a product prior, the layers of the network approximately converge to the same denoisers used in Bayes AMP. We also provide extensive numerical experiments for compressed sensing and rank-one matrix estimation demonstrating the advantages of our unrolled architecture --- in addition to being able to obliviously adapt to general priors, it exhibits improvements over Bayes AMP in more general settings of low dimensions, non-Gaussian designs, and non-product priors.


Customized Subgraph Selection and Encoding for Drug-drug Interaction Prediction

Drug-drug Interaction Prediction;Neural Architecture Search;Graph Neural Networks

Summary: We propose to efficiently and robustly search for data-specific subgraph-based pipeline components for drug-drug interaction prediction.

Abstract: Subgraph-based methods have proven to be effective and interpretable in predicting drug-drug interactions (DDIs), which are essential for medical practice and drug development. Subgraph selection and encoding are critical stages in these methods, yet customizing these components remains underexplored due to the high cost of manual adjustments. In this study, inspired by the success of neural architecture search (NAS), we propose a method to search for data-specific components within subgraph-based frameworks. Specifically, we introduce extensive subgraph selection and encoding spaces that account for the diverse contexts of drug interactions in DDI prediction. To address the challenge of large search spaces and high sampling costs, we design a relaxation mechanism that uses an approximation strategy to efficiently explore optimal subgraph configurations. This approach allows for robust exploration of the search space. Extensive experiments demonstrate the effectiveness and superiority of the proposed method, with the discovered subgraphs and encoding functions highlighting the model’s adaptability.


A Versatile Diffusion Transformer with Mixture of Noise Levels for Audiovisual Generation

multimodal diffusion;multimodal generation;diffusion timestep;latent diffusion models

Summary: We present a diffusion framework that can learn a wide range of conditional distributions within audiovisual data using a single model.

Abstract: Training diffusion models for audiovisual sequences allows for a range of generation tasks by learning conditional distributions of various input-output combinations of the two modalities. Nevertheless, this strategy often requires training a separate model for each task which is expensive. Here, we propose a novel training approach to effectively learn arbitrary conditional distributions in the audiovisual space. Our key contribution lies in how we parameterize the diffusion timestep in the forward diffusion process. Instead of the standard fixed diffusion timestep, we propose applying variable diffusion timesteps across the temporal dimension and across modalities of the inputs. This formulation offers flexibility to introduce variable noise levels for various portions of the input, hence the term mixture of noise levels. We propose a transformer-based audiovisual latent diffusion model and show that it can be trained in a task-agnostic fashion using our approach to enable a variety of audiovisual generation tasks at inference time. Experiments demonstrate the versatility of our method in tackling cross-modal and multimodal interpolation tasks in the audiovisual space. Notably, our proposed approach surpasses baselines in generating temporally and perceptually consistent samples conditioned on the input. Project page: neurips13025.github.io


Online Weighted Paging with Unknown Weights

Online Learning;Online Weighted Paging;Online Algorithms;Competitive Ratio;Regret;Theory

Summary: We study the Online Weighted Paging problem, where the weights are unknown. We provide algorithm and analyze it's performance in terms of competitive ratio and regret.

Abstract:
Online paging is a fundamental problem in the field of online algorithms, in which one maintains a cache of
k
slots as requests for fetching pages arrive online. In the weighted variant of this problem, each page has its own fetching cost; a substantial line of work on this problem culminated in an (optimal)
O
(
log

k
)
-competitive randomized algorithm, due to Bansal, Buchbinder and Naor (FOCS'07).
Existing work for weighted paging assumes that page weights are known in advance, which is not always the case in practice. For example, in multi-level caching architectures, the expected cost of fetching a memory block is a function of its probability of being in a mid-level cache rather than the main memory. This complex property cannot be predicted in advance; over time, however, one may glean information about page weights through sampling their fetching cost multiple times.
We present the first algorithm for online weighted paging that does not know page weights in advance, but rather learns from weight samples. In terms of techniques, this requires providing (integral) samples to a fractional solver, requiring a delicate interface between this solver and the randomized rounding scheme; we believe that our work can inspire online algorithms to other problems that involve cost sampling.


An exactly solvable model for emergence and scaling laws in the multitask sparse parity problem

science of deep learning;emergence;skills;scaling laws

Summary: We can predict emergence in neural networks using a simple model that also demonstrates scaling laws.

Abstract: Deep learning models can exhibit what appears to be a sudden ability to solve a new problem as training time, training data, or model size increases, a phenomenon known as emergence. In this paper, we present a framework where each new ability (a skill) is represented as a basis function. We solve a simple multi-linear model in this skill-basis, finding analytic expressions for the emergence of new skills, as well as for scaling laws of the loss with training time, data size, model size, and optimal compute. We compare our detailed calculations to direct simulations of a two-layer neural network trained on multitask sparse parity, where the tasks in the dataset are distributed according to a power-law. Our simple model captures, using a single fit parameter, the sigmoidal emergence of multiple new skills as training time, data size or model size increases in the neural network.


Many-shot Jailbreaking

large language models;long context;robustness;jailbreaks;in-context learning

Summary: We investigate a simple yet effective long-context jailbreak, study the corresponding scaling laws and evaluate some mitigations against it.

Abstract: We investigate a family of simple long-context attacks on large language models: prompting with hundreds of demonstrations of undesirable behavior. This attack is newly feasible with the larger context windows recently deployed by language model providers like Google DeepMind, OpenAI and Anthropic. We find that in diverse, realistic circumstances, the effectiveness of this attack follows a power law, up to hundreds of shots. We demonstrate the success of this attack on the most widely used state-of-the-art closed-weight models, and across various tasks. Our results suggest very long contexts present a rich new attack surface for LLMs.


Can neural operators always be continuously discretized?

Summary: Discretizing injective neural operators may cause them to lose injectivity, even with very flexible discretization methods.

Abstract: In this work we consider the problem of discretization of neural operators in a general setting. Using category theory, we give a no-go theorem that shows that diffeomorphisms between Hilbert spaces may not admit any continuous approximations by diffeomorphisms on finite spaces, even if the discretization is non-linear. This shows how infinite-dimensional Hilbert spaces and finite-dimensional vector spaces fundamentally differ. A key take-away is that to obtain discretization invariance, considerable effort is needed to ensure that finite-dimensional approximations of neural operator converge not only as sequences of functions, but that their representations converge in a suitable sense as well. With this perspective, we give several positive results. We first show that strongly monotone diffeomorphism operators always admit finite-dimensional strongly monotone diffeomorphisms. Next we show that bilipschitz neural operators may always be written via the repeated alternating composition of strongly monotone neural operators and invertible linear maps. We also show that such operators may be inverted locally via iteration provided that such inverse exists. Finally, we conclude by showing how our framework may be used `out of the box' to prove quantitative approximation results for discretization of neural operators.


Self-Consuming Generative Models with Curated Data Provably Optimize Human Preferences

Summary: We theoretically show that iteratively retraining a generative model on its own generated samples with human curation optimizes human preferences

Abstract: The rapid progress in generative models has resulted in impressive leaps in generation quality, blurring the lines between synthetic and real data. Web-scale datasets are now prone to the inevitable contamination by synthetic data, directly impacting the training of future generated models. Already, some theoretical results on self-consuming generative models (a.k.a., iterative retraining) have emerged in the literature, showcasing that either model collapse or stability could be possible depending on the fraction of generated data used at each retraining step. However, in practice, synthetic data is often subject to human feedback and curated by users before being used and uploaded online. For instance, many interfaces of popular text-to-image generative models, such as Stable Diffusion or Midjourney, produce several variations of an image for a given query which can eventually be curated by the users. In this paper, we theoretically study the impact of data curation on iterated retraining of generative models and show that it can be seen as an implicit preference optimization mechanism. However, unlike standard preference optimization, the generative model does not have access to the reward function or negative samples needed for pairwise comparisons. Moreover, our study doesn't require access to the density function, only to samples. We prove that, if the data is curated according to a reward model, then the expected reward of the iterative retraining procedure is maximized. We further provide theoretical results on the stability of the retraining loop when using a positive fraction of real data at each step. Finally, we conduct illustrative experiments on both synthetic datasets and on CIFAR10 showing that such a procedure amplifies biases of the reward model.


Knowledge Graph Completion by Intermediate Variables Regularization

Knowledge Graph Completion;Tensor Decomposition;Regularization

Summary: We propose a regularization to alleviate the overfitting problem of tensor decomposition based models for knowledge graph completion.

Abstract: Knowledge graph completion (KGC) can be framed as a 3-order binary tensor completion task. Tensor decomposition-based (TDB) models have demonstrated strong performance in KGC. In this paper, we provide a summary of existing TDB models and derive a general form for them, serving as a foundation for further exploration of TDB models. Despite the expressiveness of TDB models, they are prone to overfitting. Existing regularization methods merely minimize the norms of embeddings to regularize the model, leading to suboptimal performance. Therefore, we propose a novel regularization method for TDB models that addresses this limitation. The regularization is applicable to most TDB models and ensures tractable computation. Our method minimizes the norms of intermediate variables involved in the different ways of computing the predicted tensor. To support our regularization method, we provide a theoretical analysis that proves its effect in promoting low trace norm of the predicted tensor to reduce overfitting. Finally, we conduct experiments to verify the effectiveness of our regularization technique as well as the reliability of our theoretical analysis. The code is available at https://github.com/changyi7231/IVR.


RankUp: Boosting Semi-Supervised Regression with an Auxiliary Ranking Classifier

Semi-Supervised Learning;Weakly Supervised Learning;Regression

Summary: RankUp adapts semi-supervised classification techniques for regression by converting regression to a ranking problem.

Abstract: State-of-the-art (SOTA) semi-supervised learning techniques, such as FixMatch and it's variants, have demonstrated impressive performance in classification tasks. However, these methods are not directly applicable to regression tasks. In this paper, we present RankUp, a simple yet effective approach that adapts existing semi-supervised classification techniques to enhance the performance of regression tasks. RankUp achieves this by converting the original regression task into a ranking problem and training it concurrently with the original regression objective. This auxiliary ranking classifier outputs a classification result, thus enabling integration with existing semi-supervised classification methods. Moreover, we introduce regression distribution alignment (RDA), a complementary technique that further enhances RankUp's performance by refining pseudo-labels through distribution alignment. Despite its simplicity, RankUp, with or without RDA, achieves SOTA results in across a range of regression benchmarks, including computer vision, audio, and natural language processing tasks. Our code and log data are open-sourced at https://github.com/pm25/semi-supervised-regression.


EPIC: Effective Prompting for Imbalanced-Class Data Synthesis in Tabular Data Classification via Large Language Models

Large language model;In-context learning;Few-shot learning;Class imbalance;Tabular data;Synthetic data generation

Summary: Can LLMs effectively generate synthetic tabular data to address class imbalance for classification tasks via in-context learning? How should prompts be structured to achieve this goal?

Abstract: Large language models (LLMs) have demonstrated remarkable in-context learning capabilities across diverse applications. In this work, we explore the effectiveness of LLMs for generating realistic synthetic tabular data, identifying key prompt design elements to optimize performance. We introduce EPIC, a novel approach that leverages balanced, grouped data samples and consistent formatting with unique variable mapping to guide LLMs in generating accurate synthetic data across all classes, even for imbalanced datasets. Evaluations on real-world datasets show that EPIC achieves state-of-the-art machine learning classification performance, significantly improving generation efficiency. These findings highlight the effectiveness of EPIC for synthetic tabular data generation, particularly in addressing class imbalance.


Context-Aware Testing: A New Paradigm for Model Testing with Large Language Models

model testing;tabular data;large language models

Summary: We introduce context-aware testing (CAT) which uses context to guide the search for meaningful model failures

Abstract: The predominant de facto paradigm of testing ML models relies on either using only held-out data to compute aggregate evaluation metrics or by assessing the performance on different subgroups. However, such data-only testing methods operate under the restrictive assumption that the available empirical data is the sole input for testing ML models, disregarding valuable contextual information that could guide model testing. In this paper, we challenge the go-to approach of data-only testing and introduce Context-Aware Testing (CAT) which uses context as an inductive bias to guide the search for meaningful model failures. We instantiate the first CAT system, SMART Testing, which employs large language models to hypothesize relevant and likely failures, which are evaluated on data using a self-falsification mechanism. Through empirical evaluations in diverse settings, we show that SMART automatically identifies more relevant and impactful failures than alternatives, demonstrating the potential of CAT as a testing paradigm.


SpaFL: Communication-Efficient Federated Learning With Sparse Models And Low Computational Overhead

Federated Learning;Communication and Computation Efficiency;Pruning

Summary: We find optimal structured sparse models by communicating trainable thresholds

Abstract: The large communication and computation overhead of federated learning (FL) is one of the main challenges facing its practical deployment over resource-constrained clients and systems. In this work, SpaFL: a communication-efficient FL framework is proposed to optimize sparse model structures with low computational overhead. In SpaFL, a trainable threshold is defined for each filter/neuron to prune its all connected parameters, thereby leading to structured sparsity. To optimize the pruning process itself, only thresholds are communicated between a server and clients instead of parameters, thereby learning how to prune. Further, global thresholds are used to update model parameters by extracting aggregated parameter importance. The generalization bound of SpaFL is also derived, thereby proving key insights on the relation between sparsity and performance. Experimental results show that SpaFL improves accuracy while requiring much less communication and computing resources compared to sparse baselines. The code is available at https://github.com/news-vt/SpaFL_NeruIPS_2024


Towards Understanding How Transformers Learn In-context Through a Representation Learning Lens

Abstract: Pre-trained large language models based on Transformers have demonstrated remarkable in-context learning (ICL) abilities. With just a few demonstration examples, the models can implement new tasks without any parameter updates. However, it is still an open question to understand the mechanism of ICL. In this paper, we attempt to explore the ICL process in Transformers through a lens of representation learning. Initially, leveraging kernel methods, we figure out a dual model for one softmax attention layer. The ICL inference process of the attention layer aligns with the training procedure of its dual model, generating token representation predictions that are equivalent to the dual model's test outputs. We delve into the training process of this dual model from a representation learning standpoint and further derive a generalization error bound related to the quantity of demonstration tokens. Subsequently, we extend our theoretical conclusions to more complicated scenarios, including one Transformer layer and multiple attention layers. Furthermore, drawing inspiration from existing representation learning methods especially contrastive learning, we propose potential modifications for the attention layer. Finally, experiments are designed to support our findings.


Probabilistic size-and-shape functional mixed models

statistical shape analysis;size-and-shape perturbation model;Bayesian random effects model;norm-preserving transformation;phase function

Summary: We develop a Bayesian mixed effects model for inference on the functional size-and-shape mean via a combination of size-and-shape preserving and altering random effects.

Abstract: The reliable recovery and uncertainty quantification of a fixed effect function $\mu$ in a functional mixed model, for modeling population- and object-level variability in noisily observed functional data, is a notoriously challenging task: variations along the $x$ and $y$ axes are confounded with additive measurement error, and cannot in general be disentangled. The question then as to what properties of $\mu$ may be reliably recovered becomes important. We demonstrate that it is possible to recover the size-and-shape of a square-integrable $\mu$ under a Bayesian functional mixed model. The size-and-shape of $\mu$ is a geometric property invariant to a family of space-time unitary transformations, viewed as rotations of the Hilbert space, that jointly transform the $x$ and $y$ axes. A random object-level unitary transformation then captures size-and-shape preserving deviations of $\mu$ from an individual function, while a random linear term and measurement error capture size-and-shape altering deviations. The model is regularized by appropriate priors on the unitary transformations, posterior summaries of which may then be suitably interpreted as optimal data-driven rotations of a fixed orthonormal basis for the Hilbert space. Our numerical experiments demonstrate utility of the proposed model, and superiority over the current state-of-the-art.


Thinking Forward: Memory-Efficient Federated Finetuning of Language Models

Federated Learning;Large Language Models;Forward-mode Automatic Differentiation;Forward-mode AD;Memory-efficient Finetuning;Memory-efficiency;Data Heterogeneity

Summary: Spry is a federated learning algorithm that enables finetuning LLMs using Forward-mode Auto Differentiation; to achieve low memory footprint, high accuracy, and fast convergence.

Abstract:
Finetuning large language models (LLMs) in federated learning (FL) settings has become increasingly important as it allows resource-constrained devices to finetune a model using private data. However, finetuning LLMs using backpropagation requires excessive memory (especially from intermediate activations) for resource-constrained devices. While Forward-mode Auto-Differentiation (AD) can significantly reduce memory footprint from activations, we observe that directly applying it to LLM finetuning results in slow convergence and poor accuracy. In this paper, we introduce Spry, an FL algorithm that splits trainable weights of an LLM among participating clients, such that each client computes gradients using forward-mode AD that are closer estimations of the true gradients. Spry achieves a low memory footprint, high accuracy, and fast convergence. We formally prove that the global gradients in Spry are unbiased estimators of true global gradients for homogeneous data distributions across clients, while heterogeneity increases bias of the estimates. We also derive Spry's convergence rate, showing that the gradients decrease inversely proportional to the number of FL rounds, indicating the convergence up to the limits of heterogeneity. Empirically, Spry reduces the memory footprint during training by 1.4-7.1
×
in contrast to backpropagation, while reaching comparable accuracy, across a wide range of language tasks, models, and FL settings. Spry reduces the convergence time by 1.2-20.3
×
and achieves 5.2-13.5% higher accuracy against state-of-the-art zero-order methods. When finetuning Llama2-7B with LoRA, compared to the peak memory consumption of 33.9GB of backpropagation, Spry only consumes 6.2GB of peak memory. For OPT13B, the reduction is from 76.5GB to 10.8GB. Spry makes feasible previously impossible FL deployments on commodity mobile and edge devices. Our source code is available for replication at https://github.com/Astuary/Spry.


UMFC: Unsupervised Multi-Domain Feature Calibration for Vision-Language Models

Summary: This paper proposes UMFC, which calibrate features from multi-domain in a label-free and training-free way.

Abstract: Pre-trained vision-language models (e.g., CLIP) have shown powerful zero-shot transfer capabilities. But they still struggle with domain shifts and typically require labeled data to adapt to downstream tasks, which could be costly. In this work, we aim to leverage unlabeled data that naturally spans multiple domains to enhance the transferability of vision-language models. Under this unsupervised multi-domain setting, we have identified inherent model bias within CLIP, notably in its visual and text encoders. Specifically, we observe that CLIP’s visual encoder tends to prioritize encoding domain over discriminative category information, meanwhile its text encoder exhibits a preference for domain-relevant classes. To mitigate this model bias, we propose a training-free and label-free feature calibration method, Unsupervised Multi-domain Feature Calibration (UMFC). UMFC estimates image-level biases from domain-specific features and text-level biases from the direction of domain transition. These biases are subsequently subtracted from original image and text features separately, to render them domain-invariant. We evaluate our method on multiple settings including transductive learning and test-time adaptation. Extensive experiments show that our method outperforms CLIP and performs on par with the state-of-the-arts that need additional annotations or optimization. Our code is available at https://github.com/GIT-LJc/UMFC.


Towards the Dynamics of a DNN Learning Symbolic Interactions

deep learning theory;learning theory;knowledge representation

Summary: We prove the two-phase dynamics of a DNN learning interactions in the training process.

Abstract: This study proves the two-phase dynamics of a deep neural network (DNN) learning interactions. Despite the long disappointing view of the faithfulness of post-hoc explanation of a DNN, a series of theorems have been proven [27] in recent years to show that for a given input sample, a small set of interactions between input variables can be considered as primitive inference patterns that faithfully represent a DNN's detailed inference logic on that sample. Particularly, Zhang et al. [41] have observed that various DNNs all learn interactions of different complexities in two distinct phases, and this two-phase dynamics well explains how a DNN changes from under-fitting to over-fitting. Therefore, in this study, we mathematically prove the two-phase dynamics of interactions, providing a theoretical mechanism for how the generalization power of a DNN changes during the training process. Experiments show that our theory well predicts the real dynamics of interactions on different DNNs trained for various tasks.


MetaAligner: Towards Generalizable Multi-Objective Alignment of Language Models

Language Models;Multi-objective Alignment;Preference Optimization

Summary: We propose MetaAligner, the first policy-agnostic and generalizable method for multi-objective preference alignment.

Abstract: Recent advancements in large language models (LLMs) focus on aligning to heterogeneous human expectations and values via multi-objective preference alignment. However, existing methods are dependent on the policy model parameters, which require high-cost repetition of their alignment algorithms for each new policy model, and they cannot expand to unseen objectives due to their static alignment objectives. In this work, we propose Meta-Objective Aligner (MetaAligner), the first policy-agnostic and generalizable method for multi-objective preference alignment. MetaAligner models multi-objective alignment into three stages: (1) dynamic objectives reformulation algorithm reorganizes traditional alignment datasets to supervise the model on performing flexible alignment across different objectives; (2) conditional weak-to-strong correction paradigm aligns the weak outputs of fixed policy models to approach strong outputs with higher preferences in the corresponding alignment objectives, enabling plug-and-play inferences on any policy models, which significantly reduces training costs and facilitates alignment on close-source policy models; (3) generalizable inference method flexibly adjusts target objectives by updating their text descriptions in the prompts, facilitating generalizable alignment to unseen objectives. Experimental results show that MetaAligner achieves significant and balanced improvements in multi-objective alignments on 10 state-of-the-art policy models, and saves up to 93.63% of GPU training hours compared to previous alignment methods. The model also effectively aligns unseen objectives, marking the first step towards generalizable multi-objective preference alignment.


Neural Model Checking

Formal Verification;SystemVerilog;Temporal Logic;Neuro-symbolic AI;Neural Certificates

Summary: Hardware model checking using neural certificates

Abstract: We introduce a machine learning approach to model checking temporal logic, with application to formal hardware verification. Model checking answers the question of whether every execution of a given system satisfies a desired temporal logic specification. Unlike testing, model checking provides formal guarantees. Its application is expected standard in silicon design and the EDA industry has invested decades into the development of performant symbolic model checking algorithms. Our new approach combines machine learning and symbolic reasoning by using neural networks as formal proof certificates for linear temporal logic. We train our neural certificates from randomly generated executions of the system and we then symbolically check their validity using satisfiability solving which, upon the affirmative answer, establishes that the system provably satisfies the specification. We leverage the expressive power of neural networks to represent proof certificates as well as the fact that checking a certificate is much simpler than finding one. As a result, our machine learning procedure for model checking is entirely unsupervised, formally sound, and practically effective. We experimentally demonstrate that our method outperforms the state-of-the-art academic and commercial model checkers on a set of standard hardware designs written in SystemVerilog.


Constrained Diffusion with Trust Sampling

diffusion models;guidance;image generation;human motion

Summary: A new optimization-based training-free guided diffusion method, applicable to drastically different domains such as image and human motion generation

Abstract: Diffusion models have demonstrated significant promise in various generative tasks; however, they often struggle to satisfy challenging constraints. Our approach addresses this limitation by rethinking training-free loss-guided diffusion from an optimization perspective. We formulate a series of constrained optimizations throughout the inference process of a diffusion model. In each optimization, we allow the sample to take multiple steps along the gradient of the proxy constraint function until we can no longer trust the proxy, according to the variance at each diffusion level. Additionally, we estimate the state manifold of diffusion model to allow for early termination when the sample starts to wander away from the state manifold at each diffusion step. Trust sampling effectively balances between following the unconditional diffusion model and adhering to the loss guidance, enabling more flexible and accurate constrained generation. We demonstrate the efficacy of our method through extensive experiments on complex tasks, and in drastically different domains of images and 3D motion generation, showing significant improvements over existing methods in terms of generation quality. Our implementation is available at https://github.com/will-s-h/trust-sampling.


QUEST: Quality-Aware Metropolis-Hastings Sampling for Machine Translation

Summary: This paper presents a method to generate diverse and high-quality machine translations by sampling from a Gibbs distribution using the Metropolis-Hastings algorithm.

Abstract:
An important challenge in machine translation (MT) is to generate high-quality and diverse translations. Prior work has shown that the estimated likelihood from the MT model correlates poorly with translation quality. In contrast, quality evaluation metrics (such as COMET or BLEURT) exhibit high correlations with human judgments, which has motivated their use as rerankers (such as quality-aware and minimum Bayes risk decoding). However, relying on a single translation with high estimated quality increases the chances of "gaming the metric''. In this paper, we address the problem of sampling a set of high-quality and diverse translations. We provide a simple and effective way to avoid over-reliance on noisy quality estimates by using them as the energy function of a Gibbs distribution. Instead of looking for a mode in the distribution, we generate multiple samples from high-density areas through the Metropolis-Hastings algorithm, a simple Markov chain Monte Carlo approach. The results show that our proposed method leads to high-quality and diverse outputs across multiple language pairs (English
↔
{German, Russian}) with two strong decoder-only LLMs (Alma-7b, Tower-7b).


Breaking the curse of dimensionality in structured density estimation

nonparametric statistics;density estimation;graphical models;sample complexity;curse of dimensionality

Summary: This work presents a new graphical quantity and shows that, when one assumes the Markov property over this graph, it leads to much faster rates for nonparametric density estimation.

Abstract: We consider the problem of estimating a structured multivariate density, subject to Markov conditions implied by an undirected graph. In the worst case, without Markovian assumptions, this problem suffers from the curse of dimensionality. Our main result shows how the curse of dimensionality can be avoided or greatly alleviated under the Markov property, and applies to arbitrary graphs. While existing results along these lines focus on sparsity or manifold assumptions, we introduce a new graphical quantity called ``graph resilience'' and show that it dictates the optimal sample complexity. Surprisingly, although one might expect the sample complexity of this problem to scale with local graph parameters such as the degree, this turns out not to be the case. Through explicit examples, we compute uniform deviation bounds and illustrate how the curse of dimensionality in density estimation can thus be circumvented. Notable examples where the rate improves substantially include sequential, hierarchical, and spatial data.


Generalizing CNNs to graphs with learnable neighborhood quantization

graph convolutional networks;graph neural networks;quantization

Summary: We present a novel GCN framework that properly generalizes CNNs to graph structured data.

Abstract: Convolutional neural networks (CNNs) have led to a revolution in analyzing array data. However, many important sources of data, such as biological and social networks, are naturally structured as graphs rather than arrays, making the design of graph neural network (GNN) architectures that retain the strengths of CNNs an active and exciting area of research. Here, we introduce Quantized Graph Convolution Networks (QGCNs), the first framework for GNNs that formally and directly extends CNNs to graphs. QGCNs do this by decomposing the convolution operation into non-overlapping sub-kernels, allowing them to fit graph data while reducing to a 2D CNN layer on array data. We generalize this approach to graphs of arbitrary size and dimension by approaching sub-kernel assignment as a learnable multinomial assignment problem. Integrating this approach into a residual network architecture, we demonstrate performance that matches or exceeds other state-of-the-art GNNs on benchmark graph datasets and for predicting properties of nonlinear dynamics on a new finite element graph dataset. In summary, QGCNs are a novel GNN framework that generalizes CNNs and their strengths to graph data, allowing for more accurate and expressive models.


Active Learning for Derivative-Based Global Sensitivity Analysis with Gaussian Processes

Global Sensitivity Analysis;Gaussian Processes;Bayesian Active Learning;Bayesian optimization

Summary: We propose several uncertainty based and information gain acquisition functions for derivative based global sensitivity analysis

Abstract: We consider the problem of active learning for global sensitivity analysis of expensive black-box functions. Our aim is to efficiently learn the importance of different input variables, e.g., in vehicle safety experimentation, we study the impact of the thickness of various components on safety objectives. Since function evaluations are expensive, we use active learning to prioritize experimental resources where they yield the most value. We propose novel active learning acquisition functions that directly target key quantities of derivative-based global sensitivity measures (DGSMs) under Gaussian process surrogate models. We showcase the first application of active learning directly to DGSMs, and develop tractable uncertainty reduction and information gain acquisition functions for these measures. Through comprehensive evaluation on synthetic and real-world problems, our study demonstrates how these active learning acquisition strategies substantially enhance the sample efficiency of DGSM estimation, particularly with limited evaluation budgets. Our work paves the way for more efficient and accurate sensitivity analysis in various scientific and engineering applications.


FUSE: Fast Unified Simulation and Estimation for PDEs

Forward and Inverse Problems;PDEs;Neural Operators;Neural Posterior Estimation

Summary: This work presents a framework to unify forward and inverse problems in scientific computing by optimizing a joint objective derived from operator learning.

Abstract: The joint prediction of continuous fields and statistical estimation of the underlying discrete parameters is a common problem for many physical systems, governed by PDEs. Hitherto, it has been separately addressed by employing operator learning surrogates for field prediction while using simulation-based inference (and its variants) for statistical parameter determination. Here, we argue that solving both problems within the same framework can lead to consistent gains in accuracy and robustness. To this end, we propose a novel and flexible formulation of the operator learning problem that jointly predicts continuous quantities and infers distributions of discrete parameters, thereby amortizing the cost of both the inverse and the surrogate models to a joint pre-training step. We present the capabilities of the proposed methodology for predicting continuous and discrete biomarkers in full-body haemodynamics simulations under different levels of missing information. We also consider a test case for atmospheric large-eddy simulation of a two-dimensional dry cold bubble, where we infer both continuous time-series and information about the system's conditions. We present comparisons against different baselines to showcase significantly increased accuracy in both the inverse and the surrogate tasks.


QuaRot: Outlier-Free 4-Bit Inference in Rotated LLMs

quantization;efficient inference;large language models

Summary: We present a quantization scheme that enables 4-bit quantization of all weights, activations and KV-caches of LLMs during inference

Abstract: We introduce QuaRot, a new Quantization scheme based on Rotations, which is able to quantize LLMs end-to-end, including all weights, activations, and KV cache in 4 bits. QuaRot rotates LLMs in a way that removes outliers from the hidden state without changing the output, making quantization easier. This computational invariance is applied to the hidden state (residual) of the LLM, as well as to the activations of the feed-forward components, aspects of the attention mechanism, and to the KV cache. The result is a quantized model where all matrix multiplications are performed in 4 bits, without any channels identified for retention in higher precision. Our 4-bit quantized LLAMA2-70B model has losses of at most 0.47 WikiText-2 perplexity and retains 99% of the zero-shot performance. We also show that QuaRot can provide lossless 6 and 8 bit LLAMA-2 models without any calibration data using round-to-nearest quantization. Code is available at github.com/spcl/QuaRot.


Molecule Design by Latent Prompt Transformer

latent space generative modeling; Latent Prompt Transformer; molecule design

Summary: We propose the Latent Prompt Transformer, a novel latent space generative model with both offline and online learning algorithms for molecule design.

Abstract: This work explores the challenging problem of molecule design by framing it as a conditional generative modeling task, where target biological properties or desired chemical constraints serve as conditioning variables. We propose the Latent Prompt Transformer (LPT), a novel generative model comprising three components: (1) a latent vector with a learnable prior distribution modeled by a neural transformation of Gaussian white noise; (2) a molecule generation model based on a causal Transformer, which uses the latent vector as a prompt; and (3) a property prediction model that predicts a molecule's target properties and/or constraint values using the latent prompt. LPT can be learned by maximum likelihood estimation on molecule-property pairs. During property optimization, the latent prompt is inferred from target properties and constraints through posterior sampling and then used to guide the autoregressive molecule generation. After initial training on existing molecules and their properties, we adopt an online learning algorithm to progressively shift the model distribution towards regions that support desired target properties. Experiments demonstrate that LPT not only effectively discovers useful molecules across single-objective, multi-objective, and structure-constrained optimization tasks, but also exhibits strong sample efficiency.


Implicitly Guided Design with PropEn: Match your Data to Follow the Gradient

matching;property enhancement;gradient approximation;design optimization;shape optimization;antibodies

Summary: A method inspired by ``matching'' that allows for implicit guidance, sidestepping the need for a discriminator. Training with a matched dataset approximates the gradient of a property and applies to design optimization in real-world datasets.

Abstract: Across scientific domains, generating new models or optimizing existing ones while meeting specific criteria is crucial. Traditional machine learning frameworks for guided design use a generative model and a surrogate model (discriminator), requiring large datasets. However, real-world scientific applications often have limited data and complex landscapes, making data-hungry models inefficient or impractical. We propose a new framework, PropEn, inspired by ``matching'', which enables implicit guidance without training a discriminator. By matching each sample with a similar one that has a better property value, we create a larger training dataset that inherently indicates the direction of improvement. Matching, combined with an encoder-decoder architecture, forms a domain-agnostic generative framework for property enhancement. We show that training with a matched dataset approximates the gradient of the property of interest while remaining within the data distribution, allowing efficient design optimization. Extensive evaluations in toy problems and scientific applications, such as therapeutic protein design and airfoil optimization, demonstrate PropEn's advantages over common baselines. Notably, the protein design results are validated with wet lab experiments, confirming the competitiveness and effectiveness of our approach. Our code is available at https://github.com/prescient-design/propen.


Geometric Exploitation for Indoor Panoramic Semantic Segmentation

indoor panoramic semantic segmentation;vertical relative distance

Summary: We propose a new approach for Indoor Panoramic Semantic Segmentation

Abstract: PAnoramic Semantic Segmentation (PASS) is an important task in computer vision, as it enables semantic understanding of a 360° environment. Currently, most of existing works have focused on addressing the distortion issues in 2D panoramic images without considering spatial properties of indoor scene. This restricts PASS methods in perceiving contextual attributes to deal with the ambiguity when working with monocular images. In this paper, we propose a novel approach for indoor panoramic semantic segmentation. Unlike previous works, we consider the panoramic image as a composition of segment groups: oversampled segments, representing planar structures such as floors and ceilings, and under-sampled segments, representing other scene elements. To optimize each group, we first enhance over-sampled segments by jointly optimizing with a dense depth estimation task. Then, we introduce a transformer-based context module that aggregates different geometric representations of the scene, combined with a simple high-resolution branch, it serves as a robust hybrid decoder for estimating under-sampled segments, effectively preserving the resolution of predicted masks while leveraging various indoor geometric properties. Experimental results on both real-world (Stanford2D3DS, Matterport3D) and synthetic (Structured3D) datasets demonstrate the robustness of our framework, by setting new state-of-the-arts in almost evaluations, The code and updated results are available at: https://github.com/caodinhduc/vertical_relative_distance.


Semi-Supervised Sparse Gaussian Classification: Provable Benefits of Unlabeled Data

semi-supervised learning;gaussian mixture models;high-dimensional statistics;sparsity;statistical-computational gaps

Abstract:
The premise of semi-supervised learning (SSL) is that combining labeled and unlabeled data yields significantly more accurate models. Despite empirical successes, the theoretical understanding of SSL is still far from complete. In this work, we study SSL for high dimensional sparse Gaussian classification. To construct an accurate classifier a key task is feature selection, detecting the few variables that separate the two classes. For this SSL setting, we analyze information theoretic lower bounds for accurate feature selection as well as computational lower bounds, assuming the low-degree likelihood hardness conjecture. Our key contribution is the identification of a regime in the problem parameters (dimension, sparsity, number of labeled and unlabeled samples) where SSL is guaranteed to be advantageous for classification. Specifically, there is a regime where it is possible to construct in polynomial time an accurate SSL classifier. However, any computationally efficient supervised or unsupervised learning schemes, that separately use only the labeled or unlabeled data would fail.
Our work highlights the provable benefits of combining labeled and unlabeled data for classification and feature selection in high dimensions. We present simulations that complement our theoretical analysis.


Scalable DBSCAN with Random Projections

Density-based clustering;random projections;extreme order statistics

Summary: Scale up DBSCAN and OPTICS with random projections

Abstract: We present sDBSCAN, a scalable density-based clustering algorithm in high dimensions with cosine distance. sDBSCAN leverages recent advancements in random projections given a significantly large number of random vectors to quickly identify core points and their neighborhoods, the primary hurdle of density-based clustering. Theoretically, sDBSCAN preserves the DBSCAN’s clustering structure under mild conditions with high probability. To facilitate sDBSCAN, we present sOPTICS, a scalable visual tool to guide the parameter setting of sDBSCAN. We also extend sDBSCAN and sOPTICS to L2, L1, χ2, and Jensen-Shannon distances via random kernel features. Empirically, sDBSCAN is significantly faster and provides higher accuracy than competitive DBSCAN variants on real-world million-point data sets. On these data sets, sDBSCAN and sOPTICS run in a few minutes, while the scikit-learn counterparts and other clustering competitors demand several hours or cannot run on our hardware due to memory constraints. Our code is available at https://github.com/NinhPham/sDbscan.


Dynamics of Supervised and Reinforcement Learning in the Non-Linear Perceptron

Learning Dynamics;non-linear perceptron;supervised learning;reinforcement learning

Summary: We derive learning dynamics for a non-linear perceptron performing a binary Gaussian classification task.

Abstract: The ability of a brain or a neural network to efficiently learn depends crucially on both the task structure and the learning rule. Previous works have analyzed the dynamical equations describing learning in the relatively simplified context of the perceptron under assumptions of a student-teacher framework or a linearized output. While these assumptions have facilitated theoretical understanding, they have precluded a detailed understanding of the roles of the nonlinearity and input-data distribution in determining the learning dynamics, limiting the applicability of the theories to real biological or artificial neural networks. Here, we use a stochastic-process approach to derive flow equations describing learning, applying this framework to the case of a nonlinear perceptron performing binary classification. We characterize the effects of the learning rule (supervised or reinforcement learning, SL/RL) and input-data distribution on the perceptron's learning curve and the forgetting curve as subsequent tasks are learned. In particular, we find that the input-data noise differently affects the learning speed under SL vs. RL, as well as determines how quickly learning of a task is overwritten by subsequent learning. Additionally, we verify our approach with real data using the MNIST dataset. This approach points a way toward analyzing learning dynamics for more-complex circuit architectures.


Approximately Equivariant Neural Processes

equivariance;neural processes;meta learning;deep learning;probabilistic methods

Summary: A general approach to constructing approximately equivariant architectures with applications to neural processes

Abstract: Equivariant deep learning architectures exploit symmetries in learning problems to improve the sample efficiency of neural-network-based models and their ability to generalise. However, when modelling real-world data, learning problems are often not exactly equivariant, but only approximately. For example, when estimating the global temperature field from weather station observations, local topographical features like mountains break translation equivariance. In these scenarios, it is desirable to construct architectures that can flexibly depart from exact equivariance in a data-driven way. Current approaches to achieving this cannot usually be applied out-of-the-box to any architecture and symmetry group. In this paper, we develop a general approach to achieving this using existing equivariant architectures. Our approach is agnostic to both the choice of symmetry group and model architecture, making it widely applicable. We consider the use of approximately equivariant architectures in neural processes (NPs), a popular family of meta-learning models. We demonstrate the effectiveness of our approach on a number of synthetic and real-world regression experiments, showing that approximately equivariant NP models can outperform both their non-equivariant and strictly equivariant counterparts.


Divide-and-Conquer Predictive Coding: a structured Bayesian inference algorithm

bioplausible;predictive coding;neuroscience;variational Bayes;VAE;deep generative model;probabilistic graphical models

Summary: We design a nested Sequential Monte Carlo algorithm based on predictive coding in neuroscience, and demonstrate both its biological plausibility and its performance in deep generative modeling.

Abstract: Unexpected stimuli induce "error" or "surprise" signals in the brain. The theory of predictive coding promises to explain these observations in terms of Bayesian inference by suggesting that the cortex implements variational inference in a probabilistic graphical model. However, when applied to machine learning tasks, this family of algorithms has yet to perform on par with other variational approaches in high-dimensional, structured inference problems. To address this, we introduce a novel predictive coding algorithm for structured generative models, that we call divide-and-conquer predictive coding (DCPC); it differs from other formulations of predictive coding, as it respects the correlation structure of the generative model and provably performs maximum-likelihood updates of model parameters, all without sacrificing biological plausibility. Empirically, DCPC achieves better numerical performance than competing algorithms and provides accurate inference in a number of problems not previously addressed with predictive coding. We provide an open implementation of DCPC in Pyro on Github.


Fair Secretaries with Unfair Predictions

Secretary problem;fairness;algorithms with predictions;online algorithms

Summary: We study fairness in the context of the secretary problem with predictions.

Abstract:
Algorithms with predictions is a recent framework for decision-making under uncertainty that leverages the power of machine-learned predictions without making any assumption about their quality. The goal in this framework is for algorithms to achieve an improved performance when the predictions are accurate while maintaining acceptable guarantees when the predictions are erroneous. A serious concern with algorithms that use predictions is that these predictions can be biased and, as a result, cause the algorithm to make decisions that are deemed unfair. We show that this concern manifests itself in the classical secretary problem in the learning-augmented setting---the state-of-the-art algorithm can have zero probability of accepting the best candidate, which we deem unfair, despite promising to accept a candidate whose expected value is at least
max
Ω
(
1
)
,
1
−
O
(
ε
)
times the optimal value, where
ε
is the prediction error. We show how to preserve this promise while also guaranteeing to accept the best candidate with probability
Ω
(
1
)
. Our algorithm and analysis are based on a new ``pegging'' idea that diverges from existing works and simplifies/unifies some of their results. Finally, we extend to the
k
-secretary problem and complement our theoretical analysis with experiments.


Introducing Spectral Attention for Long-Range Dependency in Time Series Forecasting

Time series forecasting;Long-range dependency;Low-pass filter;Spectral attention;Long term trend

Summary: Introduce low-pass filter based spectral attention to address long-range dependency in time series forecasting

Abstract: Sequence modeling faces challenges in capturing long-range dependencies across diverse tasks. Recent linear and transformer-based forecasters have shown superior performance in time series forecasting. However, they are constrained by their inherent inability to effectively address long-range dependencies in time series data, primarily due to using fixed-size inputs for prediction. Furthermore, they typically sacrifice essential temporal correlation among consecutive training samples by shuffling them into mini-batches. To overcome these limitations, we introduce a fast and effective Spectral Attention mechanism, which preserves temporal correlations among samples and facilitates the handling of long-range information while maintaining the base model structure. Spectral Attention preserves long-period trends through a low-pass filter and facilitates gradient to flow between samples. Spectral Attention can be seamlessly integrated into most sequence models, allowing models with fixed-sized look-back windows to capture long-range dependencies over thousands of steps. Through extensive experiments on 11 real-world time series datasets using 7 recent forecasting models, we consistently demonstrate the efficacy of our Spectral Attention mechanism, achieving state-of-the-art results.