Daily Papers

Residual neural networks are state-of-the-art deep learning models. Their continuous-depth analog, neural ordinary differential equations (ODEs), are also widely used. Despite their success, the link between the discrete and continuous models still lacks a solid mathematical foundation. In this article, we take a step in this direction by establishing an implicit regularization of deep residual networks towards neural ODEs, for nonlinear networks trained with gradient flow. We prove that if the network is initialized as a discretization of a neural ODE, then such a discretization holds throughout training. Our results are valid for a finite training time, and also as the training time tends to infinity provided that the network satisfies a Polyak-Lojasiewicz condition. Importantly, this condition holds for a family of residual networks where the residuals are two-layer perceptrons with an overparameterization in width that is only linear, and implies the convergence of gradient flow to a global minimum. Numerical experiments illustrate our results.

We provide a rigorous analysis of implicit regularization in an overparametrized tensor factorization problem beyond the lazy training regime. For matrix factorization problems, this phenomenon has been studied in a number of works. A particular challenge has been to design universal initialization strategies which provably lead to implicit regularization in gradient-descent methods. At the same time, it has been argued by Cohen et. al. 2016 that more general classes of neural networks can be captured by considering tensor factorizations. However, in the tensor case, implicit regularization has only been rigorously established for gradient flow or in the lazy training regime. In this paper, we prove the first tensor result of its kind for gradient descent rather than gradient flow. We focus on the tubal tensor product and the associated notion of low tubal rank, encouraged by the relevance of this model for image data. We establish that gradient descent in an overparametrized tensor factorization model with a small random initialization exhibits an implicit bias towards solutions of low tubal rank. Our theoretical findings are illustrated in an extensive set of numerical simulations show-casing the dynamics predicted by our theory as well as the crucial role of using a small random initialization.

In deep learning, often the training process finds an interpolator (a solution with 0 training loss), but the test loss is still low. This phenomenon, known as benign overfitting, is a major mystery that received a lot of recent attention. One common mechanism for benign overfitting is implicit regularization, where the training process leads to additional properties for the interpolator, often characterized by minimizing certain norms. However, even for a simple sparse linear regression problem y = beta^{*top} x +xi with sparse beta^*, neither minimum ell_1 or ell_2 norm interpolator gives the optimal test loss. In this work, we give a different parametrization of the model which leads to a new implicit regularization effect that combines the benefit of ell_1 and ell_2 interpolators. We show that training our new model via gradient descent leads to an interpolator with near-optimal test loss. Our result is based on careful analysis of the training dynamics and provides another example of implicit regularization effect that goes beyond norm minimization.

In this paper, we propose to use the general L^2-based Sobolev norms, i.e., H^s norms where sin R, to measure the data discrepancy due to noise in image processing tasks that are formulated as optimization problems. As opposed to a popular trend of developing regularization methods, we emphasize that an implicit regularization effect can be achieved through the class of Sobolev norms as the data-fitting term. Specifically, we analyze that the implicit regularization comes from the weights that the H^s norm imposes on different frequency contents of an underlying image. We further analyze the underlying noise assumption of using the Sobolev norm as the data-fitting term from a Bayesian perspective, build the connections with the Sobolev gradient-based methods and discuss the preconditioning effects on the convergence rate of the gradient descent algorithm, leading to a better understanding of functional spaces/metrics and the optimization process involved in image processing. Numerical results in full waveform inversion, image denoising and deblurring demonstrate the implicit regularization effects.

In this paper, we study the implicit regularization of stochastic gradient descent (SGD) through the lens of {\em dynamical stability} (Wu et al., 2018). We start by revising existing stability analyses of SGD, showing how the Frobenius norm and trace of Hessian relate to different notions of stability. Notably, if a global minimum is linearly stable for SGD, then the trace of Hessian must be less than or equal to 2/eta, where eta denotes the learning rate. By contrast, for gradient descent (GD), the stability imposes a similar constraint but only on the largest eigenvalue of Hessian. We then turn to analyze the generalization properties of these stable minima, focusing specifically on two-layer ReLU networks and diagonal linear networks. Notably, we establish the {\em equivalence} between these metrics of sharpness and certain parameter norms for the two models, which allows us to show that the stable minima of SGD provably generalize well. By contrast, the stability-induced regularization of GD is provably too weak to ensure satisfactory generalization. This discrepancy provides an explanation of why SGD often generalizes better than GD. Note that the learning rate (LR) plays a pivotal role in the strength of stability-induced regularization. As the LR increases, the regularization effect becomes more pronounced, elucidating why SGD with a larger LR consistently demonstrates superior generalization capabilities. Additionally, numerical experiments are provided to support our theoretical findings.

The estimation of optical flow and 6-DoF ego-motion, two fundamental tasks in 3D vision, has typically been addressed independently. For neuromorphic vision (e.g., event cameras), however, the lack of robust data association makes solving the two problems separately an ill-posed challenge, especially in the absence of supervision via ground truth. Existing works mitigate this ill-posedness by either enforcing the smoothness of the flow field via an explicit variational regularizer or leveraging explicit structure-and-motion priors in the parametrization to improve event alignment. The former notably introduces bias in results and computational overhead, while the latter, which parametrizes the optical flow in terms of the scene depth and the camera motion, often converges to suboptimal local minima. To address these issues, we propose an unsupervised framework that jointly optimizes egomotion and optical flow via implicit spatial-temporal and geometric regularization. First, by modeling camera's egomotion as a continuous spline and optical flow as an implicit neural representation, our method inherently embeds spatial-temporal coherence through inductive biases. Second, we incorporate structure-and-motion priors through differential geometric constraints, bypassing explicit depth estimation while maintaining rigorous geometric consistency. As a result, our framework (called E-MoFlow) unifies egomotion and optical flow estimation via implicit regularization under a fully unsupervised paradigm. Experiments demonstrate its versatility to general 6-DoF motion scenarios, achieving state-of-the-art performance among unsupervised methods and competitive even with supervised approaches.

This position paper argues that the theoretical inconsistency often observed among Responsible AI (RAI) metrics, such as differing fairness definitions or tradeoffs between accuracy and privacy, should be embraced as a valuable feature rather than a flaw to be eliminated. We contend that navigating these inconsistencies, by treating metrics as divergent objectives, yields three key benefits: (1) Normative Pluralism: Maintaining a full suite of potentially contradictory metrics ensures that the diverse moral stances and stakeholder values inherent in RAI are adequately represented. (2) Epistemological Completeness: The use of multiple, sometimes conflicting, metrics allows for a more comprehensive capture of multifaceted ethical concepts, thereby preserving greater informational fidelity about these concepts than any single, simplified definition. (3) Implicit Regularization: Jointly optimizing for theoretically conflicting objectives discourages overfitting to one specific metric, steering models towards solutions with enhanced generalization and robustness under real-world complexities. In contrast, efforts to enforce theoretical consistency by simplifying or pruning metrics risk narrowing this value diversity, losing conceptual depth, and degrading model performance. We therefore advocate for a shift in RAI theory and practice: from getting trapped in inconsistency to characterizing acceptable inconsistency thresholds and elucidating the mechanisms that permit robust, approximated consistency in practice.

The remarkable success of large language pretraining and the discovery of scaling laws signify a paradigm shift in machine learning. Notably, the primary objective has evolved from minimizing generalization error to reducing approximation error, and the most effective strategy has transitioned from regularization (in a broad sense) to scaling up models. This raises a critical question: Do the established principles that proved successful in the generalization-centric era remain valid in this new era of scaling? This paper examines several influential regularization-based principles that may no longer hold true in the scaling-centric, large language model (LLM) era. These principles include explicit L2 regularization and implicit regularization through small batch sizes and large learning rates. Additionally, we identify a new phenomenon termed ``scaling law crossover,'' where two scaling curves intersect at a certain scale, implying that methods effective at smaller scales may not generalize to larger ones. Together, these observations highlight two fundamental questions within this new paradigm: bullet Guiding Principles for Scaling: If regularization is no longer the primary guiding principle for model design, what new principles are emerging to guide scaling? bullet Model Comparison at Scale: How to reliably and effectively compare models at the scale where only a single experiment is feasible?

Two different approaches exist to handle missing values for prediction: either imputation, prior to fitting any predictive algorithms, or dedicated methods able to natively incorporate missing values. While imputation is widely (and easily) use, it is unfortunately biased when low-capacity predictors (such as linear models) are applied afterward. However, in practice, naive imputation exhibits good predictive performance. In this paper, we study the impact of imputation in a high-dimensional linear model with MCAR missing data. We prove that zero imputation performs an implicit regularization closely related to the ridge method, often used in high-dimensional problems. Leveraging on this connection, we establish that the imputation bias is controlled by a ridge bias, which vanishes in high dimension. As a predictor, we argue in favor of the averaged SGD strategy, applied to zero-imputed data. We establish an upper bound on its generalization error, highlighting that imputation is benign in the d sqrt n regime. Experiments illustrate our findings.

It is widely believed that the implicit regularization of SGD is fundamental to the impressive generalization behavior we observe in neural networks. In this work, we demonstrate that non-stochastic full-batch training can achieve comparably strong performance to SGD on CIFAR-10 using modern architectures. To this end, we show that the implicit regularization of SGD can be completely replaced with explicit regularization even when comparing against a strong and well-researched baseline. Our observations indicate that the perceived difficulty of full-batch training may be the result of its optimization properties and the disproportionate time and effort spent by the ML community tuning optimizers and hyperparameters for small-batch training.

In this work, we investigate the implicit regularization induced by teacher-student learning dynamics in self-distillation. To isolate its effect, we describe a simple experiment where we consider teachers at random initialization instead of trained teachers. Surprisingly, when distilling a student into such a random teacher, we observe that the resulting model and its representations already possess very interesting characteristics; (1) we observe a strong improvement of the distilled student over its teacher in terms of probing accuracy. (2) The learned representations are data-dependent and transferable between different tasks but deteriorate strongly if trained on random inputs. (3) The student checkpoint contains sparse subnetworks, so-called lottery tickets, and lies on the border of linear basins in the supervised loss landscape. These observations have interesting consequences for several important areas in machine learning: (1) Self-distillation can work solely based on the implicit regularization present in the gradient dynamics without relying on any dark knowledge, (2) self-supervised learning can learn features even in the absence of data augmentation and (3) training dynamics during the early phase of supervised training do not necessarily require label information. Finally, we shed light on an intriguing local property of the loss landscape: the process of feature learning is strongly amplified if the student is initialized closely to the teacher. These results raise interesting questions about the nature of the landscape that have remained unexplored so far. Code is available at https://github.com/safelix/dinopl.

Continual post-training (CPT) is a popular and effective technique for adapting foundation models like multimodal large language models to specific and ever-evolving downstream tasks. While existing research has primarily concentrated on methods like data replay, model expansion, or parameter regularization, the fundamental role of the learning paradigm within CPT remains largely unexplored. This paper presents a comparative analysis of two core post-training paradigms: supervised fine-tuning (SFT) and reinforcement fine-tuning (RFT), investigating their respective impacts on knowledge retention during CPT. Our experiments are conducted on a benchmark comprising seven diverse multimodal tasks, utilizing Qwen2.5-VL-7B-Instruct as the base model for continual post-training. The investigation yields two significant findings: (1) When continuously learning on downstream tasks, SFT leads to catastrophic forgetting of previously learned tasks. In contrast, RFT inherently preserves prior knowledge and achieve performance comparable to multi-task training. (2) RFT successfully protects and even enhances the model's general knowledge on standard benchmarks (e.g., MMMU and MMLU-Pro). Conversely, SFT degrades general model capabilities severely. Further analysis shows that explicit mechanisms, such as KL penalty and chain-of-thought reasoning, are not the primary factors. Instead, we find that the implicit regularization inherent to RFT is a key factor in mitigating forgetting. Finally, we propose a rollout-based instance filtering algorithm to improve the stability and efficiency of RFT. Our comprehensive study demonstrates the superiority of RFT as a robust paradigm for continual post-training.

Stochastic Gradient Descent (SGD) stands as a cornerstone optimization algorithm with proven real-world empirical successes but relatively limited theoretical understanding. Recent research has illuminated a key factor contributing to its practical efficacy: the implicit regularization it instigates. Several studies have investigated the linear stability property of SGD in the vicinity of a stationary point as a predictive proxy for sharpness and generalization error in overparameterized neural networks (Wu et al., 2022; Jastrzebski et al., 2019; Cohen et al., 2021). In this paper, we delve deeper into the relationship between linear stability and sharpness. More specifically, we meticulously delineate the necessary and sufficient conditions for linear stability, contingent on hyperparameters of SGD and the sharpness at the optimum. Towards this end, we introduce a novel coherence measure of the loss Hessian that encapsulates pertinent geometric properties of the loss function that are relevant to the linear stability of SGD. It enables us to provide a simplified sufficient condition for identifying linear instability at an optimum. Notably, compared to previous works, our analysis relies on significantly milder assumptions and is applicable for a broader class of loss functions than known before, encompassing not only mean-squared error but also cross-entropy loss.

Regularization of inverse problems is of paramount importance in computational imaging. The ability of neural networks to learn efficient image representations has been recently exploited to design powerful data-driven regularizers. While state-of-the-art plug-and-play (PnP) methods rely on an implicit regularization provided by neural denoisers, alternative Bayesian approaches consider Maximum A Posteriori (MAP) estimation in the latent space of a generative model, thus with an explicit regularization. However, state-of-the-art deep generative models require a huge amount of training data compared to denoisers. Besides, their complexity hampers the optimization involved in latent MAP derivation. In this work, we first propose to use compressive autoencoders instead. These networks, which can be seen as variational autoencoders with a flexible latent prior, are smaller and easier to train than state-of-the-art generative models. As a second contribution, we introduce the Variational Bayes Latent Estimation (VBLE) algorithm, which performs latent estimation within the framework of variational inference. Thanks to a simple yet efficient parameterization of the variational posterior, VBLE allows for fast and easy (approximate) posterior sampling. Experimental results on image datasets BSD and FFHQ demonstrate that VBLE reaches similar performance as state-of-the-art PnP methods, while being able to quantify uncertainties significantly faster than other existing posterior sampling techniques. The code associated to this paper is available in https://github.com/MaudBqrd/VBLE.

Double descent presents a counter-intuitive aspect within the machine learning domain, and researchers have observed its manifestation in various models and tasks. While some theoretical explanations have been proposed for this phenomenon in specific contexts, an accepted theory to account for its occurrence in deep learning remains yet to be established. In this study, we revisit the phenomenon of double descent and demonstrate that its occurrence is strongly influenced by the presence of noisy data. Through conducting a comprehensive analysis of the feature space of learned representations, we unveil that double descent arises in imperfect models trained with noisy data. We argue that double descent is a consequence of the model first learning the noisy data until interpolation and then adding implicit regularization via over-parameterization acquiring therefore capability to separate the information from the noise.

This manuscript considers the problem of learning a random Gaussian network function using a fully connected network with frozen intermediate layers and trainable readout layer. This problem can be seen as a natural generalization of the widely studied random features model to deeper architectures. First, we prove Gaussian universality of the test error in a ridge regression setting where the learner and target networks share the same intermediate layers, and provide a sharp asymptotic formula for it. Establishing this result requires proving a deterministic equivalent for traces of the deep random features sample covariance matrices which can be of independent interest. Second, we conjecture the asymptotic Gaussian universality of the test error in the more general setting of arbitrary convex losses and generic learner/target architectures. We provide extensive numerical evidence for this conjecture, which requires the derivation of closed-form expressions for the layer-wise post-activation population covariances. In light of our results, we investigate the interplay between architecture design and implicit regularization.

This paper introduces CURLoRA, a novel approach to fine-tuning large language models (LLMs) that leverages CUR matrix decomposition in the context of Low-Rank Adaptation (LoRA). Our method addresses two critical challenges in LLM fine-tuning: mitigating catastrophic forgetting during continual learning and reducing the number of trainable parameters. We propose a unique modification to the CUR decomposition process, utilizing inverted probabilities for column and row selection which acts as an implicit regularization, and initializing the U matrix as a zero matrix, and only fine-tuning it. We demonstrate through experiments on multiple datasets that CURLoRA outperforms standard LoRA in mitigating catastrophic forgetting. It maintains model stability and performance across tasks while significantly reducing the number of trainable parameters. Our results show that CURLoRA achieves very good and stable task accuracy while maintaining base model's perplexity scores fixed compared to LoRA upon continual fine-tuning, particularly in scenarios with limited data.

Weight decay is a broadly used technique for training state-of-the-art deep networks from image classification to large language models. Despite its widespread usage and being extensively studied in the classical literature, its role remains poorly understood for deep learning. In this work, we highlight that the role of weight decay in modern deep learning is different from its regularization effect studied in classical learning theory. For deep networks on vision tasks trained with multipass SGD, we show how weight decay modifies the optimization dynamics enhancing the ever-present implicit regularization of SGD via the loss stabilization mechanism. In contrast, for large language models trained with nearly one-epoch training, we describe how weight decay balances the bias-variance tradeoff in stochastic optimization leading to lower training loss and improved training stability. Overall, we present a unifying perspective from ResNets on vision tasks to LLMs: weight decay is never useful as an explicit regularizer but instead changes the training dynamics in a desirable way. The code is available at https://github.com/tml-epfl/why-weight-decay

We showcase important features of the dynamics of the Stochastic Gradient Descent (SGD) in the training of neural networks. We present empirical observations that commonly used large step sizes (i) lead the iterates to jump from one side of a valley to the other causing loss stabilization, and (ii) this stabilization induces a hidden stochastic dynamics orthogonal to the bouncing directions that biases it implicitly toward sparse predictors. Furthermore, we show empirically that the longer large step sizes keep SGD high in the loss landscape valleys, the better the implicit regularization can operate and find sparse representations. Notably, no explicit regularization is used so that the regularization effect comes solely from the SGD training dynamics influenced by the step size schedule. Therefore, these observations unveil how, through the step size schedules, both gradient and noise drive together the SGD dynamics through the loss landscape of neural networks. We justify these findings theoretically through the study of simple neural network models as well as qualitative arguments inspired from stochastic processes. Finally, this analysis allows us to shed a new light on some common practice and observed phenomena when training neural networks. The code of our experiments is available at https://github.com/tml-epfl/sgd-sparse-features.

We study data distillation for auto-regressive machine learning tasks, where the input and output have a strict left-to-right causal structure. More specifically, we propose Farzi, which summarizes an event sequence dataset into a small number of synthetic sequences -- Farzi Data -- which are optimized to maintain (if not improve) model performance compared to training on the full dataset. Under the hood, Farzi conducts memory-efficient data distillation by (i) deriving efficient reverse-mode differentiation of the Adam optimizer by leveraging Hessian-Vector Products; and (ii) factorizing the high-dimensional discrete event-space into a latent-space which provably promotes implicit regularization. Empirically, for sequential recommendation and language modeling tasks, we are able to achieve 98-120% of downstream full-data performance when training state-of-the-art models on Farzi Data of size as little as 0.1% of the original dataset. Notably, being able to train better models with significantly less data sheds light on the design of future large auto-regressive models, and opens up new opportunities to further scale up model and data sizes.

Diffusion models have achieved remarkable success across a wide range of generative tasks. A key challenge is understanding the mechanisms that prevent their memorization of training data and allow generalization. In this work, we investigate the role of the training dynamics in the transition from generalization to memorization. Through extensive experiments and theoretical analysis, we identify two distinct timescales: an early time τ_gen at which models begin to generate high-quality samples, and a later time τ_mem beyond which memorization emerges. Crucially, we find that τ_mem increases linearly with the training set size n, while τ_gen remains constant. This creates a growing window of training times with n where models generalize effectively, despite showing strong memorization if training continues beyond it. It is only when n becomes larger than a model-dependent threshold that overfitting disappears at infinite training times. These findings reveal a form of implicit dynamical regularization in the training dynamics, which allow to avoid memorization even in highly overparameterized settings. Our results are supported by numerical experiments with standard U-Net architectures on realistic and synthetic datasets, and by a theoretical analysis using a tractable random features model studied in the high-dimensional limit.

Pose-free neural radiance fields (NeRF) aim to train NeRF with unposed multi-view images and it has achieved very impressive success in recent years. Most existing works share the pipeline of training a coarse pose estimator with rendered images at first, followed by a joint optimization of estimated poses and neural radiance field. However, as the pose estimator is trained with only rendered images, the pose estimation is usually biased or inaccurate for real images due to the domain gap between real images and rendered images, leading to poor robustness for the pose estimation of real images and further local minima in joint optimization. We design IR-NeRF, an innovative pose-free NeRF that introduces implicit pose regularization to refine pose estimator with unposed real images and improve the robustness of the pose estimation for real images. With a collection of 2D images of a specific scene, IR-NeRF constructs a scene codebook that stores scene features and captures the scene-specific pose distribution implicitly as priors. Thus, the robustness of pose estimation can be promoted with the scene priors according to the rationale that a 2D real image can be well reconstructed from the scene codebook only when its estimated pose lies within the pose distribution. Extensive experiments show that IR-NeRF achieves superior novel view synthesis and outperforms the state-of-the-art consistently across multiple synthetic and real datasets.

Modern neural networks demonstrate state-of-the-art performance on numerous existing benchmarks; however, their high computational requirements and energy consumption prompt researchers to seek more efficient solutions for real-world deployment. Logic gate networks (LGNs) learns a large network of logic gates for efficient image classification. However, learning a network that can solve a simple problem like CIFAR-10 can take days to weeks to train. Even then, almost half of the network remains unused, causing a discretization gap. This discretization gap hinders real-world deployment of LGNs, as the performance drop between training and inference negatively impacts accuracy. We inject Gumbel noise with a straight-through estimator during training to significantly speed up training, improve neuron utilization, and decrease the discretization gap. We theoretically show that this results from implicit Hessian regularization, which improves the convergence properties of LGNs. We train networks 4.5 times faster in wall-clock time, reduce the discretization gap by 98%, and reduce the number of unused gates by 100%.

Nerf-based Generative models have shown impressive capacity in generating high-quality images with consistent 3D geometry. Despite successful synthesis of fake identity images randomly sampled from latent space, adopting these models for generating face images of real subjects is still a challenging task due to its so-called inversion issue. In this paper, we propose a universal method to surgically fine-tune these NeRF-GAN models in order to achieve high-fidelity animation of real subjects only by a single image. Given the optimized latent code for an out-of-domain real image, we employ 2D loss functions on the rendered image to reduce the identity gap. Furthermore, our method leverages explicit and implicit 3D regularizations using the in-domain neighborhood samples around the optimized latent code to remove geometrical and visual artifacts. Our experiments confirm the effectiveness of our method in realistic, high-fidelity, and 3D consistent animation of real faces on multiple NeRF-GAN models across different datasets.

Learning compact discrete representations of data is a key task on its own or for facilitating subsequent processing of data. In this paper we present a model that produces Discrete InfoMax Codes (DIMCO); we learn a probabilistic encoder that yields k-way d-dimensional codes associated with input data. Our model's learning objective is to maximize the mutual information between codes and labels with a regularization, which enforces entries of a codeword to be as independent as possible. We show that the infomax principle also justifies previous loss functions (e.g., cross-entropy) as its special cases. Our analysis also shows that using shorter codes, as DIMCO does, reduces overfitting in the context of few-shot classification. Through experiments in various domains, we observe this implicit meta-regularization effect of DIMCO. Furthermore, we show that the codes learned by DIMCO are efficient in terms of both memory and retrieval time compared to previous methods.

Gradient regularization (GR) is a method that penalizes the gradient norm of the training loss during training. While some studies have reported that GR can improve generalization performance, little attention has been paid to it from the algorithmic perspective, that is, the algorithms of GR that efficiently improve the performance. In this study, we first reveal that a specific finite-difference computation, composed of both gradient ascent and descent steps, reduces the computational cost of GR. Next, we show that the finite-difference computation also works better in the sense of generalization performance. We theoretically analyze a solvable model, a diagonal linear network, and clarify that GR has a desirable implicit bias to so-called rich regime and finite-difference computation strengthens this bias. Furthermore, finite-difference GR is closely related to some other algorithms based on iterative ascent and descent steps for exploring flat minima. In particular, we reveal that the flooding method can perform finite-difference GR in an implicit way. Thus, this work broadens our understanding of GR for both practice and theory.

Large language models (LLMs) have revolutionized the role of AI, yet also pose potential risks of propagating unethical content. Alignment technologies have been introduced to steer LLMs towards human preference, gaining increasing attention. Despite notable breakthroughs in this direction, existing methods heavily rely on high-quality positive-negative training pairs, suffering from noisy labels and the marginal distinction between preferred and dispreferred response data. Given recent LLMs' proficiency in generating helpful responses, this work pivots towards a new research focus: achieving alignment using solely human-annotated negative samples, preserving helpfulness while reducing harmfulness. For this purpose, we propose Distributional Dispreference Optimization (D^2O), which maximizes the discrepancy between the generated responses and the dispreferred ones to effectively eschew harmful information. We theoretically demonstrate that D^2O is equivalent to learning a distributional instead of instance-level preference model reflecting human dispreference against the distribution of negative responses. Besides, D^2O integrates an implicit Jeffrey Divergence regularization to balance the exploitation and exploration of reference policies and converges to a non-negative one during training. Extensive experiments demonstrate that our method achieves comparable generation quality and surpasses the latest baselines in producing less harmful and more informative responses with better training stability and faster convergence.

Standing-up control is crucial for humanoid robots, with the potential for integration into current locomotion and loco-manipulation systems, such as fall recovery. Existing approaches are either limited to simulations that overlook hardware constraints or rely on predefined ground-specific motion trajectories, failing to enable standing up across postures in real-world scenes. To bridge this gap, we present HoST (Humanoid Standing-up Control), a reinforcement learning framework that learns standing-up control from scratch, enabling robust sim-to-real transfer across diverse postures. HoST effectively learns posture-adaptive motions by leveraging a multi-critic architecture and curriculum-based training on diverse simulated terrains. To ensure successful real-world deployment, we constrain the motion with smoothness regularization and implicit motion speed bound to alleviate oscillatory and violent motions on physical hardware, respectively. After simulation-based training, the learned control policies are directly deployed on the Unitree G1 humanoid robot. Our experimental results demonstrate that the controllers achieve smooth, stable, and robust standing-up motions across a wide range of laboratory and outdoor environments. Videos and code are available at https://taohuang13.github.io/humanoid-standingup.github.io/.

In this paper, we propose a generative multi-column network for image inpainting. This network synthesizes different image components in a parallel manner within one stage. To better characterize global structures, we design a confidence-driven reconstruction loss while an implicit diversified MRF regularization is adopted to enhance local details. The multi-column network combined with the reconstruction and MRF loss propagates local and global information derived from context to the target inpainting regions. Extensive experiments on challenging street view, face, natural objects and scenes manifest that our method produces visual compelling results even without previously common post-processing.

Representation rank is an important concept for understanding the role of Neural Networks (NNs) in Deep Reinforcement learning (DRL), which measures the expressive capacity of value networks. Existing studies focus on unboundedly maximizing this rank; nevertheless, that approach would introduce overly complex models in the learning, thus undermining performance. Hence, fine-tuning representation rank presents a challenging and crucial optimization problem. To address this issue, we find a guiding principle for adaptive control of the representation rank. We employ the Bellman equation as a theoretical foundation and derive an upper bound on the cosine similarity of consecutive state-action pairs representations of value networks. We then leverage this upper bound to propose a novel regularizer, namely BEllman Equation-based automatic rank Regularizer (BEER). This regularizer adaptively regularizes the representation rank, thus improving the DRL agent's performance. We first validate the effectiveness of automatic control of rank on illustrative experiments. Then, we scale up BEER to complex continuous control tasks by combining it with the deterministic policy gradient method. Among 12 challenging DeepMind control tasks, BEER outperforms the baselines by a large margin. Besides, BEER demonstrates significant advantages in Q-value approximation. Our code is available at https://github.com/sweetice/BEER-ICLR2024.

Neural rendering of implicit surfaces performs well in 3D vision applications. However, it requires dense input views as supervision. When only sparse input images are available, output quality drops significantly due to the shape-radiance ambiguity problem. We note that this ambiguity can be constrained when a 3D point is visible in multiple views, as is the case in multi-view stereo (MVS). We thus propose to regularize neural rendering optimization with an MVS solution. The use of an MVS probability volume and a generalized cross entropy loss leads to a noise-tolerant optimization process. In addition, neural rendering provides global consistency constraints that guide the MVS depth hypothesis sampling and thus improves MVS performance. Given only three sparse input views, experiments show that our method not only outperforms generic neural rendering models by a large margin but also significantly increases the reconstruction quality of MVS models. Project page: https://hao-yu-wu.github.io/s-volsdf/.

Recovery of an underlying scene geometry from multiview images stands as a long-time challenge in computer vision research. The recent promise leverages neural implicit surface learning and differentiable volume rendering, and achieves both the recovery of scene geometry and synthesis of novel views, where deep priors of neural models are used as an inductive smoothness bias. While promising for object-level surfaces, these methods suffer when coping with complex scene surfaces. In the meanwhile, traditional multi-view stereo can recover the geometry of scenes with rich textures, by globally optimizing the local, pixel-wise correspondences across multiple views. We are thus motivated to make use of the complementary benefits from the two strategies, and propose a method termed Helix-shaped neural implicit Surface learning or HelixSurf; HelixSurf uses the intermediate prediction from one strategy as the guidance to regularize the learning of the other one, and conducts such intertwined regularization iteratively during the learning process. We also propose an efficient scheme for differentiable volume rendering in HelixSurf. Experiments on surface reconstruction of indoor scenes show that our method compares favorably with existing methods and is orders of magnitude faster, even when some of existing methods are assisted with auxiliary training data. The source code is available at https://github.com/Gorilla-Lab-SCUT/HelixSurf.

Likelihood training and maximization-based decoding result in dull and repetitive generated texts even when using powerful language models (Holtzman et al., 2019). Adding a loss function for regularization was shown to improve text generation output by helping avoid unwanted properties, such as contradiction or repetition (Li at al., 2020). In this work, we propose fine-tuning a language model by using policy gradient reinforcement learning, directly optimizing for better generation. We apply this approach to minimizing repetition in generated text, and show that, when combined with unlikelihood training (Welleck et al., 2020), our method further reduces repetition without impacting the language model quality. We also evaluate other methods for improving generation at training and decoding time, and compare them using various metrics aimed at control for better text generation output.

3D Reconstruction of moving articulated objects without additional information about object structure is a challenging problem. Current methods overcome such challenges by employing category-specific skeletal models. Consequently, they do not generalize well to articulated objects in the wild. We treat an articulated object as an unknown, semi-rigid skeletal structure surrounded by nonrigid material (e.g., skin). Our method simultaneously estimates the visible (explicit) representation (3D shapes, colors, camera parameters) and the implicit skeletal representation, from motion cues in the object video without 3D supervision. Our implicit representation consists of four parts. (1) Skeleton, which specifies how semi-rigid parts are connected. (2) black{Skinning Weights}, which associates each surface vertex with semi-rigid parts with probability. (3) Rigidity Coefficients, specifying the articulation of the local surface. (4) Time-Varying Transformations, which specify the skeletal motion and surface deformation parameters. We introduce an algorithm that uses physical constraints as regularization terms and iteratively estimates both implicit and explicit representations. Our method is category-agnostic, thus eliminating the need for category-specific skeletons, we show that our method outperforms state-of-the-art across standard video datasets.

Recent self-supervised methods for image representation learning are based on maximizing the agreement between embedding vectors from different views of the same image. A trivial solution is obtained when the encoder outputs constant vectors. This collapse problem is often avoided through implicit biases in the learning architecture, that often lack a clear justification or interpretation. In this paper, we introduce VICReg (Variance-Invariance-Covariance Regularization), a method that explicitly avoids the collapse problem with a simple regularization term on the variance of the embeddings along each dimension individually. VICReg combines the variance term with a decorrelation mechanism based on redundancy reduction and covariance regularization, and achieves results on par with the state of the art on several downstream tasks. In addition, we show that incorporating our new variance term into other methods helps stabilize the training and leads to performance improvements.

We propose a novel framework for video inpainting by adopting an internal learning strategy. Unlike previous methods that use optical flow for cross-frame context propagation to inpaint unknown regions, we show that this can be achieved implicitly by fitting a convolutional neural network to known regions. Moreover, to handle challenging sequences with ambiguous backgrounds or long-term occlusion, we design two regularization terms to preserve high-frequency details and long-term temporal consistency. Extensive experiments on the DAVIS dataset demonstrate that the proposed method achieves state-of-the-art inpainting quality quantitatively and qualitatively. We further extend the proposed method to another challenging task: learning to remove an object from a video giving a single object mask in only one frame in a 4K video.

Implicit Neural Representations (INR) or neural fields have emerged as a popular framework to encode multimedia signals such as images and radiance fields while retaining high-quality. Recently, learnable feature grids proposed by Instant-NGP have allowed significant speed-up in the training as well as the sampling of INRs by replacing a large neural network with a multi-resolution look-up table of feature vectors and a much smaller neural network. However, these feature grids come at the expense of large memory consumption which can be a bottleneck for storage and streaming applications. In this work, we propose SHACIRA, a simple yet effective task-agnostic framework for compressing such feature grids with no additional post-hoc pruning/quantization stages. We reparameterize feature grids with quantized latent weights and apply entropy regularization in the latent space to achieve high levels of compression across various domains. Quantitative and qualitative results on diverse datasets consisting of images, videos, and radiance fields, show that our approach outperforms existing INR approaches without the need for any large datasets or domain-specific heuristics. Our project page is available at http://shacira.github.io .

In recent years, neural implicit surface reconstruction has emerged as a popular paradigm for multi-view 3D reconstruction. Unlike traditional multi-view stereo approaches, the neural implicit surface-based methods leverage neural networks to represent 3D scenes as signed distance functions (SDFs). However, they tend to disregard the reconstruction of individual objects within the scene, which limits their performance and practical applications. To address this issue, previous work ObjectSDF introduced a nice framework of object-composition neural implicit surfaces, which utilizes 2D instance masks to supervise individual object SDFs. In this paper, we propose a new framework called ObjectSDF++ to overcome the limitations of ObjectSDF. First, in contrast to ObjectSDF whose performance is primarily restricted by its converted semantic field, the core component of our model is an occlusion-aware object opacity rendering formulation that directly volume-renders object opacity to be supervised with instance masks. Second, we design a novel regularization term for object distinction, which can effectively mitigate the issue that ObjectSDF may result in unexpected reconstruction in invisible regions due to the lack of constraint to prevent collisions. Our extensive experiments demonstrate that our novel framework not only produces superior object reconstruction results but also significantly improves the quality of scene reconstruction. Code and more resources can be found in https://qianyiwu.github.io/objectsdf++

Current works in the generation of personalized dialogue primarily contribute to the agent presenting a consistent personality and driving a more informative response. However, we found that the generated responses from most previous models tend to be self-centered, with little care for the user in the dialogue. Moreover, we consider that human-like conversation is essentially built based on inferring information about the persona of the other party. Motivated by this, we propose a novel personalized dialogue generator by detecting an implicit user persona. Because it is hard to collect a large number of detailed personas for each user, we attempted to model the user's potential persona and its representation from dialogue history, with no external knowledge. The perception and fader variables were conceived using conditional variational inference. The two latent variables simulate the process of people being aware of each other's persona and producing a corresponding expression in conversation. Finally, posterior-discriminated regularization was presented to enhance the training procedure. Empirical studies demonstrate that, compared to state-of-the-art methods, our approach is more concerned with the user's persona and achieves a considerable boost across the evaluations.

Vector graphics are essential in design, providing artists with a versatile medium for creating resolution-independent and highly editable visual content. Recent advancements in vision-language and diffusion models have fueled interest in text-to-vector graphics generation. However, existing approaches often suffer from over-parameterized outputs or treat the layered structure - a core feature of vector graphics - as a secondary goal, diminishing their practical use. Recognizing the importance of layered SVG representations, we propose NeuralSVG, an implicit neural representation for generating vector graphics from text prompts. Inspired by Neural Radiance Fields (NeRFs), NeuralSVG encodes the entire scene into the weights of a small MLP network, optimized using Score Distillation Sampling (SDS). To encourage a layered structure in the generated SVG, we introduce a dropout-based regularization technique that strengthens the standalone meaning of each shape. We additionally demonstrate that utilizing a neural representation provides an added benefit of inference-time control, enabling users to dynamically adapt the generated SVG based on user-provided inputs, all with a single learned representation. Through extensive qualitative and quantitative evaluations, we demonstrate that NeuralSVG outperforms existing methods in generating structured and flexible SVG.

We study the problem of sample efficient reinforcement learning, where prior data such as demonstrations are provided for initialization in lieu of a dense reward signal. A natural approach is to incorporate an imitation learning objective, either as regularization during training or to acquire a reference policy. However, imitation learning objectives can ultimately degrade long-term performance, as it does not directly align with reward maximization. In this work, we propose to use prior data solely for guiding exploration via noise added to the policy, sidestepping the need for explicit behavior cloning constraints. The key insight in our framework, Data-Guided Noise (DGN), is that demonstrations are most useful for identifying which actions should be explored, rather than forcing the policy to take certain actions. Our approach achieves up to 2-3x improvement over prior reinforcement learning from offline data methods across seven simulated continuous control tasks.

Recently, GRPO-based reinforcement learning has shown remarkable progress in optimizing flow-matching models, effectively improving their alignment with task-specific rewards. Within these frameworks, the policy update relies on importance-ratio clipping to constrain overconfident positive and negative gradients. However, in practice, we observe a systematic shift in the importance-ratio distribution-its mean falls below 1 and its variance differs substantially across timesteps. This left-shifted and inconsistent distribution prevents positive-advantage samples from entering the clipped region, causing the mechanism to fail in constraining overconfident positive updates. As a result, the policy model inevitably enters an implicit over-optimization stage-while the proxy reward continues to increase, essential metrics such as image quality and text-prompt alignment deteriorate sharply, ultimately making the learned policy impractical for real-world use. To address this issue, we introduce GRPO-Guard, a simple yet effective enhancement to existing GRPO frameworks. Our method incorporates ratio normalization, which restores a balanced and step-consistent importance ratio, ensuring that PPO clipping properly constrains harmful updates across denoising timesteps. In addition, a gradient reweighting strategy equalizes policy gradients over noise conditions, preventing excessive updates from particular timestep regions. Together, these designs act as a regulated clipping mechanism, stabilizing optimization and substantially mitigating implicit over-optimization without relying on heavy KL regularization. Extensive experiments on multiple diffusion backbones (e.g., SD3.5M, Flux.1-dev) and diverse proxy tasks demonstrate that GRPO-Guard significantly reduces over-optimization while maintaining or even improving generation quality.

Learning implicit templates as neural fields has recently shown impressive performance in unsupervised shape correspondence. Despite the success, we observe current approaches, which solely rely on geometric information, often learn suboptimal deformation across generic object shapes, which have high structural variability. In this paper, we highlight the importance of part deformation consistency and propose a semantic-aware implicit template learning framework to enable semantically plausible deformation. By leveraging semantic prior from a self-supervised feature extractor, we suggest local conditioning with novel semantic-aware deformation code and deformation consistency regularizations regarding part deformation, global deformation, and global scaling. Our extensive experiments demonstrate the superiority of the proposed method over baselines in various tasks: keypoint transfer, part label transfer, and texture transfer. More interestingly, our framework shows a larger performance gain under more challenging settings. We also provide qualitative analyses to validate the effectiveness of semantic-aware deformation. The code is available at https://github.com/mlvlab/PDC.

This paper presents a neural incremental Structure-from-Motion (SfM) approach, Level-S^2fM, which estimates the camera poses and scene geometry from a set of uncalibrated images by learning coordinate MLPs for the implicit surfaces and the radiance fields from the established keypoint correspondences. Our novel formulation poses some new challenges due to inevitable two-view and few-view configurations in the incremental SfM pipeline, which complicates the optimization of coordinate MLPs for volumetric neural rendering with unknown camera poses. Nevertheless, we demonstrate that the strong inductive basis conveying in the 2D correspondences is promising to tackle those challenges by exploiting the relationship between the ray sampling schemes. Based on this, we revisit the pipeline of incremental SfM and renew the key components, including two-view geometry initialization, the camera poses registration, the 3D points triangulation, and Bundle Adjustment, with a fresh perspective based on neural implicit surfaces. By unifying the scene geometry in small MLP networks through coordinate MLPs, our Level-S^2fM treats the zero-level set of the implicit surface as an informative top-down regularization to manage the reconstructed 3D points, reject the outliers in correspondences via querying SDF, and refine the estimated geometries by NBA (Neural BA). Not only does our Level-S^2fM lead to promising results on camera pose estimation and scene geometry reconstruction, but it also shows a promising way for neural implicit rendering without knowing camera extrinsic beforehand.

We present a novel approach for recovering 3D shape and view dependent appearance from a few colored images, enabling efficient 3D reconstruction and novel view synthesis. Our method learns an implicit neural representation in the form of a Signed Distance Function (SDF) and a radiance field. The model is trained progressively through ray marching enabled volumetric rendering, and regularized with learning-free multi-view stereo (MVS) cues. Key to our contribution is a novel implicit neural shape function learning strategy that encourages our SDF field to be as linear as possible near the level-set, hence robustifying the training against noise emanating from the supervision and regularization signals. Without using any pretrained priors, our method, called SparseCraft, achieves state-of-the-art performances both in novel-view synthesis and reconstruction from sparse views in standard benchmarks, while requiring less than 10 minutes for training.

In the face of the deep learning model's vulnerability to domain shift, source-free domain adaptation (SFDA) methods have been proposed to adapt models to new, unseen target domains without requiring access to source domain data. Although the potential benefits of applying data augmentation to SFDA are attractive, several challenges arise such as the dependence on prior knowledge of class-preserving transformations and the increase in memory and computational requirements. In this paper, we propose Source-free Domain Adaptation Through the Lens of Data Augmentation (SF(DA)^2), a novel approach that leverages the benefits of data augmentation without suffering from these challenges. We construct an augmentation graph in the feature space of the pretrained model using the neighbor relationships between target features and propose spectral neighborhood clustering to identify partitions in the prediction space. Furthermore, we propose implicit feature augmentation and feature disentanglement as regularization loss functions that effectively utilize class semantic information within the feature space. These regularizers simulate the inclusion of an unlimited number of augmented target features into the augmentation graph while minimizing computational and memory demands. Our method shows superior adaptation performance in SFDA scenarios, including 2D image and 3D point cloud datasets and a highly imbalanced dataset.

Since its inception in "Attention Is All You Need", transformer architecture has led to revolutionary advancements in NLP. The attention layer within the transformer admits a sequence of input tokens X and makes them interact through pairwise similarities computed as softmax(XQK^top X^top), where (K,Q) are the trainable key-query parameters. In this work, we establish a formal equivalence between the optimization geometry of self-attention and a hard-margin SVM problem that separates optimal input tokens from non-optimal tokens using linear constraints on the outer-products of token pairs. This formalism allows us to characterize the implicit bias of 1-layer transformers optimized with gradient descent: (1) Optimizing the attention layer with vanishing regularization, parameterized by (K,Q), converges in direction to an SVM solution minimizing the nuclear norm of the combined parameter W=KQ^top. Instead, directly parameterizing by W minimizes a Frobenius norm objective. We characterize this convergence, highlighting that it can occur toward locally-optimal directions rather than global ones. (2) Complementing this, we prove the local/global directional convergence of gradient descent under suitable geometric conditions. Importantly, we show that over-parameterization catalyzes global convergence by ensuring the feasibility of the SVM problem and by guaranteeing a benign optimization landscape devoid of stationary points. (3) While our theory applies primarily to linear prediction heads, we propose a more general SVM equivalence that predicts the implicit bias with nonlinear heads. Our findings are applicable to arbitrary datasets and their validity is verified via experiments. We also introduce several open problems and research directions. We believe these findings inspire the interpretation of transformers as a hierarchy of SVMs that separates and selects optimal tokens.

Neural implicit fields are powerful for representing 3D scenes and generating high-quality novel views, but it remains challenging to use such implicit representations for creating a 3D human avatar with a specific identity and artistic style that can be easily animated. Our proposed method, AvatarCraft, addresses this challenge by using diffusion models to guide the learning of geometry and texture for a neural avatar based on a single text prompt. We carefully design the optimization framework of neural implicit fields, including a coarse-to-fine multi-bounding box training strategy, shape regularization, and diffusion-based constraints, to produce high-quality geometry and texture. Additionally, we make the human avatar animatable by deforming the neural implicit field with an explicit warping field that maps the target human mesh to a template human mesh, both represented using parametric human models. This simplifies animation and reshaping of the generated avatar by controlling pose and shape parameters. Extensive experiments on various text descriptions show that AvatarCraft is effective and robust in creating human avatars and rendering novel views, poses, and shapes. Our project page is: https://avatar-craft.github.io/.

Cosine-similarity is the cosine of the angle between two vectors, or equivalently the dot product between their normalizations. A popular application is to quantify semantic similarity between high-dimensional objects by applying cosine-similarity to a learned low-dimensional feature embedding. This can work better but sometimes also worse than the unnormalized dot-product between embedded vectors in practice. To gain insight into this empirical observation, we study embeddings derived from regularized linear models, where closed-form solutions facilitate analytical insights. We derive analytically how cosine-similarity can yield arbitrary and therefore meaningless `similarities.' For some linear models the similarities are not even unique, while for others they are implicitly controlled by the regularization. We discuss implications beyond linear models: a combination of different regularizations are employed when learning deep models; these have implicit and unintended effects when taking cosine-similarities of the resulting embeddings, rendering results opaque and possibly arbitrary. Based on these insights, we caution against blindly using cosine-similarity and outline alternatives.

The combination of deep learning, artist-curated scans, and Implicit Functions (IF), is enabling the creation of detailed, clothed, 3D humans from images. However, existing methods are far from perfect. IF-based methods recover free-form geometry, but produce disembodied limbs or degenerate shapes for novel poses or clothes. To increase robustness for these cases, existing work uses an explicit parametric body model to constrain surface reconstruction, but this limits the recovery of free-form surfaces such as loose clothing that deviates from the body. What we want is a method that combines the best properties of implicit representation and explicit body regularization. To this end, we make two key observations: (1) current networks are better at inferring detailed 2D maps than full-3D surfaces, and (2) a parametric model can be seen as a "canvas" for stitching together detailed surface patches. Based on these, our method, ECON, has three main steps: (1) It infers detailed 2D normal maps for the front and back side of a clothed person. (2) From these, it recovers 2.5D front and back surfaces, called d-BiNI, that are equally detailed, yet incomplete, and registers these w.r.t. each other with the help of a SMPL-X body mesh recovered from the image. (3) It "inpaints" the missing geometry between d-BiNI surfaces. If the face and hands are noisy, they can optionally be replaced with the ones of SMPL-X. As a result, ECON infers high-fidelity 3D humans even in loose clothes and challenging poses. This goes beyond previous methods, according to the quantitative evaluation on the CAPE and Renderpeople datasets. Perceptual studies also show that ECON's perceived realism is better by a large margin. Code and models are available for research purposes at econ.is.tue.mpg.de

Sparse-view 3D reconstruction is essential for applications in which dense image acquisition is impractical, such as robotics, augmented/virtual reality (AR/VR), and autonomous systems. In these settings, minimal image overlap prevents reliable correspondence matching, causing traditional methods, such as structure-from-motion (SfM) and multiview stereo (MVS), to fail. This survey reviews the latest advances in neural implicit models (e.g., NeRF and its regularized versions), explicit point-cloud-based approaches (e.g., 3D Gaussian Splatting), and hybrid frameworks that leverage priors from diffusion and vision foundation models (VFMs).We analyze how geometric regularization, explicit shape modeling, and generative inference are used to mitigate artifacts such as floaters and pose ambiguities in sparse-view settings. Comparative results on standard benchmarks reveal key trade-offs between the reconstruction accuracy, efficiency, and generalization. Unlike previous reviews, our survey provides a unified perspective on geometry-based, neural implicit, and generative (diffusion-based) methods. We highlight the persistent challenges in domain generalization and pose-free reconstruction and outline future directions for developing 3D-native generative priors and achieving real-time, unconstrained sparse-view reconstruction.

Deep learning (DL) applied to a device's radio-frequency fingerprint~(RFF) has attracted significant attention in physical-layer authentication due to its extraordinary classification performance. Conventional DL-RFF techniques are trained by adopting maximum likelihood estimation~(MLE). Although their discriminability has recently been extended to unknown devices in open-set scenarios, they still tend to overfit the channel statistics embedded in the training dataset. This restricts their practical applications as it is challenging to collect sufficient training data capturing the characteristics of all possible wireless channel environments. To address this challenge, we propose a DL framework of disentangled representation~(DR) learning that first learns to factor the signals into a device-relevant component and a device-irrelevant component via adversarial learning. Then, it shuffles these two parts within a dataset for implicit data augmentation, which imposes a strong regularization on RFF extractor learning to avoid the possible overfitting of device-irrelevant channel statistics, without collecting additional data from unknown channels. Experiments validate that the proposed approach, referred to as DR-based RFF, outperforms conventional methods in terms of generalizability to unknown devices even under unknown complicated propagation environments, e.g., dispersive multipath fading channels, even though all the training data are collected in a simple environment with dominated direct line-of-sight~(LoS) propagation paths.

Direct Preference Optimization (DPO) has emerged as a simple alternative to reinforcement learning from human feedback (RLHF) for aligning language models, but its reliance on hard pairwise labels makes it brittle under noise; our experiments show performance degrading by up to 93 percent in noisy settings. We introduce Anchored Direct Preference Optimization (ADPO), a unified framework that addresses this fragility through reference anchoring. By minimizing KL(q || softmax((l - l_ref) / tau_anc)), where l_ref are reference policy log probabilities, ADPO provides three key advantages: (1) it unifies major learning paradigms, including supervised fine-tuning, knowledge distillation, maximum-entropy reinforcement learning, and DPO, as special cases through different choices of target distribution q, anchor policy pi_ref, and temperature tau_anc; (2) it induces an implicit trust region governed by the softmax Fisher metric with curvature scaling as 1 / tau_anc^2, providing geometric regularization absent in standard methods; and (3) it enables flexible anchor strategies tailored to different learning contexts. Empirically, ADPO consistently outperforms standard DPO by 12 to 93 percent across twelve noisy scenarios, with listwise variants achieving top performance in eleven of twelve cases. In offline distillation, ADPO reduces student-teacher KL by 4 to 49 times while achieving superior returns (for example, 279.3 vs -309.0 for knowledge distillation on HalfCheetah). We further uncover a task-dependent tradeoff: dynamic anchors excel at online exploration in noisy environments (plus 5 to 11 percent), while fixed anchors enable stable offline distillation. Our work establishes anchoring as a general principle for robust policy optimization, with clear practical guidance for anchor selection across diverse learning scenarios.