Daily Papers

Generating high-fidelity 3D geometries under explicit parameter constraints is central to engineering design, yet current methods often require large datasets and fail to provide reliable control beyond the training distribution. We introduce LAMP, a data-efficient framework for controllable and interpretable 3D generation that aligns signed distance function (SDF) decoders by overfitting each exemplar from a shared initialization, then generates new designs by solving a parameter-constrained affine mixing problem in the aligned weight space. To improve reliability, we propose a linearity-mismatch safety metric that detects when mixed decoders leave the valid local regime. We evaluate LAMP on DrivAerNet++, BlendedNet, and additional industry-level vehicle families, including sports cars, SUVs, and convertibles. LAMP enables controlled interpolation with as few as 50 samples, safe extrapolation up to 100% beyond training ranges, and performance-guided optimization under fixed parameters, outperforming conditional autoencoder and Deep Network Interpolation (DNI) baselines in extrapolation, data efficiency, and parameter fidelity. Our results demonstrate that LAMP advances controllable, data-efficient, and safe 3D generation for design exploration, dataset generation, and performance-driven optimization.

Directed energy deposition (DED) produces complex thermo-mechanical responses that can lead to distortion and reduced dimensional accuracy of a manufactured part. Thermo-mechanical finite element simulations are widely used to estimate these effects, but their computational cost and the complexity of accurately capturing DED physics limit their use in design iteration and process optimization. This paper introduces FLARE (Field Prediction via Linear Affine Reconstruction in wEight-space), a data-efficient surrogate modeling framework for predicting post-cooling displacement fields in DED from geometric and process parameters. We develop a predefined-geometry DED simulation workflow using an open-source finite element framework and generate a dataset of simulations with varying geometry, laser power, and deposition velocity. Each simulation provides full-field displacement, stress, strain, and temperature data throughout the manufacturing process. FLARE encodes each simulation as an implicit neural field and regularizes the corresponding neural-network weights so that they follow the affine structure of the input parameter space. This enables prediction of unseen parameter combinations by reconstructing network weights through affine mixing of training examples. On this DED benchmark, the method shows improved accuracy compared to baseline methods in both in-distribution and extrapolation settings. Although the present study focuses on DED displacement prediction, the proposed affine weight-space reconstruction framework offers a promising approach for data-efficient surrogate modeling of physical fields.

Language model performance depends on identifying the optimal mixture of data groups to train on (e.g., law, code, math). Prior work has proposed a diverse set of methods to efficiently learn mixture proportions, ranging from fitting regression models over training runs to dynamically updating proportions throughout training. Surprisingly, we find that no existing method consistently outperforms a simple stratified sampling baseline in terms of average test perplexity. To understand this inconsistency, we unify existing methods into a standard framework, showing they are equivalent to solving a common optimization problem: minimize average loss subject to a method-specific mixing law -- an implicit assumption on the relationship between loss and mixture proportions. This framework suggests that measuring the fidelity of a method's mixing law can offer insights into its performance. Empirically, we find that existing methods set their mixing law parameters inaccurately, resulting in the inconsistent mixing performance we observe. Using this insight, we derive a new online method named Aioli, which directly estimates the mixing law parameters throughout training and uses them to dynamically adjust proportions. Aioli outperforms stratified sampling on 6 out of 6 datasets by an average of 0.27 test perplexity points, whereas existing methods fail to consistently beat stratified sampling, doing up to 6.9 points worse. Moreover, in a practical setting where proportions are learned on shorter runs due to computational constraints, Aioli can dynamically adjust these proportions over the full training run, consistently improving performance over existing methods by up to 12.012 test perplexity points.

Multi-layer perceptron (MLP) is a fundamental component of deep learning that has been extensively employed for various problems. However, recent empirical successes in MLP-based architectures, particularly the progress of the MLP-Mixer, have revealed that there is still hidden potential in improving MLPs to achieve better performance. In this study, we reveal that the MLP-Mixer works effectively as a wide MLP with certain sparse weights. Initially, we clarify that the mixing layer of the Mixer has an effective expression as a wider MLP whose weights are sparse and represented by the Kronecker product. This expression naturally defines a permuted-Kronecker (PK) family, which can be regarded as a general class of mixing layers and is also regarded as an approximation of Monarch matrices. Subsequently, because the PK family effectively constitutes a wide MLP with sparse weights, one can apply the hypothesis proposed by Golubeva, Neyshabur and Gur-Ari (2021) that the prediction performance improves as the width (sparsity) increases when the number of weights is fixed. We empirically verify this hypothesis by maximizing the effective width of the MLP-Mixer, which enables us to determine the appropriate size of the mixing layers quantitatively.

Recent vision transformers, large-kernel CNNs and MLPs have attained remarkable successes in broad vision tasks thanks to their effective information fusion in the global scope. However, their efficient deployments, especially on mobile devices, still suffer from noteworthy challenges due to the heavy computational costs of self-attention mechanisms, large kernels, or fully connected layers. In this work, we apply conventional convolution theorem to deep learning for addressing this and reveal that adaptive frequency filters can serve as efficient global token mixers. With this insight, we propose Adaptive Frequency Filtering (AFF) token mixer. This neural operator transfers a latent representation to the frequency domain via a Fourier transform and performs semantic-adaptive frequency filtering via an elementwise multiplication, which mathematically equals to a token mixing operation in the original latent space with a dynamic convolution kernel as large as the spatial resolution of this latent representation. We take AFF token mixers as primary neural operators to build a lightweight neural network, dubbed AFFNet. Extensive experiments demonstrate the effectiveness of our proposed AFF token mixer and show that AFFNet achieve superior accuracy and efficiency trade-offs compared to other lightweight network designs on broad visual tasks, including visual recognition and dense prediction tasks.

Conditional normalizing flows can generate diverse image samples for solving inverse problems. Most normalizing flows for inverse problems in imaging employ the conditional affine coupling layer that can generate diverse images quickly. However, unintended severe artifacts are occasionally observed in the output of them. In this work, we address this critical issue by investigating the origins of these artifacts and proposing the conditions to avoid them. First of all, we empirically and theoretically reveal that these problems are caused by "exploding inverse" in the conditional affine coupling layer for certain out-of-distribution (OOD) conditional inputs. Then, we further validated that the probability of causing erroneous artifacts in pixels is highly correlated with a Mahalanobis distance-based OOD score for inverse problems in imaging. Lastly, based on our investigations, we propose a remark to avoid exploding inverse and then based on it, we suggest a simple remedy that substitutes the affine coupling layers with the modified rational quadratic spline coupling layers in normalizing flows, to encourage the robustness of generated image samples. Our experimental results demonstrated that our suggested methods effectively suppressed critical artifacts occurring in normalizing flows for super-resolution space generation and low-light image enhancement.

Music mixing involves combining individual tracks into a cohesive mixture, a task characterized by subjectivity where multiple valid solutions exist for the same input. Existing automatic mixing systems treat this task as a deterministic regression problem, thus ignoring this multiplicity of solutions. Here we introduce MEGAMI (Multitrack Embedding Generative Auto MIxing), a generative framework that models the conditional distribution of professional mixes given unprocessed tracks. MEGAMI uses a track-agnostic effects processor conditioned on per-track generated embeddings, handles arbitrary unlabeled tracks through a permutation-equivariant architecture, and enables training on both dry and wet recordings via domain adaptation. Our objective evaluation using distributional metrics shows consistent improvements over existing methods, while listening tests indicate performances approaching human-level quality across diverse musical genres.

Diffusion models and their variations, such as rectified flows, generate diverse and high-quality images, but they are still hindered by slow iterative sampling caused by the highly curved generative paths they learn. An important cause of high curvature, as shown by previous work, is independence between the source distribution (standard Gaussian) and the data distribution. In this work, we tackle this limitation by two complementary contributions. First, we attempt to break away from the standard Gaussian assumption by introducing κ-FC, a general formulation that conditions the source distribution on an arbitrary signal κ that aligns it better with the data distribution. Then, we present MixFlow, a simple but effective training strategy that reduces the generative path curvatures and considerably improves sampling efficiency. MixFlow trains a flow model on linear mixtures of a fixed unconditional distribution and a κ-FC-based distribution. This simple mixture improves the alignment between the source and data, provides better generation quality with less required sampling steps, and accelerates the training convergence considerably. On average, our training procedure improves the generation quality by 12\% in FID compared to standard rectified flow and 7\% compared to previous baselines under a fixed sampling budget. Code available at: https://github.com/NazirNayal8/MixFlow{https://github.com/NazirNayal8/MixFlow}

We combine the capacity of sparsely gated Mixture-of-Experts (MoE) with the speed and stability of linear, mixing transformations to design the Sparse Mixer encoder model. Sparse Mixer slightly outperforms (<1%) BERT on GLUE and SuperGLUE, but more importantly trains 65% faster and runs inference 61% faster. We also present a faster variant, prosaically named Fast Sparse Mixer, that marginally underperforms BERT on SuperGLUE, but trains and runs nearly twice as fast. We justify the design of these two models by carefully ablating through various mixing mechanisms, MoE configurations and hyperparameters. Sparse Mixer overcomes many of the latency and stability concerns of MoE models and offers the prospect of serving sparse student models, without resorting to distilling them to dense variants.

We consider a family of convex quadratic programs in which the coefficients of the linear objective term and the righthand side of the constraints are affine functions of a parameter. It is well known that the solution of such a parametrized quadratic program is a piecewise affine function of the parameter. The number of (polyhedral) regions in the solution map can grow exponentially in problem size, but when the number of regions is moderate, a so-called explicit solver is practical. Such a solver computes the coefficients of the affine functions and the linear inequalities defining the polyhedral regions offline; to solve a problem instance online it simply evaluates this explicit solution map. Potential advantages of an explicit solver over a more general purpose iterative solver can include transparency, interpretability, reliability, and speed. In this paper we describe how code generation can be used to automatically generate an explicit solver from a high level description of a parametrized quadratic program. Our method has been implemented in the open-source software CVXPYgen, which is part of CVXPY, a domain specific language for general convex optimization.

Have you ever imagined what a corgi-alike coffee machine or a tiger-alike rabbit would look like? In this work, we attempt to answer these questions by exploring a new task called semantic mixing, aiming at blending two different semantics to create a new concept (e.g., corgi + coffee machine -- > corgi-alike coffee machine). Unlike style transfer, where an image is stylized according to the reference style without changing the image content, semantic blending mixes two different concepts in a semantic manner to synthesize a novel concept while preserving the spatial layout and geometry. To this end, we present MagicMix, a simple yet effective solution based on pre-trained text-conditioned diffusion models. Motivated by the progressive generation property of diffusion models where layout/shape emerges at early denoising steps while semantically meaningful details appear at later steps during the denoising process, our method first obtains a coarse layout (either by corrupting an image or denoising from a pure Gaussian noise given a text prompt), followed by injection of conditional prompt for semantic mixing. Our method does not require any spatial mask or re-training, yet is able to synthesize novel objects with high fidelity. To improve the mixing quality, we further devise two simple strategies to provide better control and flexibility over the synthesized content. With our method, we present our results over diverse downstream applications, including semantic style transfer, novel object synthesis, breed mixing, and concept removal, demonstrating the flexibility of our method. More results can be found on the project page https://magicmix.github.io

User data confidentiality protection is becoming a rising challenge in the present deep learning research. Without access to data, conventional data-driven model compression faces a higher risk of performance degradation. Recently, some works propose to generate images from a specific pretrained model to serve as training data. However, the inversion process only utilizes biased feature statistics stored in one model and is from low-dimension to high-dimension. As a consequence, it inevitably encounters the difficulties of generalizability and inexact inversion, which leads to unsatisfactory performance. To address these problems, we propose MixMix based on two simple yet effective techniques: (1) Feature Mixing: utilizes various models to construct a universal feature space for generalized inversion; (2) Data Mixing: mixes the synthesized images and labels to generate exact label information. We prove the effectiveness of MixMix from both theoretical and empirical perspectives. Extensive experiments show that MixMix outperforms existing methods on the mainstream compression tasks, including quantization, knowledge distillation, and pruning. Specifically, MixMix achieves up to 4% and 20% accuracy uplift on quantization and pruning, respectively, compared to existing data-free compression work.

Invertible neural networks based on coupling flows (CF-INNs) have various machine learning applications such as image synthesis and representation learning. However, their desirable characteristics such as analytic invertibility come at the cost of restricting the functional forms. This poses a question on their representation power: are CF-INNs universal approximators for invertible functions? Without a universality, there could be a well-behaved invertible transformation that the CF-INN can never approximate, hence it would render the model class unreliable. We answer this question by showing a convenient criterion: a CF-INN is universal if its layers contain affine coupling and invertible linear functions as special cases. As its corollary, we can affirmatively resolve a previously unsolved problem: whether normalizing flow models based on affine coupling can be universal distributional approximators. In the course of proving the universality, we prove a general theorem to show the equivalence of the universality for certain diffeomorphism classes, a theoretical insight that is of interest by itself.

Vision transformers have delivered tremendous success in representation learning. This is primarily due to effective token mixing through self attention. However, this scales quadratically with the number of pixels, which becomes infeasible for high-resolution inputs. To cope with this challenge, we propose Adaptive Fourier Neural Operator (AFNO) as an efficient token mixer that learns to mix in the Fourier domain. AFNO is based on a principled foundation of operator learning which allows us to frame token mixing as a continuous global convolution without any dependence on the input resolution. This principle was previously used to design FNO, which solves global convolution efficiently in the Fourier domain and has shown promise in learning challenging PDEs. To handle challenges in visual representation learning such as discontinuities in images and high resolution inputs, we propose principled architectural modifications to FNO which results in memory and computational efficiency. This includes imposing a block-diagonal structure on the channel mixing weights, adaptively sharing weights across tokens, and sparsifying the frequency modes via soft-thresholding and shrinkage. The resulting model is highly parallel with a quasi-linear complexity and has linear memory in the sequence size. AFNO outperforms self-attention mechanisms for few-shot segmentation in terms of both efficiency and accuracy. For Cityscapes segmentation with the Segformer-B3 backbone, AFNO can handle a sequence size of 65k and outperforms other efficient self-attention mechanisms.

Learning PDE dynamics with neural solvers can significantly improve wall-clock efficiency and accuracy compared with classical numerical solvers. In recent years, foundation models for PDEs have largely adopted multi-scale windowed self-attention, with the scOT backbone in Poseidon serving as a representative example. However, because of their locality, truly globally consistent spectral coupling can only be propagated gradually through deep stacking and window shifting. This weakens global coupling and leads to error accumulation and drift during closed-loop rollouts. To address this, we propose DRIFT-Net. It employs a dual-branch design comprising a spectral branch and an image branch. The spectral branch is responsible for capturing global, large-scale low-frequency information, whereas the image branch focuses on local details and nonstationary structures. Specifically, we first perform controlled, lightweight mixing within the low-frequency range. Then we fuse the spectral and image paths at each layer via bandwise weighting, which avoids the width inflation and training instability caused by naive concatenation. The fused result is transformed back into the spatial domain and added to the image branch, thereby preserving both global structure and high-frequency details across scales. Compared with strong attention-based baselines, DRIFT-Net achieves lower error and higher throughput with fewer parameters under identical training settings and budget. On Navier--Stokes benchmarks, the relative L_{1} error is reduced by 7\%--54\%, the parameter count decreases by about 15\%, and the throughput remains higher than scOT. Ablation studies and theoretical analyses further demonstrate the stability and effectiveness of this design. The code is available at https://github.com/cruiseresearchgroup/DRIFT-Net.

Sequence and channel mixers, the core mechanism in sequence models, have become the de facto standard in time series analysis (TSA). However, recent studies have questioned the necessity of complex sequence mixers, such as attention mechanisms, demonstrating that simpler architectures can achieve comparable or even superior performance. This suggests that the benefits attributed to complex sequencemixers might instead emerge from other architectural or optimization factors. Based on this observation, we pose a central question: Are common sequence mixers necessary for time-series analysis? Therefore, we propose JustDense, an empirical study that systematically replaces sequence mixers in various well-established TSA models with dense layers. Grounded in the MatrixMixer framework, JustDense treats any sequence mixer as a mixing matrix and replaces it with a dense layer. This substitution isolates the mixing operation, enabling a clear theoretical foundation for understanding its role. Therefore, we conducted extensive experiments on 29 benchmarks covering five representative TSA tasks using seven state-of-the-art TSA models to address our research question. The results show that replacing sequence mixers with dense layers yields comparable or even superior performance. In the cases where dedicated sequence mixers still offer benefits, JustDense challenges the assumption that "deeper and more complex architectures are inherently better" in TSA.

Invariance and equivariance to geometrical transformations have proven to be very useful inductive biases when training (convolutional) neural network models, especially in the low-data regime. Much work has focused on the case where the symmetry group employed is compact or abelian, or both. Recent work has explored enlarging the class of transformations used to the case of Lie groups, principally through the use of their Lie algebra, as well as the group exponential and logarithm maps. The applicability of such methods to larger transformation groups is limited by the fact that depending on the group of interest G, the exponential map may not be surjective. Further limitations are encountered when G is neither compact nor abelian. Using the structure and geometry of Lie groups and their homogeneous spaces, we present a framework by which it is possible to work with such groups primarily focusing on the Lie groups G = GL^{+}(n, R) and G = SL(n, R), as well as their representation as affine transformations R^{n} rtimes G. Invariant integration as well as a global parametrization is realized by decomposing the `larger` groups into subgroups and submanifolds which can be handled individually. Under this framework, we show how convolution kernels can be parametrized to build models equivariant with respect to affine transformations. We evaluate the robustness and out-of-distribution generalisation capability of our model on the standard affine-invariant benchmark classification task, where we outperform all previous equivariant models as well as all Capsule Network proposals.

Flow matching (FM) is a general framework for defining probability paths via Ordinary Differential Equations (ODEs) to transform between noise and data samples. Recent approaches attempt to straighten these flow trajectories to generate high-quality samples with fewer function evaluations, typically through iterative rectification methods or optimal transport solutions. In this paper, we introduce Consistency Flow Matching (Consistency-FM), a novel FM method that explicitly enforces self-consistency in the velocity field. Consistency-FM directly defines straight flows starting from different times to the same endpoint, imposing constraints on their velocity values. Additionally, we propose a multi-segment training approach for Consistency-FM to enhance expressiveness, achieving a better trade-off between sampling quality and speed. Preliminary experiments demonstrate that our Consistency-FM significantly improves training efficiency by converging 4.4x faster than consistency models and 1.7x faster than rectified flow models while achieving better generation quality. Our code is available at: https://github.com/YangLing0818/consistency_flow_matching

Data mixing strategies (e.g., CutMix) have shown the ability to greatly improve the performance of convolutional neural networks (CNNs). They mix two images as inputs for training and assign them with a mixed label with the same ratio. While they are shown effective for vision transformers (ViTs), we identify a token fluctuation phenomenon that has suppressed the potential of data mixing strategies. We empirically observe that the contributions of input tokens fluctuate as forward propagating, which might induce a different mixing ratio in the output tokens. The training target computed by the original data mixing strategy can thus be inaccurate, resulting in less effective training. To address this, we propose a token-label alignment (TL-Align) method to trace the correspondence between transformed tokens and the original tokens to maintain a label for each token. We reuse the computed attention at each layer for efficient token-label alignment, introducing only negligible additional training costs. Extensive experiments demonstrate that our method improves the performance of ViTs on image classification, semantic segmentation, objective detection, and transfer learning tasks. Code is available at: https://github.com/Euphoria16/TL-Align.

Data mixing augmentation have proved to be effective in improving the generalization ability of deep neural networks. While early methods mix samples by hand-crafted policies (e.g., linear interpolation), recent methods utilize saliency information to match the mixed samples and labels via complex offline optimization. However, there arises a trade-off between precise mixing policies and optimization complexity. To address this challenge, we propose a novel automatic mixup (AutoMix) framework, where the mixup policy is parameterized and serves the ultimate classification goal directly. Specifically, AutoMix reformulates the mixup classification into two sub-tasks (i.e., mixed sample generation and mixup classification) with corresponding sub-networks and solves them in a bi-level optimization framework. For the generation, a learnable lightweight mixup generator, Mix Block, is designed to generate mixed samples by modeling patch-wise relationships under the direct supervision of the corresponding mixed labels. To prevent the degradation and instability of bi-level optimization, we further introduce a momentum pipeline to train AutoMix in an end-to-end manner. Extensive experiments on nine image benchmarks prove the superiority of AutoMix compared with state-of-the-art in various classification scenarios and downstream tasks.

A DJ mix is a sequence of music tracks concatenated seamlessly, typically rendered for audiences in a live setting by a DJ on stage. As a DJ mix is produced in a studio or the live version is recorded for music streaming services, computational methods to analyze DJ mixes, for example, extracting track information or understanding DJ techniques, have drawn research interests. Many of previous works are, however, limited to identifying individual tracks in a mix or segmenting it, and the sizes of the datasets are usually small. In this paper, we provide an in-depth analysis of DJ music by aligning a mix to its original music tracks. We set up the subsequence alignment such that the audio features are less sensitive to the tempo or key change of the original track in a mix. This approach provides temporally tight mix-to-track matching from which we can obtain cue-points, transition length, mix segmentation, and musical changes in DJ performance. Using 1,557 mixes from 1001Tracklists including 13,728 tracks and 20,765 transitions, we conduct the proposed analysis and show a wide range of statistics, which may elucidate the creative process of DJ music making.

Softmax attention is the cornerstone of modern large language models, but its memory scales linearly and compute quadratically with sequence length. Linear recurrent models, such as linear attention and state space models, have become widely studied as alternatives to attention due to their linear compute and constant memory. While these sub-quadratic token mixing methods, or mixers, achieve promising efficiency gains and competitive results on a wide range of benchmarks, current linear recurrent models still lag behind on tasks that require long-context retrieval or in-context learning. A growing body of work studies hybrid architectures that attempt to mitigate these trade-offs by statically interleaving or merging attention and recurrent blocks. In this work, we explore a new axis of developing hybrid models: across the token sequence. We propose Oryx, a hybrid model that can, throughout a sequence, flexibly switch between different mixers, for example quadratic attention for rich context utilization and linear recurrences for efficient generation. Oryx ties at least 90% of its parameters across mixers, enabling attention and recurrent modes to operate over shared internal representations. We validate our design with Mamba-2 and Gated DeltaNet variants, up to 1.4B models. Under fixed token budgets and a mixed-training strategy, Oryx achieves comparable or better performance than its single-mixer baselines. At the 1.4B scale, all instances of Oryx outperform their respective baselines by at least 0.7 percentage points on averaged language modeling tasks. On retrieval tasks, Oryx achieves performance comparable to the Transformer baseline even when processing only a tiny fraction (<10%) of the tokens in attention mode. These results suggest that attention and linear recurrent models can share internal representations, and motivate sequence-axis hybridization as a promising direction.

Data mixing augmentation has been widely applied to improve the generalization ability of deep neural networks. Recently, offline data mixing augmentation, e.g. handcrafted and saliency information-based mixup, has been gradually replaced by automatic mixing approaches. Through minimizing two sub-tasks, namely, mixed sample generation and mixup classification in an end-to-end way, AutoMix significantly improves accuracy on image classification tasks. However, as the optimization objective is consistent for the two sub-tasks, this approach is prone to generating consistent instead of diverse mixed samples, which results in overfitting for target task training. In this paper, we propose AdAutomixup, an adversarial automatic mixup augmentation approach that generates challenging samples to train a robust classifier for image classification, by alternatively optimizing the classifier and the mixup sample generator. AdAutomixup comprises two modules, a mixed example generator, and a target classifier. The mixed sample generator aims to produce hard mixed examples to challenge the target classifier, while the target classifier's aim is to learn robust features from hard mixed examples to improve generalization. To prevent the collapse of the inherent meanings of images, we further introduce an exponential moving average (EMA) teacher and cosine similarity to train AdAutomixup in an end-to-end way. Extensive experiments on seven image benchmarks consistently prove that our approach outperforms the state of the art in various classification scenarios. The source code is available at https://github.com/JinXins/Adversarial-AutoMixup.

Designing machine learning architectures for processing neural networks in their raw weight matrix form is a newly introduced research direction. Unfortunately, the unique symmetry structure of deep weight spaces makes this design very challenging. If successful, such architectures would be capable of performing a wide range of intriguing tasks, from adapting a pre-trained network to a new domain to editing objects represented as functions (INRs or NeRFs). As a first step towards this goal, we present here a novel network architecture for learning in deep weight spaces. It takes as input a concatenation of weights and biases of a pre-trained MLP and processes it using a composition of layers that are equivariant to the natural permutation symmetry of the MLP's weights: Changing the order of neurons in intermediate layers of the MLP does not affect the function it represents. We provide a full characterization of all affine equivariant and invariant layers for these symmetries and show how these layers can be implemented using three basic operations: pooling, broadcasting, and fully connected layers applied to the input in an appropriate manner. We demonstrate the effectiveness of our architecture and its advantages over natural baselines in a variety of learning tasks.

Data mixing decides how to combine different sources or types of data and is a consequential problem throughout language model training. In pretraining, data composition is a key determinant of model quality; in continual learning and adaptation, it governs what is retained and acquired. Yet existing data mixing methods address only one phase of this lifecycle at a time: some require smaller proxy models tied to a single training phase, others assume a fixed domain set, and continual learning lacks principled guidance altogether. We argue that data mixing is fundamentally an online decision making problem -- one that recurs throughout training and demands a single, unified solution. We introduce OP-Mix (On-Policy Mix), a data mixing algorithm that operates across the entire language model training lifecycle. Our main insight is that candidate data mixtures can be cheaply simulated by interpolating between low-rank adapters trained directly on the current model, eliminating separate proxy models and ensuring the search is always grounded in the model's actual learning dynamics. Across pretraining, continual midtraining, and continual instruction tuning, OP-Mix consistently finds near-optimal mixtures while using a fraction of the compute of the baselines. In pretraining, OP-Mix improves upon training without mixing by 6.3% in average perplexity. For continual learning, OP-Mix matches the performance of both retraining and on-policy distillation while using 66% and 95% less overall compute, respectively. OP-Mix suggests a different view of language model training: not a sequence of distinct phases, but a single continuous process of learning from data.

Mixup data augmentation approaches have been applied for various tasks of deep learning to improve the generalization ability of deep neural networks. Some existing approaches CutMix, SaliencyMix, etc. randomly replace a patch in one image with patches from another to generate the mixed image. Similarly, the corresponding labels are linearly combined by a fixed ratio lambda by l. The objects in two images may be overlapped during the mixing process, so some semantic information is corrupted in the mixed samples. In this case, the mixed image does not match the mixed label information. Besides, such a label may mislead the deep learning model training, which results in poor performance. To solve this problem, we proposed a novel approach named SUMix to learn the mixing ratio as well as the uncertainty for the mixed samples during the training process. First, we design a learnable similarity function to compute an accurate mix ratio. Second, an approach is investigated as a regularized term to model the uncertainty of the mixed samples. We conduct experiments on five image benchmarks, and extensive experimental results imply that our method is capable of improving the performance of classifiers with different cutting-based mixup approaches. The source code is available at https://github.com/JinXins/SUMix.

A central challenge in gradient-free MCMC is designing algorithms that simultaneously bypass manual tuning, scale efficiently with dimension, and adapt to local target geometry. While adaptive strategies can auto-tune generic frameworks like random walk Metropolis, they offer slow, linear-order scaling of mixing times with dimension. Elliptical slice sampling (ESS) offers a promising alternative: it is tuning-free, adjusts to local geometry, and can achieve nearly dimension-free scaling under favorable conditions. However, its efficiency degrades rapidly if there is a mismatch between the target distribution and the distribution used to generate the ellipse-defining auxiliary variables, precluding its use in high-dimensional settings. We demonstrate that a careful synthesis of ESS and diminishing adaptation directly resolves these bottlenecks. The resulting adaptive generalized elliptical slice sampler (AGESS) self-corrects from a slow-mixing to a fast-mixing regime, while preserving ergodicity across a wide variety of target densities satisfying mild regularity conditions. The algorithm's utility is demonstrated across a broad collection of challenging applications, including generalized regression, deep Gaussian process surrogate modeling, and high-dimensional sparse regression. Together, our theoretical results and the case studies give evidence of the efficiency and robustness of AGESS across target distributions that are non-elliptical, non-differentiable, multi-modal, or high-dimensional.

We present an open-source Python library for simulating two-dimensional incompressible Kelvin-Helmholtz instabilities in stratified shear flows. The solver employs a fractional-step projection method with spectral Poisson solution via Fast Sine Transform, achieving second-order spatial accuracy. Implementation leverages NumPy, SciPy, and Numba JIT compilation for efficient computation. Four canonical test cases explore Reynolds numbers 1000--5000 and Richardson numbers 0.1--0.3: classical shear layer, double shear configuration, rotating flow, and forced turbulence. Statistical analysis using Shannon entropy and complexity indices reveals that double shear layers achieve 2.8times higher mixing rates than forced turbulence despite lower Reynolds numbers. The solver runs efficiently on standard desktop hardware, with 384times192 grid simulations completing in approximately 31 minutes. Results demonstrate that mixing efficiency depends on instability generation pathways rather than intensity measures alone, challenging Richardson number-based parameterizations and suggesting refinements for subgrid-scale representation in climate models.

We generalize quasi-arithmetic means beyond scalars by considering the gradient map of a Legendre type real-valued function. The gradient map of a Legendre type function is proven strictly comonotone with a global inverse. It thus yields a generalization of strictly mononotone and differentiable functions generating scalar quasi-arithmetic means. Furthermore, the Legendre transformation gives rise to pairs of dual quasi-arithmetic averages via the convex duality. We study the invariance and equivariance properties under affine transformations of quasi-arithmetic averages via the lens of dually flat spaces of information geometry. We show how these quasi-arithmetic averages are used to express points on dual geodesics and sided barycenters in the dual affine coordinate systems. We then consider quasi-arithmetic mixtures and describe several parametric and non-parametric statistical models which are closed under the quasi-arithmetic mixture operation.

The data mixture used in the pre-training of a language model is a cornerstone of its final performance. However, a static mixing strategy is suboptimal, as the model's learning preferences for various data domains shift dynamically throughout training. Crucially, observing these evolving preferences in a computationally efficient manner remains a significant challenge. To address this, we propose TiKMiX, a method that dynamically adjusts the data mixture according to the model's evolving preferences. TiKMiX introduces Group Influence, an efficient metric for evaluating the impact of data domains on the model. This metric enables the formulation of the data mixing problem as a search for an optimal, influence-maximizing distribution. We solve this via two approaches: TiKMiX-D for direct optimization, and TiKMiX-M, which uses a regression model to predict a superior mixture. We trained models with different numbers of parameters, on up to 1 trillion tokens. TiKMiX-D exceeds the performance of state-of-the-art methods like REGMIX while using just 20% of the computational resources. TiKMiX-M leads to an average performance gain of 2% across 9 downstream benchmarks. Our experiments reveal that a model's data preferences evolve with training progress and scale, and we demonstrate that dynamically adjusting the data mixture based on Group Influence, a direct measure of these preferences, significantly improves performance by mitigating the underdigestion of data seen with static ratios.

Hyper-Connections (HC) generalize residual connections into multiple streams, employing residual matrices for cross-stream feature mixing to enrich model expressivity. However, unconstrained mixing disrupts the identity mapping property intrinsic to the residual connection, causing unstable training. To address this, Manifold-Constrained Hyper-Connections (mHC) and its variant restrict these matrices to the Birkhoff polytope (doubly stochastic matrices) via Sinkhorn iterations or permutation-based parameterizations. We reveal three limitations of this polytope constraint: (1) identity degeneration, where learned matrices collapse around the identity and diminish cross-stream interactions, (2) an expressivity bottleneck, as the non-negativity constraint prevents subtractive feature disentanglement, and (3) parameterization inefficiencies, manifesting as unstable Sinkhorn iterations or the factorial-scaling overhead of permutation-based parameterizations. To overcome these flaws, we propose Spectral-Sphere-Constrained Hyper-Connections (sHC). By geometrically shifting the feasible set from a rigid polytope to a spectral norm sphere, sHC allows negative entries, unlocking subtractive interactions for selective feature diversification. This shift eliminates unstable Sinkhorn projections and factorial parameterization, enabling expressive, non-degenerate residual matrices while preserving training stability.

The data used to pretrain large language models has a decisive impact on a model's downstream performance, which has led to a large body of work on data selection methods that aim to automatically determine the most suitable data to use for pretraining. Existing data selection methods suffer from slow and computationally expensive processes, a problem amplified by the increasing size of models and of pretraining datasets. Data mixing, on the other hand, reduces the complexity of data selection by grouping data points together and determining sampling probabilities across entire groups. However, data mixing proportions are typically fixed before training and therefore cannot adapt to changing training dynamics. To address these limitations, we develop an efficient algorithm for Online Data Mixing (ODM) that combines elements from both data selection and data mixing. Based on multi-armed bandit algorithms, our online approach optimizes the data mixing proportions during training. Remarkably, our method trains a model that reaches the final perplexity of the next best method with 19\% fewer training iterations, and improves performance on the 5-shot MMLU benchmark by 1.9% relative accuracy, while adding negligible wall-clock time during pretraining.

Rectified flow and reflow procedures have significantly advanced fast generation by progressively straightening ordinary differential equation (ODE) flows. They operate under the assumption that image and noise pairs, known as couplings, can be approximated by straight trajectories with constant velocity. However, we observe that modeling with constant velocity and using reflow procedures have limitations in accurately learning straight trajectories between pairs, resulting in suboptimal performance in few-step generation. To address these limitations, we introduce Constant Acceleration Flow (CAF), a novel framework based on a simple constant acceleration equation. CAF introduces acceleration as an additional learnable variable, allowing for more expressive and accurate estimation of the ODE flow. Moreover, we propose two techniques to further improve estimation accuracy: initial velocity conditioning for the acceleration model and a reflow process for the initial velocity. Our comprehensive studies on toy datasets, CIFAR-10, and ImageNet 64x64 demonstrate that CAF outperforms state-of-the-art baselines for one-step generation. We also show that CAF dramatically improves few-step coupling preservation and inversion over Rectified flow. Code is available at https://github.com/mlvlab/CAF{https://github.com/mlvlab/CAF}.

A wide variety of deep learning techniques from style transfer to multitask learning rely on training affine transformations of features. Most prominent among these is the popular feature normalization technique BatchNorm, which normalizes activations and then subsequently applies a learned affine transform. In this paper, we aim to understand the role and expressive power of affine parameters used to transform features in this way. To isolate the contribution of these parameters from that of the learned features they transform, we investigate the performance achieved when training only these parameters in BatchNorm and freezing all weights at their random initializations. Doing so leads to surprisingly high performance considering the significant limitations that this style of training imposes. For example, sufficiently deep ResNets reach 82% (CIFAR-10) and 32% (ImageNet, top-5) accuracy in this configuration, far higher than when training an equivalent number of randomly chosen parameters elsewhere in the network. BatchNorm achieves this performance in part by naturally learning to disable around a third of the random features. Not only do these results highlight the expressive power of affine parameters in deep learning, but - in a broader sense - they characterize the expressive power of neural networks constructed simply by shifting and rescaling random features.

While large and diverse datasets have driven recent advances in large models, identifying the optimal data mixture for pre-training and post-training remains a significant open problem. We address this challenge with FASTMIX, a novel framework that automates data mixture discovery while training only a single proxy model. Instead of relying on predefined heuristics or resource-intensive simulations, FASTMIX jointly optimizes mixture coefficients and model parameters, substantially improving efficiency and scalability over prior approaches. At the core of FASTMIX is a reformulation of mixture selection as a bilevel optimization problem. Under this reformulation, we show that optimizing mixture ratios is mathematically equivalent to assigning per-source loss weights under uniform source sampling. This embeds the mixture coefficients directly into the differentiable iterative optimization objective, enabling efficient, gradient-based optimization of both mixture and model. To solve the optimization problem, FASTMIX implements an approximate iterative optimization procedure, alternating between (i) updating model parameters on data sampled according to current mixture ratios (inner loop) and (ii) updating mixture ratios based on validation feedback (outer loop). Across pre- and post-training, FASTMIX outperforms baselines while drastically reducing search cost. Code (https://github.com/hrtan/fastmix)

Creating novel images by fusing visual cues from multiple sources is a fundamental yet underexplored problem in image-to-image generation, with broad applications in artistic creation, virtual reality and visual media. Existing methods often face two key challenges: coexistent generation, where multiple objects are simply juxtaposed without true integration, and bias generation, where one object dominates the output due to semantic imbalance. To address these issues, we propose Visual Mixing Diffusion (VMDiff), a simple yet effective diffusion-based framework that synthesizes a single, coherent object by integrating two input images at both noise and latent levels. Our approach comprises: (1) a hybrid sampling process that combines guided denoising, inversion, and spherical interpolation with adjustable parameters to achieve structure-aware fusion, mitigating coexistent generation; and (2) an efficient adaptive adjustment module, which introduces a novel similarity-based score to automatically and adaptively search for optimal parameters, countering semantic bias. Experiments on a curated benchmark of 780 concept pairs demonstrate that our method outperforms strong baselines in visual quality, semantic consistency, and human-rated creativity.

Linear recurrent neural networks (RNNs) and state-space models (SSMs) such as Mamba have become promising alternatives to softmax-attention as sequence mixing layers in Transformer architectures. Current models, however, do not exhibit the full state-tracking expressivity of RNNs because they rely on channel-wise (i.e. diagonal) sequence mixing. In this paper, we investigate parameterizations of a large class of dense linear RNNs as fixed-points of parallelizable diagonal linear RNNs. The resulting models can naturally trade expressivity for efficiency at a fixed number of parameters and achieve state-of-the-art results on the state-tracking benchmarks A_5 and S_5, while matching performance on copying and other tasks.

Data mixing -- determining the ratios of data from different domains -- is a first-order concern for training language models (LMs). While existing mixing methods show promise, they fall short when applied during real-world LM development. We present Olmix, a framework that addresses two such challenges. First, the configuration space for developing a mixing method is not well understood -- design choices across existing methods lack justification or consensus and overlook practical issues like data constraints. We conduct a comprehensive empirical study of this space, identifying which design choices lead to a strong mixing method. Second, in practice, the domain set evolves throughout LM development as datasets are added, removed, partitioned, and revised -- a problem setting largely unaddressed by existing works, which assume fixed domains. We study how to efficiently recompute the mixture after the domain set is updated, leveraging information from past mixtures. We introduce mixture reuse, a mechanism that reuses existing ratios and recomputes ratios only for domains affected by the update. Over a sequence of five domain-set updates mirroring real-world LM development, mixture reuse matches the performance of fully recomputing the mix after each update with 74% less compute and improves over training without mixing by 11.6% on downstream tasks.

A new class of affine scaling matrices for the interior point Newton-type methods is considered to solve the nonlinear systems with simple bounds. We review the essential properties of a scaling matrix and consider several well-known scaling matrices proposed in the literature. We define a new scaling matrix that is the convex combination of these matrices. The proposed scaling matrix inherits those interesting properties of the individual matrices and satisfies additional desired requirements. The numerical experiments demonstrate the superiority of the new scaling matrix in solving several important test problems.

Optimizing pretraining data composition is pivotal for LLM generalization. While dynamic mixing outperforms static strategies by capturing evolving training dynamics, current methods fail to reconcile computational efficiency with sample efficiency and structural flexibility for diverse pipelines.We introduce Actor--Critic Online Data Mixing (AC-ODM), which approaches data mixing from a reinforcement learning perspective with a parameterized policy that we theoretically prove to act as a dynamic linear surrogate maximizing the constructive interference of gradients. To enhance practical flexibility, AC-ODM supports two operational modes: (i) a proxy mode for fixed, pre-prepared corpora, where a policy learned on a small model is transferred to a larger target; and (ii) a non-proxy mode for direct end-to-end training from scratch without priors. Empirically, AC-ODM significantly outperforms prior methods in convergence speed and downstream accuracy across various architectures. On Pythia-1B, it reaches optimal validation perplexity using up to 66% fewer training steps than competitive baselines, delivering a 27.5% relative improvement in MMLU accuracy and a 2.23 x higher pass@1 on HumanEval, all while incurring a virtually negligible (0.4%) per-step wall-clock increase and only 2% additional memory overhead. Code is available at https://github.com/DANG-ai/AC-ODM.

Self-distillation (SD) is the process of retraining a student on a mixture of ground-truth labels and the teacher's own predictions using the same architecture and training data. Although SD has been empirically shown to often improve generalization, its formal guarantees remain limited. We study SD for ridge regression in unconstrained setting in which the mixing weight ξ may be outside the unit interval. Conditioned on the training data and without any distributional assumptions, we prove that for any squared prediction risk (including out-of-distribution), the optimally mixed student strictly improves upon the ridge teacher for every regularization level λ> 0 at which the teacher ridge risk R(λ) is nonstationary (i.e., R'(λ) neq 0). We obtain a closed-form expression for the optimal mixing weight ξ^star(λ) for any value of λ and show that it obeys the sign rule: sign(ξ^star(λ))=-sign(R'(λ)). In particular, ξ^star(λ) can be negative, which is the case in over-regularized regimes. To quantify the risk improvement due to SD, we derive exact deterministic equivalents for the optimal SD risk in the proportional asymptotics regime (where the sample and feature sizes n and p both diverge but their aspect ratio p/n converges) under general anisotropic covariance and deterministic signals. Our asymptotic analysis extends standard second-order ridge deterministic equivalents to their fourth-order analogs using block linearization, which may be of independent interest. From a practical standpoint, we propose a consistent one-shot tuning method to estimate ξ^star without grid search, sample splitting, or refitting. Experiments on real-world datasets and pretrained neural network features support our theory and the one-shot tuning method.

We release Super Apriel, a 15B-parameter supernet in which every decoder layer provides four trained mixer choices -- Full Attention (FA), Sliding Window Attention (SWA), Kimi Delta Attention (KDA), and Gated DeltaNet (GDN). A placement selects one mixer per layer; placements can be switched between requests at serving time without reloading weights, enabling multiple speed presets from a single checkpoint. The shared checkpoint also enables speculative decoding without a separate draft model. The all-FA preset matches the Apriel 1.6 teacher on all reported benchmarks; recommended hybrid presets span 2.9times to 10.7times decode throughput at 96% to 77% quality retention, with throughput advantages that compound at longer context lengths. With four mixer types across 48 layers, the configuration space is vast. A surrogate that predicts placement quality from the per-layer mixer assignment makes the speed-quality landscape tractable and identifies the best tradeoffs at each speed level. We investigate whether the best configurations at each speed level can be identified early in training or only after convergence. Rankings stabilize quickly at 0.5B scale, but the most efficient configurations exhibit higher instability at 15B, cautioning against extrapolation from smaller models. Super Apriel is trained by stochastic distillation from a frozen Apriel 1.6 teacher, followed by supervised fine-tuning. We release the supernet weights, Fast-LLM training code, vLLM serving code, and a placement optimization toolkit.

While prior research has proposed a plethora of methods that build neural classifiers robust against adversarial robustness, practitioners are still reluctant to adopt them due to their unacceptably severe clean accuracy penalties. This paper significantly alleviates this accuracy-robustness trade-off by mixing the output probabilities of a standard classifier and a robust classifier, where the standard network is optimized for clean accuracy and is not robust in general. We show that the robust base classifier's confidence difference for correct and incorrect examples is the key to this improvement. In addition to providing intuitions and empirical evidence, we theoretically certify the robustness of the mixed classifier under realistic assumptions. Furthermore, we adapt an adversarial input detector into a mixing network that adaptively adjusts the mixture of the two base models, further reducing the accuracy penalty of achieving robustness. The proposed flexible method, termed "adaptive smoothing", can work in conjunction with existing or even future methods that improve clean accuracy, robustness, or adversary detection. Our empirical evaluation considers strong attack methods, including AutoAttack and adaptive attack. On the CIFAR-100 dataset, our method achieves an 85.21% clean accuracy while maintaining a 38.72% ell_infty-AutoAttacked (epsilon = 8/255) accuracy, becoming the second most robust method on the RobustBench CIFAR-100 benchmark as of submission, while improving the clean accuracy by ten percentage points compared with all listed models. The code that implements our method is available at https://github.com/Bai-YT/AdaptiveSmoothing.

Time series forecasting is widely used in extensive applications, such as traffic planning and weather forecasting. However, real-world time series usually present intricate temporal variations, making forecasting extremely challenging. Going beyond the mainstream paradigms of plain decomposition and multiperiodicity analysis, we analyze temporal variations in a novel view of multiscale-mixing, which is based on an intuitive but important observation that time series present distinct patterns in different sampling scales. The microscopic and the macroscopic information are reflected in fine and coarse scales respectively, and thereby complex variations can be inherently disentangled. Based on this observation, we propose TimeMixer as a fully MLP-based architecture with Past-Decomposable-Mixing (PDM) and Future-Multipredictor-Mixing (FMM) blocks to take full advantage of disentangled multiscale series in both past extraction and future prediction phases. Concretely, PDM applies the decomposition to multiscale series and further mixes the decomposed seasonal and trend components in fine-to-coarse and coarse-to-fine directions separately, which successively aggregates the microscopic seasonal and macroscopic trend information. FMM further ensembles multiple predictors to utilize complementary forecasting capabilities in multiscale observations. Consequently, TimeMixer is able to achieve consistent state-of-the-art performances in both long-term and short-term forecasting tasks with favorable run-time efficiency.

Inversion-based image editing in flow matching models has emerged as a powerful paradigm for training-free, text-guided image manipulation. A central challenge in this paradigm is the injection dilemma: injecting source features during denoising preserves the background of the original image but simultaneously suppresses the model's ability to synthesize edited content. Existing methods address this with fixed injection strategies -- binary on/off temporal schedules, uniform spatial mixing ratios, and channel-agnostic latent perturbation -- that ignore the inherently heterogeneous nature of injection demand across both the temporal and channel dimensions. In this paper, we present AdaEdit, a training-free adaptive editing framework that resolves this dilemma through two complementary innovations. First, we propose a Progressive Injection Schedule that replaces hard binary cutoffs with continuous decay functions (sigmoid, cosine, or linear), enabling a smooth transition from source-feature preservation to target-feature generation and eliminating feature discontinuity artifacts. Second, we introduce Channel-Selective Latent Perturbation, which estimates per-channel importance based on the distributional gap between the inverted and random latents and applies differentiated perturbation strengths accordingly -- strongly perturbing edit-relevant channels while preserving structure-encoding channels. Extensive experiments on the PIE-Bench benchmark (700 images, 10 editing types) demonstrate that AdaEdit achieves an 8.7% reduction in LPIPS, a 2.6% improvement in SSIM, and a 2.3% improvement in PSNR over strong baselines, while maintaining competitive CLIP similarity. AdaEdit is fully plug-and-play and compatible with multiple ODE solvers including Euler, RF-Solver, and FireFlow. Code is available at https://github.com/leeguandong/AdaEdit

Normalizing flows are a promising tool for modeling probability distributions in physical systems. While state-of-the-art flows accurately approximate distributions and energies, applications in physics additionally require smooth energies to compute forces and higher-order derivatives. Furthermore, such densities are often defined on non-trivial topologies. A recent example are Boltzmann Generators for generating 3D-structures of peptides and small proteins. These generative models leverage the space of internal coordinates (dihedrals, angles, and bonds), which is a product of hypertori and compact intervals. In this work, we introduce a class of smooth mixture transformations working on both compact intervals and hypertori. Mixture transformations employ root-finding methods to invert them in practice, which has so far prevented bi-directional flow training. To this end, we show that parameter gradients and forces of such inverses can be computed from forward evaluations via the inverse function theorem. We demonstrate two advantages of such smooth flows: they allow training by force matching to simulation data and can be used as potentials in molecular dynamics simulations.

Diffusion models have shown great promise for image and video generation, but sampling from state-of-the-art models requires expensive numerical integration of a generative ODE. One approach for tackling this problem is rectified flows, which iteratively learn smooth ODE paths that are less susceptible to truncation error. However, rectified flows still require a relatively large number of function evaluations (NFEs). In this work, we propose improved techniques for training rectified flows, allowing them to compete with knowledge distillation methods even in the low NFE setting. Our main insight is that under realistic settings, a single iteration of the Reflow algorithm for training rectified flows is sufficient to learn nearly straight trajectories; hence, the current practice of using multiple Reflow iterations is unnecessary. We thus propose techniques to improve one-round training of rectified flows, including a U-shaped timestep distribution and LPIPS-Huber premetric. With these techniques, we improve the FID of the previous 2-rectified flow by up to 72% in the 1 NFE setting on CIFAR-10. On ImageNet 64times64, our improved rectified flow outperforms the state-of-the-art distillation methods such as consistency distillation and progressive distillation in both one-step and two-step settings and rivals the performance of improved consistency training (iCT) in FID. Code is available at https://github.com/sangyun884/rfpp.

The scalability of Large Language Models to long sequences is hindered by the quadratic cost of attention and the limitations of positional encodings. To address these, we introduce Caracal, a novel architecture that replaces attention with a parameter-efficient, O(L log(L)) Multi-Head Fourier (MHF) module. Our contributions are threefold: (1) We leverage the Fast Fourier Transform (FFT) for sequence mixing, inherently addressing both bottlenecks mentioned above. (2) We apply a frequency-domain causal masking technique that enforces autoregressive capabilities via asymmetric padding and truncation, overcoming a critical barrier for Fourier-based generative models. (3) Unlike efficient models relying on hardware-specific implementations (e.g., Mamba), we uses standard library operators. This ensures robust portability, eliminating common deployment barriers. Evaluations demonstrate that Caracal performs competitively with Transformer and SSM baselines, offering a scalable and simple pathway for efficient long-sequence modeling. Code is available in Appendix.

Pan-sharpening aims to generate a high-resolution multispectral (HRMS) image by integrating the spectral information of a low-resolution multispectral (LRMS) image with the texture details of a high-resolution panchromatic (PAN) image. It essentially inherits the ill-posed nature of the super-resolution (SR) task that diverse HRMS images can degrade into an LRMS image. However, existing deep learning-based methods recover only one HRMS image from the LRMS image and PAN image using a deterministic mapping, thus ignoring the diversity of the HRMS image. In this paper, to alleviate this ill-posed issue, we propose a flow-based pan-sharpening network (PanFlowNet) to directly learn the conditional distribution of HRMS image given LRMS image and PAN image instead of learning a deterministic mapping. Specifically, we first transform this unknown conditional distribution into a given Gaussian distribution by an invertible network, and the conditional distribution can thus be explicitly defined. Then, we design an invertible Conditional Affine Coupling Block (CACB) and further build the architecture of PanFlowNet by stacking a series of CACBs. Finally, the PanFlowNet is trained by maximizing the log-likelihood of the conditional distribution given a training set and can then be used to predict diverse HRMS images. The experimental results verify that the proposed PanFlowNet can generate various HRMS images given an LRMS image and a PAN image. Additionally, the experimental results on different kinds of satellite datasets also demonstrate the superiority of our PanFlowNet compared with other state-of-the-art methods both visually and quantitatively.

Though Rectified Flows (ReFlows) with distillation offers a promising way for fast sampling, its fast inversion transforms images back to structured noise for recovery and following editing remains unsolved. This paper introduces FireFlow, a simple yet effective zero-shot approach that inherits the startling capacity of ReFlow-based models (such as FLUX) in generation while extending its capabilities to accurate inversion and editing in 8 steps. We first demonstrate that a carefully designed numerical solver is pivotal for ReFlow inversion, enabling accurate inversion and reconstruction with the precision of a second-order solver while maintaining the practical efficiency of a first-order Euler method. This solver achieves a 3times runtime speedup compared to state-of-the-art ReFlow inversion and editing techniques, while delivering smaller reconstruction errors and superior editing results in a training-free mode. The code is available at https://github.com/HolmesShuan/FireFlow{this URL}.

Despite recent advances in generative modeling for text-to-speech synthesis, these models do not yet have the same fine-grained adjustability of pitch-conditioned deterministic models such as FastPitch and FastSpeech2. Pitch information is not only low-dimensional, but also discontinuous, making it particularly difficult to model in a generative setting. Our work explores several techniques for handling the aforementioned issues in the context of Normalizing Flow models. We also find this problem to be very well suited for Neural Spline flows, which is a highly expressive alternative to the more common affine-coupling mechanism in Normalizing Flows.

Instruction tuning aligns large language models, including multimodal ones, with diverse user intents, but scaling to heterogeneous mixtures is hindered by gradient interference and bandwidth-heavy synchronization. We ask whether these two bottlenecks can be addressed jointly by training parts of the mixture independently and reconciling them once in parameter space. We develop a local quadratic theory inside a shared flat basin that yields three results: weight merging produces a curvature-weighted variance reduction; PCA-aligned conflict splitting maximizes this gain along high-curvature directions; and merging additionally acts as spectral filtering with implicit norm regularization. These results directly motivate MERIT, a decentralized merge-ready instruction-tuning pipeline that estimates dataset-level gradient conflicts, partitions the mixture along the top PCA conflict axes, fine-tunes each partition independently with no inter-partition communication, and merges once via token-weighted averaging. On Qwen2.5-VL-3B with 136 Vision-FLAN tasks, MERIT improves the 8-benchmark average from 54.3 (joint training) to 57.0. The same recipe scales to a 7B model on a 1.6M-example, 176-source mixture -- matching or exceeding centralized joint training with minimal cost overhead -- and transfers to text-only FLAN. Our code is available at https://github.com/naver-ai/merit.

Pretraining data of large language models composes multiple domains (e.g., web texts, academic papers, codes), whose mixture proportions crucially impact the competence of outcome models. While existing endeavors rely on heuristics or qualitative strategies to tune the proportions, we discover the quantitative predictability of model performance regarding the mixture proportions in function forms, which we refer to as the data mixing laws. Fitting such functions on sample mixtures unveils model performance on unseen mixtures before actual runs, thus guiding the selection of an ideal data mixture. Furthermore, we propose nested use of the scaling laws of training steps, model sizes, and our data mixing law to enable predicting the performance of large models trained on massive data under various mixtures with only small-scale training. Moreover, experimental results verify that our method effectively optimizes the training mixture of a 1B model trained for 100B tokens in RedPajama, reaching a performance comparable to the one trained for 48% more steps on the default mixture. Extending the application of data mixing laws to continual training accurately predicts the critical mixture proportion that avoids catastrophic forgetting and outlooks the potential for dynamic data schedules

This work presents mixed variational flows (MixFlows), a new variational family that consists of a mixture of repeated applications of a map to an initial reference distribution. First, we provide efficient algorithms for i.i.d. sampling, density evaluation, and unbiased ELBO estimation. We then show that MixFlows have MCMC-like convergence guarantees when the flow map is ergodic and measure-preserving, and provide bounds on the accumulation of error for practical implementations where the flow map is approximated. Finally, we develop an implementation of MixFlows based on uncorrected discretized Hamiltonian dynamics combined with deterministic momentum refreshment. Simulated and real data experiments show that MixFlows can provide more reliable posterior approximations than several black-box normalizing flows, as well as samples of comparable quality to those obtained from state-of-the-art MCMC methods.

Mixup is a highly successful technique to improve generalization of neural networks by augmenting the training data with combinations of random pairs. Selective mixup is a family of methods that apply mixup to specific pairs, e.g. only combining examples across classes or domains. These methods have claimed remarkable improvements on benchmarks with distribution shifts, but their mechanisms and limitations remain poorly understood. We examine an overlooked aspect of selective mixup that explains its success in a completely new light. We find that the non-random selection of pairs affects the training distribution and improve generalization by means completely unrelated to the mixing. For example in binary classification, mixup across classes implicitly resamples the data for a uniform class distribution - a classical solution to label shift. We show empirically that this implicit resampling explains much of the improvements in prior work. Theoretically, these results rely on a regression toward the mean, an accidental property that we identify in several datasets. We have found a new equivalence between two successful methods: selective mixup and resampling. We identify limits of the former, confirm the effectiveness of the latter, and find better combinations of their respective benefits.

This study introduces a novel and interpretable model, DiffVox, for matching vocal effects in music production. DiffVox, short for ``Differentiable Vocal Fx", integrates parametric equalisation, dynamic range control, delay, and reverb with efficient differentiable implementations to enable gradient-based optimisation for parameter estimation. Vocal presets are retrieved from two datasets, comprising 70 tracks from MedleyDB and 365 tracks from a private collection. Analysis of parameter correlations highlights strong relationships between effects and parameters, such as the high-pass and low-shelf filters often behaving together to shape the low end, and the delay time correlates with the intensity of the delayed signals. Principal component analysis reveals connections to McAdams' timbre dimensions, where the most crucial component modulates the perceived spaciousness while the secondary components influence spectral brightness. Statistical testing confirms the non-Gaussian nature of the parameter distribution, highlighting the complexity of the vocal effects space. These initial findings on the parameter distributions set the foundation for future research in vocal effects modelling and automatic mixing. Our source code and datasets are accessible at https://github.com/SonyResearch/diffvox.

Conditional flow matching (CFM) has emerged as a powerful framework for training continuous normalizing flows due to its computational efficiency and effectiveness. However, standard CFM often produces paths that deviate significantly from straight-line interpolations between prior and target distributions, making generation slower and less accurate due to the need for fine discretization at inference. Recent methods enhance CFM performance by inducing shorter and straighter trajectories but typically rely on computationally expensive mini-batch optimal transport (OT). Drawing insights from entropic optimal transport (EOT), we propose Weighted Conditional Flow Matching (W-CFM), a novel approach that modifies the classical CFM loss by weighting each training pair (x, y) with a Gibbs kernel. We show that this weighting recovers the entropic OT coupling up to some bias in the marginals, and we provide the conditions under which the marginals remain nearly unchanged. Moreover, we establish an equivalence between W-CFM and the minibatch OT method in the large-batch limit, showing how our method overcomes computational and performance bottlenecks linked to batch size. Empirically, we test our method on unconditional generation on various synthetic and real datasets, confirming that W-CFM achieves comparable or superior sample quality, fidelity, and diversity to other alternative baselines while maintaining the computational efficiency of vanilla CFM.

A wide array of sequence models are built on a framework modeled after Transformers, comprising alternating sequence mixer and channel mixer layers. This paper studies a unifying matrix mixer view of sequence mixers that can be conceptualized as a linear map on the input sequence. This framework encompasses a broad range of well-known sequence models, including the self-attention of Transformers as well as recent strong alternatives such as structured state space models (SSMs), and allows understanding downstream characteristics such as efficiency and expressivity through properties of their structured matrix class. We identify a key axis of matrix parameterizations termed sequence alignment, which increases the flexibility and performance of matrix mixers, providing insights into the strong performance of Transformers and recent SSMs such as Mamba. Furthermore, the matrix mixer framework offers a systematic approach to developing sequence mixers with desired properties, allowing us to develop several new sub-quadratic sequence models. In particular, we propose a natural bidirectional extension of the Mamba model (Hydra), parameterized as a quasiseparable matrix mixer, which demonstrates superior performance over other sequence models including Transformers on non-causal tasks. As a drop-in replacement for attention layers, Hydra outperforms BERT by 0.8 points on the GLUE benchmark and ViT by 2% Top-1 accuracy on ImageNet.

A central task of a Disc Jockey (DJ) is to create a mixset of mu-sic with seamless transitions between adjacent tracks. In this paper, we explore a data-driven approach that uses a generative adversarial network to create the song transition by learning from real-world DJ mixes. In particular, the generator of the model uses two differentiable digital signal processing components, an equalizer (EQ) and a fader, to mix two tracks selected by a data generation pipeline. The generator has to set the parameters of the EQs and fader in such away that the resulting mix resembles real mixes created by humanDJ, as judged by the discriminator counterpart. Result of a listening test shows that the model can achieve competitive results compared with a number of baselines.

Deep neural networks tend to memorize noisy labels, severely degrading their generalization performance. Although Mixup has demonstrated effectiveness in improving generalization and robustness, existing Mixup-based methods typically perform indiscriminate mixing without principled guidance on sample selection and mixing strategy, inadvertently propagating noisy supervision. To overcome these limitations, we propose SelectMix, a confidence-guided mixing framework explicitly tailored for noisy labels. SelectMix first identifies potentially noisy or ambiguous samples through confidence based mismatch analysis using K-fold cross-validation, then selectively blends identified uncertain samples with confidently predicted peers from their potential classes. Furthermore, SelectMix employs soft labels derived from all classes involved in the mixing process, ensuring the labels accurately represent the composition of the mixed samples, thus aligning supervision signals closely with the actual mixed inputs. Through extensive theoretical analysis and empirical evaluations on multiple synthetic (MNIST, Fashion-MNIST, CIFAR-10, CIFAR-100) and real-world benchmark datasets (CIFAR-N, MNIST and Clothing1M), we demonstrate that SelectMix consistently outperforms strong baseline methods, validating its effectiveness and robustness in learning with noisy labels.

Online Class-Incremental (OCI) learning has sparked new approaches to expand the previously trained model knowledge from sequentially arriving data streams with new classes. Unfortunately, OCI learning can suffer from catastrophic forgetting (CF) as the decision boundaries for old classes can become inaccurate when perturbated by new ones. Existing literature have applied the data augmentation (DA) to alleviate the model forgetting, while the role of DA in OCI has not been well understood so far. In this paper, we theoretically show that augmented samples with lower correlation to the original data are more effective in preventing forgetting. However, aggressive augmentation may also reduce the consistency between data and corresponding labels, which motivates us to exploit proper DA to boost the OCI performance and prevent the CF problem. We propose the Enhanced Mixup (EnMix) method that mixes the augmented samples and their labels simultaneously, which is shown to enhance the sample diversity while maintaining strong consistency with corresponding labels. Further, to solve the class imbalance problem, we design an Adaptive Mixup (AdpMix) method to calibrate the decision boundaries by mixing samples from both old and new classes and dynamically adjusting the label mixing ratio. Our approach is demonstrated to be effective on several benchmark datasets through extensive experiments, and it is shown to be compatible with other replay-based techniques.

The inability of deep learning models to handle data drawn from unseen distributions has sparked much interest in unsupervised out-of-distribution (U-OOD) detection, as it is crucial for reliable deep learning models. Despite considerable attention, theoretically-motivated approaches are few and far between, with most methods building on top of some form of heuristic. Recently, U-OOD was formalized in the context of data invariants, allowing a clearer understanding of how to characterize U-OOD, and methods leveraging affine invariants have attained state-of-the-art results on large-scale benchmarks. Nevertheless, the restriction to affine invariants hinders the expressiveness of the approach. In this work, we broaden the affine invariants formulation to a more general case and propose a framework consisting of a normalizing flow-like architecture capable of learning non-linear invariants. Our novel approach achieves state-of-the-art results on an extensive U-OOD benchmark, and we demonstrate its further applicability to tabular data. Finally, we show our method has the same desirable properties as those based on affine invariants.

Token mixing layers play a key role in how language models can learn and generate long-range dependencies. Their efficiency relies on the necessary trade-off between decoding speed and the memory requirements, along with the cache size. Considering causal generation, this paper explores new trade-offs thanks to a unified framework which separates two crucial features: (i) the direct influence of inputs on outputs in one generation step; (ii) the recurrent propagation of information through past outputs. This framework encompasses major architectures such as attention and state-space models, but also generalizes the recurrence equations by allowing each state to depend on multiple past states rather than only the immediate predecessor. By introducing structure, we design new recurrence patterns that provably achieve the desired complexity, while providing theoretical insights on their expressivity -- trading runtime for expressivity in a principled way. Empirical validation is performed on synthetic tasks, along with language modeling. Together, these results provide a unified toolkit for the understanding and design of efficient and expressive token mixers across model families.

Retrieval systems rely on representations learned by increasingly powerful models. However, due to the high training cost and inconsistencies in learned representations, there is significant interest in facilitating communication between representations and ensuring compatibility across independently trained neural networks. In the literature, two primary approaches are commonly used to adapt different learned representations: affine transformations, which adapt well to specific distributions but can significantly alter the original representation, and orthogonal transformations, which preserve the original structure with strict geometric constraints but limit adaptability. A key challenge is adapting the latent spaces of updated models to align with those of previous models on downstream distributions while preserving the newly learned representation spaces. In this paper, we impose a relaxed orthogonality constraint, namely λ-Orthogonality regularization, while learning an affine transformation, to obtain distribution-specific adaptation while retaining the original learned representations. Extensive experiments across various architectures and datasets validate our approach, demonstrating that it preserves the model's zero-shot performance and ensures compatibility across model updates. Code available at: https://github.com/miccunifi/lambda_orthogonality.git{https://github.com/miccunifi/lambda\_orthogonality}.

A new generalized matrix inverse is derived which is consistent with respect to arbitrary nonsingular diagonal transformations, e.g., it preserves units associated with variables under state space transformations, thus providing a general solution to a longstanding open problem relevant to a wide variety of applications in robotics, tracking, and control systems. The new inverse complements the Drazin inverse (which is consistent with respect to similarity transformations) and the Moore-Penrose inverse (which is consistent with respect to unitary/orthonormal transformations) to complete a trilogy of generalized matrix inverses that exhausts the standard family of analytically-important linear system transformations. Results are generalized to obtain unit-consistent and unit-invariant matrix decompositions and examples of their use are described.

We propose an end-to-end music mixing style transfer system that converts the mixing style of an input multitrack to that of a reference song. This is achieved with an encoder pre-trained with a contrastive objective to extract only audio effects related information from a reference music recording. All our models are trained in a self-supervised manner from an already-processed wet multitrack dataset with an effective data preprocessing method that alleviates the data scarcity of obtaining unprocessed dry data. We analyze the proposed encoder for the disentanglement capability of audio effects and also validate its performance for mixing style transfer through both objective and subjective evaluations. From the results, we show the proposed system not only converts the mixing style of multitrack audio close to a reference but is also robust with mixture-wise style transfer upon using a music source separation model.

While scaling laws for recommendation models have gained significant traction, existing architectures such as Wukong, HiFormer and DHEN, often struggle with sub-optimal designs and hardware under-utilization, limiting their practical scalability. Our previous TokenMixer architecture (introduced in RankMixer paper) addressed effectiveness and efficiency by replacing self-attention with a ightweight token-mixing operator; however, it faced critical bottlenecks in deeper configurations, including sub-optimal residual paths, vanishing gradients, incomplete MoE sparsification and constrained scalability. In this paper, we propose TokenMixer-Large, a systematically evolved architecture designed for extreme-scale recommendation. By introducing a mixing-and-reverting operation, inter-layer residuals and the auxiliary loss, we ensure stable gradient propagation even as model depth increases. Furthermore, we incorporate a Sparse Per-token MoE to enable efficient parameter expansion. TokenMixer-Large successfully scales its parameters to 7-billion and 15-billion on online traffic and offline experiments, respectively. Currently deployed in multiple scenarios at ByteDance, TokenMixer-Large has achieved significant offline and online performance gains, delivering an increase of +1.66\% in orders and +2.98\% in per-capita preview payment GMV for e-commerce, improving ADSS by +2.0\% in advertising and achieving a +1.4\% revenue growth for live streaming.

Network calibration aims to accurately estimate the level of confidences, which is particularly important for employing deep neural networks in real-world systems. Recent approaches leverage mixup to calibrate the network's predictions during training. However, they do not consider the problem that mixtures of labels in mixup may not accurately represent the actual distribution of augmented samples. In this paper, we present RankMixup, a novel mixup-based framework alleviating the problem of the mixture of labels for network calibration. To this end, we propose to use an ordinal ranking relationship between raw and mixup-augmented samples as an alternative supervisory signal to the label mixtures for network calibration. We hypothesize that the network should estimate a higher level of confidence for the raw samples than the augmented ones (Fig.1). To implement this idea, we introduce a mixup-based ranking loss (MRL) that encourages lower confidences for augmented samples compared to raw ones, maintaining the ranking relationship. We also propose to leverage the ranking relationship among multiple mixup-augmented samples to further improve the calibration capability. Augmented samples with larger mixing coefficients are expected to have higher confidences and vice versa (Fig.1). That is, the order of confidences should be aligned with that of mixing coefficients. To this end, we introduce a novel loss, M-NDCG, in order to reduce the number of misaligned pairs of the coefficients and confidences. Extensive experimental results on standard benchmarks for network calibration demonstrate the effectiveness of RankMixup.

We address the problem of synthesizing multi-view optical illusions: images that change appearance upon a transformation, such as a flip or rotation. We propose a simple, zero-shot method for obtaining these illusions from off-the-shelf text-to-image diffusion models. During the reverse diffusion process, we estimate the noise from different views of a noisy image, and then combine these noise estimates together and denoise the image. A theoretical analysis suggests that this method works precisely for views that can be written as orthogonal transformations, of which permutations are a subset. This leads to the idea of a visual anagram--an image that changes appearance under some rearrangement of pixels. This includes rotations and flips, but also more exotic pixel permutations such as a jigsaw rearrangement. Our approach also naturally extends to illusions with more than two views. We provide both qualitative and quantitative results demonstrating the effectiveness and flexibility of our method. Please see our project webpage for additional visualizations and results: https://dangeng.github.io/visual_anagrams/

Flow matching in the continuous simplex has emerged as a promising strategy for DNA sequence design, but struggles to scale to higher simplex dimensions required for peptide and protein generation. We introduce Gumbel-Softmax Flow and Score Matching, a generative framework on the simplex based on a novel Gumbel-Softmax interpolant with a time-dependent temperature. Using this interpolant, we introduce Gumbel-Softmax Flow Matching by deriving a parameterized velocity field that transports from smooth categorical distributions to distributions concentrated at a single vertex of the simplex. We alternatively present Gumbel-Softmax Score Matching which learns to regress the gradient of the probability density. Our framework enables high-quality, diverse generation and scales efficiently to higher-dimensional simplices. To enable training-free guidance, we propose Straight-Through Guided Flows (STGFlow), a classifier-based guidance method that leverages straight-through estimators to steer the unconditional velocity field toward optimal vertices of the simplex. STGFlow enables efficient inference-time guidance using classifiers pre-trained on clean sequences, and can be used with any discrete flow method. Together, these components form a robust framework for controllable de novo sequence generation. We demonstrate state-of-the-art performance in conditional DNA promoter design, sequence-only protein generation, and target-binding peptide design for rare disease treatment.

Multiplications are responsible for most of the computational cost involved in neural network training and inference. Recent research has thus looked for ways to reduce the cost associated with them. Inspired by Mogami (2020), we replace multiplication with a cheap piecewise affine approximation that is achieved by adding the bit representation of the floating point numbers together as integers. We show that transformers can be trained with the resulting modified matrix multiplications on both vision and language tasks with little to no performance impact, and without changes to the training hyperparameters. We further replace all non-linearities in the networks making them fully and jointly piecewise affine in both inputs and weights. Finally, we show that we can eliminate all multiplications in the entire training process, including operations in the forward pass, backward pass and optimizer update, demonstrating the first successful training of modern neural network architectures in a fully multiplication-free fashion.

We present Piecewise Rectified Flow (PeRFlow), a flow-based method for accelerating diffusion models. PeRFlow divides the sampling process of generative flows into several time windows and straightens the trajectories in each interval via the reflow operation, thereby approaching piecewise linear flows. PeRFlow achieves superior performance in a few-step generation. Moreover, through dedicated parameterizations, the obtained PeRFlow models show advantageous transfer ability, serving as universal plug-and-play accelerators that are compatible with various workflows based on the pre-trained diffusion models. The implementations of training and inference are fully open-sourced. https://github.com/magic-research/piecewise-rectified-flow

Data mixing augmentation has proved effective in training deep models. Recent methods mix labels mainly based on the mixture proportion of image pixels. As the main discriminative information of a fine-grained image usually resides in subtle regions, methods along this line are prone to heavy label noise in fine-grained recognition. We propose in this paper a novel scheme, termed as Semantically Proportional Mixing (SnapMix), which exploits class activation map (CAM) to lessen the label noise in augmenting fine-grained data. SnapMix generates the target label for a mixed image by estimating its intrinsic semantic composition, and allows for asymmetric mixing operations and ensures semantic correspondence between synthetic images and target labels. Experiments show that our method consistently outperforms existing mixed-based approaches on various datasets and under different network depths. Furthermore, by incorporating the mid-level features, the proposed SnapMix achieves top-level performance, demonstrating its potential to serve as a solid baseline for fine-grained recognition. Our code is available at https://github.com/Shaoli-Huang/SnapMix.git.

The composition of training data, governed by the diversity of sources and their mixing strategy, is a cornerstone of Large Language Model (LLM) pre-training. Online Data Mixing (ODM), the technique of adaptively adjusting data mixtures during training, has emerged as a promising direction to improve efficiency. However, existing methods are constrained by their reliance on a singular optimization perspective, which fundamentally overlooks the need for complex LLM pre-training to consider the dynamic data composition from multiple dimensions. To overcome this limitation, we introduce the Holistic Data Scheduler (HDS), a novel online data mixing framework. HDS formulates the data scheduling challenge as a reinforcement learning problem in a continuous control space and leverages the Soft Actor-Critic (SAC) algorithm for its stability and sample efficiency in exploring the high-dimensional policy space. At the core of HDS lies a novel multi-objective, holistic reward function that integrates three critical perspectives: a data-driven reward for quality, a loss-driven reward capturing inter-domain influence, and a model-driven reward based on weight norms. To validate our design and determine its optimal configuration, we conducted systematic experiments on LLMs of various sizes. On The Pile benchmark, HDS reaches the final validation perplexity of the next best method with 44% fewer training iterations. Furthermore, it achieves a 7.2% improvement on the MMLU 0-shot task along with consistent gains on other benchmarks, showcasing its ability to enhance both training efficiency and final model capability.

We consider in this work quantities that can be obtained as limits of powers of parametrized matrices, for instance the inverse matrix or the logarithm of the determinant. Under the assumption of affine dependence in the parameters, we use the Empirical Interpolation Method (EIM) to derive an approximation for powers of these matrices, from which we derive a nonintrusive approximation for the aforementioned limits. We derive upper bounds of the error made by the obtained formula. Finally, numerical comparisons with classical intrusive and nonintrusive approximation techniques are provided: in the considered test-cases, our algorithm performs well compared to the nonintrusive ones.

Flow-based generative models are powerful exact likelihood models with efficient sampling and inference. Despite their computational efficiency, flow-based models generally have much worse density modeling performance compared to state-of-the-art autoregressive models. In this paper, we investigate and improve upon three limiting design choices employed by flow-based models in prior work: the use of uniform noise for dequantization, the use of inexpressive affine flows, and the use of purely convolutional conditioning networks in coupling layers. Based on our findings, we propose Flow++, a new flow-based model that is now the state-of-the-art non-autoregressive model for unconditional density estimation on standard image benchmarks. Our work has begun to close the significant performance gap that has so far existed between autoregressive models and flow-based models. Our implementation is available at https://github.com/aravindsrinivas/flowpp

In this paper, we develop and implement an efficient asymptotic-preserving (AP) scheme to solve the gas mixture of Boltzmann equations under the disparate mass scaling relevant to the so-called "epochal relaxation" phenomenon. The disparity in molecular masses, ranging across several orders of magnitude, leads to significant challenges in both the evaluation of collision operators and the designing of time-stepping schemes to capture the multi-scale nature of the dynamics. A direct implementation of the spectral method faces prohibitive computational costs as the mass ratio increases due to the need to resolve vastly different thermal velocities. Unlike [I. M. Gamba, S. Jin, and L. Liu, Commun. Math. Sci., 17 (2019), pp. 1257-1289], we propose an alternative approach based on proper truncation of asymptotic expansions of the collision operators, which significantly reduces the computational complexity and works well for small varepsilon. By incorporating the separation of three time scales in the model's relaxation process [P. Degond and B. Lucquin-Desreux, Math. Models Methods Appl. Sci., 6 (1996), pp. 405-436], we design an AP scheme that captures the specific dynamics of the disparate mass model while maintaining computational efficiency. Numerical experiments demonstrate the effectiveness of the proposed scheme in handling large mass ratios of heavy and light species, as well as capturing the epochal relaxation phenomenon.

This paper studies the training-testing discrepancy (a.k.a. exposure bias) problem for improving the diffusion models. During training, the input of a prediction network at one training timestep is the corresponding ground-truth noisy data that is an interpolation of the noise and the data, and during testing, the input is the generated noisy data. We present a novel training approach, named MixFlow, for improving the performance. Our approach is motivated by the Slow Flow phenomenon: the ground-truth interpolation that is the nearest to the generated noisy data at a given sampling timestep is observed to correspond to a higher-noise timestep (termed slowed timestep), i.e., the corresponding ground-truth timestep is slower than the sampling timestep. MixFlow leverages the interpolations at the slowed timesteps, named slowed interpolation mixture, for post-training the prediction network for each training timestep. Experiments over class-conditional image generation (including SiT, REPA, and RAE) and text-to-image generation validate the effectiveness of our approach. Our approach MixFlow over the RAE models achieve strong generation results on ImageNet: 1.43 FID (without guidance) and 1.10 (with guidance) at 256 x 256, and 1.55 FID (without guidance) and 1.10 (with guidance) at 512 x 512.

Recent advances in deep learning, exemplified by Hyper-Connections (HC), have expanded the residual connection paradigm by introducing wider residual streams and diverse connectivity patterns. While these innovations yield significant performance gains, they compromise the identity mapping property of residual connections, leading to training instability, limited scalability, and increased memory overhead. To address these challenges, we propose JPmHC (Jacobian-spectrum Preserving manifold-constrained Hyper-Connections), a framework that replaces identity skips with a trainable linear mixer acting on n parallel streams while explicitly controlling gradient conditioning. By constraining the mixer M on operator-norm-bounded manifolds (e.g., bistochastic, Stiefel, Grassmann), JPmHC prevents gradient pathologies and enhances stability. JPmHC introduces three key contributions: (i) a free-probability analysis that predicts Jacobian spectra for structured skips, providing actionable design rules for mixer selection; (ii) memory-efficient implicit differentiation for fixed-point projections, reducing activation memory and synchronization overhead; and (iii) a Stiefel-constrained mixer via Cayley transforms, ensuring orthogonality without post-hoc normalization. Empirical evaluations on ARC-AGI demonstrate that JPmHC achieves faster convergence, higher accuracy, and lower computational cost compared to bistochastic baselines, with a rank-p Grassmannian variant tracking between the two -- consistent with the spectral theory predictions. As a flexible and scalable extension of HC, JPmHC advances spectrum-aware, stable, and efficient deep learning, offering insights into topological architecture design and foundational model evolution. \newline \newline

Neural vocoders often struggle with aliasing in latent feature spaces, caused by time-domain nonlinear operations and resampling layers. Aliasing folds high-frequency components into the low-frequency range, making aliased and original frequency components indistinguishable and introducing two practical issues. First, aliasing complicates the waveform generation process, as the subsequent layers must address these aliasing effects, increasing the computational complexity. Second, it limits extrapolation performance, particularly in handling high fundamental frequencies, which degrades the perceptual quality of generated speech waveforms. This paper demonstrates that 1) time-domain nonlinear operations inevitably introduce aliasing but provide a strong inductive bias for harmonic generation, and 2) time-frequency-domain processing can achieve aliasing-free waveform synthesis but lacks the inductive bias for effective harmonic generation. Building on this insight, we propose Wavehax, an aliasing-free neural WAVEform generator that integrates 2D convolution and a HArmonic prior for reliable Complex Spectrogram estimation. Experimental results show that Wavehax achieves speech quality comparable to existing high-fidelity neural vocoders and exhibits exceptional robustness in scenarios requiring high fundamental frequency extrapolation, where aliasing effects become typically severe. Moreover, Wavehax requires less than 5% of the multiply-accumulate operations and model parameters compared to HiFi-GAN V1, while achieving over four times faster CPU inference speed.

Recent test-time adaptation methods heavily rely on nuanced adjustments of batch normalization (BN) parameters. However, one critical assumption often goes overlooked: that of independently and identically distributed (i.i.d.) test batches with respect to unknown labels. This oversight leads to skewed BN statistics and undermines the reliability of the model under non-i.i.d. scenarios. To tackle this challenge, this paper presents a novel method termed 'Un-Mixing Test-Time Normalization Statistics' (UnMix-TNS). Our method re-calibrates the statistics for each instance within a test batch by mixing it with multiple distinct statistics components, thus inherently simulating the i.i.d. scenario. The core of this method hinges on a distinctive online unmixing procedure that continuously updates these statistics components by incorporating the most similar instances from new test batches. Remarkably generic in its design, UnMix-TNS seamlessly integrates with a wide range of leading test-time adaptation methods and pre-trained architectures equipped with BN layers. Empirical evaluations corroborate the robustness of UnMix-TNS under varied scenarios-ranging from single to continual and mixed domain shifts, particularly excelling with temporally correlated test data and corrupted non-i.i.d. real-world streams. This adaptability is maintained even with very small batch sizes or single instances. Our results highlight UnMix-TNS's capacity to markedly enhance stability and performance across various benchmarks. Our code is publicly available at https://github.com/devavratTomar/unmixtns.

Transformer attention is typically implemented using softmax normalization, which enforces attention weights with unit sum normalization. While effective in many settings, this constraint can limit flexibility in controlling attention magnitudes and may contribute to overly concentrated or unstable attention patterns during training. Prior work has explored modifications such as attention sinks or gating mechanisms, but these approaches provide only limited or indirect control over attention reweighting. We propose Affine-Scaled Attention, a simple extension to standard attention that introduces input-dependent scaling and a corresponding bias term applied to softmax-normalized attention weights. This design relaxes the strict normalization constraint while maintaining aggregation of value representations, allowing the model to adjust both the relative distribution and the scale of attention in a controlled manner. We empirically evaluate Affine-Scaled Attention in large-scale language model pretraining across multiple model sizes. Experimental results show consistent improvements in training stability, optimization behavior, and downstream task performance compared to standard softmax attention and attention sink baselines. These findings suggest that modest reweighting of attention outputs provides a practical and effective way to improve attention behavior in Transformer models.

Diffusion models produce high-quality text-to-image results, but their iterative denoising is computationally expensive.Distribution Matching Distillation (DMD) emerges as a promising path to few-step distillation, but suffers from diversity collapse and fidelity degradation when reduced to two steps or fewer. We present 1.x-Distill, the first fractional-step distillation framework that breaks the integer-step constraint of prior few-step methods and establishes 1.x-step generation as a practical regime for distilled diffusion models.Specifically, we first analyze the overlooked role of teacher CFG in DMD and introduce a simple yet effective modification to suppress mode collapse. Then, to improve performance under extreme steps, we introduce Stagewise Focused Distillation, a two-stage strategy that learns coarse structure through diversity-preserving distribution matching and refines details with inference-consistent adversarial distillation. Furthermore, we design a lightweight compensation module for Distill--Cache co-Training, which naturally incorporates block-level caching into our distillation pipeline.Experiments on SD3-Medium and SD3.5-Large show that 1.x-Distill surpasses prior few-step methods, achieving better quality and diversity at 1.67 and 1.74 effective NFEs, respectively, with up to 33x speedup over original 28x2 NFE sampling.

Diffusion models have revolutionized text-to-image generation with its exceptional quality and creativity. However, its multi-step sampling process is known to be slow, often requiring tens of inference steps to obtain satisfactory results. Previous attempts to improve its sampling speed and reduce computational costs through distillation have been unsuccessful in achieving a functional one-step model. In this paper, we explore a recent method called Rectified Flow, which, thus far, has only been applied to small datasets. The core of Rectified Flow lies in its reflow procedure, which straightens the trajectories of probability flows, refines the coupling between noises and images, and facilitates the distillation process with student models. We propose a novel text-conditioned pipeline to turn Stable Diffusion (SD) into an ultra-fast one-step model, in which we find reflow plays a critical role in improving the assignment between noise and images. Leveraging our new pipeline, we create, to the best of our knowledge, the first one-step diffusion-based text-to-image generator with SD-level image quality, achieving an FID (Frechet Inception Distance) of 23.3 on MS COCO 2017-5k, surpassing the previous state-of-the-art technique, progressive distillation, by a significant margin (37.2 rightarrow 23.3 in FID). By utilizing an expanded network with 1.7B parameters, we further improve the FID to 22.4. We call our one-step models InstaFlow. On MS COCO 2014-30k, InstaFlow yields an FID of 13.1 in just 0.09 second, the best in leq 0.1 second regime, outperforming the recent StyleGAN-T (13.9 in 0.1 second). Notably, the training of InstaFlow only costs 199 A100 GPU days. Project page:~https://github.com/gnobitab/InstaFlow.

Temporal causal representation learning methods assume that causal mechanisms switch instantaneously between discrete domains, yet real-world systems often exhibit continuous mechanism transitions. For example, a vehicle's dynamics evolve gradually through a turning maneuver, and human gait shifts smoothly from walking to running. We formalize this setting by modeling transitional mechanisms as convex combinations of finitely many atomic mechanisms, governed by time-varying mixing coefficients. Our theoretical contributions establish that both the latent causal variables and the continuous mixing trajectory are jointly identifiable. We further propose TRACE, a Mixture-of-Experts framework where each expert learns one atomic mechanism during training, enabling recovery of mechanism trajectories at test time. This formulation generalizes to intermediate mechanism states never observed during training. Experiments on synthetic and real-world data demonstrate that TRACE recovers mixing trajectories with up to 0.99 correlation, substantially outperforming discrete-switching baselines.

Let S be a rational projective surface given by means of a projective rational parametrization whose base locus satisfies a mild assumption. In this paper we present an algorithm that provides three rational maps f,g,h:A^2 --to Ssubset P^n such that the union of the three images covers S. As a consequence, we present a second algorithm that generates two rational maps f,g:A^2 --to S, such that the union of their images covers the affine surface Scap A^n. In the affine case, the number of rational maps involved in the cover is in general optimal.

We introduce Jukebox, a model that generates music with singing in the raw audio domain. We tackle the long context of raw audio using a multi-scale VQ-VAE to compress it to discrete codes, and modeling those using autoregressive Transformers. We show that the combined model at scale can generate high-fidelity and diverse songs with coherence up to multiple minutes. We can condition on artist and genre to steer the musical and vocal style, and on unaligned lyrics to make the singing more controllable. We are releasing thousands of non cherry-picked samples at https://jukebox.openai.com, along with model weights and code at https://github.com/openai/jukebox

This paper presents a new state-of-the-art algorithm for exact 3times3 matrix multiplication over general non-commutative rings, achieving a rank-23 scheme with only 58 scalar additions. This improves the previous best additive complexity of 60 additions without a change of basis. The result was discovered through an automated search combining ternary-restricted flip-graph exploration with greedy intersection reduction for common subexpression elimination. The resulting scheme uses only coefficients from {-1, 0, 1}, ensuring both efficiency and portability across arbitrary fields. The total scalar operation count is reduced from 83 to 81.

We resolve the open question regarding the sample complexity of policy learning for maximizing the long-run average reward associated with a uniformly ergodic Markov decision process (MDP), assuming a generative model. In this context, the existing literature provides a sample complexity upper bound of widetilde O(|S||A|t_{mix}^2 epsilon^{-2}) and a lower bound of Omega(|S||A|t_{mix} epsilon^{-2}). In these expressions, |S| and |A| denote the cardinalities of the state and action spaces respectively, t_{mix} serves as a uniform upper limit for the total variation mixing times, and epsilon signifies the error tolerance. Therefore, a notable gap of t_{mix} still remains to be bridged. Our primary contribution is the development of an estimator for the optimal policy of average reward MDPs with a sample complexity of widetilde O(|S||A|t_{mix}epsilon^{-2}). This marks the first algorithm and analysis to reach the literature's lower bound. Our new algorithm draws inspiration from ideas in Li et al. (2020), Jin and Sidford (2021), and Wang et al. (2023). Additionally, we conduct numerical experiments to validate our theoretical findings.

Diffusion-based generative models have demonstrated their powerful performance across various tasks, but this comes at a cost of the slow sampling speed. To achieve both efficient and high-quality synthesis, various distillation-based accelerated sampling methods have been developed recently. However, they generally require time-consuming fine tuning with elaborate designs to achieve satisfactory performance in a specific number of function evaluation (NFE), making them difficult to employ in practice. To address this issue, we propose Simple and Fast Distillation (SFD) of diffusion models, which simplifies the paradigm used in existing methods and largely shortens their fine-tuning time up to 1000times. We begin with a vanilla distillation-based sampling method and boost its performance to state of the art by identifying and addressing several small yet vital factors affecting the synthesis efficiency and quality. Our method can also achieve sampling with variable NFEs using a single distilled model. Extensive experiments demonstrate that SFD strikes a good balance between the sample quality and fine-tuning costs in few-step image generation task. For example, SFD achieves 4.53 FID (NFE=2) on CIFAR-10 with only 0.64 hours of fine-tuning on a single NVIDIA A100 GPU. Our code is available at https://github.com/zju-pi/diff-sampler.

Recent advances in deep learning have mainly relied on Transformers due to their data dependency and ability to learn at scale. The attention module in these architectures, however, exhibits quadratic time and space in input size, limiting their scalability for long-sequence modeling. Despite recent attempts to design efficient and effective architecture backbone for multi-dimensional data, such as images and multivariate time series, existing models are either data independent, or fail to allow inter- and intra-dimension communication. Recently, State Space Models (SSMs), and more specifically Selective State Space Models, with efficient hardware-aware implementation, have shown promising potential for long sequence modeling. Motivated by the success of SSMs, we present MambaMixer, a new architecture with data-dependent weights that uses a dual selection mechanism across tokens and channels, called Selective Token and Channel Mixer. MambaMixer connects selective mixers using a weighted averaging mechanism, allowing layers to have direct access to early features. As a proof of concept, we design Vision MambaMixer (ViM2) and Time Series MambaMixer (TSM2) architectures based on the MambaMixer block and explore their performance in various vision and time series forecasting tasks. Our results underline the importance of selective mixing across both tokens and channels. In ImageNet classification, object detection, and semantic segmentation tasks, ViM2 achieves competitive performance with well-established vision models and outperforms SSM-based vision models. In time series forecasting, TSM2 achieves outstanding performance compared to state-of-the-art methods while demonstrating significantly improved computational cost. These results show that while Transformers, cross-channel attention, and MLPs are sufficient for good performance in time series forecasting, neither is necessary.

Riemannian submanifold optimization with momentum is computationally challenging because, to ensure that the iterates remain on the submanifold, we often need to solve difficult differential equations. Here, we simplify such difficulties for a class of structured symmetric positive-definite matrices with the affine-invariant metric. We do so by proposing a generalized version of the Riemannian normal coordinates that dynamically orthonormalizes the metric and locally converts the problem into an unconstrained problem in the Euclidean space. We use our approach to simplify existing approaches for structured covariances and develop matrix-inverse-free 2^nd-order optimizers for deep learning in low precision settings. Code: https://github.com/yorkerlin/StructuredNGD-DL

Rectified flow models have become a de facto standard in image generation due to their stable sampling trajectories and high-fidelity outputs. Despite their strong generative capabilities, they face critical limitations in image editing tasks: inaccurate inversion processes for mapping real images back into the latent space, and gradient entanglement issues during editing often result in outputs that do not faithfully reflect the target prompt. Recent efforts have attempted to directly map source and target distributions via ODE-based approaches without inversion; however,these methods still yield suboptimal editing quality. In this work, we propose a flow decomposition-and-aggregation framework built upon an inversion-free formulation to address these limitations. Specifically, we semantically decompose the target prompt into multiple sub-prompts, compute an independent flow for each, and aggregate them to form a unified editing trajectory. While we empirically observe that decomposing the original flow enhances diversity in the target space, generating semantically aligned outputs still requires consistent guidance toward the full target prompt. To this end, we design a projection and soft-aggregation mechanism for flow, inspired by gradient conflict resolution in multi-task learning. This approach adaptively weights the sub-target velocity fields, suppressing semantic redundancy while emphasizing distinct directions, thereby preserving both diversity and consistency in the final edited output. Experimental results demonstrate that our method outperforms existing zero-shot editing approaches in terms of semantic fidelity and attribute disentanglement. The code is available at https://github.com/Harvard-AI-and-Robotics-Lab/SplitFlow.

We introduce a new family of physics-inspired generative models termed PFGM++ that unifies diffusion models and Poisson Flow Generative Models (PFGM). These models realize generative trajectories for N dimensional data by embedding paths in N{+}D dimensional space while still controlling the progression with a simple scalar norm of the D additional variables. The new models reduce to PFGM when D{=}1 and to diffusion models when D{to}infty. The flexibility of choosing D allows us to trade off robustness against rigidity as increasing D results in more concentrated coupling between the data and the additional variable norms. We dispense with the biased large batch field targets used in PFGM and instead provide an unbiased perturbation-based objective similar to diffusion models. To explore different choices of D, we provide a direct alignment method for transferring well-tuned hyperparameters from diffusion models (D{to} infty) to any finite D values. Our experiments show that models with finite D can be superior to previous state-of-the-art diffusion models on CIFAR-10/FFHQ 64{times}64 datasets, with FID scores of 1.91/2.43 when D{=}2048/128. In class-conditional setting, D{=}2048 yields current state-of-the-art FID of 1.74 on CIFAR-10. In addition, we demonstrate that models with smaller D exhibit improved robustness against modeling errors. Code is available at https://github.com/Newbeeer/pfgmpp

Recent studies show that self-attentions behave like low-pass filters (as opposed to convolutions) and enhancing their high-pass filtering capability improves model performance. Contrary to this idea, we investigate existing convolution-based models with spectral analysis and observe that improving the low-pass filtering in convolution operations also leads to performance improvement. To account for this observation, we hypothesize that utilizing optimal token mixers that capture balanced representations of both high- and low-frequency components can enhance the performance of models. We verify this by decomposing visual features into the frequency domain and combining them in a balanced manner. To handle this, we replace the balancing problem with a mask filtering problem in the frequency domain. Then, we introduce a novel token-mixer named SPAM and leverage it to derive a MetaFormer model termed as SPANet. Experimental results show that the proposed method provides a way to achieve this balance, and the balanced representations of both high- and low-frequency components can improve the performance of models on multiple computer vision tasks. Our code is available at https://doranlyong.github.io/projects/spanet/{https://doranlyong.github.io/projects/spanet/}.

The Reduced Basis Method can be exploited in an efficient way only if the so-called affine dependence assumption on the operator and right-hand side of the considered problem with respect to the parameters is satisfied. When it is not, the Empirical Interpolation Method is usually used to recover this assumption approximately. In both cases, the Reduced Basis Method requires to access and modify the assembly routines of the corresponding computational code, leading to an intrusive procedure. In this work, we derive variants of the EIM algorithm and explain how they can be used to turn the Reduced Basis Method into a nonintrusive procedure. We present examples of aeroacoustic problems solved by integral equations and show how our algorithms can benefit from the linear algebra tools available in the considered code.

Training data compositions for Large Language Models (LLMs) can significantly affect their downstream performance. However, a thorough data ablation study exploring large sets of candidate data mixtures is typically prohibitively expensive since the full effect is seen only after training the models; this can lead practitioners to settle for sub-optimal data mixtures. We propose an efficient method for approximating data ablations which trains individual models on subsets of a training corpus and reuses them across evaluations of combinations of subsets. In continued pre-training experiments, we find that, given an arbitrary evaluation set, the perplexity score of a single model trained on a candidate set of data is strongly correlated with perplexity scores of parameter averages of models trained on distinct partitions of that data. From this finding, we posit that researchers and practitioners can conduct inexpensive simulations of data ablations by maintaining a pool of models that were each trained on partitions of a large training corpus, and assessing candidate data mixtures by evaluating parameter averages of combinations of these models. This approach allows for substantial improvements in amortized training efficiency -- scaling only linearly with respect to new data -- by enabling reuse of previous training computation, opening new avenues for improving model performance through rigorous, incremental data assessment and mixing.

Despite recent advances in inversion-based editing, text-guided image manipulation remains challenging for diffusion models. The primary bottlenecks include 1) the time-consuming nature of the inversion process; 2) the struggle to balance consistency with accuracy; 3) the lack of compatibility with efficient consistency sampling methods used in consistency models. To address the above issues, we start by asking ourselves if the inversion process can be eliminated for editing. We show that when the initial sample is known, a special variance schedule reduces the denoising step to the same form as the multi-step consistency sampling. We name this Denoising Diffusion Consistent Model (DDCM), and note that it implies a virtual inversion strategy without explicit inversion in sampling. We further unify the attention control mechanisms in a tuning-free framework for text-guided editing. Combining them, we present inversion-free editing (InfEdit), which allows for consistent and faithful editing for both rigid and non-rigid semantic changes, catering to intricate modifications without compromising on the image's integrity and explicit inversion. Through extensive experiments, InfEdit shows strong performance in various editing tasks and also maintains a seamless workflow (less than 3 seconds on one single A40), demonstrating the potential for real-time applications. Project Page: https://sled-group.github.io/InfEdit/

Recent advancements in image mixing and generative data augmentation have shown promise in enhancing image classification. However, these techniques face the challenge of balancing semantic fidelity with diversity. Specifically, image mixing involves interpolating two images to create a new one, but this pixel-level interpolation can compromise fidelity. Generative augmentation uses text-to-image generative models to synthesize or modify images, often limiting diversity to avoid generating out-of-distribution data that potentially affects accuracy. We propose that this fidelity-diversity dilemma partially stems from the whole-image paradigm of existing methods. Since an image comprises the class-dependent part (CDP) and the class-independent part (CIP), where each part has fundamentally different impacts on the image's fidelity, treating different parts uniformly can therefore be misleading. To address this fidelity-diversity dilemma, we introduce Decoupled Data Augmentation (De-DA), which resolves the dilemma by separating images into CDPs and CIPs and handling them adaptively. To maintain fidelity, we use generative models to modify real CDPs under controlled conditions, preserving semantic consistency. To enhance diversity, we replace the image's CIP with inter-class variants, creating diverse CDP-CIP combinations. Additionally, we implement an online randomized combination strategy during training to generate numerous distinct CDP-CIP combinations cost-effectively. Comprehensive empirical evaluations validate the effectiveness of our method.

Instruction Tuning involves finetuning a language model on a collection of instruction-formatted datasets in order to enhance the generalizability of the model to unseen tasks. Studies have shown the importance of balancing different task proportions during finetuning, but finding the right balance remains challenging. Unfortunately, there's currently no systematic method beyond manual tuning or relying on practitioners' intuition. In this paper, we introduce SMART (Submodular data Mixture strAtegy for instRuction Tuning) - a novel data mixture strategy which makes use of a submodular function to assign importance scores to tasks which are then used to determine the mixture weights. Given a fine-tuning budget, SMART redistributes the budget among tasks and selects non-redundant samples from each task. Experimental results demonstrate that SMART significantly outperforms traditional methods such as examples proportional mixing and equal mixing. Furthermore, SMART facilitates the creation of data mixtures based on a few representative subsets of tasks alone and through task pruning analysis, we reveal that in a limited budget setting, allocating budget among a subset of representative tasks yields superior performance compared to distributing the budget among all tasks. The code for reproducing our results is open-sourced at https://github.com/kowndinya-renduchintala/SMART.

The convolutional layers of standard convolutional neural networks (CNNs) are equivariant to translation. However, the convolution and fully-connected layers are not equivariant or invariant to other affine geometric transformations. Recently, a new class of CNNs is proposed in which the conventional layers of CNNs are replaced with equivariant convolution, pooling, and batch-normalization layers. The final classification layer in equivariant neural networks is invariant to different affine geometric transformations such as rotation, reflection and translation, and the scalar value is obtained by either eliminating the spatial dimensions of filter responses using convolution and down-sampling throughout the network or average is taken over the filter responses. In this work, we propose to integrate the orthogonal moments which gives the high-order statistics of the function as an effective means for encoding global invariance with respect to rotation, reflection and translation in fully-connected layers. As a result, the intermediate layers of the network become equivariant while the classification layer becomes invariant. The most widely used Zernike, pseudo-Zernike and orthogonal Fourier-Mellin moments are considered for this purpose. The effectiveness of the proposed work is evaluated by integrating the invariant transition and fully-connected layer in the architecture of group-equivariant CNNs (G-CNNs) on rotated MNIST and CIFAR10 datasets.

Mixup is a powerful data augmentation method that interpolates between two or more examples in the input or feature space and between the corresponding target labels. Many recent mixup methods focus on cutting and pasting two or more objects into one image, which is more about efficient processing than interpolation. However, how to best interpolate images is not well defined. In this sense, mixup has been connected to autoencoders, because often autoencoders "interpolate well", for instance generating an image that continuously deforms into another. In this work, we revisit mixup from the interpolation perspective and introduce AlignMix, where we geometrically align two images in the feature space. The correspondences allow us to interpolate between two sets of features, while keeping the locations of one set. Interestingly, this gives rise to a situation where mixup retains mostly the geometry or pose of one image and the texture of the other, connecting it to style transfer. More than that, we show that an autoencoder can still improve representation learning under mixup, without the classifier ever seeing decoded images. AlignMix outperforms state-of-the-art mixup methods on five different benchmarks.

Cool (approx 10^4K), dense material permeates the hot (approx 10^6K), tenuous solar corona in form of coronal condensations, for example prominences and coronal rain. As the solar atmosphere evolves, turbulence can drive mixing between the condensations and the surrounding corona, with the mixing layer exhibiting an enhancement in emission from intermediate temperature (approx10^5K) spectral lines, which is often attributed to turbulent heating within the mixing layer. However, radiative cooling is highly efficient at intermediate temperatures and numerical simulations have shown that radiative cooling can far exceed turbulent heating in prominence-corona mixing scenarios. As such the mixing layer can have a net loss of thermal energy, i.e., the mixing layer is cooling rather than heating. Here, we investigate the observational signatures of cooling processes in Kelvin-Helmholtz mixing between a prominence thread and the surrounding solar corona through 2D numerical simulations. Optically thin emission is synthesised for Si IV, along with optically thick emission for Halpha, Ca II K and Mg II h using Lightweaver The Mg II h probes the turbulent mixing layer, whereas Halpha and Ca II K form within the thread and along its boundary respectively. As the mixing evolves, intermediate temperatures form leading to an increase in Si IV emission, which coincides with increased radiative losses. The simulation is dominated by cooling in the mixing layer, rather than turbulent heating, and yet enhanced emission in warm lines is produced. As such, an observational signature of decreased emission in cooler lines and increased emission in hotter lines may be a signature of mixing, rather than an implication of heating.

As foundational models reshape scientific discovery, a bottleneck persists in dynamical system reconstruction (DSR): the ability to learn across system hierarchies. Many meta-learning approaches have been applied successfully to single systems, but falter when confronted with sparse, loosely related datasets requiring multiple hierarchies to be learned. Mixture of Experts (MoE) offers a natural paradigm to address these challenges. Despite their potential, we demonstrate that naive MoEs are inadequate for the nuanced demands of hierarchical DSR, largely due to their gradient descent-based gating update mechanism which leads to slow updates and conflicted routing during training. To overcome this limitation, we introduce MixER: Mixture of Expert Reconstructors, a novel sparse top-1 MoE layer employing a custom gating update algorithm based on K-means and least squares. Extensive experiments validate MixER's capabilities, demonstrating efficient training and scalability to systems of up to ten parametric ordinary differential equations. However, our layer underperforms state-of-the-art meta-learners in high-data regimes, particularly when each expert is constrained to process only a fraction of a dataset composed of highly related data points. Further analysis with synthetic and neuroscientific time series suggests that the quality of the contextual representations generated by MixER is closely linked to the presence of hierarchical structure in the data.

We study the problem of designing models for machine learning tasks defined on sets. In contrast to traditional approach of operating on fixed dimensional vectors, we consider objective functions defined on sets that are invariant to permutations. Such problems are widespread, ranging from estimation of population statistics poczos13aistats, to anomaly detection in piezometer data of embankment dams Jung15Exploration, to cosmology Ntampaka16Dynamical,Ravanbakhsh16ICML1. Our main theorem characterizes the permutation invariant functions and provides a family of functions to which any permutation invariant objective function must belong. This family of functions has a special structure which enables us to design a deep network architecture that can operate on sets and which can be deployed on a variety of scenarios including both unsupervised and supervised learning tasks. We also derive the necessary and sufficient conditions for permutation equivariance in deep models. We demonstrate the applicability of our method on population statistic estimation, point cloud classification, set expansion, and outlier detection.

Discrete diffusion models (DDMs) have shown powerful generation ability for discrete data modalities like text and molecules. However, their practical application is hindered by inefficient sampling, requiring a large number of sampling steps. Accelerating DDMs by using larger step sizes typically introduces significant problems in generation quality, as it amplifies the impact of both the compounding decoding error due to factorized predictions and discretization error from numerical approximations, leading to a significant decrease in sampling quality. To address these challenges, we propose learnable sampler distillation (LSD), a novel approach to train fast and high-fidelity samplers for DDMs. LSD employs a distillation approach where a student sampler with a few steps learns to align its intermediate score trajectory with that of a high-quality teacher sampler with numerous steps. This alignment is achieved by optimizing learnable sampler coefficients that adaptively adjust sampling dynamics. Additionally, we further propose LSD+, which also learns time schedules that allocate steps non-uniformly. Experiments across text generation, image generation, and synthetic tasks demonstrate that our proposed approaches outperform existing samplers for DDMs, achieving substantially higher sampling quality with significantly fewer sampling steps. Our code is available at https://github.com/feiyangfu/LSD{https://github.com/feiyangfu/LSD}.

In this work, we introduce a novel approach for predicting thermodynamic properties of binary mixtures, which we call the similarity-based method (SBM). The method is based on quantifying the pairwise similarity of components, which we achieve by comparing quantum-chemical descriptors of the components, namely σ-profiles. The basic idea behind the approach is that mixtures with similar pairs of components will have similar thermodynamic properties. The SBM is trained on a matrix that contains some data for a given property for different binary mixtures; the missing entries are then predicted by the SBM. As an example, we consider the prediction of isothermal activity coefficients at infinite dilution (γ^infty_{ij}) and show that the SBM outperforms the well-established physical methods modified UNIFAC (Dortmund) and COSMO-SAC-dsp. In this case, the matrix is only sparsely occupied, and it is shown that the SBM works also if only a limited number of data for similar mixtures is available. The SBM idea can be transferred to any mixture property and is a powerful tool for generating essential data for many applications.

Machine learning based solvers have garnered much attention in physical simulation and scientific computing, with a prominent example, physics-informed neural networks (PINNs). However, PINNs often struggle to solve high-frequency and multi-scale PDEs, which can be due to spectral bias during neural network training. To address this problem, we resort to the Gaussian process (GP) framework. To flexibly capture the dominant frequencies, we model the power spectrum of the PDE solution with a student t mixture or Gaussian mixture. We apply the inverse Fourier transform to obtain the covariance function (by Wiener-Khinchin theorem). The covariance derived from the Gaussian mixture spectrum corresponds to the known spectral mixture kernel. Next, we estimate the mixture weights in the log domain, which we show is equivalent to placing a Jeffreys prior. It automatically induces sparsity, prunes excessive frequencies, and adjusts the remaining toward the ground truth. Third, to enable efficient and scalable computation on massive collocation points, which are critical to capture high frequencies, we place the collocation points on a grid, and multiply our covariance function at each input dimension. We use the GP conditional mean to predict the solution and its derivatives so as to fit the boundary condition and the equation itself. As a result, we can derive a Kronecker product structure in the covariance matrix. We use Kronecker product properties and multilinear algebra to promote computational efficiency and scalability, without low-rank approximations. We show the advantage of our method in systematic experiments. The code is released at https://github.com/xuangu-fang/Gaussian-Process-Slover-for-High-Freq-PDE.

Diffusion models have greatly improved visual generation but are hindered by slow generation speed due to the computationally intensive nature of solving generative ODEs. Rectified flow, a widely recognized solution, improves generation speed by straightening the ODE path. Its key components include: 1) using the diffusion form of flow-matching, 2) employing boldsymbol v-prediction, and 3) performing rectification (a.k.a. reflow). In this paper, we argue that the success of rectification primarily lies in using a pretrained diffusion model to obtain matched pairs of noise and samples, followed by retraining with these matched noise-sample pairs. Based on this, components 1) and 2) are unnecessary. Furthermore, we highlight that straightness is not an essential training target for rectification; rather, it is a specific case of flow-matching models. The more critical training target is to achieve a first-order approximate ODE path, which is inherently curved for models like DDPM and Sub-VP. Building on this insight, we propose Rectified Diffusion, which generalizes the design space and application scope of rectification to encompass the broader category of diffusion models, rather than being restricted to flow-matching models. We validate our method on Stable Diffusion v1-5 and Stable Diffusion XL. Our method not only greatly simplifies the training procedure of rectified flow-based previous works (e.g., InstaFlow) but also achieves superior performance with even lower training cost. Our code is available at https://github.com/G-U-N/Rectified-Diffusion.

Diffusion and flow-matching models achieve remarkable generative performance but at the cost of many sampling steps, this slows inference and limits applicability to time-critical tasks. The ReFlow procedure can accelerate sampling by straightening generation trajectories. However, ReFlow is an iterative procedure, typically requiring training on simulated data, and results in reduced sample quality. To mitigate sample deterioration, we examine the design space of ReFlow and highlight potential pitfalls in prior heuristic practices. We then propose seven improvements for training dynamics, learning and inference, which are verified with thorough ablation studies on CIFAR10 32 times 32, AFHQv2 64 times 64, and FFHQ 64 times 64. Combining all our techniques, we achieve state-of-the-art FID scores (without / with guidance, resp.) for fast generation via neural ODEs: 2.23 / 1.98 on CIFAR10, 2.30 / 1.91 on AFHQv2, 2.84 / 2.67 on FFHQ, and 3.49 / 1.74 on ImageNet-64, all with merely 9 neural function evaluations.

When finetuning large language models for specialized tasks such as mathematical reasoning, models exhibit catastrophic forgetting, losing previously learned capabilities. We investigate this by finetuning Flan-T5-Base (250M parameters) on the DeepMind Mathematics dataset and measuring forgetting on MultiNLI. Math-only training improves mathematical accuracy from 3.1\% to 12.0\% but causes NLI accuracy to collapse from 81.0\% to 16.5\%--a 64.5 percentage point drop occurring within the first 1,000 training steps. We propose mixed training strategies that interleave mathematical and NLI examples during training. Our results demonstrate that mixed training completely eliminates catastrophic forgetting while maintaining equivalent mathematical performance: the balanced 1:1 ratio achieves 12.0\% math accuracy (matching math-only) while preserving 86.2\% NLI accuracy. We systematically explore mixing ratios from 1:1 to 15:1, finding that even minimal NLI exposure (6.2\%) provides effective regularization. These findings demonstrate that specialization need not require forgetting general capabilities, with implications for scaling to larger models where mixed training may confer additional benefits beyond forgetting prevention.

Let F be a field, and n geq r>0 be integers, with r even. Denote by A_n(F) the space of all n-by-n alternating matrices with entries in F. We consider the problem of determining the greatest possible dimension for an affine subspace of A_n(F) in which every matrix has rank equal to r (or rank at least r). Recently Rubei has solved this problem over the field of real numbers. We extend her result to all fields with large enough cardinality. Provided that n geq r+3 and |F|geq minbigl(r-1,r{2}+2bigr), we also determine the affine subspaces of rank r matrices in A_n(F) that have the greatest possible dimension, and we point to difficulties for the corresponding problem in the case nleq r+2.

Generative adversarial network (GAN) based vocoders have achieved significant attention in speech synthesis with high quality and fast inference speed. However, there still exist many noticeable spectral artifacts, resulting in the quality decline of synthesized speech. In this work, we adopt a novel GAN-based vocoder designed for few artifacts and high fidelity, called FA-GAN. To suppress the aliasing artifacts caused by non-ideal upsampling layers in high-frequency components, we introduce the anti-aliased twin deconvolution module in the generator. To alleviate blurring artifacts and enrich the reconstruction of spectral details, we propose a novel fine-grained multi-resolution real and imaginary loss to assist in the modeling of phase information. Experimental results reveal that FA-GAN outperforms the compared approaches in promoting audio quality and alleviating spectral artifacts, and exhibits superior performance when applied to unseen speaker scenarios.

Flow matching is a powerful framework for generating high-quality samples in various applications, especially image synthesis. However, the intensive computational demands of these models, especially during the fine-tuning process and sampling processes, pose significant challenges for low-resource scenarios. This paper introduces Bellman Optimal Step-size Straightening (BOSS) technique for distilling flow-matching generative models: it aims specifically for a few-step efficient image sampling while adhering to a computational budget constraint. First, this technique involves a dynamic programming algorithm that optimizes the step sizes of the pretrained network. Then, it refines the velocity network to match the optimal step sizes, aiming to straighten the generation paths. Extensive experimental evaluations across image generation tasks demonstrate the efficacy of BOSS in terms of both resource utilization and image quality. Our results reveal that BOSS achieves substantial gains in efficiency while maintaining competitive sample quality, effectively bridging the gap between low-resource constraints and the demanding requirements of flow-matching generative models. Our paper also fortifies the responsible development of artificial intelligence, offering a more sustainable generative model that reduces computational costs and environmental footprints. Our code can be found at https://github.com/nguyenngocbaocmt02/BOSS.

We study the problem of training a flow-based generative model, parametrized by a two-layer autoencoder, to sample from a high-dimensional Gaussian mixture. We provide a sharp end-to-end analysis of the problem. First, we provide a tight closed-form characterization of the learnt velocity field, when parametrized by a shallow denoising auto-encoder trained on a finite number n of samples from the target distribution. Building on this analysis, we provide a sharp description of the corresponding generative flow, which pushes the base Gaussian density forward to an approximation of the target density. In particular, we provide closed-form formulae for the distance between the mean of the generated mixture and the mean of the target mixture, which we show decays as Theta_n(1{n}). Finally, this rate is shown to be in fact Bayes-optimal.

Large pre-trained models for zero/few-shot learning excel in language and vision domains but encounter challenges in multivariate time series (TS) due to the diverse nature and scarcity of publicly available pre-training data. Consequently, there has been a recent surge in utilizing pre-trained large language models (LLMs) with token adaptations for TS forecasting. These approaches employ cross-domain transfer learning and surprisingly yield impressive results. However, these models are typically very slow and large (~billion parameters) and do not consider cross-channel correlations. To address this, we present Tiny Time Mixers (TTM), a significantly small model based on the lightweight TSMixer architecture. TTM marks the first success in developing fast and tiny general pre-trained models (<1M parameters), exclusively trained on public TS datasets, with effective transfer learning capabilities for forecasting. To tackle the complexity of pre-training on multiple datasets with varied temporal resolutions, we introduce several novel enhancements such as adaptive patching, dataset augmentation via downsampling, and resolution prefix tuning. Moreover, we employ a multi-level modeling strategy to effectively model channel correlations and infuse exogenous signals during fine-tuning, a crucial capability lacking in existing benchmarks. TTM shows significant accuracy gains (12-38\%) over popular benchmarks in few/zero-shot forecasting. It also drastically reduces the compute needs as compared to LLM-TS methods, with a 14X cut in learnable parameters, 106X less total parameters, and substantial reductions in fine-tuning (65X) and inference time (54X). In fact, TTM's zero-shot often surpasses the few-shot results in many popular benchmarks, highlighting the efficacy of our approach. Code and pre-trained models will be open-sourced.

Model merging combines several independently fine-tuned experts into a single multi-task model without any training data, reducing the storage, serving, and decentralized-development costs of large foundation models. State-of-the-art merging methods formulate merging as a layer-wise quadratic interference minimization problem. Although this problem admits an exact closed-form pseudoinverse solution, that solution underperforms hundreds of iterations of gradient descent in practice. The iterative loop dominates the cost of the pipeline, yet its effectiveness has remained unexplained. We revisit this regime and show that the iterative solver does not primarily act as an optimizer; rather, it serves as an implicit spectral regularizer for an ill-posed normal equation, where small-eigenvalue directions of the per-layer interference operator amplify proxy noise. Building on this finding, we formalize multi-task model merging as a noisy linear inverse problem and propose a spectral filtering estimator parameterized by a per-direction filter. We instantiate this estimator with SWUDI, a closed-form method that combines a soft exponential filter, which matches the gradient-flow trajectory of iterative descent, with a hard top-K truncation that suppresses noise-amplifying small-eigenvalue directions. Furthermore, we propose SWUDI-A, an adaptive variant that replaces the global rank hyperparameter with per-layer rank rules, further improving robustness across architectures. Both variants share a single symmetric eigendecomposition per linear layer and require no training data or optimizer state. Across four general benchmarks and a multimodal merging benchmark spanning VQA, Geometry, Chart, OCR, Grounding, and modality merging, our proposed spectral solvers match or outperform state-of-the-art merging methods. Crucially, they reduce wall-clock time by 28-72x and peak GPU memory by up to 50%.

Majorities of distillation methods on pre-trained diffusion models or on pre-trained rectified flow, focus on either the distillation outputs or the trajectories between random noises and clean images to speed up sample generations from pre-trained models. In those trajectory-based distillation methods, consistency distillation requires the self-consistent trajectory projection to regulate the trajectory, which might avoid the common ODE approximation error {while still be concerning about sampling efficiencies}. At the same time, rectified flow distillations enforce straight trajectory for fast sampling, although an ODE solver is still required. In this work, we propose a trajectory distillation method, \modelname, that enjoys the benefits of both and enables few-step generations. TraFlow adopts the settings of consistency trajectory models, and further enforces the properties of self-consistency and straightness throughout the entire trajectory. These two properties are pursued by reaching a balance with following three targets: (1) reconstruct the output from pre-trained models; (2) learn the amount of changes by pre-trained models; (3) satisfy the self-consistency over its trajectory. Extensive experimental results have shown the effectiveness of our proposed method.

While deep neural networks achieve great performance on fitting the training distribution, the learned networks are prone to overfitting and are susceptible to adversarial attacks. In this regard, a number of mixup based augmentation methods have been recently proposed. However, these approaches mainly focus on creating previously unseen virtual examples and can sometimes provide misleading supervisory signal to the network. To this end, we propose Puzzle Mix, a mixup method for explicitly utilizing the saliency information and the underlying statistics of the natural examples. This leads to an interesting optimization problem alternating between the multi-label objective for optimal mixing mask and saliency discounted optimal transport objective. Our experiments show Puzzle Mix achieves the state of the art generalization and the adversarial robustness results compared to other mixup methods on CIFAR-100, Tiny-ImageNet, and ImageNet datasets. The source code is available at https://github.com/snu-mllab/PuzzleMix.

Transport maps can ease the sampling of distributions with non-trivial geometries by transforming them into distributions that are easier to handle. The potential of this approach has risen with the development of Normalizing Flows (NF) which are maps parameterized with deep neural networks trained to push a reference distribution towards a target. NF-enhanced samplers recently proposed blend (Markov chain) Monte Carlo methods with either (i) proposal draws from the flow or (ii) a flow-based reparametrization. In both cases, the quality of the learned transport conditions performance. The present work clarifies for the first time the relative strengths and weaknesses of these two approaches. Our study concludes that multimodal targets can be reliably handled with flow-based proposals up to moderately high dimensions. In contrast, methods relying on reparametrization struggle with multimodality but are more robust otherwise in high-dimensional settings and under poor training. To further illustrate the influence of target-proposal adequacy, we also derive a new quantitative bound for the mixing time of the Independent Metropolis-Hastings sampler.