Daily Papers

We develop a linear perturbative formalism to compute the response of an inhomogeneous stellar disk embedded in a non-responsive dark matter halo to perturbations like bars, spiral arms and satellite galaxy encounters. Without self-gravity to reinforce it, the response of a Fourier mode phase mixes away due to an intrinsic spread in the vertical (Omega_z), radial (Omega_r) and azimuthal (Omega_phi) frequencies, giving rise to local phase-space spirals. Collisional diffusion due to scattering of stars by structures like giant molecular clouds causes super-exponential damping of the phase-spiral amplitude. The z-v_z phase-spiral is 1-armed (2-armed) for vertically anti-symmetric (symmetric) bending (breathing) modes. Only transient perturbations with timescales (tau_{P}) comparable to the vertical oscillation period (tau_z sim 1/Omega_z) trigger z-v_z phase-spirals. Each (n,l,m) mode of the response to impulsive (tau_{P}<tau=1/(nOmega_z+lOmega_r+mOmega_phi)) perturbations is power law (sim tau_{P}/tau) suppressed, but that to adiabatic (tau_{P}>tau) perturbations is exponentially weak (sim left[-left(tau_{mathrm{P}/tauright)^alpharight]}) except resonant (tauto infty) modes. Slower (tau_{P}>tau_z) perturbations, e.g., distant encounters with satellite galaxies, induce stronger bending modes. If the Gaia phase-spiral was triggered by a satellite, Sagittarius is the leading contender as it dominates the Solar neighborhood response of the Milky Way disk to satellite encounters. However, survival against collisional damping necessitates that the impact occurred within sim 0.6-0.7 Gyr ago. We discuss how the detailed galactic potential dictates the phase-spiral shape: phase mixing occurs slower and phase-spirals are less wound in the outer disk and in presence of an ambient halo.

We introduce a data-driven diagnostic that combines the singular value decomposition (SVD) with an information-theoretic entropy to quantify the phase-space complexity of perturbed distribution functions in gyrokinetic turbulence. Applying this framework to nonlinear flux-tube simulations that solve the time evolution of the ion distribution function represented by Fourier modes with the wavenumber for real space, we define the von Neumann entropy (vNE) to analyze the velocity-space structure. A global survey in the wavenumber space reveals a wavenumber-dependent variation of the vNE in velocity-space structure: the vNE remains low at low wavenumber but increases across k_perpρ_{ti}sim 1. Hermite/Laguerre decompositions revealed that the finite Larmor radius (FLR) phase mixing in the perpendicular (magnetic-moment) direction is active. Simultaneously, the systematic increase in vNE for k_perpρ_{ti} correlates with the broadening of the Hermite spectrum, suggesting enhanced parallel phase mixing (Landau resonance) as the primary mechanism for the observed wave number dependence. These results demonstrate that the SVD-based vNE provides a compact measure of kinetic complexity without assuming a predefined basis and enables a global mapping of its wavenumber dependence of phase-mixing processes in gyrokinetic turbulence.

We study the response of mono-energetic stellar populations with initially isotropic kinematics to impulsive and adiabatic changes to an underlying dark matter potential. Half-light radii expand and velocity dispersions decrease as enclosed dark matter is removed. The details of this expansion and cooling depend on the time scale on which the underlying potential changes. In the adiabatic regime, the product of half-light radius and average velocity dispersion is conserved. We show that the stellar populations maintain centrally isotropic kinematics throughout their adiabatic evolution, and their densities can be approximated by a family of analytical radial profiles. Metallicity gradients within the galaxy flatten as dark matter is slowly removed. In the case of strong impulsive perturbations, stellar populations develop power-law-like density tails with radially biased kinematics. We show that the distribution of stellar binding energies within the dark matter halo substantially widens after an impulsive perturbation, no matter the sign of the perturbation. This allows initially energetically separated stellar populations to mix, to the extent that previously chemo-dynamically distinct populations may masquerade as a single population with large metallicity and energy spread. Finally, we show that in response to an impulsive perturbation, stellar populations that are deeply embedded in cored dark matter halos undergo a series of damped oscillations before reaching a virialised equilibrium state, driven by inefficient phase mixing in the harmonic potentials of cored halos. This slow return to equilibrium adds substantial systematic uncertainty to dynamical masses estimated from Jeans modeling or the virial theorem.

Multi-agent systems can improve reliability, yet under a fixed inference budget they often help, saturate, or even collapse. We develop a minimal and calibratable theory that predicts these regimes from three binding constraints of modern agent stacks: finite context windows, lossy inter-agent communication, and shared failures among similar agents. Each leaf agent is summarized by a compute-performance scaling exponent β; communication is captured by a message-length fidelity curve γ(m); dependence is captured by an effective shared-error correlation ρ; and a context window W imposes hard fan-in limits that make hierarchy necessary. For binary success/failure tasks with majority aggregation, we prove a sharp phase transition for deep b-ary trees with correlated inputs and lossy communication: a single scalar α_ρ (combining γ(m), ρ, and fan-in b) determines whether weak signal is amplified to a nontrivial fixed point or washed out to chance. In the amplifying regime, we derive an organization exponent s and show that budgeted synergy, i.e., outperforming the best single agent under the same total budget, occurs exactly when s>β, yielding closed-form compute allocation rules and explicit budget thresholds. We further characterize saturation via a mixing depth and provide a conservative clipped predictor that remains accurate across growth and saturation. A continuous-performance warm-up gives closed-form risks for star, chain, and tree organizations, making correlation- and communication-induced floors explicit and exposing the core design trade-offs in a smooth setting. Finally, we validate the predicted phase boundaries in controlled synthetic simulations and show how the same mechanisms explain the dominant bottlenecks reported in recent large-scale matched-budget studies of LLM agent-system scaling.

The post-training phase of large language models is essential for enhancing capabilities such as instruction-following, reasoning, and alignment with human preferences. However, it demands extensive high-quality data and poses risks like overfitting, alongside significant computational costs due to repeated post-training and evaluation after each base model update. This paper introduces ParamΔ, a novel method that streamlines post-training by transferring knowledge from an existing post-trained model to a newly updated base model with ZERO additional training. By computing the difference between post-trained model weights (Θ_post) and base model weights (Θ_base), and adding this to the updated base model (Θ'_base), we define ParamΔ Model as: Θ_{ParamΔ} = Θ_post - Θ_base + Θ'_base. This approach surprisingly equips the new base model with post-trained capabilities, achieving performance comparable to direct post-training. We did analysis on LLama3, Llama3.1, Qwen, and DeepSeek-distilled models. Results indicate ParamΔ Model effectively replicates traditional post-training. For example, the ParamΔ Model obtained from 70B Llama3-inst, Llama3-base, Llama3.1-base models attains approximately 95\% of Llama3.1-inst model's performance on average. ParamΔ brings a new perspective on how to fully leverage models in the open-weight community, where checkpoints for base and instruct models are readily available and frequently updated, by providing a cost-free framework to accelerate the iterative cycle of model development.

Phase stability in multicomponent solid solutions depends on configurational entropy beyond the ideal mixing limit, but capturing it together with vibrational entropy within the same atomistic framework remains challenging. Here, we extend non-equilibrium thermodynamic integration to composition-dependent transformations through an alchemical interpolation of the interactions, combined with Monte Carlo identity exchange moves and molecular dynamics that sample the vibrational and non-ideal configurational entropy along the integration path. We apply the framework to the Au-Cu binary alloy using Atomic Cluster Expansion potentials trained on density functional theory data using the LDA, PBE, and r2SCAN functionals, and construct composition-temperature phase diagrams directly from atomistic free energies. We find that explicit configurational sampling lowers the AuCu order-disorder transition temperature predicted by the ACE potential trained on LDA data from approximately 810 K to 710 K, closer to the experimental value of 683 K, and substantially widens the stability range of the solid solution. At the same time, the much larger sensitivity to the exchange-correlation functional shows that this level of agreement should not be interpreted as general predictive accuracy. Non-ideal configurational entropy must therefore be sampled explicitly, alongside a careful choice of functional, for a reliable atomistic description of binary phase diagrams.

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.

Pretraining large language models effectively requires strategic data selection, blending and ordering. However, key details about data mixtures especially their scalability to longer token horizons and larger model sizes remain underexplored due to limited disclosure by model developers. To address this, we formalize the concept of two-phase pretraining and conduct an extensive systematic study on how to select and mix data to maximize model accuracies for the two phases. Our findings illustrate that a two-phase approach for pretraining outperforms random data ordering and natural distribution of tokens by 3.4% and 17% on average accuracies. We provide in-depth guidance on crafting optimal blends based on quality of the data source and the number of epochs to be seen. We propose to design blends using downsampled data at a smaller scale of 1T tokens and then demonstrate effective scaling of our approach to larger token horizon of 15T tokens and larger model size of 25B model size. These insights provide a series of steps practitioners can follow to design and scale their data blends.

Online surgical phase recognition (SPR) underpins context-aware operating-room systems and requires committing to a prediction at every frame from past context alone. Surgical video poses three demands that natural-video recognizers do not jointly address: procedures span tens of thousands of frames, time flows non-uniformly as long routine stretches are punctuated by brief phase-defining transitions, and the visual domain is narrow so backbone features are strongly correlated across channels. Existing recognizers either let per-frame cost grow with elapsed length, or hold cost bounded but advance state at a uniform rate with channel-independent dynamics, leaving the latter two demands unaddressed. We present SurgicalMamba, a causal SPR model built on Mamba2's structured state-space duality (SSD) that holds per-frame cost at O(d). It introduces three SSD-compatible components, each targeting one demand: a dual-path SSD block that separates long- and short-term regimes at the level of recurrent state; intensity-modulated stepping, a continuous-time time-warp that adapts the slow path's effective rate to phase-relevant information; and state regramming, a per-chunk Cayley rotation that opens cross-channel mixing in the otherwise axis-aligned SSM recurrence. The learned rotation planes inherit a phase-aligned structure without any direct supervision, offering an interpretable internal signature of surgical workflow. Across seven public SPR benchmarks, SurgicalMamba reaches state-of-the-art accuracy and phase-level Jaccard under strict online evaluation: 94.6%/82.7% on Cholec80 (+0.7 pp/+2.2 pp over the strongest prior) and 89.5%/68.9% on AutoLaparo (+1.7 pp/+2.0 pp), at 119 fps on a single GPU. Ablations isolate the contribution of each component. The code is publicly available at https://github.com/sukjuoh/Surgical-Mamba.

Handheld data collection systems, such as the Universal Manipulation Interface (UMI), enable scalable data collection across diverse environments but only capture observed actions rather than the desired actions executed by a robot controller. In contrast, teleoperation captures desired actions directly, but is prohibitively time-consuming to collect. We revisit this trade-off through the lens of action validity across task phases. We observe that handheld trajectories provide valid supervision in tolerant, free-space phases, but lack dynamic feasibility in contact-sensitive phases, where tracking observed trajectories at high stiffness produces large, unsafe contact forces. We study the interaction between these two supervision types for contact-rich manipulation and find that training policies that combine handheld data with a small number of targeted teleoperated demonstrations provide an efficient hybrid strategy. Specifically, rather than teleoperating the entire task, we only collect partial teleoperated demonstrations for task segments where base handheld policies fail. However, naively mixing handheld and teleoperated phase-specific data yields worse performance than training on handheld data alone. To address this mismatch between observed and desired supervision, we propose Bi-modal Routing for Imitation Data via Gated Experts (BRIDGE), a mixture of diffusion policy experts that routes between specialist task phase heads conditioned on the current robot state. Notably, our approach enables task-phase specific use of desired actions during contact sensitive segments and improves success rates over handheld-only baselines by up to 36.7% across three contact-rich manipulation tasks.

Text-to-image diffusion models have recently become highly capable, yet their behavior in multi-object scenes remains unreliable: models often produce an incorrect number of instances and exhibit semantics leaking across objects. We trace these failures to vague instance boundaries; self-attention already reveals instance layouts early in the denoising process, but existing approaches act only on semantic signals. We introduce ISAC (Instance-to-Semantic Attention Control), a training-free, model-agnostic objective that performs hierarchical attention control by first carving out instance layouts from self-attention and then binding semantics to these instances. In Phase 1, ISAC clusters self-attention into the number of instances and repels overlaps, establishing an instance-level structural hierarchy; in Phase 2, it injects these instance cues into cross-attention to obtain instance-aware semantic masks and decomposes mixing semantics by tying attributes within each instance. ISAC yields consistent gains on T2I-CompBench, HRS-Bench, and IntraCompBench, our new benchmark for intra-class compositions where failures are most frequent, with improvements of at least 50% in multi-class accuracy and 7% in multi-instance accuracy on IntraCompBench, without any fine-tuning or external models. Beyond text-to-image setups, ISAC also strengthens layout-to-image controllers under overlapping boxes by refining coarse box layouts into dense instance masks, indicating that hierarchical decoupling of instance formation and semantic assignment is a key principle for robust, controllable multi-object generation. Code will be released upon publication.

Midtraining, the practice of mixing specialized data with more general pretraining data in an intermediate training phase, has become widespread in language model development, yet there is little understanding of what makes it effective. We propose that midtraining functions as distributional bridging by providing better initialization for posttraining. We conduct controlled pretraining experiments, and find that midtraining benefits are largest for domains distant from general pretraining data, such as code and math, and scale with the proximity advantage the midtraining data provides toward the target distribution. In these domains, midtraining consistently outperforms continued pretraining on specialized data alone both in-domain and in terms of mitigating forgetting. We further conduct an investigation on the starting time and mixture weight of midtraining data, using code as a case study, and find that time of introduction and mixture weight interact strongly such that early introduction of specialized data is amenable to high mixture weights, while late introduction requires lower ones. This suggests that late introduction of specialized data outside a plasticity window cannot be compensated for by increasing data mixtures later in training. Beyond midtraining itself, this suggests that distributional transitions between any training phases may benefit from similar bridging strategies.

The rapid advancement of Large Language Models (LLMs) has resulted in a significant knowledge gap between the open-source community and industry, primarily because the latter relies on closed-source, high-quality data and training recipes. To address this, we introduce PCMind-2.1-Kaiyuan-2B, a fully open-source 2-billion-parameter model focused on improving training efficiency and effectiveness under resource constraints. Our methodology includes three key innovations: a Quantile Data Benchmarking method for systematically comparing heterogeneous open-source datasets and providing insights on data mixing strategies; a Strategic Selective Repetition scheme within a multi-phase paradigm to effectively leverage sparse, high-quality data; and a Multi-Domain Curriculum Training policy that orders samples by quality. Supported by a highly optimized data preprocessing pipeline and architectural modifications for FP16 stability, Kaiyuan-2B achieves performance competitive with state-of-the-art fully open-source models, demonstrating practical and scalable solutions for resource-limited pretraining. We release all assets (including model weights, data, and code) under Apache 2.0 license at https://huggingface.co/thu-pacman/PCMind-2.1-Kaiyuan-2B.

A wide range of deep learning-based machine learning techniques are extensively applied to the design of high-entropy alloys (HEAs), yielding numerous valuable insights. Kolmogorov-Arnold Networks (KAN) is a recently developed architecture that aims to improve both the accuracy and interpretability of input features. In this work, we explore three different datasets for HEA design and demonstrate the application of KAN for both classification and regression models. In the first example, we use a KAN classification model to predict the probability of single-phase formation in high-entropy carbide ceramics based on various properties such as mixing enthalpy and valence electron concentration. In the second example, we employ a KAN regression model to predict the yield strength and ultimate tensile strength of HEAs based on their chemical composition and process conditions including annealing time, cold rolling percentage, and homogenization temperature. The third example involves a KAN classification model to determine whether a certain composition is an HEA or non-HEA, followed by a KAN regressor model to predict the bulk modulus of the identified HEA, aiming to identify HEAs with high bulk modulus. In all three examples, KAN either outperform or match the performance in terms of accuracy such as F1 score for classification and Mean Square Error (MSE), and coefficient of determination (R2) for regression of the multilayer perceptron (MLP) by demonstrating the efficacy of KAN in handling both classification and regression tasks. We provide a promising direction for future research to explore advanced machine learning techniques, which lead to more accurate predictions and better interpretability of complex materials, ultimately accelerating the discovery and optimization of HEAs with desirable properties.

Dusty post-red giant branch (post-RGB) stars are low- and intermediate-mass stars where the RGB evolution was prematurely terminated by a poorly understood binary interaction. These binary stars are considered to be low-luminosity analogues of post-asymptotic giant branch (post-AGB) binary stars. In this study, we investigated the chemical composition of two dusty post-RGB binary stars, SZ Mon and DF Cyg, using multi-wavelength spectroscopic data from HERMES/Mercator (optical) and the APOGEE survey (near-infrared). Owing to challenges posed by existing spectral analysis tools for the study of evolved stars with complex atmospheres, we developed E-iSpec: a dedicated spectral analysis tool for evolved stars, to consistently determine atmospheric parameters, elemental abundances, and carbon isotopic ratios. Our abundance analysis revealed that observed depletion patterns and estimated depletion efficiencies resemble those found in post-AGB binary stars. However, the onset of chemical depletion in post-RGB targets occurs at higher condensation temperatures (T_{rm turn-off, post-RGB}approx1400 K), than in most post-AGB stars (T_{rm turn-off, post-AGB}approx1100 K). Additionally, our study resulted in the first estimates of carbon isotopic ratios for post-RGB stars (^{12}C/^{13}C_{rm SZ Mon}=8pm4, ^{12}C/^{13}C_{rm DF Cyg}=12pm3). We found that the observationally derived CNO abundances and the carbon isotopic ratios of our post-RGB binary targets are in good agreement with theoretical predictions from the ATON single star evolutionary models involving first dredge-up and moderately-deep extra mixing. This agreement emphasises that in post-RGB binary targets, the observed CNO abundances reflect the chemical composition expected from single star nucleosynthesis (i.e., convective and non-convective mixing processes) occurring during the RGB phase before it is terminated.

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.

Synchronization in one dimension displays generic scale invariance with universal properties previously observed in surface kinetic roughening and the wider context of the Kardar-Parisi-Zhang (KPZ) universality class. This has been established for phase oscillators and also for some limit-cycle oscillators, both in the presence of columnar (quenched) disorder and of time-dependent noise, by extensive numerical simulations, and has been analytically motivated by continuum approximations in the strong oscillator coupling limit. The robustness and the precise boundaries in parameter space for such critical behavior remain unclear, however, which may preclude further developments, including the extension of these results to higher dimensions and the experimental observation of nonequilibrium criticality in synchronizing (e.g.~electronic or chemical) oscillators. We here present complete numerical phase diagrams of one-dimensional synchronization, including saturation times and values, but, most importantly, also dynamical features giving insight into the gradual emergence of synchronous dynamics, based on systems of phase oscillators with either type of randomness. In the absence of synchronization, the dynamics evolves as expected for random deposition (for time-dependent noise) or linear growth (for columnar disorder), while a crossover from Edwards-Wilkinson to Kardar-Parisi-Zhang behavior (with the corresponding type of randomness) is observed as the randomness strength, or the nonoddity of the coupling among oscillators, is increased in the synchronous region -- their combined effect being partially captured by the so-called KPZ coupling. The distortion of scaling due to phase slips near the desynchronization boundary, a feature that is likely to play a role in experimental contexts, is also discussed.

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.

Deep learning has become an area of interest in most scientific areas, including physical sciences. Modern networks apply real-valued transformations on the data. Particularly, convolutions in convolutional neural networks discard phase information entirely. Many deterministic signals, such as seismic data or electrical signals, contain significant information in the phase of the signal. We explore complex-valued deep convolutional networks to leverage non-linear feature maps. Seismic data commonly has a lowcut filter applied, to attenuate noise from ocean waves and similar long wavelength contributions. Discarding the phase information leads to low-frequency aliasing analogous to the Nyquist-Shannon theorem for high frequencies. In non-stationary data, the phase content can stabilize training and improve the generalizability of neural networks. While it has been shown that phase content can be restored in deep neural networks, we show how including phase information in feature maps improves both training and inference from deterministic physical data. Furthermore, we show that the reduction of parameters in a complex network outperforms larger real-valued networks.

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.

We present a comprehensive analysis of how two-layer neural networks learn features to solve the modular addition task. Our work provides a full mechanistic interpretation of the learned model and a theoretical explanation of its training dynamics. While prior work has identified that individual neurons learn single-frequency Fourier features and phase alignment, it does not fully explain how these features combine into a global solution. We bridge this gap by formalizing a diversification condition that emerges during training when overparametrized, consisting of two parts: phase symmetry and frequency diversification. We prove that these properties allow the network to collectively approximate a flawed indicator function on the correct logic for the modular addition task. While individual neurons produce noisy signals, the phase symmetry enables a majority-voting scheme that cancels out noise, allowing the network to robustly identify the correct sum. Furthermore, we explain the emergence of these features under random initialization via a lottery ticket mechanism. Our gradient flow analysis proves that frequencies compete within each neuron, with the "winner" determined by its initial spectral magnitude and phase alignment. From a technical standpoint, we provide a rigorous characterization of the layer-wise phase coupling dynamics and formalize the competitive landscape using the ODE comparison lemma. Finally, we use these insights to demystify grokking, characterizing it as a three-stage process involving memorization followed by two generalization phases, driven by the competition between loss minimization and weight decay.

Strategies for the generation of periodic discrete structures with identical two-point correlation are developed. Starting from a pair of root structures, which are not related by translation, phase inversion or axis reflections, child structures of arbitrary resolution (i.e., pixel or voxel numbers) and number of phases (i.e., material phases/species) can be generated by means of trivial embedding based phase extension, application of kernels and/or phase coalescence, such that the generated structures inherit the two-point-correlation equivalence. Proofs of the inheritance property are provided by means of the Discrete Fourier Transform theory. A Python 3 implementation of the results is offered by the authors through the Github repository https://github.com/DataAnalyticsEngineering/EQ2PC in order to make the provided results reproducible and useful for all interested readers. Examples for the generation of structures are demonstrated, together with applications in the homogenization theory of periodic media.

While deep learning has advanced speech enhancement (SE), effective phase modeling remains challenging, as conventional networks typically operate within a flat Euclidean feature space, which is not easy to model the underlying circular topology of the phase. To address this, we propose a manifold-aware magnitude-phase dual-stream framework that aligns the phase stream with its intrinsic circular geometry by enforcing Global Rotation Equivariance (GRE) characteristic. Specifically, we introduce a Magnitude-Phase Interactive Convolutional Module (MPICM) for modulus-based information exchange and a Hybrid-Attention Dual-FFN (HADF) bottleneck for unified feature fusion, both of which are designed to preserve GRE in the phase stream. Comprehensive evaluations are conducted across phase retrieval, denoising, dereverberation, and bandwidth extension tasks to validate the superiority of the proposed method over multiple advanced baselines. Notably, the proposed architecture reduces Phase Distance by over 20\% in the phase retrieval task and improves PESQ by more than 0.1 in zero-shot cross-corpus denoising evaluations. The overall superiority is also established in universal SE tasks involving mixed distortions. Qualitative analysis further reveals that the learned phase features exhibit distinct periodic patterns, which are consistent with the intrinsic circular nature of the phase. The source code is available at https://github.com/wangchengzhong/RENet.

Neural vocoders have recently advanced waveform generation, yielding natural and expressive audio. Among these approaches, iSTFT-based vocoders have recently gained attention. They predict a complex-valued spectrogram and then synthesize the waveform via iSTFT, thereby avoiding learned upsampling stages that can increase computational cost. However, current approaches use real-valued networks that process the real and imaginary parts independently. This separation limits their ability to capture the inherent structure of complex spectrograms. We present ComVo, a Complex-valued neural Vocoder whose generator and discriminator use native complex arithmetic. This enables an adversarial training framework that provides structured feedback in complex-valued representations. To guide phase transformations in a structured manner, we introduce phase quantization, which discretizes phase values and regularizes the training process. Finally, we propose a block-matrix computation scheme to improve training efficiency by reducing redundant operations. Experiments demonstrate that ComVo achieves higher synthesis quality than comparable real-valued baselines, and that its block-matrix scheme reduces training time by 25%. Audio samples and code are available at https://hs-oh-prml.github.io/ComVo/.

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.

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.

Reciprocity is a fundamental symmetry present in many natural phenomena and engineered systems. Distinct situations where this symmetry is broken are typically grouped under the umbrella term "nonreciprocity", colloquially defined by: the action of A on B neq the action of B on A. In this review, we elucidate what nonreciprocity is by providing an introduction to its most salient classes: nonvariational dynamics, violations of Newton's third law, broken detailed balance, nonreciprocal responses and nonreciprocity of arbitrary linear operators. Next, we point out where to find these manifestations of non-reciprocity, from ensembles of particles with field mediated interactions to synthetic neural networks and open quantum systems. Given this breadth of contexts and the lack of an all-encompassing definition, it makes it all the more intriguing that some general conclusions can be gathered, when distinct definitions of nonreciprocity overlap. We explore what these universal consequences are with a special emphasis on collective phenomena that arise in nonreciprocal many-body systems. The topics covered include nonreciprocal phase transitions and non-normal amplification of noise and perturbations. We conclude with some open questions.

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.

Music source separation in the time-frequency domain is commonly achieved by applying a soft or binary mask to the magnitude component of (complex) spectrograms. The phase component is usually not estimated, but instead copied from the mixture and applied to the magnitudes of the estimated isolated sources. While this method has several practical advantages, it imposes an upper bound on the performance of the system, where the estimated isolated sources inherently exhibit audible "phase artifacts". In this paper we address these shortcomings by directly estimating masks in the complex domain, extending recent work from the speech enhancement literature. The method is particularly well suited for multi-instrument musical source separation since residual phase artifacts are more pronounced for spectrally overlapping instrument sources, a common scenario in music. We show that complex masks result in better separation than masks that operate solely on the magnitude component.

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.

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.

Sonification -- the mapping of data to non-speech audio -- offers an underexplored channel for representing complex dynamical systems. We treat El Niño-Southern Oscillation (ENSO), a canonical example of low-dimensional climate chaos, as a test case for culturally-situated sonification evaluated through complex systems diagnostics. Using parameter-mapping sonification of the Niño 3.4 sea surface temperature anomaly index (1870--2024), we encode ENSO variability into two traditional Javanese gamelan pentatonic systems (pelog and slendro) across four composition strategies, then analyze the resulting audio as trajectories in a two-dimensional acoustic phase space. Recurrence-based diagnostics, convex hull geometry, and coupling analysis reveal that the sonification pipeline preserves key dynamical signatures: alternating modes produce the highest trajectory recurrence rates, echoing ENSO's quasi-periodicity; layered polyphonic modes explore the broadest phase space regions; and the two scale families induce qualitatively distinct coupling regimes between spectral brightness and energy -- predominantly anti-phase in pelog but near-independent in slendro. Phase space trajectory analysis provides a rigorous geometric framework for comparing sonification designs within a complex systems context. Perceptual validation remains necessary; we contribute the dynamical systems methodology for evaluating such mappings.

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.

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 estimation and clustering in Gaussian mixture models under variance misspecification. Observations are generated with true variance σ^2, while the component means are estimated using a likelihood with variance τ^2, yielding a family of mismatched likelihood functions parameterized by the ratio ρ=τ/σ. We show that the interplay between ρ and the signal-to-noise ratio (SNR) induces a sharp phase diagram. Under correct specification (ρ=1), maximum likelihood recovers the true means, independently of the SNR. However, once the model is misspecified, two different regimes emerge. Under under-smoothing (ρ<1), the estimated Gaussian means are displaced from the truth, and in low SNR this discrepancy grows as the SNR decreases: for every fixed ρ<1, the squared error scales as SNR^{-1}. Under over-smoothing (ρ>1), the fitted likelihood blurs the cluster separation, causing distinct component means to collapse towards the overall mixture center once ρ^2 exceeds a threshold of the form 1 + λ,SNR, where λ depends on the geometry of the true means. We further show that the hard assignment objective arises as the limit τto 0 of the same mismatched likelihood family, and derive corresponding low- and high-SNR results for hard-assignment mean estimation and latent-label recovery. Furthermore, in low SNR, Bayes-optimal clustering is close to random guessing, and the hard-assignment target remains far from the true means. These results show that in low-SNR applications, even mild variance misspecification or hard-assignment procedures can induce substantial bias, whereas in high SNR these effects are largely absent.

Materials that undergo internal transformations are usually described in solid mechanics by multi-well energy functions that account for both elastic and transformational behavior. In order to separate the two effects, physicists use instead phase-field-type theories where conventional linear elastic strain is quadratically coupled to an additional field that describes the evolution of the reference state and solely accounts for nonlinearity. In this paper we propose a systematic method allowing one to split the non-convex energy into harmonic and nonharmonic parts and to convert a nonconvex mechanical problem into a partially linearized phase-field problem. The main ideas are illustrated using the simplest framework of the Peierls-Nabarro dislocation model.

Flow matching (FM) enables high-fidelity generation, while self-supervised learning (SSL) speech models provide hierarchical representations spanning acoustic and phonetic levels. However, existing FM-based speech enhancement (SE) methods operate primarily in the spectral domain, treating SSL features only as external conditions rather than modeling directly in the SSL latent space. To fully exploit the structural richness of SSL representations, we propose PhASE-Flow, an FM-based SE framework that operates entirely in the SSL space. It models the conditional distribution of clean acoustic representations given phonetic ones, reconstructing the waveform via a neural vocoder. Experiments show that PhASE-Flow outperforms state-of-the-art baselines in perceptual quality and intelligibility. Notably, it achieves competitive performance with only four sampling steps, enabling highly efficient inference. Audio demos are available at https://anonymous.4open.science/w/phase-flow_demo-E6E1/.

In contrast to entropy, which increases monotonically, the "complexity" or "interestingness" of closed systems seems intuitively to increase at first and then decrease as equilibrium is approached. For example, our universe lacked complex structures at the Big Bang and will also lack them after black holes evaporate and particles are dispersed. This paper makes an initial attempt to quantify this pattern. As a model system, we use a simple, two-dimensional cellular automaton that simulates the mixing of two liquids ("coffee" and "cream"). A plausible complexity measure is then the Kolmogorov complexity of a coarse-grained approximation of the automaton's state, which we dub the "apparent complexity." We study this complexity measure, and show analytically that it never becomes large when the liquid particles are non-interacting. By contrast, when the particles do interact, we give numerical evidence that the complexity reaches a maximum comparable to the "coffee cup's" horizontal dimension. We raise the problem of proving this behavior analytically.

The presence of thermal gradients in alloys often leads to non-uniformity in concentration profiles, which can induce the thermomigration of microstructural features such as precipitates. To investigate such microstructural changes, we present a phase-field model that incorporates coupling between concentration and thermal gradients. First, we simulated the evolution of non-uniform concentration profiles in the single-phase regions of Fe-C and Fe-N alloy systems due to imposed thermal gradients. To validate our model with the classical experiments performed by Darken and Oriani, we studied the evolution of spatially varying concentration profiles where thermal gradients encompass single-phase and two-phase regions. We developed a parameterized thermodynamic description of the two-phase region of a binary alloy to systematically study the effect of interactions between chemically-driven and thermal gradient-driven diffusion of solute on the evolution of precipitates. Our simulations show how thermal gradient, precipitate size, and interparticle distance influence the migration and associated morphological changes of precipitates. The composition profiles and migration rates obtained from single-particle simulations show an exact match with our analytical model. We use twoparticle simulations to show conditions under which thermomigration induces the growth of the smaller particle and shrinkage of the larger one in contrast to the isothermal Ostwald ripening behavior. Our multiparticle simulations show similar behavior during coarsening. Moreover, in the presence of a thermal gradient, there is a shift in the center of mass of the precipitates towards the high-temperature region. Thus, our study offers new insights into the phenomena of microstructure evolution in the presence of thermal gradient.

I introduce a novel mathematical framework integrating topological dynamics, operator algebras, and ergodic geometry to study lattices of asynchronous metric dynamical systems. Each node in the lattice carries an internal flow represented by a one-parameter family of operators, evolving on its own time scale. I formalize stratified state spaces capturing multiple levels of synchronized behavior, define an asynchronous evolution metric that quantifies phase-offset distances between subsystems, and characterize emergent coherent topologies arising when subsystems synchronize. Within this framework, I develop formal operators for the evolution of each subsystem and give precise conditions under which phase-aligned synchronization occurs across the lattice. The main results include: (1) the existence and uniqueness of coherent (synchronized) states under a contractive coupling condition, (2) stability of these coherent states and criteria for their emergence as a collective phase transition in a continuous operator topology, and (3) the influence of symmetries, with group-invariant coupling leading to flow-invariant synchrony subspaces and structured cluster dynamics. Proofs are given for each theorem, demonstrating full mathematical rigor. In a final section, I discuss hypothetical applications of this framework to symbolic lattice systems (e.g. subshifts), to invariant group actions on dynamical lattices, and to operator fields over stratified manifolds in the spirit of noncommutative geometry. Throughout, I write in the first person to emphasize the exploratory nature of this work. The paper avoids any reference to cosmology or observers, focusing instead on clean, formal mathematics suitable for a broad array of dynamical systems.

The singlet-doublet vector-like fermion dark matter model has been extensively studied in the literature over the past decade. An important parameter in this model is the singlet-doublet mixing angle (sintheta). All the previous studies have primarily focused on annihilation and co-annihilation processes for obtaining the correct dark matter relic density, assuming that the singlet and doublet components decouple at the same epoch. In this work, we demonstrate that this assumption holds only for larger mixing angles with a dependency on the mass of the dark matter. However, it badly fails for the mixing angle sintheta<0.05. We present a systematic study of the parameter space of the singlet-doublet dark matter relic, incorporating annihilation, co-annihilation, and, for the first time, co-scattering processes. Additionally, the freeze-in parameter space is also explored. We found that due to the inclusion of co-scattering processes, the correct relic density parameter space is shifted towards the detection sensitivity range of the LHC and MATHUSLA via displaced vertex signatures.

Understanding how structured internal structure emerges during neural network training is central to the study of deep learning. We investigate this phenomenon through the group composition task, where a two-layer neural network is trained to predict g_1 star g_2 for elements of a finite group G. By lifting the projected gradient flow to the Fourier domain, we demonstrate that the training dynamics are governed by a Riemannian gradient ascent on a representation-theoretic energy functional. We prove that, under random initialization, this flow drives each neuron to converge almost surely toward a single irreducible representation, while the cross-layer Fourier coefficients achieve a rotational rank-one alignment. This framework provides a representation-theoretic account of feature learning and characterizes a novel low-rank compression phenomenon for matrix-valued group representations. Moreover, for Abelian groups, we provide a complete population-level description: random initialization promotes uniform diversification across nontrivial representations and induces Haar-uniform phases, jointly approximating the indicator via a majority-vote mechanism. We further prove that both phase alignment and representation competition emerge with exponential convergence rates.

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.

Music demixing is the task of separating different tracks from the given single audio signal into components, such as drums, bass, and vocals from the rest of the accompaniment. Separation of sources is useful for a range of areas, including entertainment and hearing aids. In this paper, we introduce two new benchmarks for the sound source separation tasks and compare popular models for sound demixing, as well as their ensembles, on these benchmarks. For the models' assessments, we provide the leaderboard at https://mvsep.com/quality_checker/, giving a comparison for a range of models. The new benchmark datasets are available for download. We also develop a novel approach for audio separation, based on the ensembling of different models that are suited best for the particular stem. The proposed solution was evaluated in the context of the Music Demixing Challenge 2023 and achieved top results in different tracks of the challenge. The code and the approach are open-sourced on GitHub.

This project focuses on a method to extract a frequency comb in mechanical means, for general interest and numerous practical applications in MEMS. The method of execution is the implementation of a beam that is exhibiting non-linear dynamics that is perturbed and analyzed for its transverse vibrations. The perturbation is an external harmonic driver with a chosen small amplitude and frequency (which is slightly detuned from the beam eigenfrequency), that when engaged with the unperturbed beam oscillations, causes it reach a state of "injection pulling" - an effect that occurs when one harmonic oscillator is coupled with a second one and causes it to oscillate in a frequency near its own. This causes the beam to reach SNIC bifurcation, rendering a frequency comb as desired. Theoretical analysis showed that the problem can be modelled using a non-linear equation of the beam, that translates to a form of the non-linear Duffing equation. While a solution to the dynamics function of the beam is hard to obtain in practice due to mathematical difficulties, a slow evolution model is suggested that is composed of functions of a amplitude and phase. Using several additional mathematical assumptions, the amplitude is seen to be related to the phase, while the phase equation solution is seen to be of the form of Adler's equation. These assumptions ultimately reduce the entire behaviour of the beam to a relatively simple solution to the Adler equation, which has a known analytical solution. Computerized numerical simulations are run on it to check the results and compare them to the theory and desired outcome. The results agreed with the theory and produce the expected frequency comb, showing the assumptions to be valid in extracting the comb.

Standard diffusion corrupts data using Gaussian noise whose Fourier coefficients have random magnitudes and random phases. While effective for unconditional or text-to-image generation, corrupting phase components destroys spatial structure, making it ill-suited for tasks requiring geometric consistency, such as re-rendering, simulation enhancement, and image-to-image translation. We introduce Phase-Preserving Diffusion φ-PD, a model-agnostic reformulation of the diffusion process that preserves input phase while randomizing magnitude, enabling structure-aligned generation without architectural changes or additional parameters. We further propose Frequency-Selective Structured (FSS) noise, which provides continuous control over structural rigidity via a single frequency-cutoff parameter. φ-PD adds no inference-time cost and is compatible with any diffusion model for images or videos. Across photorealistic and stylized re-rendering, as well as sim-to-real enhancement for driving planners, φ-PD produces controllable, spatially aligned results. When applied to the CARLA simulator, φ-PD improves CARLA-to-Waymo planner performance by 50\%. The method is complementary to existing conditioning approaches and broadly applicable to image-to-image and video-to-video generation. Videos, additional examples, and code are available on our https://yuzeng-at-tri.github.io/ppd-page/{project page}.

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

Audio mixing style encompasses the artistic and technical decisions a mix engineer makes, including level balancing, spatialization, and the choice, ordering, and parameterization of audio effects (FX) on each stem. FX chains are a key determinant of this style, yet existing approaches to modeling them remain limited. Some operate on stereo mixtures without explicit per-stem FX chain modeling, others fix the number or type of effects per track, and many require differentiable effect implementations or scarce multitrack datasets. We present StemFX, a framework that learns mixing style representations by autoregressively predicting variable-length FX chains on source-separated stems. A Transformer decoder predicts tokenized FX chains autoregressively, while a band-split multi-band CNN encoder with FiLM conditioning captures per-stem spectral structure. To enable large-scale paired training, we extract pseudo-stems from about 105K songs via source separation and augment them using MultiAFx, a toolkit unifying 85 audio effects from 7 Python libraries. Evaluated on mixing style retrieval, StemFX outperforms all baseline models across all tested chain lengths. On paired mixing style transfer, StemFX achieves the best spectral fidelity and the highest listener preference, over 4000 times faster than iterative optimization.

The transition of an impulsively excited kink oscillation of a solar coronal loop to an oscillation with a stationary amplitude, i.e., the damping pattern, is determined using the low-dimensional self-oscillation model. In the model, the decayless kink oscillations are sustained by the interaction of the oscillating loop with an external quasi-steady flow. The analytical solution is based on the assumption that the combined effect of the effective dissipation, for example, by resonant absorption, and interaction with an external flow, is weak. The effect is characterised by a dimensionless coupling parameter. The damping pattern is found to depend upon the initial amplitude and the coupling parameter. The approximate expression shows a good agreement with a numerical solution of the self-oscillation equation. The plausibility of the established damping pattern is demonstrated by an observational example. Notably, the damping pattern is not exponential, and the characteristic decay time is different from the time determined by the traditionally used exponential damping fit. Implications of this finding for seismology of the solar coronal plasmas are discussed. In particular, it is suggested that a very rapid, in less than the oscillation period, decay of the oscillation to the stationary level, achieved for larger values of the coupling parameter, can explain the relative rareness of the kink oscillation events.

Proper weight initialization prior to training has historically been one of the key factors that helped kick off the deep learning revolution. Initialization is even more crucial in "reservoir computing", where the weights of a readout layer are learned linearly while the reservoir weights are fixed and largely determine the richness, stability and memory of the resulting dynamics. In the infinite-width limit it has been shown that meaningful initializations are those sitting at an effective critical point of the randomly initialized model. The phase transition is controlled by the weight variance g^2 and separates an ordered phase from a chaotic one where information progressively degrades. Here we derive a simple criterion to estimate the critical g_c for a broad class of recurrent architectures and we show that it closely tracks the gain at which a gated-RNN reservoir achieves peak performance on a chaotic forecasting task. Finally, we argue that our criterion can serve as a design principle for future initialization schemes.

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.

Image-to-Video diffusion models leverage input images to generate visually stunning content, yet frequently produce motion that violates physical laws. We reveal a surprising finding: a 2-step generation often exhibits better physical consistency than a 50-step output from the same model. Through spectral analysis, we trace this to phase erosion during denoising; the phase degrades significantly (dropping by approx 18% from step 2 to step 50), whereas the magnitude remains relatively stable. Building on this insight, we propose PhaseLock, a training-free framework that preserves the valid motion priors from few-step inference throughout the denoising trajectory. Rather than relying on full-step inference for physical consistency, PhaseLock extracts a motion prior from just 2 steps and enforces it onto high-fidelity generation via Latent Delta Guidance. Our approach effectively mitigates phase degradation, improving physical consistency by an average of 6.2 points across diverse models while largely maintaining visual fidelity, with negligible overhead (1.06times time, 1.02times memory) and reduced reliance on expensive external guidance methods (sim5times time).

Holographic Metasurface Transceivers (HMTs) are emerging as cost-effective substitutes to large antenna arrays for beamforming in Millimeter and TeraHertz wave communication. However, to achieve desired channel gains through beamforming in HMT, phase-shifts of a large number of elements need to be appropriately set, which is challenging. Also, these optimal phase-shifts depend on the location of the receivers, which could be unknown. In this work, we develop a learning algorithm using a {\it fixed-budget multi-armed bandit framework} to beamform and maximize received signal strength at the receiver for far-field regions. Our algorithm, named \Algo exploits the parametric form of channel gains of the beams, which can be expressed in terms of two {\it phase-shifting parameters}. Even after parameterization, the problem is still challenging as phase-shifting parameters take continuous values. To overcome this, {\it\HB} works with the discrete values of phase-shifting parameters and exploits their unimodal relations with channel gains to learn the optimal values faster. We upper bound the probability of {\it\HB} incorrectly identifying the (discrete) optimal phase-shift parameters in terms of the number of pilots used in learning. We show that this probability decays exponentially with the number of pilot signals. We demonstrate that {\it\HB} outperforms state-of-the-art algorithms through extensive simulations.

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.

We investigate the coupling effects of the two-phase interface, viscosity ratio, and density ratio of the dispersed phase to the continuous phase on the flow statistics in two-phase Taylor-Couette turbulence at a system Reynolds number of 6000 and a system Weber number of 10 using interface-resolved three-dimensional direct numerical simulations with the volume-of-fluid method. Our study focuses on four different scenarios: neutral droplets, low-viscosity droplets, light droplets, and low-viscosity light droplets. We find that neutral droplets and low-viscosity droplets primarily contribute to drag enhancement through the two-phase interface, while light droplets reduce the system's drag by explicitly reducing Reynolds stress due to the density dependence of Reynolds stress. Additionally, low-viscosity light droplets contribute to greater drag reduction by further reducing momentum transport near the inner cylinder and implicitly reducing Reynolds stress. While interfacial tension enhances turbulent kinetic energy (TKE) transport, drag enhancement is not strongly correlated with TKE transport for both neutral droplets and low-viscosity droplets. Light droplets primarily reduce the production term by diminishing Reynolds stress, whereas the density contrast between the phases boosts TKE transport near the inner wall. Therefore, the reduction in the dissipation rate is predominantly attributed to decreased turbulence production, causing drag reduction. For low-viscosity light droplets, the production term diminishes further, primarily due to their greater reduction in Reynolds stress, while reduced viscosity weakens the density difference's contribution to TKE transport near the inner cylinder, resulting in a more pronounced reduction in the dissipation rate and consequently stronger drag reduction. Our findings provide new insights into the turbulence modulation in two-phase flow.

In heterogeneous networks of coupled oscillators, phase frustration typically prevents the emergence of synchronization in the Sakaguchi--Kuramoto (SK) model. In this study, we propose an analytical framework to overcome this barrier and induce complete synchronization at a specified small coupling value in oscillators governed by phase-frustrated bi-harmonic coupling. We derive an optimal set of natural frequencies that is robust against added noise and correlated with the network degree heterogeneity, along with the parameters involved in the bi-harmonic coupling function that lead to complete synchronization (r = 1). In addition, we find complete synchronization transitions accompanied by hysteresis in scale-free networks, indicating a first-order (discontinuous) phase transition, whereas Erdős--Rényi networks exhibit complete synchronization through a second-order (continuous) phase transition. Furthermore, we use the mean-field approximation in the presence of optimal frequencies to determine the critical coupling strength associated with the synchronization transition in the pure second-harmonic Sakaguchi--Kuramoto model. Here, the obtained optimal natural frequencies scale linearly with the node degree, and the critical coupling strength for the onset of synchronization is derived analytically from the self-consistent equations. In this specific regime, we observe a perfectly ordered two-cluster synchronized state. These findings remain robust for higher-order harmonic coupling schemes, as well as across a diverse range of synthetic and empirical networks, including scale-free, Erdős--Rényi, Zachary Karate Club, and the C.~elegans neural network, demonstrating their general applicability.

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.

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.

In recent years, rapid progress has been made on the problem of single-channel sound separation using supervised training of deep neural networks. In such supervised approaches, a model is trained to predict the component sources from synthetic mixtures created by adding up isolated ground-truth sources. Reliance on this synthetic training data is problematic because good performance depends upon the degree of match between the training data and real-world audio, especially in terms of the acoustic conditions and distribution of sources. The acoustic properties can be challenging to accurately simulate, and the distribution of sound types may be hard to replicate. In this paper, we propose a completely unsupervised method, mixture invariant training (MixIT), that requires only single-channel acoustic mixtures. In MixIT, training examples are constructed by mixing together existing mixtures, and the model separates them into a variable number of latent sources, such that the separated sources can be remixed to approximate the original mixtures. We show that MixIT can achieve competitive performance compared to supervised methods on speech separation. Using MixIT in a semi-supervised learning setting enables unsupervised domain adaptation and learning from large amounts of real world data without ground-truth source waveforms. In particular, we significantly improve reverberant speech separation performance by incorporating reverberant mixtures, train a speech enhancement system from noisy mixtures, and improve universal sound separation by incorporating a large amount of in-the-wild data.

Motivated by realistic scattering processes of composite systems, we study the dynamics of a two-particle bound system which is scattered at a mirror. The physics of the scattering process will be discussed in the cases when only one particle interacts directly with the mirror and when both particles are scattered directly. It is shown that the coherence between the transmitted and the reflected wave-packet becomes reduced due to the scattering process. When both particles interact directly with the mirror, the system exhibits long-lived resonances. The results should be of interest for interference experiments with composite systems.

We present a 380-520 GHz balanced superconductor-insulator-superconductor (SIS) mixer on a single silicon substrate. All radio-frequency (RF) circuit components are fabricated on a 9 μm thick membrane. The intermediate frequency (IF) is separately amplified and combined. The balanced mixer chip, using Nb/Al/Al_{2}O_{3}/Nb SIS junctions, is mounted in a tellurium copper waveguide block at 4.2 K using Au beam lead contacts. We find uncorrected minimum receiver double-sideband noise temperatures of 70 K and a noise suppression of up to 18 dB, measured within a 440-495 GHz RF and a 4-8 GHz IF bandwidth, representing state-of-the-art device performance.

Knowledge of mixtures' phase equilibria is crucial in nature and technical chemistry. Phase equilibria calculations of mixtures require activity coefficients. However, experimental data on activity coefficients is often limited due to high cost of experiments. For an accurate and efficient prediction of activity coefficients, machine learning approaches have been recently developed. However, current machine learning approaches still extrapolate poorly for activity coefficients of unknown molecules. In this work, we introduce the SMILES-to-Properties-Transformer (SPT), a natural language processing network to predict binary limiting activity coefficients from SMILES codes. To overcome the limitations of available experimental data, we initially train our network on a large dataset of synthetic data sampled from COSMO-RS (10 Million data points) and then fine-tune the model on experimental data (20 870 data points). This training strategy enables SPT to accurately predict limiting activity coefficients even for unknown molecules, cutting the mean prediction error in half compared to state-of-the-art models for activity coefficient predictions such as COSMO-RS, UNIFAC, and improving on recent machine learning approaches.

We study the sparse phase retrieval problem, which seeks to recover a sparse signal from a limited set of magnitude-only measurements. In contrast to prevalent sparse phase retrieval algorithms that primarily use first-order methods, we propose an innovative second-order algorithm that employs a Newton-type method with hard thresholding. This algorithm overcomes the linear convergence limitations of first-order methods while preserving their hallmark per-iteration computational efficiency. We provide theoretical guarantees that our algorithm converges to the s-sparse ground truth signal x^{natural} in R^n (up to a global sign) at a quadratic convergence rate after at most O(log (Vertx^{natural} Vert /x_{min}^{natural})) iterations, using Omega(s^2log n) Gaussian random samples. Numerical experiments show that our algorithm achieves a significantly faster convergence rate than state-of-the-art methods.

Recent theoretical and practical research has focused on multi-component High Entropy Alloys (HEAs), which have superior mechanical and functional properties than standard alloys based on a single major element, thereby establishing a new field. A multi-component HEA contains five or more primary elements at concentrations ranging from 5 to 35 atomic percent. We examined the microstructure and mechanical properties of TiVCoNiMn2 HEA. The mixing enthalpy and other thermodynamic parameters were determined using Meidma's model. TiVCoNiMn2 exhibits a mixing enthalpy of -15.6 kJ/mol and an atomic radius mismatch of approximately 10.03%. HEA is derived from both hydride and non-hydride-producing elements. This could be a useful hydrogen storage material. The hydrogen absorption/desorption capabilities of these HEAs are promising.

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.

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

A fully differential calculation in perturbative quantum chromodynamics is presented for the production of massive photon pairs at hadron colliders. All next-to-leading order perturbative contributions from quark-antiquark, gluon-(anti)quark, and gluon-gluon subprocesses are included, as well as all-orders resummation of initial-state gluon radiation valid at next-to-next-to-leading logarithmic accuracy. The region of phase space is specified in which the calculation is most reliable. Good agreement is demonstrated with data from the Fermilab Tevatron, and predictions are made for more detailed tests with CDF and DO data. Predictions are shown for distributions of diphoton pairs produced at the energy of the Large Hadron Collider (LHC). Distributions of the diphoton pairs from the decay of a Higgs boson are contrasted with those produced from QCD processes at the LHC, showing that enhanced sensitivity to the signal can be obtained with judicious selection of events.

A cylindrical TM_{0,1,0} mode microwave cavity resonator was excited using a balanced interferometric configuration that allowed manipulation of the electric field and potential within the resonator by adjusting the phase and amplitude of the interferometer arms driving the resonator. With precise tuning of the phase and amplitude, 25 dB suppression of the electric field at the resonance frequency was achieved while simultaneously resonantly enhancing the time-varying electric-scalar potential. Under these conditions, the system demonstrated electromagnetically induced absorption in the cavity response due to the annulment of the electric field at the resonance frequency. This phenomena can be regarded as a form of extreme dispersion, and led to a sharp increase in the cavity phase versus frequency response by an order of magnitude when compared to the cavity Q-factor. This work presents an experimental setup that will allow the electric-scalar Aharonov-Bohm effect to be tested under conditions involving a time-varying electric-scalar potential, without the presence of an electric field or magnetic vector potential, an experiment that has not yet been realised.

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 revisit quantum phase estimation algorithms for the purpose of obtaining the energy levels of many-body Hamiltonians and pay particular attention to the statistical analysis of their outputs. We introduce the mean phase direction of the parent distribution associated with eigenstate inputs as a new post-processing tool. By connecting it with the unknown phase, we find that if used as its direct estimator, it exceeds the accuracy of the standard majority rule using one less bit of resolution, making evident that it can also be inverted to provide unbiased estimation. Moreover, we show how to directly use this quantity to accurately find the energy levels when the initialized state is an eigenstate of the simulated propagator during the whole time evolution, which allows for shallower algorithms. We then use IBM Q hardware to carry out the digital quantum simulation of three toy models: a two-level system, a two-spin Ising model and a two-site Hubbard model at half-filling. Methodologies are provided to implement Trotterization and reduce the variability of results in noisy intermediate scale quantum computers.

Generative Adversarial Networks (GANs) are a popular formulation to train generative models for complex high dimensional data. The standard method for training GANs involves a gradient descent-ascent (GDA) procedure on a minimax optimization problem. This procedure is hard to analyze in general due to the nonlinear nature of the dynamics. We study the local dynamics of GDA for training a GAN with a kernel-based discriminator. This convergence analysis is based on a linearization of a non-linear dynamical system that describes the GDA iterations, under an isolated points model assumption from [Becker et al. 2022]. Our analysis brings out the effect of the learning rates, regularization, and the bandwidth of the kernel discriminator, on the local convergence rate of GDA. Importantly, we show phase transitions that indicate when the system converges, oscillates, or diverges. We also provide numerical simulations that verify our claims.

We report an optical method of generating arbitrary polarization states by manipulating the thicknesses of a pair of uniaxial birefringent plates, the optical axes of which are set at a crossing angle of {\pi}/4. The method has the remarkable feature of being able to generate a distribution of arbitrary polarization states in a group of highly discrete spectra without spatially separating the individual spectral components. The target polarization-state distribution is obtained as an optimal solution through an exploration. Within a realistic exploration range, a sufficient number of near-optimal solutions are found. This property is also reproduced well by a concise model based on a distribution of exploration points on a Poincar\'e sphere, showing that the number of near-optimal solutions behaves according to a power law with respect to the number of spectral components of concern. As a typical example of an application, by applying this method to a set of phase-locked highly discrete spectra, we numerically demonstrate the continuous generation of a vector-like optical electric field waveform, the helicity of which is alternated within a single optical cycle in the time domain.

In the present article we study diffuse interface models for two-phase biomembranes. We will do so by starting off with a diffuse interface model on R^n defined by two coupled phase fields u,v. The first phase field u is the diffuse approximation of the interior of the membrane; the second phase field v is the diffuse approximation of the two phases of the membrane. We prove a compactness result and a lower bound in the sense of Gamma-convergence for pairs of phase functions (u_varepsilon,v_varepsilon). As an application of this first result, we consider a diffuse approximation of a two-phase Willmore functional plus line tension energy.

Generalist robot policies trained on large-scale, visually homogeneous datasets can be susceptible to shortcut learning, which impairs their out-of-distribution (OOD) generalization. While generative data augmentation is a common approach to introduce diversity, it presents a subtle challenge: data composition. Naively mixing real and synthetic data can corrupt the learning signal, as this process often prioritizes visual diversity at the expense of information fidelity. This paper suggests that robust generalization depends on principled, fidelity-aware data composition. We introduce Coherent Information Fidelity Tuning (CIFT), a framework that treats data composition as an optimization problem. CIFT uses a practical proxy for Information Fidelity based on the feature-space geometry of a dataset. This enables the identification of a phase transition, termed the Decoherence Point, where training stability degrades. The framework includes a generative engine, Multi-View Video Augmentation (MVAug), to synthesize a causally disentangled data spectrum for this tuning process. Applying CIFT to policy architectures such as pi_0 and Diffusion Policy improves OOD success rates by over 54\%. These results indicate that fidelity-aware composition, beyond data synthesis alone, is an important component for developing robust, general-purpose robots.

Distribution Matching Distillation (DMD) distills score-based generative models into efficient one-step generators, without requiring a one-to-one correspondence with the sampling trajectories of their teachers. However, limited model capacity causes one-step distilled models underperform on complex generative tasks, e.g., synthesizing intricate object motions in text-to-video generation. Directly extending DMD to multi-step distillation increases memory usage and computational depth, leading to instability and reduced efficiency. While prior works propose stochastic gradient truncation as a potential solution, we observe that it substantially reduces the generation diversity of multi-step distilled models, bringing it down to the level of their one-step counterparts. To address these limitations, we propose Phased DMD, a multi-step distillation framework that bridges the idea of phase-wise distillation with Mixture-of-Experts (MoE), reducing learning difficulty while enhancing model capacity. Phased DMD is built upon two key ideas: progressive distribution matching and score matching within subintervals. First, our model divides the SNR range into subintervals, progressively refining the model to higher SNR levels, to better capture complex distributions. Next, to ensure the training objective within each subinterval is accurate, we have conducted rigorous mathematical derivations. We validate Phased DMD by distilling state-of-the-art image and video generation models, including Qwen-Image (20B parameters) and Wan2.2 (28B parameters). Experimental results demonstrate that Phased DMD preserves output diversity better than DMD while retaining key generative capabilities. We will release our code and models.

The superfluid phase transition dynamics and associated spontaneous vortex formation with the crossing of the critical temperature in a disk geometry is studied in the framework of the AdS/CFT correspondence by solving the Einstein-Abelian-Higgs model in an AdS_4 black hole. For a slow quench, the vortex density admits a universal scaling law with the cooling rate as predicted by the Kibble-Zurek mechanism (KZM), while for fast quenches, the density shows a universal scaling behavior as a function of the final temperature, that lies beyond the KZM prediction. The vortex number distribution in both the power-law and saturation regimes can be approximated by a normal distribution. However, the study of the universal scaling of the cumulants reveals non-normal features and indicates that vortex statistics in the newborn superfluid is best described by the Poisson binomial distribution, previously predicted in the KZM regime [Phys. Rev. Lett. 124, 240602 (2020)]. This is confirmed by studying the cumulant scalings as a function of the quench time and the quench depth. Our work supports the existence of a universal defect number distribution that accommodates the KZM scaling, its breakdown at fast quenches, and the additional universal scaling laws as a function of the final value of the control parameter.

Bayes' rule tells us how to invert a causal process in order to update our beliefs in light of new evidence. If the process is believed to have a complex compositional structure, we may ask whether composing the inversions of the component processes gives the same belief update as the inversion of the whole. We answer this question affirmatively, showing that the relevant compositional structure is precisely that of the lens pattern, and that we can think of Bayesian inversion as a particular instance of a state-dependent morphism in a corresponding fibred category. We define a general notion of (mixed) Bayesian lens, and discuss the (un)lawfulness of these lenses when their contravariant components are exact Bayesian inversions. We prove our main result both abstractly and concretely, for both discrete and continuous states, taking care to illustrate the common structures.

Code-mixing is a well-studied linguistic phenomenon when two or more languages are mixed in text or speech. Several works have been conducted on building datasets and performing downstream NLP tasks on code-mixed data. Although it is not uncommon to observe code-mixing of three or more languages, most available datasets in this domain contain code-mixed data from only two languages. In this paper, we introduce OffMix-3L, a novel offensive language identification dataset containing code-mixed data from three different languages. We experiment with several models on this dataset and observe that BanglishBERT outperforms other transformer-based models and GPT-3.5.

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.

Intelligent robots need to interact with diverse objects across various environments. The appearance and state of objects frequently undergo complex transformations depending on the object properties, e.g., phase transitions. However, in the vision community, segmenting dynamic objects with phase transitions is overlooked. In light of this, we introduce the concept of phase in segmentation, which categorizes real-world objects based on their visual characteristics and potential morphological and appearance changes. Then, we present a new benchmark, Multi-Phase, Multi-Transition, and Multi-Scenery Video Object Segmentation (M^3-VOS), to verify the ability of models to understand object phases, which consists of 479 high-resolution videos spanning over 10 distinct everyday scenarios. It provides dense instance mask annotations that capture both object phases and their transitions. We evaluate state-of-the-art methods on M^3-VOS, yielding several key insights. Notably, current appearance-based approaches show significant room for improvement when handling objects with phase transitions. The inherent changes in disorder suggest that the predictive performance of the forward entropy-increasing process can be improved through a reverse entropy-reducing process. These findings lead us to propose ReVOS, a new plug-andplay model that improves its performance by reversal refinement. Our data and code will be publicly available at https://zixuan-chen.github.io/M-cube-VOS.github.io/.

The use of machine learning algorithms to investigate phase transitions in physical systems is a valuable way to better understand the characteristics of these systems. Neural networks have been used to extract information of phases and phase transitions directly from many-body configurations. However, one limitation of neural networks is that they require the definition of the model architecture and parameters previous to their application, and such determination is itself a difficult problem. In this paper, we investigate for the first time the relationship between the accuracy of neural networks for information of phases and the network configuration (that comprises the architecture and hyperparameters). We formulate the phase analysis as a regression task, address the question of generating data that reflects the different states of the physical system, and evaluate the performance of neural architecture search for this task. After obtaining the optimized architectures, we further implement smart data processing and analytics by means of neuron coverage metrics, assessing the capability of these metrics to estimate phase transitions. Our results identify the neuron coverage metric as promising for detecting phase transitions in physical systems.

Fourier Neural Operators (FNO) learn solution operators of partial differential equations by parameterizing global convolutions in the complex Fourier domain. For real-valued PDE solutions, the complex FFT carries representational redundancy through conjugate symmetry. We introduce the Hartley Neural Operator (HNO), the exact real-valued mirror of FNO: it replaces the FFT with the purely real Discrete Hartley Transform and learns a single real multiplier per retained spectral mode, with no complex arithmetic. Because the real Hartley spectrum is not halved by conjugate symmetry, HNO retains twice as many frequency corners as FNO but one real weight where FNO carries a complex pair, so the two operators are iso-parametric at equal width and differ only in spectral basis. Our central thesis is that the best basis is a property of the operator. Self-adjoint elliptic operators (Poisson, biharmonic) have real, symmetric Green's functions that the real Hartley multiplier diagonalizes exactly, and HNO is favored there. Time-dependent operators carry phase, from oscillation in the wave equation to transport in advection, Burgers, and Navier-Stokes, which a real diagonal multiplier cannot represent, so FNO is favored there, and increasingly so with the operator's phase content, leaving the phaseless heat equation as the borderline case. Training both operators identically and benchmarking across PDE classes, initial-condition families, and boundary conditions, we find an elliptic-versus-time-dependent split that is monotone in operator phase content and matches the Green's-function theory we develop. Rather than a universal winner, our findings give a predictive rule: match the spectral basis to the symmetry of the solution operator.

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.

We study in detail a one-dimensional lattice model of a continuum, conserved field (mass) that is transferred deterministically between neighbouring random sites. The model falls in a wider class of lattice models capturing the joint effect of random advection and diffusion and encompassing as specific cases, some models studied in the literature, like the Kang-Redner, Kipnis-Marchioro-Presutti, Takayasu-Taguchi, etc. The motivation for our setup comes from a straightforward interpretation as advection of particles in one-dimensional turbulence, but it is also related to a problem of synchronization of dynamical systems driven by common noise. For finite lattices, we study both the coalescence of an initially spread field (interpreted as roughening), and the statistical steady-state properties. We distinguish two main size-dependent regimes, depending on the strength of the diffusion term and on the lattice size. Using numerical simulations and mean-field approach, we study the statistics of the field. For weak diffusion, we unveil a characteristic hierarchical structure of the field. We also connect the model and the iterated function systems concept.

Based on a time-dependent Ginzburg-Landau system of equations and finite element modeling, we present novel results related with the physics of phase-slippage in superconducting wires surrounded by a non-superconductive environment. These results are obtained within our previously reported approach related to superconducting rings and superconductive gravitational wave detector transducers. It is shown that the phase-slip centers (PSCs) can be effective in originating not only positive but also negative thermal fluxes. With an appropriate design utilizing thermal diodes, PSCs can serve as cryocooling engines. Operating at Tsim 1 K cryostat cold-finger, they can achieve sub-Kelvin temperatures without using ^3He.

We present the quark weak-mixing component of a Froggatt--Nielsen program, with one flavon and three messengers, in which a single hierarchy parameter B (with εequiv 1/B) and a rational-exponent ``B-lattice'' organize fermion Yukawa textures. Building on companion mass-fit work, we translate the lattice into sharp predictions for quark mixing. The four-magnitude parameterization serves as a practical interface between the flavon Yukawa textures and quark weak mixing observables, yielding coefficient-free ratio tests of the lattice structure.

We consider the problem of modeling high-speed flows using machine learning methods. While most prior studies focus on low-speed fluid flows in which uniform time-stepping is practical, flows approaching and exceeding the speed of sound exhibit sudden changes such as shock waves. In such cases, it is essential to use adaptive time-stepping methods to allow a temporal resolution sufficient to resolve these phenomena while simultaneously balancing computational costs. Here, we propose a two-phase machine learning method, known as ShockCast, to model high-speed flows with adaptive time-stepping. In the first phase, we propose to employ a machine learning model to predict the timestep size. In the second phase, the predicted timestep is used as an input along with the current fluid fields to advance the system state by the predicted timestep. We explore several physically-motivated components for timestep prediction and introduce timestep conditioning strategies inspired by neural ODE and Mixture of Experts. As ShockCast is the first framework for learning high-speed flows, we evaluate our methods by generating two supersonic flow datasets, available at https://huggingface.co/datasets/divelab. Our code is publicly available as part of the AIRS library (https://github.com/divelab/AIRS).

The two-body problem of variational electrodynamics possesses differential-delay equations of motion with state-dependent delays of neutral type and solutions that can have velocity discontinuities on countable sets. From a periodic orbit possessing some mild properties at breaking points, we define a synchronization function in R x R3, which is further used to construct two bounded oscillatory functions vanishing at breaking points and whose first derivatives are continuous and defined everywhere but at breaking points. The oscillatory functions are associated with a PDE identity in H2(R3), and we postulate ordering conditions for the PDE identity to define a Fredholm-Schroedinger operator with an O(1/r2) spin-orbit forcing term belonging to L2(R3). As an application, we introduce the Chemical Principle criterion to select orbits with asymptotically vanishing far-fields and estimate the Bohr radius parameter of the Fredholm-Schroedinger PDE using the boundary-layer of orbits chosen according to the Chemical Principle criterion. Last, working backward, we derive a Chemical Principle-like condition from the ordering conditions.

The mixing of two or more languages is called Code-Mixing (CM). CM is a social norm in multilingual societies. Neural Language Models (NLMs) like transformers have been effective on many NLP tasks. However, NLM for CM is an under-explored area. Though transformers are capable and powerful, they cannot always encode positional information since they are non-recurrent. Therefore, to enrich word information and incorporate positional information, positional encoding is defined. We hypothesize that Switching Points (SPs), i.e., junctions in the text where the language switches (L1 -> L2 or L2 -> L1), pose a challenge for CM Language Models (LMs), and hence give special emphasis to SPs in the modeling process. We experiment with several positional encoding mechanisms and show that rotatory positional encodings along with switching point information yield the best results. We introduce CONFLATOR: a neural language modeling approach for code-mixed languages. CONFLATOR tries to learn to emphasize switching points using smarter positional encoding, both at unigram and bigram levels. CONFLATOR outperforms the state-of-the-art on two tasks based on code-mixed Hindi and English (Hinglish): (i) sentiment analysis and (ii) machine translation.

In an experiment on a turbulent jet, we detect interfacial turbulent layers in a frame that moves, on average, along with the \tnti. This significantly prolongs the observation time of scalar and velocity structures and enables the measurement of two types of Lagrangian coherent structures. One structure, the finite-time Lyapunov field (FTLE), quantifies advective transport barriers of fluid parcels while the other structure highlights barriers of diffusive momentum transport. These two complementary structures depend on large-scale and small-scale motion and are therefore associated with the growth of the turbulent region through engulfment or nibbling, respectively. We detect the \tnti\ from cluster analysis, where we divide the measured scalar field into four clusters. Not only the \tnti\ can be found this way, but also the next, internal, turbulent-turbulent interface. Conditional averages show that these interfaces are correlated with barriers of advective and diffusive transport when the Lagrangian integration time is smaller than the integral time scale. Diffusive structures decorrelate faster since they have a smaller timescale. Conditional averages of these structures at internal turbulent-turbulent interfaces show the same pattern with a more pronounced jump at the interface indicative of a shear layer. This is quite an unexpected outcome, as the internal interface is now defined not by the presence or absence of vorticity, but by conditional vorticity corresponding to two uniform concentration zones. The long-time diffusive momentum flux along Lagrangian paths represents the growth of the turbulent flow into the irrotational domain, a direct demonstration of nibbling. The diffusive flux parallel to the \tnti\ appears to be concentrated in a diffusive superlayer whose width is comparable with the Taylor microscale, which is relatively invariant in time.

Using the weights of trained Neural Network (NN) models as data modality has recently gained traction as a research field - dubbed Weight Space Learning (WSL). Multiple recent works propose WSL methods to analyze models, evaluate methods, or synthesize weights. Weight space learning methods require populations of trained models as datasets for development and evaluation. However, existing collections of models - called `model zoos' - are unstructured or follow a rudimentary definition of diversity. In parallel, work rooted in statistical physics has identified phases and phase transitions in NN models. Models are homogeneous within the same phase but qualitatively differ from one phase to another. We combine the idea of `model zoos' with phase information to create a controlled notion of diversity in populations. We introduce 12 large-scale zoos that systematically cover known phases and vary over model architecture, size, and datasets. These datasets cover different modalities, such as computer vision, natural language processing, and scientific ML. For every model, we compute loss landscape metrics and validate full coverage of the phases. With this dataset, we provide the community with a resource with a wide range of potential applications for WSL and beyond. Evidence suggests the loss landscape phase plays a role in applications such as model training, analysis, or sparsification. We demonstrate this in an exploratory study of the downstream methods like transfer learning or model weights averaging.

Collectives of actively-moving particles can spontaneously separate into dilute and dense phases -- a fascinating phenomenon known as motility-induced phase separation (MIPS). MIPS is well-studied for randomly-moving particles with no directional bias. However, many forms of active matter exhibit collective chemotaxis, directed motion along a chemical gradient that the constituent particles can generate themselves. Here, using theory and simulations, we demonstrate that collective chemotaxis strongly competes with MIPS -- in some cases, arresting or completely suppressing phase separation, or in other cases, generating fundamentally new dynamic instabilities. We establish quantitative principles describing this competition, thereby helping to reveal and clarify the rich physics underlying active matter systems that perform chemotaxis, ranging from cells to robots.

Understanding the physics of planetary magma oceans has been the subject of growing efforts, in light of the increasing abundance of Solar system samples and extrasolar surveys. A rocky planet harboring such an ocean is likely to interact tidally with its host star, planetary companions, or satellites. To date, however, models of the tidal response and heat generation of magma oceans have been restricted to the framework of weakly viscous solids, ignoring the dynamical fluid behavior of the ocean beyond a critical melt fraction. Here we provide a handy analytical model that accommodates this phase transition, allowing for a physical estimation of the tidal response of lava worlds. We apply the model in two settings: The tidal history of the early Earth-Moon system in the aftermath of the giant impact; and the tidal interplay between short-period exoplanets and their host stars. For the former, we show that the fluid behavior of the Earth's molten surface drives efficient early Lunar recession to {sim} 25 Earth radii within 10^4{-} 10^5 years, in contrast with earlier predictions. For close-in exoplanets, we report on how their molten surfaces significantly change their spin-orbit dynamics, allowing them to evade spin-orbit resonances and accelerating their track towards tidal synchronization from a Gyr to Myr timescale. Moreover, we re-evaluate the energy budgets of detected close-in exoplanets, highlighting how the surface thermodynamics of these planets are likely controlled by enhanced, fluid-driven tidal heating, rather than vigorous insolation, and how this regime change substantially alters predictions for their surface temperatures.

In a two-band superconductor, two qualitatively different fluctuation modes related to the gap modules contribute to free energy and heat capacity, in addition to the phase fluctuations. The first mode has divergent temperature behaviour since it accounts for the critical fluctuations around the phase transition point, Tc, along with pseudo-critical ones associated with former instability of the weaker-superconductivity component. The involvement of these two factors, competing under interband interaction, results in the Ginzburg number which increases with Tc non-monotonically, allowing the reduction up to 75%. This makes fluctuations effective for revealing additional superconducting component in the system. The second mode does not diverge, but has a jump at Tc, defined uniquely by the strength of interband interaction. This mode contributes fundamentally beyond critical domain.

The Sherrington-Kirkpatrick spin-glass model used the replica symmetry method to find the phase transition of the system. In 1979-1980, Parisi proposed a solution based on replica symmetry breaking (RSB), which allowed him to identify the underlying phases of complex systems such as spin-glasses. Regardless of the method used for detection, the intrinsic phase of a system exists whether or not replicas are considered. We introduce a single replica method of spin-glass phase detection using the field's variation experienced by each spin in a system configuration. This method focuses on a single replica with quenched random couplings. Each spin inevitably observes a different field from the others. Our results show that the mean and variance of fields named "Spontaneous Configurational Field" experienced by spins are suitable indicators to explore different ferromagnetic, paramagnetic, and mixed phases. To classify different phases of the system with defined indicators we have developed an algorithm based on machine learning to analyze the desired samples.

We introduce an optical tweezer platform for assembling and individually manipulating a two-dimensional register of nuclear spin qubits. Each nuclear spin qubit is encoded in the ground ^{1}S_{0} manifold of ^{87}Sr and is individually manipulated by site-selective addressing beams. We observe that spin relaxation is negligible after 5 seconds, indicating that T_1gg5 s. Furthermore, utilizing simultaneous manipulation of subsets of qubits, we demonstrate significant phase coherence over the entire register, estimating T_2^star = left(21pm7right) s and measuring T_2^echo=left(42pm6right) s.

Simulation-to-reality translation must bridge the appearance gap between synthetic and real domains while preserving structural and semantic consistency. Conditioning-based methods achieve spatial alignment but introduce computationally expensive control modules. Paired-data methods achieve realism but rely on complex synthesis pipelines, often altering scene geometry and semantics. Training-free editing methods avoid both constraints but lack a learned appearance prior, limiting their perceptual quality. Recently proposed phase-preserving diffusion presents a promising alternative, but Fourier-domain formulations are constrained by global spectral coupling. This coupling induces spatial artifacts such as ringing and boundary leakage, thereby degrading structural and semantic consistency. We introduce Wavelet Phase Diffusion, which addresses this through two components. First, we operate in the Dual-Tree Complex Wavelet Packet Transform domain, whose localized wavelet packets enable spatially adaptive phase injection without global spectral interference. Second, Low-Frequency Randomization (LFR) replaces the low-frequency packet, decoupling the model from the synthetic illumination prior and enabling in-distribution real-world appearance. Both components train on unpaired open-domain data, and introduce negligible inference overhead. The spatial locality further enables instance-level translation, where individual objects or regions are translated to photorealistic appearance independently while the surrounding scene remains untranslated. On vKITTI to KITTI image translation, ours outperforms prior methods in realism and semantic consistency while maintaining competitive structural alignment. For CARLA video translation, ours approaches the realism of paired-data methods while reducing VLM planner ADE and FDE by 5.4% and 5.1%, respectively.

We theoretically identify the noise-induced coherent contribution to the ergotropy of a four-level quantum heat engine coupled to a unimodal quantum cavity. We utilize a protocol where the passive state's quasiprobabilities can be analytically identified from the population-coherence coupled reduced density matrix. The reduced density matrix elements are evaluated using a microscopic quantum master equation formalism. Multiple ergotropies within the same coherence interval, each characterized by a positive and pronounced coherent contribution, are observed. These ergotropies are a result of population inversion as well as quasiprobability-population inversion, controllable through the coherence measure parameters. The optimal flux and power of the engine are found to be at moderate values of ergotropy with increasing values of noise-induced coherence. The optimal power at different coherences is found to possess a constant ergotropy.

All known up to now models of chemical oscillations are based exclusively on kinetic considerations. The chemical gross-process equation is split usually by elementary steps, each step is supplied by an arrow and a differential equation, joint solution to such a construction under certain, often ad hoc chosen conditions and with ad hoc numerical coefficients leads to chemical oscillations. Kinetic perception of chemical oscillations reigns without exclusions. However, as it was recently shown by the author for the laser and for the electrochemical systems, chemical oscillations follow also from solutions to the basic expressions of discrete thermodynamics of chemical equilibria. Graphically those solutions are various fork bifurcation diagrams, and, in certain types of chemical systems, oscillations are well pronounced in the bistable bifurcation areas. In this work we describe a general thermodynamic approach to chemical oscillations as opposite to kinetic models, and depict some of their new features like spontaneity and fractality. The paper doubts exclusivity of the kinetic approach to chemical oscillations, and its aim is to discuss and exemplify thermodynamically predicted chemical oscillations in closed chemical systems.

Using the supersymmetric method of random matrix theory within the Heidelberg approach framework we provide statistical description of stationary intensity sampled in locations inside an open wave-chaotic cavity, assuming that the time-reversal invariance inside the cavity is fully broken. In particular, we show that when incoming waves are fed via a finite number M of open channels the probability density {cal P}(I) for the single-point intensity I decays as a power law for large intensities: {cal P}(I)sim I^{-(M+2)}, provided there is no internal losses. This behaviour is in marked difference with the Rayleigh law {cal P}(I)sim exp(-I/I) which turns out to be valid only in the limit Mto infty. We also find the joint probability density of intensities I_1, ldots, I_L in L>1 observation points, and then extract the corresponding statistics for the maximal intensity in the observation pattern. For Lto infty the resulting limiting extreme value statistics (EVS) turns out to be different from the classical EVS distributions.

Deep neural network based methods have been successfully applied to music source separation. They typically learn a mapping from a mixture spectrogram to a set of source spectrograms, all with magnitudes only. This approach has several limitations: 1) its incorrect phase reconstruction degrades the performance, 2) it limits the magnitude of masks between 0 and 1 while we observe that 22% of time-frequency bins have ideal ratio mask values of over~1 in a popular dataset, MUSDB18, 3) its potential on very deep architectures is under-explored. Our proposed system is designed to overcome these. First, we propose to estimate phases by estimating complex ideal ratio masks (cIRMs) where we decouple the estimation of cIRMs into magnitude and phase estimations. Second, we extend the separation method to effectively allow the magnitude of the mask to be larger than 1. Finally, we propose a residual UNet architecture with up to 143 layers. Our proposed system achieves a state-of-the-art MSS result on the MUSDB18 dataset, especially, a SDR of 8.98~dB on vocals, outperforming the previous best performance of 7.24~dB. The source code is available at: https://github.com/bytedance/music_source_separation

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.

Out-of-distribution (OOD) detection and segmentation are crucial for deploying machine learning models in safety-critical applications such as autonomous driving and robot-assisted surgery. While prior research has primarily focused on unimodal image data, real-world applications are inherently multimodal, requiring the integration of multiple modalities for improved OOD detection. A key challenge is the lack of supervision signals from unknown data, leading to overconfident predictions on OOD samples. To address this challenge, we propose Feature Mixing, an extremely simple and fast method for multimodal outlier synthesis with theoretical support, which can be further optimized to help the model better distinguish between in-distribution (ID) and OOD data. Feature Mixing is modality-agnostic and applicable to various modality combinations. Additionally, we introduce CARLA-OOD, a novel multimodal dataset for OOD segmentation, featuring synthetic OOD objects across diverse scenes and weather conditions. Extensive experiments on SemanticKITTI, nuScenes, CARLA-OOD datasets, and the MultiOOD benchmark demonstrate that Feature Mixing achieves state-of-the-art performance with a 10 times to 370 times speedup. Our source code and dataset will be available at https://github.com/mona4399/FeatureMixing.

Variational Autoencoders (VAEs) are essential for large-scale audio tasks like diffusion-based generation. However, existing open-source models often neglect auditory perceptual aspects during training, leading to weaknesses in phase accuracy and stereophonic spatial representation. To address these challenges, we propose {\epsilon}ar-VAE, an open-source music signal reconstruction model that rethinks and optimizes the VAE training paradigm. Our contributions are threefold: (i) A K-weighting perceptual filter applied prior to loss calculation to align the objective with auditory perception. (ii) Two novel phase losses: a Correlation Loss for stereo coherence, and a Phase Loss using its derivatives--Instantaneous Frequency and Group Delay--for precision. (iii) A new spectral supervision paradigm where magnitude is supervised by all four Mid/Side/Left/Right components, while phase is supervised only by the LR components. Experiments show {\epsilon}ar-VAE at 44.1kHz substantially outperforms leading open-source models across diverse metrics, showing particular strength in reconstructing high-frequency harmonics and the spatial characteristics.

We consider the solvable neural scaling model with three parameters: data complexity, target complexity, and model-parameter-count. We use this neural scaling model to derive new predictions about the compute-limited, infinite-data scaling law regime. To train the neural scaling model, we run one-pass stochastic gradient descent on a mean-squared loss. We derive a representation of the loss curves which holds over all iteration counts and improves in accuracy as the model parameter count grows. We then analyze the compute-optimal model-parameter-count, and identify 4 phases (+3 subphases) in the data-complexity/target-complexity phase-plane. The phase boundaries are determined by the relative importance of model capacity, optimizer noise, and embedding of the features. We furthermore derive, with mathematical proof and extensive numerical evidence, the scaling-law exponents in all of these phases, in particular computing the optimal model-parameter-count as a function of floating point operation budget.

There have been significant advances in deep learning for music demixing in recent years. However, there has been little attention given to how these neural networks can be adapted for real-time low-latency applications, which could be helpful for hearing aids, remixing audio streams and live shows. In this paper, we investigate the various challenges involved in adapting current demixing models in the literature for this use case. Subsequently, inspired by the Hybrid Demucs architecture, we propose the Hybrid Spectrogram Time-domain Audio Separation Network HS-TasNet, which utilises the advantages of spectral and waveform domains. For a latency of 23 ms, the HS-TasNet obtains an overall signal-to-distortion ratio (SDR) of 4.65 on the MusDB test set, and increases to 5.55 with additional training data. These results demonstrate the potential of efficient demixing for real-time low-latency music applications.

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}

This study investigates the hydrodynamics of droplet formation in a T-shaped cylindrical microfluidic device using micro-PIV experiments and CFD simulations. Devices of 150 micro-m internal diameter were fabricated from PDMS via a cost-effective embedded templating method. Flow visualization was conducted using immiscible silicone oil and deionized water, forming water-in-oil droplets. A mathematical model coupling the Navier-Stokes and conservative level-set equations was solved using the finite element method. Detailed flow fields (velocity, pressure, and phase distribution) were obtained over a wide range of flow-rate ratios (0.1-10) and capillary numbers (0.001-0.1) to characterize droplet formation mechanisms. Phase evolution revealed distinct breakup stages (lag, filling, necking, and pinch-off) and multiple regimes (squeezing, dripping, sausage flow, and parallel flow with tip streaming). A regime map delineating droplet and non-droplet regions was developed. Droplet size, curvature, and internal flow profiles exhibited strong dependence on Ca and Qr. Scaling analysis showed linear dependence of droplet size on Qr in the squeezing regime, with curvature nearly independent of Qr. In contrast, both size and curvature followed power-law dependence on Ca and Qr in the dripping regime. Velocity fields inside droplets were laminar and parabolic in the core. Fully developed plug-like profiles appeared in squeezing, whereas front and rear regions remained developing in dripping. Correlations for droplet length, curvature, and film thickness, including a novel thin-film model incorporating visco-inertial and capillary effects, enable predictive design within the studied range. These findings advance fundamental understanding of confined droplet dynamics and provide quantitative guidelines for optimizing droplet-based microfluidic systems.

Human cognition emerges from coordinated spiking dynamics in distributed neural circuits, where information is encoded via both firing rates and precise spike timing determined by brain rhythms. Inspired by this notion, we propose a brain-inspired learning primitive in which cognition-level neural synchrony emerges through iterative bottom-up and top-down interactions between micro-scale dynamics of spiking neurons and a macro-scale mechanism of oscillatory synchronization. Specifically, we model each parcel (e.g., a cortical region or an image pixel) in the target system as a spiking neuron embedded in a predefined connectivity scaffold. Low-level information is encoded in a spatiotemporal domain, where neurons are selectively grouped and fire spontaneously over time through self-organized dynamics. In the bottom-up route, oscillatory synchronization is formed from past spiking activity accumulated over a finite memory window. Since brain dynamics operate in a regime of partial and transient synchronization rather than global phase locking, we model oscillatory coordination using a time-delayed synchronization formulation, which enables a top-down modulation of heterogeneous neural spiking for a large-scale distributed system. Together, we devise a spiking-by-synchronization neural network (S2-Net) that uses rhythmic timing as a control mechanism for efficient information processing. Promising results have been achieved across a broad range of tasks, including neural activity decoding, energy-efficient signal processing, temporal binding and semantic reasoning.

Classical theories of chemical kinetics assume independent reactions in dilute solutions, whose rates are determined by mean concentrations. In condensed matter, strong interactions alter chemical activities and create inhomogeneities that can dramatically affect the reaction rate. The extreme case is that of a reaction coupled to a phase transformation, whose kinetics must depend on the order parameter -- and its gradients, at phase boundaries. This Account presents a general theory of chemical kinetics based on nonequilibrium thermodynamics. The reaction rate is a nonlinear function of the thermodynamic driving force (free energy of reaction) expressed in terms of variational chemical potentials. The Cahn-Hilliard and Allen-Cahn equations are unified and extended via a master equation for non-equilibrium chemical thermodynamics. For electrochemistry, both Marcus and Butler-Volmer kinetics are generalized for concentrated solutions and ionic solids. The theory is applied to intercalation dynamics in the phase separating Li-ion battery material Li_xFePO_4.

We investigate BZT shocks and the QCD phase transition in the dense core of a cold quark star in beta equilibrium subject to the multicomponent van der Waals (MvdW) equation of state (EoS) as a model of internal structure. When this system is expressed in terms of multiple components, it can be used to explore the impact of a phase transition from a hadronic state to a quark plasma state with a complex clustering structure. The clustering can take the form of colored diquarks or triquarks and bound colorless meson, baryon, or hyperon states at the phase transition boundary. The resulting multicomponent EoS system is nonconvex, which can give rise to Bethe-Zel'dovich-Thompson (BZT) phase changing shock waves. Using the BZT shock wave condition we find constraints on the quark density and examine how this changes the tidal deformability of the compact core. These results are then combined with the TOV equations to find the resulting mass and radius relationship. These state are compared to recent astrophysical high-mass neutron star systems, which may provide evidence for a core that has undergone a quark gluon phase transition such as PSR 0943+10 or GW 190814.

We present an open-source Python implementation of an idealized high-order pseudo-spectral solver for the one-dimensional nonlinear Schr\"odinger equation (NLSE). The solver combines Fourier spectral spatial discretization with an adaptive eighth-order Dormand-Prince time integration scheme to achieve machine-precision conservation of mass and near-perfect preservation of momentum and energy for smooth solutions. The implementation accurately reproduces fundamental NLSE phenomena including soliton collisions with analytically predicted phase shifts, Akhmediev breather dynamics, and the development of modulation instability from noisy initial conditions. Four canonical test cases validate the numerical scheme: single soliton propagation, two-soliton elastic collision, breather evolution, and noise-seeded modulation instability. The solver employs a 2/3 dealiasing rule with exponential filtering to prevent aliasing errors from the cubic nonlinearity. Statistical analysis using Shannon, R\'enyi, and Tsallis entropies quantifies the spatio-temporal complexity of solutions, while phase space representations reveal the underlying coherence structure. The implementation prioritizes code transparency and educational accessibility over computational performance, providing a valuable pedagogical tool for exploring nonlinear wave dynamics. Complete source code, documentation, and example configurations are freely available, enabling reproducible computational experiments across diverse physical contexts where the NLSE governs wave evolution, including nonlinear optics, Bose-Einstein condensates, and ocean surface waves.

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.

Using observations from GMRT and FAST, we conducted multi-wavelength studies on PSR J1948+3540 and analyzed its intensity modulation characteristics in detail. We found that the intensity modulation of this pulsar exhibits broad low-frequency modulation features. The modulation frequency/period is time-dependent, but the dominant modulation component varies with the observing frequency. Specifically, at low frequencies, the modulation is dominated by the first half of the middle component, while at high frequencies, it is dominated by the second half of the middle component. Spectral analysis revealed that the intensities of the leading and trailing components vary with the observing frequency, but the middle component does not change significantly. Besides, the polarization analyses reveal that the peak of the radiation intensity is located in the latter half of the middle component, whereas the linear polarization is dominant in the former half. However, due to the low degree of linear polarization, the change of the dominant modulation component with the observed frequency is not caused by the variation in linear polarization. The phenomenon of the dominant modulation component varying with observing frequency has not been reported before and remains difficult to understand within the current theoretical framework.

Generative image models can produce convincingly real images, with plausible shapes, textures, layouts and lighting. However, one domain in which they perform notably poorly is in the synthesis of transparent objects, which exhibit refraction, reflection, absorption and scattering. Refraction is a particular challenge, because refracted pixel rays often intersect with surfaces observed in other parts of the image, providing a constraint on the color. It is clear from inspection that generative models have not distilled the laws of optics sufficiently well to accurately render refractive objects. In this work, we consider the problem of generating images with accurate refraction, given a text prompt. We synchronize the pixels within the object's boundary with those outside by warping and merging the pixels using Snell's Law of Refraction, at each step of the generation trajectory. For those surfaces that are not directly observed in the image, but are visible via refraction or reflection, we recover their appearance by synchronizing the image with a second generated image -- a panorama centered at the object -- using the same warping and merging procedure. We demonstrate that our approach generates much more optically-plausible images that respect the physical constraints.

We put forward the dynamical study of a novel higher-order small network of Chialvo neurons arranged in a ring-star topology, with the neurons interacting via linear diffusive couplings. This model is perceived to imitate the nonlinear dynamical properties exhibited by a realistic nervous system where the neurons transfer information through higher-order multi-body interactions. We first analyze our model using the tools from nonlinear dynamics literature: fixed point analysis, Jacobian matrix, and bifurcation patterns. We observe the coexistence of chaotic attractors, and also an intriguing route to chaos starting from a fixed point, to period-doubling, to cyclic quasiperiodic closed invariant curves, to ultimately chaos. We numerically observe the existence of codimension-1 bifurcation patterns: saddle-node, period-doubling, and Neimark Sacker. We also qualitatively study the typical phase portraits of the system and numerically quantify chaos and complexity using the 0-1 test and sample entropy measure respectively. Finally, we study the collective behavior of the neurons in terms of two synchronization measures: the cross-correlation coefficient, and the Kuramoto order parameter.

Colloids play an important role in fundamental science as well as in nature and technology. They have had a strong impact on the fundamental understanding of statistical physics. For example, colloids have helped to obtain a better understanding of collective phenomena, ranging from phase transitions and glass formation to the swarming of active Brownian particles. Yet the success of colloidal systems hinges crucially on the specific physical and chemical properties of the colloidal particles, i.e. particles with the appropriate characteristics must be available. Here we present an idea to create particles with freely selectable properties. The properties might depend, for example, on the presence of other particles (hence mimicking specific pair or many-body interactions), previous configurations (hence introducing some memory or feedback), or a directional bias (hence changing the dynamics). Without directly interfering with the sample, each particle is fully controlled and can receive external commands through a predefined algorithm that can take into account any input parameters. This is realized with computer-controlled colloids, which we term cybloids - short for cybernetic colloids. The potential of cybloids is illustrated by programming a time-delayed external potential acting on a single colloid and interaction potentials for many colloids. Both an attractive harmonic potential and an annular potential are implemented. For a single particle, this programming can cause subdiffusive behavior or lend activity. For many colloids, the programmed interaction potential allows to select a crystal structure at wish. Beyond these examples, we discuss further opportunities which cybloids offer.

We propose a novel framework for phase retrieval that leverages Langevin dynamics to enable efficient posterior sampling, yielding reconstructions that explicitly balance distortion and perceptual quality. Unlike conventional approaches that prioritize pixel-wise accuracy, our method navigates the perception-distortion tradeoff through a principled combination of stochastic sampling, learned denoising, and model-based updates. The framework comprises three variants of increasing complexity, integrating theoretically grounded Langevin inference, adaptive noise schedule learning, parallel reconstruction sampling, and warm-start initialization from classical solvers. Extensive experiments demonstrate that our method achieves state-of-the-art performance across multiple benchmarks, both in terms of fidelity and perceptual quality.

A primary challenge in using neural networks to approximate nonlinear dynamical systems governed by partial differential equations (PDEs) is transforming these systems into a suitable format, especially when dealing with non-linearizable dynamics or the need for infinite-dimensional spaces for linearization. This paper introduces DyMixOp, a novel neural operator framework for PDEs that integrates insights from complex dynamical systems to address this challenge. Grounded in inertial manifold theory, DyMixOp transforms infinite-dimensional nonlinear PDE dynamics into a finite-dimensional latent space, establishing a structured foundation that maintains essential nonlinear interactions and enhances physical interpretability. A key innovation is the Local-Global-Mixing (LGM) transformation, inspired by convection dynamics in turbulence. This transformation effectively captures both fine-scale details and nonlinear interactions, while mitigating spectral bias commonly found in existing neural operators. The framework is further strengthened by a dynamics-informed architecture that connects multiple LGM layers to approximate linear and nonlinear dynamics, reflecting the temporal evolution of dynamical systems. Experimental results across diverse PDE benchmarks demonstrate that DyMixOp achieves state-of-the-art performance, significantly reducing prediction errors, particularly in convection-dominated scenarios reaching up to 86.7\%, while maintaining computational efficiency and scalability.

Bayes' rule tells us how to invert a causal process in order to update our beliefs in light of new evidence. If the process is believed to have a complex compositional structure, we may observe that the inversion of the whole can be computed piecewise in terms of the component processes. We study the structure of this compositional rule, noting that it relates to the lens pattern in functional programming. Working in a suitably general axiomatic presentation of a category of Markov kernels, we see how we can think of Bayesian inversion as a particular instance of a state-dependent morphism in a fibred category. We discuss the compositional nature of this, formulated as a functor on the underlying category and explore how this can used for a more type-driven approach to statistical inference.