Daily Papers

Neural networks acquire structured representations at specific moments during training, yet identifying these transitions typically relies on retrospective, label-dependent metrics. We introduce a bifurcation theory of representation dynamics to detect these moments in real time. Analyzing a passive GMM probe attached to the evolving encoder, we show the onset of structure corresponds to a supercritical pitchfork bifurcation driven by the loss Hessian. The system exhibits a theoretically predictable zero-crossing (β_c) that, compared to the network's current state (β), yields a dynamic ratio β(t)/β_c(t): a universal, label-free phase coordinate for representation dynamics, computable entirely from hidden states. We empirically validate four distinct transition regimes predicted by this coordinate across diverse settings: SAEs on language models (Pythia), SSL (CIFAR), and grokking (modular arithmetic). Crucially, under finite dissipation, macroscopic symmetry-breaking can lag the initial zero-crossing by orders of magnitude, which providing a rigorous dynamical account of the delayed escape observed in grokking. Microscopically, the bifurcation creates a shared unstable subspace, forcing collective symmetry breaking. We term this the "feature lottery" in SAE training: a feature's terminal interpretability becomes predictable remarkably early. By only 5% of training, early atom purity robustly predicts final convergence purity, with top-decile early atoms achieving over 12x the baseline purity at convergence. Beyond explaining concept emergence, β/β_c provides a practical early-warning indicator for training health, detecting the onset of usable structure, the crystallization of feature identity, and representational collapse epochs before downstream metrics react.

Generative models have advanced significantly in sampling material systems with continuous variables, such as atomistic structures. However, their application to discrete variables, like atom types or spin states, remains underexplored. In this work, we introduce a Boltzmann generator built on discrete flow matching, specifically tailored for systems with discrete phase-space coordinates (e.g., the Ising model or crystalline compounds). This approach enables a single model to sample free energy surfaces over a wide temperature range with minimal training overhead. In addition, the model generation is scalable to larger lattice sizes than those in the training set. We demonstrate the effectiveness of our approach on the 2D Ising model, showing efficient and reliable free energy sampling. This framework provides a scalable and computationally efficient solution for discrete coordinate systems and can be extended to sample the alchemical degrees of freedom in crystalline compounds.

The integration of Supernumerary Limbs (SLs) on humanoid robots poses a significant stability challenge due to the dynamic perturbations they introduce. This thesis addresses this issue by designing a novel hierarchical control architecture to improve humanoid locomotion stability with SLs. The core of this framework is a decoupled strategy that combines learning-based locomotion with model-based balancing. The low-level component consists of a walking gait for a Unitree H1 humanoid through imitation learning and curriculum learning. The high-level component actively utilizes the SLs for dynamic balancing. The effectiveness of the system is evaluated in a physics-based simulation under three conditions: baseline gait for an unladen humanoid (baseline walking), walking with a static SL payload (static payload), and walking with the active dynamic balancing controller (dynamic balancing). Our evaluation shows that the dynamic balancing controller improves stability. Compared to the static payload condition, the balancing strategy yields a gait pattern closer to the baseline and decreases the Dynamic Time Warping (DTW) distance of the CoM trajectory by 47\%. The balancing controller also improves the re-stabilization within gait cycles and achieves a more coordinated anti-phase pattern of Ground Reaction Forces (GRF). The results demonstrate that a decoupled, hierarchical design can effectively mitigate the internal dynamic disturbances arising from the mass and movement of the SLs, enabling stable locomotion for humanoids equipped with functional limbs. Code and videos are available here: https://github.com/heyzbw/HuSLs.

While numerous frameworks have been developed to enhance the reasoning abilities of large language models (LLMs), there is a scarcity of methods that effectively balance the trade-off between cost and quality. In this paper, we introduce Fleet of Agents (FoA), a novel and intuitive yet principled framework utilizing LLMs as agents to navigate through dynamic tree searches, employing a genetic-type particle filtering approach. FoA spawns a multitude of agents, each exploring the search space autonomously, followed by a selection phase where resampling based on a heuristic value function optimizes the balance between exploration and exploitation. This mechanism enables dynamic branching, adapting the exploration strategy based on discovered solutions. We conduct extensive experiments on three benchmark tasks, ``Game of 24'', ``Mini-Crosswords'', and ``WebShop'', utilizing four different LLMs, ``GPT-3.5'', ``GPT-4'', ``LLaMA3.2-11B'', and ``LLaMA3.2-90B''. On average across all tasks and LLMs, FoA obtains a quality improvement of ~5% while requiring only ~40% of the cost of previous SOTA methods. Notably, our analyses reveal that (1) FoA achieves the best cost-quality trade-off among all benchmarked methods and (2) FoA + LLaMA3.2-11B surpasses the Llama3.2-90B model. FoA is publicly available at https://github.com/au-clan/FoA.

Advances in computer vision and machine learning techniques have led to significant development in 2D and 3D human pose estimation from RGB cameras, LiDAR, and radars. However, human pose estimation from images is adversely affected by occlusion and lighting, which are common in many scenarios of interest. Radar and LiDAR technologies, on the other hand, need specialized hardware that is expensive and power-intensive. Furthermore, placing these sensors in non-public areas raises significant privacy concerns. To address these limitations, recent research has explored the use of WiFi antennas (1D sensors) for body segmentation and key-point body detection. This paper further expands on the use of the WiFi signal in combination with deep learning architectures, commonly used in computer vision, to estimate dense human pose correspondence. We developed a deep neural network that maps the phase and amplitude of WiFi signals to UV coordinates within 24 human regions. The results of the study reveal that our model can estimate the dense pose of multiple subjects, with comparable performance to image-based approaches, by utilizing WiFi signals as the only input. This paves the way for low-cost, broadly accessible, and privacy-preserving algorithms for human sensing.

Vision Language Models (VLMs) demonstrate strong qualitative visual understanding, but struggle with metrically precise spatial reasoning required for embodied applications. The agentic paradigm promises that VLMs can use a wide variety of tools that could augment these capabilities, such as depth estimators, segmentation models, and pose estimators. Yet it remains an open challenge how to realize this vision without solely relying on handcrafted prompting strategies or enforcing fixed, predefined tool pipelines that limit VLMs' ability to discover optimal tool-use patterns. Reinforcement Learning could overcome this gap, but has so far been limited to reasoning with a single visual tool due to the large search space in multi-tool reasoning. We introduce Double Interactive Reinforcement Learning (DIRL), a two-phase training framework where VLMs learn to coordinate multiple tools through interactive exploration and feedback. In the teaching phase, we combine demonstrations from a single tool specialist trained via interactive RL with traces from a frontier model using all tools. In the exploration phase, the model further refines multi-tool coordination through continued RL. Our model, SpaceTools, with tool-augmented spatial reasoning ability, achieves state-of-the-art performance on spatial understanding benchmarks (RoboSpatial-Home, BLINK, BOP-ASK) and demonstrates reliable real-world manipulation using a 7-DOF robot as a tool. DIRL provides substantial improvements over the vanilla SFT (+12% on RoboSpatial) and RL (+16% on RoboSpatial) baselines. Project page: https://spacetools.github.io/.

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.

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.

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.

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.

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.

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.

As the number of seismic sensors grows, it is becoming increasingly difficult for analysts to pick seismic phases manually and comprehensively, yet such efforts are fundamental to earthquake monitoring. Despite years of improvements in automatic phase picking, it is difficult to match the performance of experienced analysts. A more subtle issue is that different seismic analysts may pick phases differently, which can introduce bias into earthquake locations. We present a deep-neural-network-based arrival-time picking method called "PhaseNet" that picks the arrival times of both P and S waves. Deep neural networks have recently made rapid progress in feature learning, and with sufficient training, have achieved super-human performance in many applications. PhaseNet uses three-component seismic waveforms as input and generates probability distributions of P arrivals, S arrivals, and noise as output. We engineer PhaseNet such that peaks in probability provide accurate arrival times for both P and S waves, and have the potential to increase the number of S-wave observations dramatically over what is currently available. This will enable both improved locations and improved shear wave velocity models. PhaseNet is trained on the prodigious available data set provided by analyst-labeled P and S arrival times from the Northern California Earthquake Data Center. The dataset we use contains more than seven million waveform samples extracted from over thirty years of earthquake recordings. We demonstrate that PhaseNet achieves much higher picking accuracy and recall rate than existing methods.

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.