Miracle-dz/UniFAR-FTUs huggingface dataset:
Lattice Models, Hamiltonian Operators, and Symmetric Functions

We give general conditions for the existence of a Hamiltonian operator whose discrete time evolution matches the partition function of certain solvable lattice models. In particular, we examine two classes of lattice models: the classical six-vertex model and a generalized family of (2n+ 4)-vertex models for each positive integer n. These models depend on a statistic called charge, and are associated to the quantum group Uq(ĝl(1|n)) [7]. Our results show a close and unexpected connection between Hamiltonian operators and solvability. The six-vertex model can be associated with Hamiltonians from classical Fock space, and we show that such a correspondence exists precisely when the Boltzmann weights are free fermionic. This allows us to prove that the free fermionic partition function is always a (skew) supersymmetric Schur function and then use the Berele-Regev formula to correct a result from [13]. In this context, the supersymmetric function involution takes us between two lattice models that generalize the vicious walker and osculating walker models. We also observe that the supersymmetric Jacobi-Trudi formula, through Wick’s Theorem, can be seen as a six-vertex analogue of the Lindström-Gessel-Viennot Lemma. Then, we prove a sharp solvability criterion for the six-vertex model with charge that provides the proper analogue of the free fermion condition. Building on results in [9], we show that this criterion exactly dictates when a charged model has a Hamiltonian operator acting on a Drinfeld twist of q-Fock space. The resulting partition function is then always a (skew) supersymmetric LLT polynomial.
Conditional Value-at-Risk for Quantitative Trading: A Direct Reinforcement Learning Approach

We propose a convex formulation for a trading system with the Conditional Value-at-Risk as a risk-adjusted performance measure under the notion of Direct Reinforcement Learning. Due to convexity, the proposed approach can uncover a lucrative trading policy in a “pure” online manner where it can interactively learn and update the policy without multi-epoch training and validation. We assess our proposed algorithm on a real financial market where it trades one of the largest US trust funds, SPDR, for three years. Numerical experiments demonstrate the algorithm's robustness in detecting central market-regime switching. Moreover, the results show the algorithm's effectiveness in extracting profitable policy while meeting an investor's risk preference under a conservative frictional market with a transaction cost of 0.15% per trade.
Finite‐Size Analysis of the Collapse of Dry Granular Columns

In this letter, we focus on the size effect of granular column collapses, which are potentially connected to the dynamics of complex geophysical flows, even if the link between microscopic structures of granular assemblies and their macroscopic behaviors is still not well understood. Using the spheropolyhedral discrete element method (DEM), we show that the column radius/grain size ratio has a strong influence on the collapse behavior. A finite‐size analysis, which is inspired by a phase transition around an inflection point, is performed to obtain a general scaling equation with critical exponents for runout distances. We further link the size effect with the strong force network and formalize a correlation length scale that exponentially scales with the effective aspect ratio. Such a scaling solution shows similarities with the percolation problem of two‐dimensional random networks and can be extended to other similar natural and engineering systems.
Optimal Targeting in Fundraising: A Causal Machine-Learning Approach

Ineffective fundraising lowers the resources charities can use to provide goods. We combine a field experiment and a causal machine-learning approach to increase a charity's fundraising effectiveness. The approach optimally targets a fundraising instrument to individuals whose expected donations exceed solicitation costs. Our results demonstrate that machine-learning-based optimal targeting allows the charity to substantially increase donations net of fundraising costs relative to uniform benchmarks in which either everybody or no one receives the gift. To that end, it (a) should direct its fundraising efforts to a subset of past donors and (b) never address individuals who were previously asked but never donated. Further, we show that the benefits of machine-learning-based optimal targeting even materialize when the charity only exploits publicly available geospatial information or applies the estimated optimal targeting rule to later fundraising campaigns conducted in similar samples. We conclude that charities not engaging in optimal targeting waste significant resources.
Non-Asymptotic Analysis for Two Time-scale TDC with General Smooth Function Approximation

Temporal-difference learning with gradient correction (TDC) is a two time-scale algorithm for policy evaluation in reinforcement learning. This algorithm was initially proposed with linear function approximation, and was later extended to the one with general smooth function approximation. The asymptotic convergence for the on-policy setting with general smooth function approximation was established in [bhatnagar2009convergent], however, the finite-sample analysis remains unsolved due to challenges in the non-linear and two-time-scale update structure, non-convex objective function and the time-varying projection onto a tangent plane. In this paper, we develop novel techniques to explicitly characterize the finite-sample error bound for the general off-policy setting with i.i. d. \ or Markovian samples, and show that it converges as fast as $\mathcal O(1/\sqrt T)$ (up to a factor of $\mathcal O(\log T)$). Our approach can be applied to a wide range of value-based reinforcement learning algorithms with general smooth function approximation.
Anderson Acceleration as a Krylov Method with Application to Asymptotic Convergence Analysis

Anderson acceleration (AA) is widely used for accelerating the convergence of nonlinear fixed-point methods $x_{k+1}=q(x_{k})$, $x_k \in \mathbb{R}^n$, but little is known about how to quantify the convergence acceleration provided by AA. As a roadway towards gaining more understanding of convergence acceleration by AA, we study AA($m$), i.e., Anderson acceleration with finite window size $m$, applied to the case of linear fixed-point iterations $x_{k+1}=M x_{k}+b$. We write AA($m$) as a Krylov method with polynomial residual update formulas, and derive recurrence relations for the AA($m$) polynomials. Writing AA($m$) as a Krylov method immediately implies that $k$ iterations of AA($m$) cannot produce a smaller residual than $k$ iterations of GMRES without restart (but without implying anything about the relative convergence speed of (windowed) AA($m$) versus restarted GMRES($m$)). We find that the AA($m$) residual polynomials observe a periodic memory effect where increasing powers of the error iteration matrix $M$ act on the initial residual as the iteration number increases. We derive several further results based on these polynomial residual update formulas, including orthogonality relations, a lower bound on the AA(1) acceleration coefficient $\beta_k$, and explicit nonlinear recursions for the AA(1) residuals and residual polynomials that do not include the acceleration coefficient $\beta_k$. Using these recurrence relations we also derive new residual convergence bounds for AA(1) in the linear case, demonstrating how the per-iteration residual reduction $||r_{k+1}||/||r_{k}||$ depends strongly on the residual reduction in the previous iteration and on the angle between the prior residual vectors $r_k$ and $r_{k-1}$. We apply these results to study the influence of the initial guess on the asymptotic convergence factor of AA(1), and to study AA(1) residual convergence patterns.
CCTrans: Simplifying and Improving Crowd Counting with Transformer

Most recent methods used for crowd counting are based on the convolutional neural network (CNN), which has a strong ability to extract local features. But CNN inherently fails in modeling the global context due to the limited receptive fields. However, the transformer can model the global context easily. In this paper, we propose a simple approach called CCTrans to simplify the design pipeline. Specifically, we utilize a pyramid vision transformer backbone to capture the global crowd information, a pyramid feature aggregation (PFA) model to combine low-level and high-level features, an efficient regression head with multi-scale dilated convolution (MDC) to predict density maps. Besides, we tailor the loss functions for our pipeline. Without bells and whistles, extensive experiments demonstrate that our method achieves new state-of-the-art results on several benchmarks both in weakly and fully-supervised crowd counting. Moreover, we currently rank No.1 on the leaderboard of NWPU-Crowd. Our code will be made available.
Smart at what cost?: characterising mobile deep neural networks in the wild

With smartphones' omnipresence in people's pockets, Machine Learning (ML) on mobile is gaining traction as devices become more powerful. With applications ranging from visual filters to voice assistants, intelligence on mobile comes in many forms and facets. However, Deep Neural Network (DNN) inference remains a compute intensive workload, with devices struggling to support intelligence at the cost of responsiveness. On the one hand, there is significant research on reducing model runtime requirements and supporting deployment on embedded devices. On the other hand, the strive to maximise the accuracy of a task is supported by deeper and wider neural networks, making mobile deployment of state-of-the-art DNNs a moving target. In this paper, we perform the first holistic study of DNN usage in the wild in an attempt to track deployed models and match how these run on widely deployed devices. To this end, we analyse over 16k of the most popular apps in the Google Play Store to characterise their DNN usage and performance across devices of different capabilities, both across tiers and generations. Simultaneously, we measure the models' energy footprint, as a core cost dimension of any mobile deployment. To streamline the process, we have developed gaugeNN, a tool that automates the deployment, measurement and analysis of DNNs on devices, with support for different frameworks and platforms. Results from our experience study paint the landscape of deep learning deployments on smartphones and indicate their popularity across app developers. Furthermore, our study shows the gap between bespoke techniques and real-world deployments and the need for optimised deployment of deep learning models in a highly dynamic and heterogeneous ecosystem.
Learning Periodic Tasks from Human Demonstrations

We develop a method for learning periodic tasks from visual demonstrations. The core idea is to leverage periodicity in the policy structure to model periodic aspects of the tasks. We use active learning to optimize parameters of rhythmic dynamic movement primitives (rDMPs) and propose an objective to maximize the similarity between the motion of objects manipulated by the robot and the desired motion in human video demonstrations. We consider tasks with deformable objects and granular matter whose states are challenging to represent and track: wiping surfaces with a cloth, winding cables, and stirring granular matter with a spoon. Our method does not require tracking markers or manual annotations. The initial training data consists of 10-minute videos of random unpaired interactions with objects by the robot and human. We use these for unsupervised learning of a keypoint model to get task-agnostic visual correspondences. Then, we use Bayesian optimization to optimize rDMPs from a single human video demonstration within few robot trials. We present simulation and hardware experiments to validate our approach.
Finite volume methods for the computation of statistical solutions of the incompressible Euler equations

We present an eﬃcient numerical scheme based on Monte Carlo integration to approximate statistical solutions of the incompressible Euler equations. The scheme is based on ﬁnite volume methods, which provide a more ﬂexible framework than previously existing spectral methods for the computation of statistical solutions for incompressible ﬂows. This ﬁnite volume scheme is rigorously proven to, under experimentally veriﬁable assumptions, converge in an appropriate topology and with increasing resolution to a statistical solution. The convergence obtained is stronger than that of measure-valued solutions, as it implies convergence of multi-point correlation marginals. We present results of numerical experiments which support the claim that the aforementioned assumptions are very natural, and appear to hold in practice.
Simultaneous rational approximation to successive powers of a real number

We develop new tools leading, for each integer n ≥ 4, to a significantly improved upper bound for the uniform exponent of rational approximation λ̂n(ξ) to successive powers 1, ξ, . , ξ of a given real transcendental number ξ. As an application, we obtain a refined lower bound for the exponent of approximation to ξ by algebraic integers of degree at most n+ 1. The new lower bound is n/2 + a √ n + 4/3 with a = (1 − log(2))/2 ≃ 0.153, instead of the current n/2 +O(1).
On the maximum luminosities of normal stripped-envelope supernovae -- brighter than explosion models allow

Stripped-envelope supernovae (SE SNe) of Type Ib and Type Ic are thought to result from explosions of massive stars having lost their outer envelopes. The favoured explosion mechanism is by core-collapse, with the shock later revived by neutrino heating. However, there is an upper limit to the amount of radioactive Nickel-56 that such models can accomplish. Recent literature point to a tension between the maximum luminosity from such simulations and observations. We use a well characterized sample of SE SNe from the Zwicky Transient Facility (ZTF) Bright Transient Survey (BTS) to collect a sample of spectroscopically classified normal Type Ibc SNe for which we use the ZTF light curves to determine the maximum luminosity. We cull the sample further based on data quality, light-curve shape, distance and colors. The methodology of the sample construction from this BTS sample can be used for many other future investigations. In total we use 129 Type Ib or Type Ic BTS SNe with an initial rough luminosity distribution peaked at Mr = -17.61 +- 0.72, and where 36% are apparently brighter than the theoretically predicted maximum brightness of Mr = -17.8. When we further cull this sample to ensure that the SNe are normal Type Ibc with good LC data within the Hubble flow, the sample of 94 objects has Mr = -17.64 +- 0.54. A main uncertainty in absolute magnitude determinations for SNe is the host galaxy extinction correction, but the reddened objects only get more luminous after corrections. If we simply exclude objects with red, unusual or uncertain colors, we are left with 14 objects at M = -17.90 +- 0.73, whereof a handful are most certainly brighter than the suggested theoretical limit. The main result of this study is thus that normal SNe Ibc do indeed reach luminosities above $10^{42.6}$ erg/s, apparently in conflict with existing explosion models.
The structure of digraphs with excess one

A digraph is ‐geodetic if for any (not necessarily distinct) vertices there is at most one directed walk from to with length not exceeding . The order of a ‐geodetic digraph with minimum out‐degree is bounded below by the directed Moore bound . The Moore bound can be met only in the trivial cases and , so it is of interest to look for ‐geodetic digraphs with out‐degree and smallest possible order , where is the excess of the digraph. Miller, Miret and Sillasen recently ruled out the existence of digraphs with excess one for and and for and . We conjecture that there are no digraphs with excess one for and in this paper we investigate the structure of minimal counterexamples to this conjecture. We severely constrain the possible structures of the outlier function and prove the nonexistence of certain digraphs with degree three and excess one, as well closing the open cases and left by the analysis of Miller et al. We further show that there are no involutary digraphs with excess one, that is, the outlier function of any such digraph must contain a cycle of length .
Entanglement and Chaos in De Sitter Holography: An SYK Example

Entanglement, chaos, and complexity are as important for de Sitter space as for AdS and for black holes. There are similarities and great differences between AdS and dS in how these concepts are manifested in the space-time geometry. In the first part of this paper the Ryu-Takayanagi prescription, the theory of fast scrambling, and the holographic complexity correspondence are reformulated for de Sitter space. Criteria are proposed for a holographic model to describe de Sitter space. The criteria can be summarized by the requirement that scrambling and complexity growth must be"hyperfast. "In the later part of the paper I show that a certain limit of SYK is a concrete, computable, holographic model of de Sitter space. Calculations are described which support the conjecture.
Small Protoplanetary Disks in the Orion Nebula Cluster and OMC1 with ALMA

The Orion Nebula Cluster (ONC) is the nearest dense star-forming region at ∼400 pc away, making it an ideal target to study the impact of high stellar density and proximity to massive stars (the Trapezium) on protoplanetary disk evolution. The OMC1 molecular cloud is a region of high extinction situated behind the Trapezium in which actively forming stars are shielded from the Trapezium’s strong radiation. In this work, we survey disks at high resolution with Atacama Large Millimeter/submillimeter Array at three wavelengths with resolutions of 0. ″095 (3 mm; Band 3), 0. ″048 (1.3 mm; Band 6), and 0. ″030 (0.85 mm; Band 7) centered on radio Source I. We detect 127 sources, including 15 new sources that have not previously been detected at any wavelength. 72 sources are spatially resolved at 3 mm, with sizes from ∼8–100 au. We classify 76 infrared-detected sources as foreground ONC disks and the remainder as embedded OMC1 disks. The two samples have similar disk sizes, but the OMC1 sources have a dense and centrally concentrated spatial distribution, indicating they may constitute a spatially distinct subcluster. We find smaller disk sizes and a lack of large (>75 au) disks in both our samples compared to other nearby star-forming regions, indicating that environmental disk truncation processes are significant. While photoevaporation from nearby massive Trapezium stars may account for the smaller disks in the ONC, the embedded sources in OMC1 are hidden from this radiation and thus must truncated by some other mechanism, possibly dynamical truncation or accretion-driven contraction.
Localizing Objects with Self-Supervised Transformers and no Labels

Localizing objects in image collections without supervision can help to avoid expensive annotation campaigns. We propose a simple approach to this problem, that leverages the activation features of a vision transformer pre-trained in a self-supervised manner. Our method, LOST, does not require any external object proposal nor any exploration of the image collection; it operates on a single image. Yet, we outperform state-of-the-art object discovery methods by up to 8 CorLoc points on PASCAL VOC 2012. We also show that training a class-agnostic detector on the discovered objects boosts results by another 7 points. Moreover, we show promising results on the unsupervised object discovery task. The code to reproduce our results can be found at https://github.com/valeoai/LOST.
A Novel Framework for Modeling Weakly Lensing Shear Using Kinematics and Imaging at Moderate Redshift

Kinematic weak lensing describes the distortion of a galaxy’s projected velocity field due to lensing shear, an effect recently reported for the first time by Gurri et al. based on a sample of 18 galaxies at z ∼ 0.1. In this paper, we develop a new formalism that combines the shape information from imaging surveys with the kinematic information from resolved spectroscopy to better constrain the lensing distortion of source galaxies and to potentially address systematic errors that affect conventional weak-lensing analyses. Using a Bayesian forward model applied to mock galaxy observations, we model distortions in the source galaxy’s velocity field simultaneously with the apparent shear-induced offset between the kinematic and photometric major axes. We show that this combination dramatically reduces the statistical uncertainty on the inferred shear, yielding statistical error gains of a factor of 2–6 compared to kinematics alone. While we have not accounted for errors from intrinsic kinematic irregularities, our approach opens kinematic lensing studies to higher redshifts where resolved spectroscopy is more challenging. For example, we show that ground-based integral-field spectroscopy of background galaxies at z ∼ 0.7 can deliver gravitational shear measurements with signal-to-noise ratio of ∼1 per source galaxy at 1 arcminute separations from a galaxy cluster at z ∼ 0.3. This suggests that even modest samples observed with existing instruments could deliver improved galaxy cluster mass measurements and well-sampled probes of their halo mass profiles to large radii.
Second-Order Neural ODE Optimizer

We propose a novel second-order optimization framework for training the emerging deep continuous-time models, specifically the Neural Ordinary Differential Equations (Neural ODEs). Since their training already involves expensive gradient computation by solving a backward ODE, deriving efficient second-order methods becomes highly nontrivial. Nevertheless, inspired by the recent Optimal Control (OC) interpretation of training deep networks, we show that a specific continuous-time OC methodology, called Differential Programming, can be adopted to derive backward ODEs for higher-order derivatives at the same O(1) memory cost. We further explore a low-rank representation of the second-order derivatives and show that it leads to efficient preconditioned updates with the aid of Kronecker-based factorization. The resulting method -- named SNOpt -- converges much faster than first-order baselines in wall-clock time, and the improvement remains consistent across various applications, e.g. image classification, generative flow, and time-series prediction. Our framework also enables direct architecture optimization, such as the integration time of Neural ODEs, with second-order feedback policies, strengthening the OC perspective as a principled tool of analyzing optimization in deep learning. Our code is available at https://github.com/ghliu/snopt.