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We present a family of local quantum channels whose steady-states exhibit stable mixed-state symmetry-protected topological (SPT) order. Motivated by recent experimental progress on "erasure conversion" techniques that allow one to identify (\emph{herald}) decoherence processes, we consider open systems with biased erasure noise, which leads to strongly symmetric heralded errors. We utilize this heralding to construct a local correction protocol that effectively confines errors into short-ranged pairs in the steady-state. Using a combination of numerical simulations and mean-field analysis, we show that our protocol stabilizes SPT order against a sufficiently low rate of decoherence. As the rate of heralded noise increases, SPT order is eventually lost through a directed percolation transition. We further find that while introducing unheralded errors destroys SPT order in the limit of long length- and time-scales, the correction protocol is sufficient for ensuring that local SPT order persists, with a correlation length that diverges as $\xi \sim (1-f_e)^{-1/2}$, where $f_e$ is the fraction of errors that are heralded., Comment: 7+20 pages. v2: fixed typos, updated reference

We develop time-series machine learning (ML) methods for closure modeling of the Unsteady Reynolds Averaged Navier Stokes (URANS) equations applied to stably stratified turbulence (SST). SST is strongly affected by fine balances between forces and becomes more anisotropic in time for decaying cases. Moreover, there is a limited understanding of the physical phenomena described by some of the terms in the URANS equations. Rather than attempting to model each term separately, it is attractive to explore the capability of machine learning to model groups of terms, i.e., to directly model the force balances. We consider decaying SST which are homogeneous and stably stratified by a uniform density gradient, enabling dimensionality reduction. We consider two time-series ML models: Long Short-Term Memory (LSTM) and Neural Ordinary Differential Equation (NODE). Both models perform accurately and are numerically stable in a posteriori tests. Furthermore, we explore the data requirements of the ML models by extracting physically relevant timescales of the complex system. We find that the ratio of the timescales of the minimum information required by the ML models to accurately capture the dynamics of the SST corresponds to the Reynolds number of the flow. The current framework provides the backbone to explore the capability of such models to capture the dynamics of higher-dimensional complex SST flows.

Nitrogen-vacancy centers are spatially resolved probes of current noise. So far, current noise sensing with NV centers has primarily been used as a way to probe equilibrium transport coefficients. We develop a framework for computing the spatiotemporal correlations of nonequilibrium current noise in the Boltzmann regime, and apply it to two-dimensional metals in current-biased steady states. We argue that the spatial structure of the noise reveals the nonequilibrium nature of the electron distribution function, and more generally reveals the nature and lifetimes of the excitations responsible for transport. We estimate the visibility of these signatures in near-term experiments., Comment: 8 pages, 3 figures

Recently, diffusion transformers have gained wide attention with its excellent performance in text-to-image and text-to-vidoe models, emphasizing the need for transformers as backbone for diffusion models. Transformer-based models have shown better generalization capability compared to CNN-based models for general vision tasks. However, much less has been explored in the existing literature regarding the capabilities of transformer-based diffusion backbones and expanding their generative prowess to other datasets. This paper focuses on enabling a single pre-trained diffusion transformer model to scale across multiple datasets swiftly, allowing for the completion of diverse generative tasks using just one model. To this end, we propose DiffScaler, an efficient scaling strategy for diffusion models where we train a minimal amount of parameters to adapt to different tasks. In particular, we learn task-specific transformations at each layer by incorporating the ability to utilize the learned subspaces of the pre-trained model, as well as the ability to learn additional task-specific subspaces, which may be absent in the pre-training dataset. As these parameters are independent, a single diffusion model with these task-specific parameters can be used to perform multiple tasks simultaneously. Moreover, we find that transformer-based diffusion models significantly outperform CNN-based diffusion models methods while performing fine-tuning over smaller datasets. We perform experiments on four unconditional image generation datasets. We show that using our proposed method, a single pre-trained model can scale up to perform these conditional and unconditional tasks, respectively, with minimal parameter tuning while performing as close as fine-tuning an entire diffusion model for that particular task.

Large diffusion-based Text-to-Image (T2I) models have shown impressive generative powers for text-to-image generation as well as spatially conditioned image generation. For most applications, we can train the model end-toend with paired data to obtain photorealistic generation quality. However, to add an additional task, one often needs to retrain the model from scratch using paired data across all modalities to retain good generation performance. In this paper, we tackle this issue and propose a novel strategy to scale a generative model across new tasks with minimal compute. During our experiments, we discovered that the variance maps of intermediate feature maps of diffusion models capture the intensity of conditioning. Utilizing this prior information, we propose MaxFusion, an efficient strategy to scale up text-to-image generation models to accommodate new modality conditions. Specifically, we combine aligned features of multiple models, hence bringing a compositional effect. Our fusion strategy can be integrated into off-the-shelf models to enhance their generative prowess.

Calcium batteries (CBs) are potential next-generation energy storage devices, offering a promising alternative to lithium-ion batteries due to their theoretically high energy density, better safety, and lower costs associated with the natural abundance of calcium. However, the limited availability of positive electrode (cathode) materials has constrained the development of CBs so far. Given the similar ionic radii of Na$^+$ and Ca$^{2+}$, structures that are effective at reversibly intercalating Na$^+$ may be able to reversibly intercalate Ca$^{2+}$ as well. In this context, transition metal fluorides (TMFs) exhibiting weberite and perovskite structures that are known for intercalating Na$^+$ form an interesting set of possible CB cathode frameworks. Thus, we use first principles calculations to explore weberite and perovskite TMFs as CB cathodes, of compositions Ca\textsubscript{x}M\textsubscript{2}F\textsubscript{7} and Ca\textsubscrpt{x}MF\textsubscript{3}, respectively, where M = Ti, V, Cr, Mn, Fe, Co, or Ni. We systematically evaluate key cathode properties, including ground state structure, average Ca-intercalation voltage, thermodynamic stability (at 0 K), theoretical capacity, and Ca$^{2+}$ migration barriers. Importantly, we identify Ca\textsubscript{x}Cr\textsubscript{2}F\textsubscript{7} and Ca\textsubscript{x}Mn\textsubscript{2}F\textsubscript{7} weberite frameworks as promising Ca-cathodes. Our study not only unveils potential CB cathodes but also paves the way for further advancement in TMF-based intercalation cathodes, diversifying the chemical space for next-generation energy storage systems.

The ground states of interacting one-dimensional metals are generically Luttinger liquids. Luttinger liquid theory is usually considered for translation invariant systems. The Luttinger liquid description remains valid for weak quasiperiodic modulations; however, as the quasiperiodic modulation gets increasingly strong, it is increasingly renormalized and eventually fails, as the system becomes localized. We explore how quasiperiodic modulation renormalizes the Luttinger parameter characterizing this emergent Luttinger liquid, using the renormalization of transmission coefficients across a barrier as a proxy that remains valid for general quasiperiodic modulation. We find, unexpectedly, that quasiperiodic modulation weakens the effects of short-range interactions, but enhances those of long-range interactions. We support the former finding with matrix-product numerics. We also discuss how interactions affect the localization phase boundary.

In chaotic quantum systems, the entanglement of a region $A$ can be described in terms of the surface tension of a spacetime membrane pinned to the boundary of $A$. Here, we interpret the tension of this entanglement membrane in terms of the rate at which information "flows" across it. For any orientation of the membrane, one can define (generically nonunitary) dynamics across the membrane; we explore this dynamics in various space-time translation-invariant (STTI) stabilizer circuits in one and two spatial dimensions. We find that the flux of information across the membrane in these STTI circuits reaches a steady state. In the cases where this dynamics is nonunitary and the steady state flux is nonzero, this occurs because the dynamics across the membrane is unitary in a subspace of extensive entropy. This generalized unitarity is present in a broad class of STTI stabilizer circuits, and is also present in some special non-stabilizer models. The existence of multiple unitary (or generalized unitary) directions forces the entanglement membrane tension to be a piecewise linear function of the orientation of the membrane; in this respect, the entanglement membrane behaves like an interface in a zero-temperature classical lattice model. We argue that entanglement membranes in random stabilizer circuits that produce volume-law entanglement are also effectively at zero temperature., Comment: 11 pages, 8 figures + 31 pages, 17 figures. v2: Revised in response to referee comments, close to published version

An adaptive algorithm for computing eigenmodes and propagation constants of optical fibers is proposed. The algorithm is built using a dual-weighted residual error estimator. The residuals are based on the eigensystem for leaky hybrid modes obtained from Maxwell equations truncated to a finite domain after a transformation by a perfectly matched layer. The adaptive algorithm is then applied to compute practically interesting modes for multiple fiber microstructures. Emerging microstructured optical fibers are characterized by complex geometrical features in their transverse cross-section. Their leaky modes, useful for confining and propagating light in their cores, often exhibit fine scale features. The adaptive algorithm automatically captures these features without any expert input. The results also show that confinement losses of these modes are captured accurately on the adaptively found meshes., Comment: 23 pages. Improved and updated results

Despite their black-box nature, deep learning models are extensively used in image-based drug discovery to extract feature vectors from single cells in microscopy images. To better understand how these networks perform representation learning, we employ visual explainability techniques (e.g., Grad-CAM). Our analyses reveal several mechanisms by which supervised models cheat, exploiting biologically irrelevant pixels when extracting morphological features from images, such as noise in the background. This raises doubts regarding the fidelity of learned single-cell representations and their relevance when investigating downstream biological questions. To address this misalignment between researcher expectations and machine behavior, we introduce Grad-CAMO, a novel single-cell interpretability score for supervised feature extractors. Grad-CAMO measures the proportion of a model's attention that is concentrated on the cell of interest versus the background. This metric can be assessed per-cell or averaged across a validation set, offering a tool to audit individual features vectors or guide the improved design of deep learning architectures. Importantly, Grad-CAMO seamlessly integrates into existing workflows, requiring no dataset or model modifications, and is compatible with both 2D and 3D Cell Painting data. Additional results are available at https://github.com/eigenvivek/Grad-CAMO.

Reliable numerical computations are central to scientific computing, but the floating-point arithmetic that enables large-scale models is error-prone. Numeric exceptions are a common occurrence and can propagate through code, leading to flawed results. This paper presents FlowFPX, a toolkit for systematically debugging floating-point exceptions by recording their flow, coalescing exception contexts, and fuzzing in select locations. These tools help scientists discover when exceptions happen and track down their origin, smoothing the way to a reliable codebase., Comment: Presented at JuliaCon 2023; to appear in JuliaCon proceedings

Nitrogen vacancy (NV) centre quantum sensors provide unique opportunities in studying condensed matter systems: they are quantitative, noninvasive, physically robust, offer nanoscale resolution, and may be used across a wide range of temperatures. These properties have been exploited in recent years to obtain nanoscale resolution measurements of static magnetic fields arising from spin order and current flow in condensed matter systems. Compared with other nanoscale magnetic-field sensors, NV centres have the unique advantage that they can probe quantities that go beyond average magnetic fields. Leveraging techniques from magnetic resonance, NV centres can perform high precision noise sensing, and have given access to diverse systems, such as fluctuating electrical currents in simple metals and graphene, as well as magnetic dynamics in yttrium iron garnet. In this review we summarise unique opportunities in condensed matter sensing by focusing on the connections between specific NV measurements and previously established physical characteristics that are more readily understood in the condensed matter community, such as correlation functions and order parameters that are inaccessible by other techniques, and we describe the technical frontier enabled by NV centre sensing.

Mixed methods for linear elasticity with strongly symmetric stresses of lowest order are studied in this paper. On each simplex, the stress space has piecewise linear components with respect to its Alfeld split (which connects the vertices to barycenter), generalizing the Johnson-Mercier two-dimensional element to higher dimensions. Further reductions in the stress space in the three-dimensional case (to 24 degrees of freedom per tetrahedron) are possible when the displacement space is reduced to local rigid displacements. Proofs of optimal error estimates of numerical solutions and improved error estimates via postprocessing and the duality argument are presented., Comment: 32 pages

Let $M$ be an $n\times n$ matrix of homogeneous linear forms over a field $\Bbbk$. If the ideal $\mathcal{I}_{n-2}(M)$ generated by minors of size $n-1$ is Cohen-Macaulay, then the Gulliksen-Neg{\aa}rd complex is a free resolution of $\mathcal{I}_{n-2}(M)$. It has recently been shown that by taking into account the syzygy modules for $\mathcal{I}_{n-2}(M)$ which can be obtained from this complex, one can derive a refined signature-based Gr\"obner basis algorithm DetGB which avoids reductions to zero when computing a grevlex Gr\"obner basis for $\mathcal{I}_{n-2}(M)$. In this paper, we establish sharp complexity bounds on DetGB. To accomplish this, we prove several results on the sizes of reduced grevlex Gr\"obner bases of reverse lexicographic ideals, thanks to which we obtain two main complexity results which rely on conjectures similar to that of Fr\"oberg. The first one states that, in the zero-dimensional case, the size of the reduced grevlex Gr\"obner basis of $\mathcal{I}_{n-2}(M)$ is bounded from below by $n^{6}$ asymptotically. The second, also in the zero-dimensional case, states that the complexity of DetGB is bounded from above by $n^{2\omega+3}$ asymptotically, where $2\le\omega\le 3$ is any complexity exponent for matrix multiplication over $\Bbbk$., Comment: 26 pages, 2 algorithms; updated remarks after Theorem 6.5

NVIDIA Tensor Cores and AMD Matrix Cores (together called Matrix Accelerators) are of growing interest in high-performance computing and machine learning owing to their high performance. Unfortunately, their numerical behaviors are not publicly documented, including the number of extra precision bits maintained, the accumulation order of addition, and predictable subnormal number handling during computations. This makes it impossible to reliably port codes across these differing accelerators. This paper contributes a collection of {\em Feature Targeted Tests for Numerical Properties} that that help determine these features across five floating-point formats, four rounding modes and additional that highlight the rounding behaviors and preservation of extra precision bits. To show the practical relevance of FTTN, we design a simple matrix-multiplication test designed with insights gathered from our feature-tests. We executed this very simple test on five platforms, producing different answers: V100, A100, and MI250X produced 0, MI100 produced 255.875, and Hopper H100 produced 191.875. Our matrix multiplication tests employ patterns found in iterative refinement-based algorithms, highlighting the need to check for significant result variability when porting code across GPUs.

Finite-temperature spin transport in integrable isotropic spin chains (i.e., spin chains with continuous nonabelian symmetries) is known to be superdiffusive, with anomalous transport properties displaying remarkable robustness to isotropic integrability-breaking perturbations. Using a discrete-time classical model, we numerically study the crossover to conventional diffusion resulting from both noisy and Floquet isotropic perturbations of strength $\lambda$. We identify an anomalously-long crossover time scale $t_\star \sim \lambda^{-\alpha}$ with $\alpha \approx 6$ in both cases. We discuss our results in terms of a kinetic theory of transport that characterizes the lifetimes of large solitons responsible for superdiffusion.

Generative artificial intelligence (AI) and large language models (LLMs) have gained rapid popularity through publicly available tools such as ChatGPT. The adoption of LLMs for personal and professional use is fueled by the natural interactions between human users and computer applications such as ChatGPT, along with powerful summarization and text generation capabilities. Given the widespread use of such generative AI tools, in this work we investigate how these tools can be deployed in a non-safety critical, strategic traffic flow management setting. Specifically, we train an LLM, CHATATC, based on a large historical data set of Ground Delay Program (GDP) issuances, spanning 2000-2023 and consisting of over 80,000 GDP implementations, revisions, and cancellations. We test the query and response capabilities of CHATATC, documenting successes (e.g., providing correct GDP rates, durations, and reason) and shortcomings (e.g,. superlative questions). We also detail the design of a graphical user interface for future users to interact and collaborate with the CHATATC conversational agent., Comment: 8 pages, 5 figures; minor revisions to address reviewer feedback for final submission to the 11th International Conference on Research in Air Transportation (ICRAT)

Large language models (LLMs) have been shown to exhibit a wide range of capabilities, such as writing robot code from language commands -- enabling non-experts to direct robot behaviors, modify them based on feedback, or compose them to perform new tasks. However, these capabilities (driven by in-context learning) are limited to short-term interactions, where users' feedback remains relevant for only as long as it fits within the context size of the LLM, and can be forgotten over longer interactions. In this work, we investigate fine-tuning the robot code-writing LLMs, to remember their in-context interactions and improve their teachability i.e., how efficiently they adapt to human inputs (measured by average number of corrections before the user considers the task successful). Our key observation is that when human-robot interactions are viewed as a partially observable Markov decision process (in which human language inputs are observations, and robot code outputs are actions), then training an LLM to complete previous interactions is training a transition dynamics model -- that can be combined with classic robotics techniques such as model predictive control (MPC) to discover shorter paths to success. This gives rise to Language Model Predictive Control (LMPC), a framework that fine-tunes PaLM 2 to improve its teachability on 78 tasks across 5 robot embodiments -- improving non-expert teaching success rates of unseen tasks by 26.9% while reducing the average number of human corrections from 2.4 to 1.9. Experiments show that LMPC also produces strong meta-learners, improving the success rate of in-context learning new tasks on unseen robot embodiments and APIs by 31.5%. See videos, code, and demos at: https://robot-teaching.github.io/.

The small-scale dynamo is typically studied by assuming that the correlation time of the velocity field is zero. Some authors have used a smooth renovating flow model to study how the properties of the dynamo are affected by the correlation time being nonzero. Here, we assume the velocity is an incompressible Gaussian random field (which need not be smooth), and derive the lowest-order corrections to the evolution equation for the two-point correlation of the magnetic field in Fourier space. Using this, we obtain the evolution equation for the longitudinal correlation function of the magnetic field ($M_L$) in nonhelical turbulence, valid for arbitrary Prandtl number. The non-resistive terms of this equation do not contain spatial derivatives of $M_L$ of order greater than two. We further simplify this equation in the limit of high Prandtl number, and find that the growth rate of the magnetic energy is much smaller than previously reported. Nevertheless, the magnetic power spectrum still retains the Kazantsev form at high Prandtl number., Comment: 20 pages, 3 figures, 1 table. Version incorporating referees' comments. Major changes: in section 3.3, pointed out an oversight in a previous work that explains some qualitative differences in the final evolution equation; discussed the validity of WKB; fixed a mistake in section 4.2.5 (that does not affect the final results); clarified the use of equation 13 based on a comment received

Given polynomials $g$ and $f_1,\dots,f_p$, all in $\Bbbk[x_1,\dots,x_n]$ for some field $\Bbbk$, we consider the problem of computing the critical points of the restriction of $g$ to the variety defined by $f_1=\cdots=f_p=0$. These are defined by the simultaneous vanishing of the $f_i$'s and all maximal minors of the Jacobian matrix associated to $(g,f_1, \ldots, f_p)$. We use the Eagon-Northcott complex associated to the ideal generated by these maximal minors to gain insight into the syzygy module of the system defining these critical points. We devise new $F_5$-type criteria to predict and avoid more reductions to zero when computing a Gr\"obner basis for the defining system of this critical locus. We give a bound for the arithmetic complexity of this enhanced $F_5$ algorithm and compare it to the best previously known bound for computing critical points using Gr\"obner bases., Comment: 10 pages, 3 algorithms, 4 figures

Local measurements cannot create entanglement, but they can convert short-range entanglement to long-range entanglement, as in quantum teleportation. This phenomenon of measurement-induced entanglement (MIE) has been widely discussed in recent work on measurement-induced entanglement phase transitions and related phenomena. Here, we situate MIE in a broader context of the growth of long-range conditional mutual information (CMI) under decoherence. We upper-bound the rate at which decoherence can generate long-range CMI, and derive a characterization of states that saturate this bound. We point out that the structure of states saturating the CMI upper bound can be very different under different decoherent dynamics and provide explicit examples. We additionally explore the dynamics of CMI in random quantum circuits subject to random local decoherence, as a function of circuit depth. We argue that the universality class of the finite-depth teleportation transition, as well as its lower critical dimension, are different for erasures than for measurements., Comment: 10+10 pages, 10 figures; improved discussion on decoupling; included a new "summary of results" section

We introduce TopoX, a Python software suite that provides reliable and user-friendly building blocks for computing and machine learning on topological domains that extend graphs: hypergraphs, simplicial, cellular, path and combinatorial complexes. TopoX consists of three packages: TopoNetX facilitates constructing and computing on these domains, including working with nodes, edges and higher-order cells; TopoEmbedX provides methods to embed topological domains into vector spaces, akin to popular graph-based embedding algorithms such as node2vec; TopoModelx is built on top of PyTorch and offers a comprehensive toolbox of higher-order message passing functions for neural networks on topological domains. The extensively documented and unit-tested source code of TopoX is available under MIT license at https://pyt-team.github.io/.

Logarithmic Number Systems (LNS) hold considerable promise in helping reduce the number of bits needed to represent a high dynamic range of real-numbers with finite precision, and also efficiently support multiplication and division. However, under LNS, addition and subtraction turn into non-linear functions that must be approximated - typically using precomputed table-based functions. Additionally, multiple layers of error correction are typically needed to improve result accuracy. Unfortunately, previous efforts have not characterized the resulting error bound. We provide the first rigorous analysis of LNS, covering detailed techniques such as co-transformation that are crucial to implementing subtraction with reasonable accuracy. We provide theorems capturing the error due to table interpolations, the finite precision of pre-computed values in the tables, and the error introduced by fix-point multiplications involved in LNS implementations. We empirically validate our analysis using a Python implementation, showing that our analytical bounds are tight, and that our testing campaign generates inputs diverse-enough to almost match (but not exceed) the analytical bounds. We close with discussions on how to adapt our analysis to LNS systems with different bases and also discuss many pragmatic ramifications of our work in the broader arena of scientific computing and machine learning., Comment: 42 pages, 14 figures, 6 tables

The Cadmium Zinc Telluride Imager (CZTI) aboard AstroSat has good sensitivity to Gamma Ray Bursts (GRBs), with close to 600 detections including about 50 discoveries undetected by other missions. However, CZTI was not designed to be a GRB monitor and lacks localisation capabilities. We introduce a new method of localising GRBs using "shadows" cast on the CZTI detector plane due to absorption and scattering by satellite components and instruments. Comparing the observed distribution of counts on the detector plane with simulated distributions with the AstroSat Mass Model, we can localise GRBs in the sky. Our localisation uncertainty is defined by a two-component model, with a narrow Gaussian component that has close to 50% probability of containing the source, and the remaining spread over a broader Gaussian component with an 11.3 times higher $\sigma$. The width ($\sigma$) of the Gaussian components scales inversely with source counts. We test this model by applying the method to GRBs with known positions and find good agreement between the model and observations. This new ability expands the utility of CZTI in the study of GRBs and other rapid high-energy transients., Comment: 9 pages, 5 figures

Foundation models that incorporate language, vision, and more recently actions have revolutionized the ability to harness internet scale data to reason about useful tasks. However, one of the key challenges of training embodied foundation models is the lack of data grounded in the physical world. In this paper, we propose AutoRT, a system that leverages existing foundation models to scale up the deployment of operational robots in completely unseen scenarios with minimal human supervision. AutoRT leverages vision-language models (VLMs) for scene understanding and grounding, and further uses large language models (LLMs) for proposing diverse and novel instructions to be performed by a fleet of robots. Guiding data collection by tapping into the knowledge of foundation models enables AutoRT to effectively reason about autonomy tradeoffs and safety while significantly scaling up data collection for robot learning. We demonstrate AutoRT proposing instructions to over 20 robots across multiple buildings and collecting 77k real robot episodes via both teleoperation and autonomous robot policies. We experimentally show that such "in-the-wild" data collected by AutoRT is significantly more diverse, and that AutoRT's use of LLMs allows for instruction following data collection robots that can align to human preferences., Comment: 26 pages, 9 figures, ICRA 2024 VLMNM Workshop

Although Regge finite element functions are not continuous, useful generalizations of nonlinear derivatives like the curvature, can be defined using them. This paper is devoted to studying the convergence of the finite element lifting of a generalized (distributional) Gauss curvature defined using a metric tensor approximation in the Regge finite element space. Specifically, we investigate the interplay between the polynomial degree of the curvature lifting by Lagrange elements and the degree of the metric tensor in the Regge finite element space. Previously, a superconvergence result, where convergence rate of one order higher than expected, was obtained when the approximate metric is the canonical Regge interpolant of the exact metric. In this work, we show that an even higher order can be obtained if the degree of the curvature lifting is reduced by one polynomial degree and if at least linear Regge elements are used. These improved convergence rates are confirmed by numerical examples.

Accurate predictions of material properties within the chemical space of transition metal fluorides (TMFs), using density functional theory (DFT) is important for advancing several technological applications. The state-of-the-art semi-local exchange-correlation functionals within DFT include the strongly constrained and appropriately normed (SCAN) and the restored regularized SCAN (r$^2$SCAN), both of which are meta generalized gradient approximation (metaGGA) functionals. Both SCAN and r$^2$SCAN are susceptible to self-interaction errors (SIEs) while modelling correlated $d$ electrons of transition metals. Hence, in this work, we evaluate the accuracy of both functionals in estimating properties of TMFs, including redox enthalpies, lattice geometries, on-site magnetic moments, and band gaps. We observe both SCAN and r$^2$SCAN to exhibit poor accuracy in estimating fluorination enthalpies among TMFs, attributable to SIEs among the $d$ electrons. Thus, we derive optimal Hubbard $U$ corrections for both functionals based on experimental fluorination enthalpies of binary TMFs. Note that the linear response theory yielded unphysical $U$ values for V, Fe, and Ni fluorides. While adding the optimal $U$ to the metaGGA functionals does not significantly affect the lattice volumes and magnetic moments, it does significantly increase the calculated band gaps. Also, we calculate the average Na intercalation voltage in Mn, Fe, Co, and Ni fluorides as a transferability check of our optimal $U$ values. Overall, we recommend using the Hubbard $U$ correction to improve predictions of redox enthalpies in other TMFs, while for band gap predictions, we suggest using the non-corrected functionals. Finally, our study should advance the accuracy of DFT-based screening studies to unearth novel TMFs, which can be used in various applications, including energy storage, catalysis, and magnetic devices.