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Diffusion MRI (dMRI) is an advanced imaging technique characterizing tissue microstructure and white matter structural connectivity of the human brain. The demand for high-quality dMRI data is growing, driven by the need for better resolution and improved tissue contrast. However, acquiring high-quality dMRI data is expensive and time-consuming. In this context, deep generative modeling emerges as a promising solution to enhance image quality while minimizing acquisition costs and scanning time. In this study, we propose a novel generative approach to perform dMRI generation using deep diffusion models. It can generate high dimension (4D) and high resolution data preserving the gradients information and brain structure. We demonstrated our method through an image mapping task aimed at enhancing the quality of dMRI images from 3T to 7T. Our approach demonstrates highly enhanced performance in generating dMRI images when compared to the current state-of-the-art (SOTA) methods. This achievement underscores a substantial progression in enhancing dMRI quality, highlighting the potential of our novel generative approach to revolutionize dMRI imaging standards., Comment: 11 pages, 3 figures

Over the past few years alone, the lensing community has discovered thousands of strong lens candidates, and spectroscopically confirmed hundreds of them. In this time of abundance, it becomes pragmatic to focus our time and resources on the few extraordinary systems, in order to most efficiently study the universe. In this paper, we present such a system: DESI-090.9854-35.9683, a cluster-scale lens at $z_{\rm l} = 0.49$, with seven observed lensed sources around the core, and additional lensed sources further out in the cluster. From the number and the textbook configuration of the lensed images, a tight constraint on the mass potential of the lens is possible. This would allow for detailed analysis on the dark and luminous matter content within galaxy clusters, as well as a probe into dark energy and high-redshift galaxies. We present our spatially resolved kinematic measurements of this system from the Very Large Telescope Multi Unit Spectroscopic Explorer, which confirm five of these source galaxies (in ascending order, at $z_{\rm s} = 0.962, 0.962, 1.166, 1.432,$ and $1.432$). With previous Hubble Space Telescope imaging in the F140W and F200LP bands, we also present a simple two power-law profile flux-based lens model that, for a cluster lens, well models the five lensed arc families with redshifts. We determine the mass to be $M(< \theta_{\rm E}) = 4.78\times10^{13} M_{\odot}$ for the primary mass potential. From the model, we extrapolate the redshift of one of the two source galaxies not yet spectroscopically confirmed to be at $z_{\rm s}=4.52^{+1.03}_{-0.71}$., Comment: 14 pages, 6 figures

Understanding the dynamics of climate variables is paramount for numerous sectors, like energy and environmental monitoring. This study focuses on the critical need for a precise mapping of environmental variables for national or regional monitoring networks, a task notably challenging when dealing with skewed data. To address this issue, we propose a novel data fusion approach, the \textit{warped multifidelity Gaussian process} (WMFGP). The method performs prediction using multiple time-series, accommodating varying reliability and resolutions and effectively handling skewness. In an extended simulation experiment the benefits and the limitations of the methods are explored, while as a case study, we focused on the wind speed monitored by the network of ARPA Lombardia, one of the regional environmental agencies operting in Italy. ARPA grapples with data gaps, and due to the connection between wind speed and air quality, it struggles with an effective air quality management. We illustrate the efficacy of our approach in filling the wind speed data gaps through two extensive simulation experiments. The case study provides more informative wind speed predictions crucial for predicting air pollutant concentrations, enhancing network maintenance, and advancing understanding of relevant meteorological and climatic phenomena.

Parcellation of white matter tractography provides anatomical features for disease prediction, anatomical tract segmentation, surgical brain mapping, and non-imaging phenotype classifications. However, parcellation does not always reach 100% accuracy due to various factors, including inter-individual anatomical variability and the quality of neuroimaging scan data. The failure to identify parcels causes a problem of missing microstructure data values, which is especially challenging for downstream tasks that analyze large brain datasets. In this work, we propose a novel deep-learning model to impute tissue microstructure: the White Matter Geometry-guided Diffusion (WMG-Diff) model. Specifically, we first propose a deep score-based guided diffusion model to impute tissue microstructure for diffusion magnetic resonance imaging (dMRI) tractography fiber clusters. Second, we propose a white matter atlas geometric relationship-guided denoising function to guide the reverse denoising process at the subject-specific level. Third, we train and evaluate our model on a large dataset with 9342 subjects. Comprehensive experiments for tissue microstructure imputation and a downstream non-imaging phenotype prediction task demonstrate that our proposed WMG-Diff outperforms state-of-the-art methods., Comment: 12 pages, 3 figures, 2 tables

Parcellation of human cerebellar pathways is essential for advancing our understanding of the human brain. Existing diffusion MRI tractography parcellation methods have been successful in defining major cerebellar fibre tracts, while relying solely on fibre tract structure. However, each fibre tract may relay information related to multiple cognitive and motor functions of the cerebellum. Hence, it may be beneficial for parcellation to consider the potential importance of the fibre tracts for individual motor and cognitive functional performance measures. In this work, we propose a multimodal data-driven method for cerebellar pathway parcellation, which incorporates both measures of microstructure and connectivity, and measures of individual functional performance. Our method involves first training a multitask deep network to predict various cognitive and motor measures from a set of fibre tract structural features. The importance of each structural feature for predicting each functional measure is then computed, resulting in a set of structure-function saliency values that are clustered to parcellate cerebellar pathways. We refer to our method as Deep Multimodal Saliency Parcellation (DeepMSP), as it computes the saliency of structural measures for predicting cognitive and motor functional performance, with these saliencies being applied to the task of parcellation. Applying DeepMSP we found that it was feasible to identify multiple cerebellar pathway parcels with unique structure-function saliency patterns that were stable across training folds.

The relationship between brain connections and non-imaging phenotypes is increasingly studied using deep neural networks. However, the local and global properties of the brain's white matter networks are often overlooked in convolutional network design. We introduce TractGraphFormer, a hybrid Graph CNN-Transformer deep learning framework tailored for diffusion MRI tractography. This model leverages local anatomical characteristics and global feature dependencies of white matter structures. The Graph CNN module captures white matter geometry and grey matter connectivity to aggregate local features from anatomically similar white matter connections, while the Transformer module uses self-attention to enhance global information learning. Additionally, TractGraphFormer includes an attention module for interpreting predictive white matter connections. In sex prediction tests, TractGraphFormer shows strong performance in large datasets of children (n=9345) and young adults (n=1065). Overall, our approach suggests that widespread connections in the WM are predictive of the sex of an individual, and consistent predictive anatomical tracts are identified across the two datasets. The proposed approach highlights the potential of integrating local anatomical information and global feature dependencies to improve prediction performance in machine learning with diffusion MRI tractography., Comment: 23 pages, 4 figures

Deep learning has been used to improve photoacoustic (PA) image reconstruction. One major challenge is that errors cannot be quantified to validate predictions when ground truth is unknown. Validation is key to quantitative applications, especially using limited-bandwidth ultrasonic linear detector arrays. Here, we propose a hybrid Bayesian convolutional neural network (Hybrid-BCNN) to jointly predict PA image and segmentation with error (uncertainty) predictions. Each output pixel represents a probability distribution where error can be quantified. The Hybrid-BCNN was trained with simulated PA data and applied to both simulations and experiments. Due to the sparsity of PA images, segmentation focuses Hybrid-BCNN on minimizing the loss function in regions with PA signals for better predictions. The results show that accurate PA segmentations and images are obtained, and error predictions are highly statistically correlated to actual errors. To leverage error predictions, confidence processing created PA images above a specific confidence level., Comment: 31 pages, 8 figures

We describe a quantum algorithm for the Planted Noisy $k$XOR problem (also known as sparse Learning Parity with Noise) that achieves a nearly quartic ($4$th power) speedup over the best known classical algorithm while also only using logarithmically many qubits. Our work generalizes and simplifies prior work of Hastings, by building on his quantum algorithm for the Tensor Principal Component Analysis (PCA) problem. We achieve our quantum speedup using a general framework based on the Kikuchi Method (recovering the quartic speedup for Tensor PCA), and we anticipate it will yield similar speedups for further planted inference problems. These speedups rely on the fact that planted inference problems naturally instantiate the Guided Sparse Hamiltonian problem. Since the Planted Noisy $k$XOR problem has been used as a component of certain cryptographic constructions, our work suggests that some of these are susceptible to super-quadratic quantum attacks., Comment: 50 pages

The Cryogenic Underground Observatory for Rare Events (CUORE) is a detector array comprised by 988 5$\;$cm$\times$5$\;$cm$\times$5$\;$cm TeO$_2$ crystals held below 20 mK, primarily searching for neutrinoless double-beta decay in $^{130}$Te. Unprecedented in size amongst cryogenic calorimetric experiments, CUORE provides a promising setting for the study of exotic through-going particles. Using the first tonne-year of CUORE's exposure, we perform a search for hypothesized fractionally charged particles (FCPs), which are well-motivated by various Standard Model extensions and would have suppressed interactions with matter. No excess of FCP candidate tracks is observed over background, setting leading limits on the underground FCP flux with charges between $e/24-e/5$ at 90\% confidence level. Using the low background environment and segmented geometry of CUORE, we establish the sensitivity of tonne-scale sub-Kelvin detectors to diverse signatures of new physics., Comment: 7 pages, 5 figures

We present a search for neutrinoless double-beta ($0\nu\beta\beta$) decay of $^{136}$Xe using the full KamLAND-Zen 800 dataset with 745 kg of enriched xenon, corresponding to an exposure of $2.097$ ton yr of $^{136}$Xe. This updated search benefits from a more than twofold increase in exposure, recovery of photo-sensor gain, and reduced background from muon-induced spallation of xenon. Combining with the search in the previous KamLAND-Zen phase, we obtain a lower limit for the $0\nu\beta\beta$ decay half-life of $T_{1/2}^{0\nu} > 3.8 \times 10^{26}$ yr at 90% C.L., a factor of 1.7 improvement over the previous limit. The corresponding upper limits on the effective Majorana neutrino mass are in the range 28-122 meV using phenomenological nuclear matrix element calculations., Comment: arXiv admin note: text overlap with arXiv:2203.02139

Semantic and syntactic bootstrapping posit that children use their prior knowledge of one linguistic domain, say syntactic relations, to help later acquire another, such as the meanings of new words. Empirical results supporting both theories may tempt us to believe that these are different learning strategies, where one may precede the other. Here, we argue that they are instead both contingent on a more general learning strategy for language acquisition: joint learning. Using a series of neural visually-grounded grammar induction models, we demonstrate that both syntactic and semantic bootstrapping effects are strongest when syntax and semantics are learnt simultaneously. Joint learning results in better grammar induction, realistic lexical category learning, and better interpretations of novel sentence and verb meanings. Joint learning makes language acquisition easier for learners by mutually constraining the hypotheses spaces for both syntax and semantics. Studying the dynamics of joint inference over many input sources and modalities represents an important new direction for language modeling and learning research in both cognitive sciences and AI, as it may help us explain how language can be acquired in more constrained learning settings.

It has been claimed that within a language, morphologically irregular words are more likely to be phonotactically simple and morphologically regular words are more likely to be phonotactically complex. This inverse correlation has been demonstrated in English for a small sample of words, but has yet to be shown for a larger sample of languages. Furthermore, frequency and word length are known to influence both phonotactic complexity and morphological irregularity, and they may be confounding factors in this relationship. Therefore, we examine the relationships between all pairs of these four variables both to assess the robustness of previous findings using improved methodology and as a step towards understanding the underlying causal relationship. Using information-theoretic measures of phonotactic complexity and morphological irregularity (Pimentel et al., 2020; Wu et al., 2019) on 25 languages from UniMorph, we find that there is evidence of a positive relationship between morphological irregularity and phonotactic complexity within languages on average, although the direction varies within individual languages. We also find weak evidence of a negative relationship between word length and morphological irregularity that had not been previously identified, and that some existing findings about the relationships between these four variables are not as robust as previously thought., Comment: To appear in Proceedings of the Society for Computation in Linguistics 2024

We present the model we developed to reconstruct the CUORE radioactive background based on the analysis of an experimental exposure of 1038.4 kg yr. The data reconstruction relies on a simultaneous Bayesian fit applied to energy spectra over a broad energy range. The high granularity of the CUORE detector, together with the large exposure and extended stable operations, allow for an in-depth exploration of both spatial and time dependence of backgrounds. We achieve high sensitivity to both bulk and surface activities of the materials of the setup, detecting levels as low as 10 nBq kg$^{-1}$ and 0.1 nBq cm$^{-2}$, respectively. We compare the contamination levels we extract from the background model with prior radio-assay data, which informs future background risk mitigation strategies. The results of this background model play a crucial role in constructing the background budget for the CUPID experiment as it will exploit the same CUORE infrastructure.

The layered van der Waals material CrCl3 exhibits very strongly bound ligand field excitons that control optoelectronic applications and are connected with magnetic ordering by virtue of their d-orbital origin. Time-resolved photoluminescence of these exciton populations at room temperature shows that their relaxation is dominated by exciton-exciton annihilation and that the spontaneous decay lifetime is very long. These observations allow the rough quantification of the exciton annihilation rate constant and contextualization in light of a recent theory of universal scaling behavior of the annihilation process.

There is growing recognition among financial institutions, financial regulators and policy makers of the importance of addressing nature-related risks and opportunities. Evaluating and assessing nature-related risks for financial institutions is challenging due to the large volume of heterogeneous data available on nature and the complexity of investment value chains and the various components' relationship to nature. The dual problem of scaling data analytics and analysing complex systems can be addressed using Artificial Intelligence (AI). We address issues such as plugging existing data gaps with discovered data, data estimation under uncertainty, time series analysis and (near) real-time updates. This report presents potential AI solutions for models of two distinct use cases, the Brazil Beef Supply Use Case and the Water Utility Use Case. Our two use cases cover a broad perspective within sustainable finance. The Brazilian cattle farming use case is an example of greening finance - integrating nature-related considerations into mainstream financial decision-making to transition investments away from sectors with poor historical track records and unsustainable operations. The deployment of nature-based solutions in the UK water utility use case is an example of financing green - driving investment to nature-positive outcomes. The two use cases also cover different sectors, geographies, financial assets and AI modelling techniques, providing an overview on how AI could be applied to different challenges relating to nature's integration into finance. This report is primarily aimed at financial institutions but is also of interest to ESG data providers, TNFD, systems modellers, and, of course, AI practitioners., Comment: 67 pages, 10 figures, UKRI (NERC) Integrated Finance and Biodiversity for a Nature Positive Future Programme

The objective of this work is to evaluate multi-agent artificial intelligence methods when deployed on teams of unmanned surface vehicles (USV) in an adversarial environment. Autonomous agents were evaluated in real-world scenarios using the Aquaticus test-bed, which is a Capture-the-Flag (CTF) style competition involving teams of USV systems. Cooperative teaming algorithms of various foundations in behavior-based optimization and deep reinforcement learning (RL) were deployed on these USV systems in two versus two teams and tested against each other during a competition period in the fall of 2023. Deep reinforcement learning applied to USV agents was achieved via the Pyquaticus test bed, a lightweight gymnasium environment that allows simulated CTF training in a low-level environment. The results of the experiment demonstrate that rule-based cooperation for behavior-based agents outperformed those trained in Deep-reinforcement learning paradigms as implemented in these competitions. Further integration of the Pyquaticus gymnasium environment for RL with MOOS-IvP in terms of configuration and control schema will allow for more competitive CTF games in future studies. As the development of experimental deep RL methods continues, the authors expect that the competitive gap between behavior-based autonomy and deep RL will be reduced. As such, this report outlines the overall competition, methods, and results with an emphasis on future works such as reward shaping and sim-to-real methodologies and extending rule-based cooperation among agents to react to safety and security events in accordance with human experts intent/rules for executing safety and security processes., Comment: Accepted to the IEEE ICRA Workshop on Field Robotics 2024

We study pseudorandomness properties of permutations on $\{0,1\}^n$ computed by random circuits made from reversible $3$-bit gates (permutations on $\{0,1\}^3$). Our main result is that a random circuit of depth $n \cdot \tilde{O}(k^2)$, with each layer consisting of $\approx n/3$ random gates in a fixed nearest-neighbor architecture, yields almost $k$-wise independent permutations. The main technical component is showing that the Markov chain on $k$-tuples of $n$-bit strings induced by a single random $3$-bit nearest-neighbor gate has spectral gap at least $1/n \cdot \tilde{O}(k)$. This improves on the original work of Gowers [Gowers96], who showed a gap of $1/\mathrm{poly}(n,k)$ for one random gate (with non-neighboring inputs); and, on subsequent work [HMMR05,BH08] improving the gap to $\Omega(1/n^2k)$ in the same setting. From the perspective of cryptography, our result can be seen as a particularly simple/practical block cipher construction that gives provable statistical security against attackers with access to $k$~input-output pairs within few rounds. We also show that the Luby--Rackoff construction of pseudorandom permutations from pseudorandom functions can be implemented with reversible circuits. From this, we make progress on the complexity of the Minimum Reversible Circuit Size Problem (MRCSP), showing that block ciphers of fixed polynomial size are computationally secure against arbitrary polynomial-time adversaries, assuming the existence of one-way functions (OWFs)., Comment: v2: added references and comparison to subsequent work, removed claim in previous Section 7.3 with error in proof

Preceding a core-collapse supernova, various processes produce an increasing amount of neutrinos of all flavors characterized by mounting energies from the interior of massive stars. Among them, the electron antineutrinos are potentially detectable by terrestrial neutrino experiments such as KamLAND and Super-Kamiokande via inverse beta decay interactions. Once these pre-supernova neutrinos are observed, an early warning of the upcoming core-collapse supernova can be provided. In light of this, KamLAND and Super-Kamiokande, both located in the Kamioka mine in Japan, have been monitoring pre-supernova neutrinos since 2015 and 2021, respectively. Recently, we performed a joint study between KamLAND and Super-Kamiokande on pre-supernova neutrino detection. A pre-supernova alert system combining the KamLAND detector and the Super-Kamiokande detector was developed and put into operation, which can provide a supernova alert to the astrophysics community. Fully leveraging the complementary properties of these two detectors, the combined alert is expected to resolve a pre-supernova neutrino signal from a 15 M$_{\odot}$ star within 510 pc of the Earth, at a significance level corresponding to a false alarm rate of no more than 1 per century. For a Betelgeuse-like model with optimistic parameters, it can provide early warnings up to 12 hours in advance., Comment: Resubmitted to ApJ. 22 pages, 16 figures, for more information about the combined pre-supernova alert system, see https://www.lowbg.org/presnalarm/

We present a novel method for quantifying the microscopic structure of brain tissue. It is based on the automated recognition of interpretable features obtained by analyzing the shapes of cells. This contrasts with prevailing methods of brain anatomical analysis in two ways. First, contemporary methods use gray-scale values derived from smoothed version of the anatomical images, which dissipated valuable information from the texture of the images. Second, contemporary analysis uses the output of black-box Convolutional Neural Networks, while our system makes decisions based on interpretable features obtained by analyzing the shapes of individual cells. An important benefit of this open-box approach is that the anatomist can understand and correct the decisions made by the computer. Our proposed system can accurately localize and identify existing brain structures. This can be used to align and coregistar brains and will facilitate connectomic studies for reverse engineering of brain circuitry.

The study of brain differences across Eastern and Western populations provides vital insights for understanding potential cultural and genetic influences on cognition and mental health. Diffusion MRI (dMRI) tractography is an important tool in assessing white matter (WM) connectivity and brain tissue microstructure across different populations. However, a comprehensive investigation into WM fiber tracts between Eastern and Western populations is challenged due to the lack of a cross-population WM atlas and the large site-specific variability of dMRI data. This study presents a dMRI tractography atlas, namely the East-West WM Atlas, for concurrent WM mapping between Eastern and Western populations and creates a large, harmonized dMRI dataset (n=306) based on the Human Connectome Project and the Chinese Human Connectome Project. The curated WM atlas, as well as subject-specific data including the harmonized dMRI data, the whole brain tractography data, and parcellated WM fiber tracts and their diffusion measures, are publicly released. This resource is a valuable addition to facilitating the exploration of brain commonalities and differences across diverse cultural backgrounds.

The matter-antimatter asymmetry underlines the incompleteness of the current understanding of particle physics. Neutrinoless double-beta ($0\nu \beta\beta$) decay may help explain this asymmetry, while unveiling the Majorana nature of the neutrino. The CUORE experiment searches for $0\nu \beta\beta$ decay of $^{130}$Te using a tonne-scale cryogenic calorimeter operated at milli-kelvin temperatures. We report no evidence for $0\nu \beta\beta$ decay and place a lower limit on the half-life of T$_{1/2}$ $>$ 3.8 $\times$ 10$^{25}$ years (90% C.I.) with over 2 tonne$\cdot$year TeO$_2$ exposure. The tools and techniques developed for this result and the 5 year stable operation of nearly 1000 detectors demonstrate the infrastructure for a next-generation experiment capable of searching for $0\nu \beta\beta$ decay across multiple isotopes.

Shape plays an important role in computer graphics, offering informative features to convey an object's morphology and functionality. Shape analysis in brain imaging can help interpret structural and functionality correlations of the human brain. In this work, we investigate the shape of the brain's 3D white matter connections and its potential predictive relationship to human cognitive function. We reconstruct brain connections as sequences of 3D points using diffusion magnetic resonance imaging (dMRI) tractography. To describe each connection, we extract 12 shape descriptors in addition to traditional dMRI connectivity and tissue microstructure features. We introduce a novel framework, Shape--fused Fiber Cluster Transformer (SFFormer), that leverages a multi-head cross-attention feature fusion module to predict subject-specific language performance based on dMRI tractography. We assess the performance of the method on a large dataset including 1065 healthy young adults. The results demonstrate that both the transformer-based SFFormer model and its inter/intra feature fusion with shape, microstructure, and connectivity are informative, and together, they improve the prediction of subject-specific language performance scores. Overall, our results indicate that the shape of the brain's connections is predictive of human language function., Comment: 2 figures, 11 pages

Languages may encode similar meanings using different sentence structures. This makes it a challenge to provide a single set of formal rules that can derive meanings from sentences in many languages at once. To overcome the challenge, we can take advantage of language-general connections between meaning and syntax, and build on cross-linguistically parallel syntactic structures. We introduce UD Type Calculus, a compositional, principled, and language-independent system of semantic types and logical forms for lexical items which builds on a widely-used language-general dependency syntax framework. We explain the essential features of UD Type Calculus, which all involve giving dependency relations denotations just like those of words. These allow UD-TC to derive correct meanings for sentences with a wide range of syntactic structures by making use of dependency labels. Finally, we present evaluation results on a large existing corpus of sentences and their logical forms, showing that UD-TC can produce meanings comparable with our baseline., Comment: 10 pages, 6 figures, 1 table. For related code, see https://github.com/McGill-NLP/ud-to-meaning

Language models (LMs) may appear insensitive to word order changes in natural language understanding (NLU) tasks. In this paper, we propose that linguistic redundancy can explain this phenomenon, whereby word order and other linguistic cues such as case markers provide overlapping and thus redundant information. Our hypothesis is that models exhibit insensitivity to word order when the order provides redundant information, and the degree of insensitivity varies across tasks. We quantify how informative word order is using mutual information (MI) between unscrambled and scrambled sentences. Our results show the effect that the less informative word order is, the more consistent the model's predictions are between unscrambled and scrambled sentences. We also find that the effect varies across tasks: for some tasks, like SST-2, LMs' prediction is almost always consistent with the original one even if the Pointwise-MI (PMI) changes, while for others, like RTE, the consistency is near random when the PMI gets lower, i.e., word order is really important., Comment: 5 pages

Simultaneous localisation and mapping (SLAM) algorithms are commonly used in robotic systems for learning maps of novel environments. Brains also appear to learn maps, but the mechanisms are not known and it is unclear how to infer these maps from neural activity data. We present BrainSLAM; a method for performing SLAM using only population activity (local field potential, LFP) data simultaneously recorded from three brain regions in rats: hippocampus, prefrontal cortex, and parietal cortex. This system uses a convolutional neural network (CNN) to decode velocity and familiarity information from wavelet scalograms of neural local field potential data recorded from rats as they navigate a 2D maze. The CNN's output drives a RatSLAM-inspired architecture, powering an attractor network which performs path integration plus a separate system which performs `loop closure' (detecting previously visited locations and correcting map aliasing errors). Together, these three components can construct faithful representations of the environment while simultaneously tracking the animal's location. This is the first demonstration of inference of a spatial map from brain recordings. Our findings expand SLAM to a new modality, enabling a new method of mapping environments and facilitating a better understanding of the role of cognitive maps in navigation and decision making., Comment: Accepted to the 23rd International Conference on Autonomous Agents and Multiagent Systems. 2024

Ternary nitrides are of growing technological importance, with applications as semiconductors, catalysts, and magnetic materials; however, new synthetic tools are needed to advance materials discovery efforts. Here, we show that Zn$_3$WN$_4$ can be synthesized via metathesis reactions between Li$_6$WN$_4$ and Zn$X_2$ ($X$ = Br, Cl, F). In situ synchrotron powder X-ray diffraction and differential scanning calorimetry show that the reaction onset is correlated with the Zn$X_2$ melting point and that product purity is inversely correlated with the reaction's exothermicity. High resolution synchrotron powder X-ray diffraction measurements show that this bulk synthesis produces a structure with substantial cation ordering, as opposed to the disordered structure initially discovered via thin film sputtering. Diffuse reflectance spectroscopy reveals that Zn$_3$WN$_4$ powders exhibit two optical absorption onsets at 2.5 eV and 4.0 eV, indicating wide-bandgap semiconducting behavior and suggesting a small amount of structural disorder. We hypothesize that this synthesis strategy is generalizable because many potential Li-$M$-N precursors (where $M$ is a metal) are available for synthesizing new ternary nitride materials. This work introduces a promising synthesis strategy that will accelerate the discovery of novel functional ternary nitrides and other currently inaccessible materials.