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The national forecasting competition WxChallenge, brainchild of Brad Illston at the University of Oklahoma in 2005, has become a cherished institution played across the United States each year. Participants include students, faculty, alumni, and industry professionals. However, forecasts are given as scalar values without expression of uncertainty, probabilities being a keystone of meteorological forecasting today, and previous attempts to add probabilistic elements to WxChallenge have failed partly due to challenges in making probability forecasting accessible to all, and inability to combine scores with different units while also appropriately rewarding forecasts using proper scoring rules. Much of the competition's maintenance relies on dedicated volunteers, highlighting need for more automation. Hence I propose three new features: (1) automated forecast problems based on morning ensemble guidance, forming prediction baselines, thresholds over which the players demonstrate skill in their later forecast; (2) a spread betting game, where the players allocate 100 confidence credits to the over-under for exceeding a percentile (e.g., 50pc) threshold of a variable (e.g., maximum temperature) derived from the ensemble baseline; and (3) a game where players distribute 100 confidence credits across bins of a continuous variable (e.g., accumulated precipitation) approximating a probability mass function. Forecasts are evaluated using Shannon information gained over the baseline forecast, yielding additive units of bits that allow score combinations of different variables and units. Information gain parallels the Brier Score and is likewise a sound measure of skill due its punishment of hedging. This proposal objective is to augment WxChallenge with two new probabilistic games that are accessible, scientifically sound, enjoyable, and optional., Comment: Manuscript is 10 pages and 2 figures. Originally submitted and rejected from Bulletin of American Meteorological Society. Future resubmission is expected

The Great Salt Lake (Utah, USA) is reducing in size, which raises several ecological concerns, including the effect of an increasing area of dry playa exposed by the retreating lake. This study focuses solely on concerns about the toxicity of metals in the dust blowing off the playa. Although considerable efforts have been made to understand aeolian dust in urban areas along the Wasatch Front, located just east and south of the Great Salt Lake, there is still a need to consolidate existing research and to conduct a compositional analysis of the dust found in these urban areas. We investigated the dust reaching urban monitoring sites around the Great Salt Lake that are managed by the Utah Division of Air Quality. By analyzing historical data, we found that the decrease in the Great Salt Lake's surface area has not led to a statistically significant increase in dust events in urban areas. Windrose plots align with prior research, indicating that heightened dust levels in urban areas coincide with winds originating from the south or west, passing over identified playas and deserts such as the Milford Flats, Sevier Dry Lake, Tule Dry Lake, Great Salt Lake Desert, Dugway Proving Grounds, and the West Desert of Utah. Metallic compositional analysis of urban dust was used to evaluate potential health risks associated with the dust using the hazard quotient, air regional screening levels, and cancer risk methods. This analysis revealed no significant increase in concentrations of toxic metals. However, this is not to preclude a risk of dust-related health concerns, especially due to pre-existing arsenic and lead levels.

Generative Artificial Intelligence (GenAI, generative AI) has rapidly become available as a tool in scientific research. To explore the use of generative AI in science, we conduct an empirical analysis using OpenAlex. Analyzing GenAI publications and other AI publications from 2017 to 2023, we profile growth patterns, the diffusion of GenAI publications across fields of study, and the geographical spread of scientific research on generative AI. We also investigate team size and international collaborations to explore whether GenAI, as an emerging scientific research area, shows different collaboration patterns compared to other AI technologies. The results indicate that generative AI has experienced rapid growth and increasing presence in scientific publications. The use of GenAI now extends beyond computer science to other scientific research domains. Over the study period, U.S. researchers contributed nearly two-fifths of global GenAI publications. The U.S. is followed by China, with several small and medium-sized advanced economies demonstrating relatively high levels of GenAI deployment in their research publications. Although scientific research overall is becoming increasingly specialized and collaborative, our results suggest that GenAI research groups tend to have slightly smaller team sizes than found in other AI fields. Furthermore, notwithstanding recent geopolitical tensions, GenAI research continues to exhibit levels of international collaboration comparable to other AI technologies., Comment: 26 pages, 4 tables, 1 figures, 1 appendix figure

Reinforcement learning (RL) algorithms for continuous control tasks require accurate sampling-based action selection. Many tasks, such as robotic manipulation, contain inherent problem symmetries. However, correctly incorporating symmetry into sampling-based approaches remains a challenge. This work addresses the challenge of preserving symmetry in sampling-based planning and control, a key component for enhancing decision-making efficiency in RL. We introduce an action sampling approach that enforces the desired symmetry. We apply our proposed method to a coordinate regression problem and show that the symmetry aware sampling method drastically outperforms the naive sampling approach. We furthermore develop a general framework for sampling-based model-based planning with Model Predictive Path Integral (MPPI). We compare our MPPI approach with standard sampling methods on several continuous control tasks. Empirical demonstrations across multiple continuous control environments validate the effectiveness of our approach, showcasing the importance of symmetry preservation in sampling-based action selection., Comment: Published at International Workshop on the Algorithmic Foundations of Robotics (WAFR) 2024. Website: http://lfzhao.com/EquivSampling

Learning navigation capabilities in different environments has long been one of the major challenges in decision-making. In this work, we focus on zero-shot navigation ability using given abstract $2$-D top-down maps. Like human navigation by reading a paper map, the agent reads the map as an image when navigating in a novel layout, after learning to navigate on a set of training maps. We propose a model-based reinforcement learning approach for this multi-task learning problem, where it jointly learns a hypermodel that takes top-down maps as input and predicts the weights of the transition network. We use the DeepMind Lab environment and customize layouts using generated maps. Our method can adapt better to novel environments in zero-shot and is more robust to noise., Comment: Published at Reinforcement Learning Conference (RLC) 2024. Website: http://lfzhao.com/map-nav/

This letter presents the measurement of the energy-dependent neutrino-nucleon cross section in tungsten and the differential flux of muon neutrinos and anti-neutrinos. The analysis is performed using proton-proton collision data at a center-of-mass energy of $13.6 \, {\rm TeV}$ and corresponding to an integrated luminosity of $(65.6 \pm 1.4) \, \mathrm{fb^{-1}}$. Using the active electronic components of the FASER detector, $338.1 \pm 21.0$ charged current muon neutrino interaction events are identified, with backgrounds from other processes subtracted. We unfold the neutrino events into a fiducial volume corresponding to the sensitive regions of the FASER detector and interpret the results in two ways: We use the expected neutrino flux to measure the cross section, and we use the predicted cross section to measure the neutrino flux. Both results are presented in six bins of neutrino energy, achieving the first differential measurement in the TeV range. The observed distributions align with Standard Model predictions. Using this differential data, we extract the contributions of neutrinos from pion and kaon decays.

We consider a finite group $G$ acting on a manifold $M$. For any equivariant Morse function, which is a generic condition, there does not always exist an equivariant metric $g$ on $M$ such that the pair $(f,g)$ is Morse-Smale. Here, the pair $(f,g)$ is called Morse-Smale if the descending and ascending manifolds intersect transversely. The best possible metrics $g$ are those that make the pair $(f,g)$ stably Morse-Smale. A diffeomorphism $\phi: M \to M$ is a reflection, if $\phi^2 = \operatorname{id}$ and the fixed point set of $\phi$ forms a codimension-one submanifold (with $M \setminus M^{\operatorname{fix}}$ not necessarily disconnected). In this note, we focus on the special case where the group $G = \{\operatorname{id}, \phi\}$. We show that the condition of being stably Morse-Smale is generic for metrics $g$. Given a stably Morse-Smale pair, we introduce a canonical equivariant Thom-Smale-Witten complex by counting certain broken trajectories. This has applications to the case when we have a manifold with boundary and when the Morse function has critical points on the boundary. We provide an alternative definition of the Thom-Smale-Witten complexes, which are quasi-isomorphic to those defined by Kronheimer and Mrowka. We also explore the case when $G$ is generated by multiple reflections. As an example, we compute the Thom-Smale-Witten complex of an upright higher-genus surface by counting broken trajectories.

With recent computer vision techniques and user-generated content, we can augment the physical world with metadata that describes attributes, such as names, geo-locations, and visual features of physical objects. To assess the benefits of these potentially ubiquitous labels for foreign vocabulary learning, we built a proof-of-concept system that displays bilingual text and sound labels on physical objects outdoors using augmented reality. Established tools for language learning have focused on effective content delivery methods such as books and flashcards. However, recent research and consumer learning tools have begun to focus on how learning can become more mobile, ubiquitous, and desirable. To test whether our system supports vocabulary learning, we conducted a preliminary between-subjects (N=44) study. Our results indicate that participants preferred learning with virtual labels on real-world objects outdoors over learning with flashcards. Our findings motivate further investigation into mobile AR-based learning systems in outdoor settings.

We investigate deformations of skew group algebras that arise from a finite cyclic group acting on a polynomial ring in positive characteristic, where characteristic divides the order of the group. We allow deformations which deform both the group action and the vector space multiplication. We fully characterize the Poincare-Birkhoff-Witt deformations which arise in this setting from multiple perspectives: a necessary and sufficient condition list, a practical road map from which one can generate examples corresponding to any choice of group algebra element, an explicit formula, and a combinatorial analysis of the class of algebras.

Equivariant neural networks have shown great success in reinforcement learning, improving sample efficiency and generalization when there is symmetry in the task. However, in many problems, only approximate symmetry is present, which makes imposing exact symmetry inappropriate. Recently, approximately equivariant networks have been proposed for supervised classification and modeling physical systems. In this work, we develop approximately equivariant algorithms in reinforcement learning (RL). We define approximately equivariant MDPs and theoretically characterize the effect of approximate equivariance on the optimal Q function. We propose novel RL architectures using relaxed group convolutions and experiment on several continuous control domains and stock trading with real financial data. Our results demonstrate that approximate equivariance matches prior work when exact symmetries are present, and outperforms them when domains exhibit approximate symmetry. As an added byproduct of these techniques, we observe increased robustness to noise at test time., Comment: Preprint

Quantifying uncertainty in networks is an important step in modelling relationships and interactions between entities. We consider the challenge of bootstrapping an inhomogeneous random graph when only a single observation of the network is made and the underlying data generating function is unknown. We utilise an exchangeable network test that can empirically validate bootstrap samples generated by any method, by testing if the observed and bootstrapped networks are statistically distinguishable. We find that existing methods fail this test. To address this, we propose a principled, novel, distribution-free network bootstrap using k-nearest neighbour smoothing, that can regularly pass this exchangeable network test in both synthetic and real-data scenarios. We demonstrate the utility of this work in combination with the popular data visualisation method t-SNE, where uncertainty estimates from bootstrapping are used to explain whether visible structures represent real statistically sound structures.

Communicating forecast uncertainty effectively is a persistent challenge in predictive endeavours such as weather forecasting. This paper explores the application of possibility theory as a complementary approach to traditional probability in risk communication. Unlike probability, possibility theory allows for the representation of uncertain events as ranges of potential, distinguished by degrees of plausibility possibility and certainty necessity. Using a simplified fuzzy-logic inference system, we generate possibility forecasts of ozone-concentration forecasts from meteorological inputs. Observations are pre-processed as degrees of an adjective, e.g., 1 m/s wind speed may belong to the adjective "calm" at degree 0.8 (perhaps represented with an adverb as "substantially"). Aggregation of all rule activations yields a possibility distribution over the output range. As possibility is an upper bound of probability, possibilities provides most value for risk-averse stakeholders sensitive to the event of interest, especially near the event's predictability horizon when there is most uncertainty to remove. By setting the forecast challenge as the possibility of an event, we effectively extend the predictability horizon: trading some specificity for detection of fainter signals of the event's future occurrence. Possibility theory appreciates uncertainty's dual nature: inherent randomness (aleatoric) and knowledge deficiency (epistemic). While the unfamiliar nature of the theory requires more accessible language before operational use and public communication, possibility offers substantial practical benefits for assessment of uncertainty at the edge of predictability limits for vulnerable users., Comment: 9 Figures, 15 Pages, unsubmitted as of 28 Oct 2024

Reinforcement Learning (RL) has the potential to enable robots to learn from their own actions in the real world. Unfortunately, RL can be prohibitively expensive, in terms of on-robot runtime, due to inefficient exploration when learning from a sparse reward signal. Designing dense reward functions is labour-intensive and requires domain expertise. In our work, we propose GCR (Goal-Contrastive Rewards), a dense reward function learning method that can be trained on passive video demonstrations. By using videos without actions, our method is easier to scale, as we can use arbitrary videos. GCR combines two loss functions, an implicit value loss function that models how the reward increases when traversing a successful trajectory, and a goal-contrastive loss that discriminates between successful and failed trajectories. We perform experiments in simulated manipulation environments across RoboMimic and MimicGen tasks, as well as in the real world using a Franka arm and a Spot quadruped. We find that GCR leads to a more-sample efficient RL, enabling model-free RL to solve about twice as many tasks as our baseline reward learning methods. We also demonstrate positive cross-embodiment transfer from videos of people and of other robots performing a task. Appendix: \url{https://tinyurl.com/gcr-appendix-2}.

We present results from data acquired by the SENSEI experiment at SNOLAB after a major upgrade in May 2023, which includes deploying 16 new sensors and replacing the copper trays that house the CCDs with a new light-tight design. We observe a single-electron event rate of $(1.39 \pm 0.11) \times 10^{-5}$ e$^-$/pix/day, corresponding to $(39.8 \pm 3.1)$ e$^-$/gram/day. This is an order-of-magnitude improvement compared to the previous lowest single-electron rate in a silicon detector and the lowest for any photon detector in the near-infrared-ultraviolet range. We use these data to obtain a 90% confidence level upper bound of $1.53 \times 10^{-5}$ e$^-$/pix/day and to set constraints on sub-GeV dark matter candidates that produce single-electron events. We hypothesize that the data taken at SNOLAB in the previous run, with an older tray design for the sensors, contained a larger rate of single-electron events due to light leaks. We test this hypothesis using data from the SENSEI detector located in the MINOS cavern at Fermilab.

We analyze near-infrared integral field spectropolarimetry of the AB Aurigae protoplanetary disk and protoplanet (AB Aur b), obtained with SCExAO/CHARIS in 22 wavelength channels covering the J, H, and K passbands ($\lambda_{\rm o}$ = 1.1--2.4 $\mu m$) over angular separations of $\rho$ $\approx$ 0.13" to 1.1" ($\sim$20--175 au). Our images resolve spiral structures in the disk in each CHARIS channel. At the longest wavelengths, the data may reveal an extension of the western spiral seen in previous polarimetric data at $\rho$ $<$ 0.3" out to larger distances clockwise from the protoplanet AB Aur b, coincident with the ALMA-detected $CO$ gas spiral. While AB Aur b is detectable in complementary total intensity data, it is a non-detection in polarized light at $\lambda$ $>$ 1.3 $\mu $m. While the observed disk color is extremely red across $JHK$, the disk has a blue intrinsic scattering color consistent with small dust grains. The disk's polarization spectrum is redder than AB Aur b's total intensity spectrum. The polarization fraction peaks at $\sim$ 0.6 along the major disk axis. Radiative transfer modeling of the CHARIS data shows that small, porous dust grains with a porosity of $p$ = 0.6--0.8 better reproduce the scattered-light appearance of the disk than more compact spheres ($p$ = 0.3), especially the polarization fraction. This work demonstrates the utility of integral field spectropolarimetry to characterize structures in protoplanetary disks and elucidate the properties of the disks' dust., Comment: 23 pages, 17 Figures, accepted to AAS Journals

The first FASER search for a light, long-lived particle decaying into a pair of photons is reported. The search uses LHC proton-proton collision data at $\sqrt{s}=13.6~\text{TeV}$ collected in 2022 and 2023, corresponding to an integrated luminosity of $57.7\text{fb}^{-1}$. A model with axion-like particles (ALPs) dominantly coupled to weak gauge bosons is the primary target. Signal events are characterised by high-energy deposits in the electromagnetic calorimeter and no signal in the veto scintillators. One event is observed, compared to a background expectation of $0.44 \pm 0.39$ events, which is entirely dominated by neutrino interactions. World-leading constraints on ALPs are obtained for masses up to $300~\text{MeV}$ and couplings to the Standard Model W gauge boson, $g_{aWW}$, around $10^{-4}$ GeV$^{-1}$, testing a previously unexplored region of parameter space. Other new particle models that lead to the same experimental signature, including ALPs coupled to gluons or photons, U(1)$_B$ gauge bosons, up-philic scalars, and a Type-I two-Higgs doublet model, are also considered for interpretation, and new constraints on previously viable parameter space are presented in this paper., Comment: 37 pages, 22 figures

We introduce LLMD, a large language model designed to analyze a patient's medical history based on their medical records. Along with domain knowledge, LLMD is trained on a large corpus of records collected over time and across facilities, as well as tasks and labels that make nuanced connections among them. This approach is critical to an accurate picture of patient health, and has distinctive advantages over models trained on knowledge alone, unlabeled records, structured EHR data, or records from a single health system. The recipe for LLMD continues pretraining a foundational model on both domain knowledge and the contents of millions of records. These span an average of 10 years of care and as many as 140 care sites per patient. LLMD is then instruction fine-tuned on structuring and abstraction tasks. The former jointly identify and normalize document metadata, provenance information, clinical named-entities, and ontology mappings, while the latter roll these into higher-level representations, such a continuous era of time a patient was on a medication. LLMD is deployed within a layered validation system that includes continual random audits and review by experts, e.g. based on uncertainty, disease-specific rules, or use-case. LLMD exhibits large gains over both more-powerful generalized models and domain-specific models. On medical knowledge benchmarks, LLMD-8B achieves state of the art accuracy on PubMedQA text responses, besting orders-of-magnitude larger models. On production tasks, we show that LLMD significantly outperforms all other models evaluated, and among alternatives, large general purpose LLMs like GPT-4o are more accurate than models emphasizing medical knowledge. We find strong evidence that accuracy on today's medical benchmarks is not the most significant factor when analyzing real-world patient data, an insight with implications for future medical LLMs.'

We introduce a operation on categories enriched in filtered spaces, whose effect is to turn categories of $E_1$-pages into categories of $E_2$-pages. This allows us to give a homotopical versions of several results that were previously implemented using $E_2$-model structures or more sophisticated machinery in higher algebra. We find that we can recover the homotopy theory of spaces from this page-turning operation on the homotopy theory of CW-complexes and filtration-shifting maps, a version of the cellular approximation theorem. In the category of filtered spectra, we show that this implements the procedure on filtered spectra sending the homotopy exact couple to its associated derived couple. Finally, we recover Pstragowski's category of synthetic spectra from applying this page-turning operation to the category of filtered modules over a spectral version of the Rees ring., Comment: 48 pages. Comments welcome

We study the task of locating a user in a mapped indoor environment using natural language queries and images from the environment. Building on recent pretrained vision-language models, we learn a similarity score between text descriptions and images of locations in the environment. This score allows us to identify locations that best match the language query, estimating the user's location. Our approach is capable of localizing on environments, text, and images that were not seen during training. One model, finetuned CLIP, outperformed humans in our evaluation., Comment: RO-MAN 2023

Mixed Reality (MR) platforms enable users to interact with three-dimensional holographic instructions during the assembly and fabrication of highly custom and parametric architectural constructions without the necessity of two-dimensional drawings. Previous MR fabrication projects have primarily relied on digital menus and custom buttons as the interface for user interaction with the MR environment. Despite this approach being widely adopted, it is limited in its ability to allow for direct human interaction with physical objects to modify fabrication instructions within the MR environment. This research integrates user interactions with physical objects through real-time gesture recognition as input to modify, update or generate new digital information enabling reciprocal stimuli between the physical and the virtual environment. Consequently, the digital environment is generative of the user's provided interaction with physical objects to allow seamless feedback in the fabrication process. This research investigates gesture recognition for feedback-based MR workflows for robotic fabrication, human assembly, and quality control in the construction of the UnLog Tower., Comment: 16 pages, 16 figures. Published in the Proceedings of the International Conference on Computational Design and Robotic Fabrication (CDRF) 2023

Classical point process models, such as the epidemic-type aftershock sequence (ETAS) model, have been widely used for forecasting the event times and locations of earthquakes for decades. Recent advances have led to Neural Point Processes (NPPs), which promise greater flexibility and improvements over classical models. However, the currently-used benchmark dataset for NPPs does not represent an up-to-date challenge in the seismological community since it lacks a key earthquake sequence from the region and improperly splits training and testing data. Furthermore, initial earthquake forecast benchmarking lacks a comparison to state-of-the-art earthquake forecasting models typically used by the seismological community. To address these gaps, we introduce EarthquakeNPP: a collection of benchmark datasets to facilitate testing of NPPs on earthquake data, accompanied by a credible implementation of the ETAS model. The datasets cover a range of small to large target regions within California, dating from 1971 to 2021, and include different methodologies for dataset generation. In a benchmarking experiment, we compare three spatio-temporal NPPs against ETAS and find that none outperform ETAS in either spatial or temporal log-likelihood. These results indicate that current NPP implementations are not yet suitable for practical earthquake forecasting. However, EarthquakeNPP will serve as a platform for collaboration between the seismology and machine learning communities with the goal of improving earthquake predictability.

Fluid flows are intrinsically characterized via the topology and dynamics of underlying vortex lines. Turbulence in common fluids like water and air, mathematically described by the incompressible Navier-Stokes equations (INSE), engenders spontaneous self-stretching and twisting of vortex lines, generating a complex hierarchy of structures. While the INSE are routinely used to describe turbulence, their regularity remains unproven; the implicit assumption being that the self-stretching is ultimately regularized by viscosity, preventing any singularities. Here, we uncover an inviscid regularizing mechanism stemming from self-stretching itself, by analyzing the flow topology as perceived by an observer aligned with the vorticity vector undergoing amplification. While, initially, vorticity amplification occurs via increasing twisting of vortex lines, a regularizing anti-twist spontaneously emerges to prevent unbounded growth. By isolating a vortex, we additionally demonstrate the genericity of this self-regularizing anti-twist. Our work, directly linking dynamics of vortices to turbulence statistics, reveals how the Navier-Stokes dynamics avoids the development of singularities even without the aid of viscosity., Comment: 12 pages, 4 figures

High-performance programmable silicon photonic circuits are considered to be a critical part of next generation architectures for optical processing, photonic quantum circuits and neural networks. Low-loss optical phase change materials (PCMs) offer a promising route towards non-volatile free-form control of light. Here, we exploit direct-write digital patterning of waveguides using layers of the PCM Sb$_2$Se$_3$ with a thickness of up to 100 nm, demonstrating the ability to strongly increase the effect per pixel compared to previous implementations where much thinner PCM layers were used. We exploit the excellent refractive index matching between Sb$_2$Se$_3$ and silicon to achieve a low-loss hybrid platform for programmable photonics. A five-fold reduction in modulation length of a Mach-Zehnder interferometer is achieved compared to previous work using thin-film Sb$_2$Se$_3$ devices, decreased to 5 $\mu$m in this work. Application of the thicker PCM layers in direct-write digital programming of a multimode interferometer (MMI) shows a three-fold reduction of the number of programmed pixels to below 10 pixels per device. The demonstrated scaling of performance with PCM layer thickness is important for establishing the optimum working range for hybrid silicon-PCM devices and holds promise for achieving ultracompact programmable photonic circuits., Comment: 24 pages, 5 figures

We describe the motivation, design, and early results for our 42-night, 125 star Subaru/SCExAO direct imaging survey for planets around accelerating stars. Unlike prior large surveys, ours focuses only on stars showing evidence for an astrometric acceleration plausibly due to the dynamical pull of an unseen planet or brown dwarf. Our program is motivated by results from a recent pilot program that found the first planet jointly discovered from direct imaging and astrometry and resulted in a planet and brown dwarf discovery rate substantially higher than previous unbiased surveys like GPIES. The first preliminary results from our program reveal multiple new companions; discovered planets and brown dwarfs can be further characterized with follow-up data, including higher-resolution spectra. Finally, we describe the critical role this program plays in supporting the Roman Space Telescope Coronagraphic Instrument, providing a currently-missing list of targets suitable for the CGI technological demonstration without which the CGI tech demo risks failure., Comment: 13 pages, 7 figures; Proc. SPIE in press

In this paper, we develop methods for calculating equivariant homology from equivariant Morse functions on a closed manifold with the action of a finite group. We show how to alter $G$-equivariant Morse functions to a stable one, where the descending manifold from a critical point $p$ has the same stabilizer group as $p$, giving a better-behaved cell structure on $M$. For an equivariant, stable Morse function, we show that a generic equivariant metric satisfies the Morse--Smale condition. In the process, we give a proof that a generic equivariant function is Morse, and that equivariant, stable Morse functions form a dense subset in the $C^0$-topology within the space of all equivariant functions. Finally, we give an expository account of equivariant homology and cohomology theories, as well as their interaction with Morse theory. We show that any equivariant Morse function gives a filtration of $M$ that induces a Morse spectral sequence, computing the equivariant homology of $M$ from information about how the stabilizer group of a critical point acts on its tangent space. In the case of a stable Morse function, we show that this can be further reduced to a Morse chain complex., Comment: 22 pages

Sparse autoencoders (SAEs) are a promising approach to interpreting the internal representations of transformer language models. However, SAEs are usually trained separately on each transformer layer, making it difficult to use them to study how information flows across layers. To solve this problem, we introduce the multi-layer SAE (MLSAE): a single SAE trained on the residual stream activation vectors from every transformer layer. Given that the residual stream is understood to preserve information across layers, we expected MLSAE latents to `switch on' at a token position and remain active at later layers. Interestingly, we find that individual latents are often active at a single layer for a given token or prompt, but this layer may differ for different tokens or prompts. We quantify these phenomena by defining a distribution over layers and considering its variance. We find that the variance of the distributions of latent activations over layers is about two orders of magnitude greater when aggregating over tokens compared with a single token. For larger underlying models, the degree to which latents are active at multiple layers increases, which is consistent with the fact that the residual stream activation vectors at adjacent layers become more similar. Finally, we relax the assumption that the residual stream basis is the same at every layer by applying pre-trained tuned-lens transformations, but our findings remain qualitatively similar. Our results represent a new approach to understanding how representations change as they flow through transformers. We release our code to train and analyze MLSAEs at https://github.com/tim-lawson/mlsae., Comment: 34 pages, 26 figures

In randomized trials, the per-protocol effect, that is, the effect of being assigned a treatment strategy and receiving treatment according to the assigned strategy, is sometimes thought to reflect the effect of the treatment strategy itself, without intervention on assignment. Here, we argue by example that this is not necessarily the case. We examine a causal structure for a randomized trial where these two causal estimands -- the per-protocol effect and the effect of the treatment strategy -- are not equal, and where their corresponding identifying observed data functionals are not the same, but both require information on assignment for identification. Our example highlights the conceptual difference between the per-protocol effect and the effect of the treatment strategy itself, the conditions under which the observed data functionals for these estimands are equal, and suggests that in some cases their identification requires information on assignment, even when assignment is randomized. An implication of these findings is that in observational analyses that aim to emulate a target randomized trial in which an analog of assignment is well-defined, the effect of the treatment strategy is not necessarily an observational analog of the per-protocol effect. Furthermore, either of these effects may be unidentifiable without information on treatment assignment, unless one makes additional assumptions; informally, that assignment does not affect the outcome except through treatment (i.e., an exclusion-restriction assumption), and that assignment is not a confounder of the treatment outcome association conditional on other variables in the analysis.

We present Subaru/SCExAO + CHARIS broadband (JHK) integral field spectroscopy of HD 34700 A in polarized light. CHARIS has the unique ability to obtain polarized integral field images at 22 wavelength channels in broadband, as the incoming light is first split into different polarization states before passing though the lenslet array. We recover the transition disk around HD 34700 A in multiband polarized light in our data. We combine our polarized intensity data with previous total intensity data to examine the scattering profiles, scattering phase functions and polarized fraction of the disk at multiple wavelengths. We also carry out 3D Monte Carlo radiative transfer simulations of the disk using MCFOST, and make qualitative comparisons between our models and data to constrain dust grain properties. We find that in addition to micron-sized dust grains, a population of sub-micron grains is needed to match the surface brightness in polarized light and polarized fraction. This could indicate the existence of a population of small grains in the disk, or it could be caused by Mie theory simulations using additional small grains to compensate for sub-micron structures of real dust aggregates. We find models that match the polarized fraction of the data but the models do not apply strong constraints on the dust grain type or compositions. We find no models that can match all observed properties of the disk. More detailed modeling using realistic dust aggregates with irregular surfaces and complex structures is required to further constrain the dust properties.

Climate change not only threatens agricultural producers but also strains related public agencies and financial institutions. These important food system actors include government entities tasked with insuring grower livelihoods and supporting response to continued global warming. We examine future risk within the U.S. Corn Belt geographic region for one such crucial institution: the U.S. Federal Crop Insurance Program. Specifically, we predict the impacts of climate-driven crop loss at a policy-salient "risk unit" scale. Built through our presented neural network Monte Carlo method, simulations anticipate both more frequent and more severe losses that would result in a costly doubling of the annual probability of maize Yield Protection insurance claims at mid-century. We also provide an open source pipeline and interactive visualization tools to explore these results with configurable statistical treatments. Altogether, we fill an important gap in current understanding for climate adaptation by bridging existing historic yield estimation and climate projection to predict crop loss metrics at policy-relevant granularity., Comment: 20 page main document followed by supplemental