We introduce MACROCAST, a lightweight Time Series Foundation Model (TSFM) for real-time macroeconomic forecasting. Existing TSFMs suffer from data leakage in two forms: temporal contamination, as the model may have seen the realized values of the series it forecasts, and revision bias, as training on fully revised data diverges from the preliminary, vintage-specific releases available to real-time forecasters. MACROCAST is, to our knowledge, the first TSFM that rules out both forms of leakage entirely: at no stage of training is the model exposed to information that would not have been available to a forecaster in real time. We train MACROCAST first on purely synthetic time series in approximately one GPU-day and then fine-tune it on synthetic time series drawn from Bayesian VARs, dynamic factor models, and ARIMA specifications estimated on vintage-specific ALFRED data. Because pretraining uses only simulated data and fine-tuning uses only real-time vintages, no observed future or revised value ever enters the model; each fine-tuning run takes nine minutes. Evaluated on the FRED-MD database in a genuine real-time out-of-sample exercise, MACROCAST improves on the AR(1) benchmark for
Alcoholic beverage properties are increasingly understood through ethanol-water structural states rather than empirical labels such as alcohol content and vintage. Yet whether chronological vintage similarly reflects an intrinsic structural state remains unclear. Here, we apply persistent homology to map the topological evolution of self-assembled molecular aggregates in strong-aroma Baijiu aged 1-10 years. The resulting fingerprints reveal a three-stage maturation pathway: rapid scaffold consolidation (B0), population-level channel stabilization (B1), and non-monotonic cavity reorganization (B2). These coupled trajectories converge toward a mature topological state rather than passively tracking chronological age. We therefore propose a universal topological attractor, in which optimal aging is defined by a system's position in persistence space relative to a mature structural domain. This framework reframes beverage aging as navigation through structural state space, providing a physical basis for quality evaluation and accelerated maturation.
Learning low-dimensional latent representations is a central topic in statistics and machine learning, and rotation methods have long been used to obtain sparse and interpretable representations. Despite nearly a century of widespread use across many fields, rigorous guarantees for valid inference for the learned representation remain lacking. In this paper, we identify a surprisingly prevalent phenomenon that suggests a reason for this gap: for a broad class of vintage rotations, the resulting estimators exhibit a non-estimable bias. Because this bias is independent of the data, it fundamentally precludes the development of valid inferential procedures, including the construction of confidence intervals and hypothesis testing. To address this challenge, we propose a novel bias-free rotation method within a general representation learning framework based on latent variables. We establish an oracle inference property for the learned sparse representations: the estimators achieve the same asymptotic variance as in the ideal setting where the latent variables are observed. To bridge the gap between theory and computation, we develop an efficient computational framework and prove that
This paper reviews two established formulations for modelling multi-year energy investments: the simple method, which aggregates all capacity regardless of commissioning year, and the vintage method, which explicitly tracks investments by year to capture differences in technical parameters over time. While the vintage method improves modelling fidelity, it significantly increases model size. To address this, we propose a novel compact formulation that maintains the ability to represent year-specific characteristics while reducing the dimensionality of the model. The proposed compact formulation is implemented in the open-source model TulipaEnergyModel.jl and offers a tractable alternative for detailed long-term energy system planning.
These lecture notes present a comprehensive and powerful many-body technique pioneered in 1960 by D. N. Zubarev. The technique, known as the Zubarev Double Time Greens Function method, was used extensively by leading solid state physicists such as John Hubbard and Laura Roth in the 1960s. We present the technique and apply it to the non-interacting electron and boson gas. We next consider the (many-body) Hubbard model and show how it yields the Stoner criterion for ferromagnetism. It is easily extendable to superconductivity and related problems. Our treatment is pedagogical and understandable to those with just an elementary understanding of second quantization.
This extended paper contributes a methodology and a detailed analysis of app installation and functionality on a 'vintage' device. Experimental results are presented that demonstrate barriers to the reuse of vintage Apple devices. and solutions are posited. 230 apps across 23 unique app categories were tested to determine if they could be downloaded, installed, and opened, and whether they appeared functional on a vintage Apple device. Only 29 (12.6%) of the apps could be downloaded directly, and in contrast 140 (60.9%) of the apps were downloadable with the aid of another Apple device. In total, 141 (61.3%) of applications downloaded either directly or indirectly were considered functional and capable of running on the device. We discuss measures Apple and developers could take to support legacy device users, prolong device use, enable reuse and, potentially, prevent functional devices from becoming e-waste.
Recent advances in audio generation have focused on text-to-audio (T2A) and video-to-audio (V2A) tasks. However, T2A or V2A methods cannot generate holistic sounds (onscreen and off-screen). This is because T2A cannot generate sounds aligning with onscreen objects, while V2A cannot generate semantically complete (offscreen sounds missing). In this work, we address the task of holistic audio generation: given a video and a text prompt, we aim to generate both onscreen and offscreen sounds that are temporally synchronized with the video and semantically aligned with text and video. Previous approaches for joint text and video-to-audio generation often suffer from modality bias, favoring one modality over the other. To overcome this limitation, we introduce VinTAGe, a flow-based transformer model that jointly considers text and video to guide audio generation. Our framework comprises two key components: a Visual-Text Encoder and a Joint VT-SiT model. To reduce modality bias and improve generation quality, we employ pretrained uni-modal text-to-audio and video-to-audio generation models for additional guidance. Due to the lack of appropriate benchmarks, we also introduce VinTAGe-Bench,
We present new or updated angular diameters, physical radii, and effective temperatures for 145 stars from the Navy Precision Optical Interferometer data archive. We used data from 1996 to late-2021, and we describe the differences between early and late data, which hinge upon an update of the beam combiner in 2002. We came across several sub-categories of stars of interest: 13 of our stars are promising targets for the Habitable World Observatory and therefore require as much study as possible, and 14 more are asteroseismic targets and have stellar masses after we combined our radii and effective temperatures with frequencies of maximum oscillation power values from the literature. In addition to this, many of the stars here show measurements to the first null in the visibility curve and beyond, which is the gateway to determining second-order effects such as direct measurements of limb-darkening. Finally, we consider the stars in the larger context of previous NPOI measurements and find the majority 75% of the angular diameters in the overall NPOI sample have uncertainties of 2% or less.
Application modernization in legacy languages such as COBOL, PL/I, and REXX faces an acute shortage of resources, both in expert availability and in high-quality human evaluation data. While Large Language Models as a Judge (LaaJ) offer a scalable alternative to expert review, their reliability must be validated before being trusted in high-stakes workflows. Without principled validation, organizations risk a circular evaluation loop, where unverified LaaJs are used to assess model outputs, potentially reinforcing unreliable judgments and compromising downstream deployment decisions. Although various automated approaches to validating LaaJs have been proposed, alignment with human judgment remains a widely used and conceptually grounded validation strategy. In many real-world domains, the availability of human-labeled evaluation data is severely limited, making it difficult to assess how well a LaaJ aligns with human judgment. We introduce SparseAlign, a formal framework for assessing LaaJ alignment with sparse human-labeled data. SparseAlign combines a novel pairwise-confidence concept with a score-sensitive alignment metric that jointly capture ranking consistency and score proxi
Vintage factor analysis is one important type of factor analysis that aims to first find a low-dimensional representation of the original data, and then to seek a rotation such that the rotated low-dimensional representation is scientifically meaningful. The most widely used vintage factor analysis is the Principal Component Analysis (PCA) followed by the varimax rotation. Despite its popularity, little theoretical guarantee can be provided to date mainly because varimax rotation requires to solve a non-convex optimization over the set of orthogonal matrices. In this paper, we propose a deflation varimax procedure that solves each row of an orthogonal matrix sequentially. In addition to its net computational gain and flexibility, we are able to fully establish theoretical guarantees for the proposed procedure in a broader context. Adopting this new deflation varimax as the second step after PCA, we further analyze this two step procedure under a general class of factor models. Our results show that it estimates the factor loading matrix in the minimax optimal rate when the signal-to-noise-ratio (SNR) is moderate or large. In the low SNR regime, we offer possible improvement over us
The on-off phenomena of opponent colors in center-surround may be the best-known facts of retinal processing of information. Apparently, however, no explicit model has been proposed that shows how neurons can be connected to produce the center-surround phenomena. Here it is shown that a previous simple model of color vision can produce these phenomena, including the detection of edge orientation and motion famously discovered by Hubel and Wiesel. The model was previously shown to produce major phenomena central to color vision, including mutually exclusive opponent colors. Although the opponencies of mutually exclusive colors and center-surround involve the same color pairs, red-green and blue-yellow, the model produces them by two different mechanisms. Perceptions of two colors are mutually exclusive because only one cone type can have the most, or least, absorption of photons. Two colors have the on-off opponency of center-surround because they have the same network designs up to the ganglion cells, with the inputs reversed there. On-off opponencies with different colors are possible, but natural selection evidently did not choose them.
We wholeheartedly congratulate Drs. Rohe and Zeng for their insightful paper \cite{rohe2020vintage} on vintage factor analysis with Varimax rotation. This note discusses the conditions to guarantee Varimax consistently recovers the subspace rotation.
The paper concerns the study of equilibrium points, or steady states, of economic systems arising in modeling optimal investment with \textit{vintage capital}, namely, systems where all key variables (capitals, investments, prices) are indexed not only by time $τ$ but also by age $s$. Capital accumulation is hence described as a partial differential equation (briefly, PDE), and equilibrium points are in fact equilibrium distributions in the variable $s$ of ages. Investments in frontier as well as non-frontier vintages are possible. Firstly a general method is developed to compute and study equilibrium points of a wide range of infinite dimensional, infinite horizon boundary control problems for linear PDEs with convex criterion, possibly applying to a wide variety of economic problems. Sufficient and necessary conditions for existence of equilibrium points are derived in this general context. In particular, for optimal investment with vintage capital, existence and uniqueness of a long run equilibrium distribution is proved for general concave revenues and convex investment costs, and analytic formulas are obtained for optimal controls and trajectories in the long run, definitely s
This paper examines whether real-time GDP announcements can reliably identify business-cycle turning points. Using U.S. real-time GDP vintages from 1947 to 2021, we construct 4,356 recession indicators based on alternative smoothing methods and scaling variations. We then combine these indicators with alternative thresholds to generate 137,457 perfect recession classifiers. The selected classifiers identify all 12 historical recessions without generating false positives or false negatives. Restricting attention to the high-precision segment yields two classifiers with a standard deviation of detection errors below three months, while the selected ensemble signals recessions, on average, 3.04 months after their official onset. The framework accurately identifies recession episodes across vintages, suggesting that discrepancies in prior work may reflect limitations of traditional dating methods in addition to data revisions. Overall, the results indicate that real-time GDP announcements provide a practical proxy for NBER-style recession dating.
Look-ahead bias (using information from after a decision epoch to make the decision at that epoch) is the dominant way a backtest or a machine-learning evaluation flatters a system that will disappoint in deployment. The field manages it with construct-specific recipes and empirical detectors, which are sound only channel by channel and certify nothing by their silence. We show that look-ahead-freedom is a formal property in disguise: fixing an epoch, the demand that the future not influence the present is temporal non-interference over a time-indexed information lattice. From this identification we develop a pipeline calculus separating a datum's availability from its reference time, and settle the problem's boundary. Where availability may depend on data values, look-ahead-freedom is undecidable (indeed Pi-0-1-hard): leakage is recursively enumerable but freedom is not. On the value-independent fragment (covering windowing, resampling, joins, point-in-time and vintage reads, and agentic retrieval) we give a type-and-effect system that is sound and decidable in linear time. An artifact confirms the theory: the check scales linearly, an independent oracle witnesses no leak in any a
We analyze how four forces restructure the AI industry over 2026-2030: the DRAM/HBM price surge, frontier-capable open-weight models (GLM-5.2), rapid inference-efficiency gains (near-Shannon-limit KV-cache compression, lightweight local runtimes), and the entry of Meta and xAI into compute resale on fleets bought before the memory repricing. Formulating inference economics in dollars per petabyte of bandwidth delivered (\$/PB) -- model-agnostic for bandwidth-bound decode -- we show the entrant-incumbent cost gap never closes: a depreciation conveyor delivers newly amortized fleets to incumbents faster than hardware prices normalize (3.2x in 2026, 1.9x in 2027, re-widening to 3-4x by 2029-30). Training bifurcates into a luxury tier (\$18-38B per frontier run by 2030) and a mass tier (previous-frontier parity via RL/distillation falling toward \$5M). Solvency of the announced buildout is confined to a corridor requiring roughly 2x annual token-demand growth for four years with sticky premium pricing; a measurement critique shows public token trackers overstate monetizable demand, and all pre-Q2-2026 projections predate the industry's shift from token maximization to token minimizatio
This paper aims to develop a theory for linear-quadratic Nash systems and Master equations in possibly infinite-dimensional Hilbert spaces. As a first step and motivated by the recent results in [31], we study a more general model in the linear quadratic case where the dependence on the distribution enters just in the objective functional through the mean. This property enables the Nash systems and the Master equation to be reduced to two systems of coupled Riccati equations and backward abstract evolution equations. We show that solutions for such systems exist and are unique for all time horizons, a result that is completely new in the literature in our setting. Finally, we apply the results to a vintage capital model, where capital depends on time and age, and the production function depends on the mean of the vintage capital.
Amortized variational inference in latent-variable forecasters creates a deployment gap: the test-time encoder approximates a training-time optimization-refined latent, but without access to future targets. This gap introduces unnecessary forecast error and interpretability challenges. In this work, we propose the Sparse Latent Factor Forecaster with Iterative Inference (SLFF), addressing this through (i) a sparse coding objective with L1 regularization for low-dimensional latents, (ii) unrolled proximal gradient descent (LISTA-style) for iterative refinement during training, and (iii) encoder alignment to ensure amortized outputs match optimization-refined solutions. Under a linearized decoder assumption, we derive a design-motivating bound on the amortization gap based on encoder-optimizer distance, with convergence rates under mild conditions; empirical checks confirm the bound is predictive for the deployed MLP decoder. To prevent mixed-frequency data leakage, we introduce an information-set-aware protocol using release calendars and vintage macroeconomic data. Interpretability is formalized via a three-stage protocol: stability (Procrustes alignment across seeds), driver valid
Deep learning has become a standard approach for the modeling of audio effects, yet strictly black-box modeling remains problematic for time-varying systems. Unlike time-invariant effects, training models on devices with internal modulation typically requires the recording or extraction of control signals to ensure the time-alignment required by standard loss functions. This paper introduces a Generative Adversarial Network (GAN) framework to model such effects using only input-output audio recordings, without requiring a modulation signal extraction. We propose a convolutional-recurrent architecture trained via a two-stage strategy: an initial adversarial phase allows the model to learn the distribution of the modulation behavior without strict phase constraints, followed by a supervised fine-tuning phase where a State Prediction Network (SPN) estimates the initial internal states required to synchronize the model with the target. Additionally, a new metric based on chirp-train signals is developed to quantify modulation accuracy. Experiments modeling a vintage hardware phaser demonstrate the method's ability to capture time-varying dynamics in a fully black-box context.
The increasing demand for high-quality digital emulations of analog audio hardware, such as vintage tube guitar amplifiers, led to numerous works on neural network-based black-box modeling, with deep learning architectures like WaveNet showing promising results. However, a key limitation in all of these models was the aliasing artifacts stemming from nonlinear activation functions in neural networks. In this paper, we investigated novel and modified activation functions aimed at mitigating aliasing within neural amplifier models. Supporting this, we introduced a novel metric, the Aliasing-to-Signal Ratio (ASR), which quantitatively assesses the level of aliasing with high accuracy. Measuring also the conventional Error-to-Signal Ratio (ESR), we conducted studies on a range of preexisting and modern activation functions with varying stretch factors. Our findings confirmed that activation functions with smoother curves tend to achieve lower ASR values, indicating a noticeable reduction in aliasing. Notably, this improvement in aliasing reduction was achievable without a substantial increase in ESR, demonstrating the potential for high modeling accuracy with reduced aliasing in neural