Notes

Score-informed note separation seeks to extract the performed waveform of all individual notes, often from a polyphonic recording. Existing deep learning systems generally only target instrument-level stems. We present, to our knowledge, the first deep learning approach to score-informed note separation, NoteSep. NoteSep extracts the queried notes by applying an extraction stage model, NoteGrab, once per note. Conditioned on pitch, onset, and offset, NoteGrab separates harmonic and percussive components in two U-Nets linked by bidirectional cross-attention; selective harmonic gating suppresses lower-octave interference while preserving percussive attacks. Finally, a joint separation stage applies Adaptive Set Ownership (ASO) to compare concurrent NoteGrab estimates and reallocate mixture energy. We curate SCNS-Train (25,729 mixtures and 743,920 targets) for training and SCNS-Eval (16 instruments, disjoint scores and libraries) for evaluation. On SCNS-Eval, NoteSep reaches a median SI-SDR of 7.39dB, compared with 2.49dB for our strongest baseline. See the demo page at https://benschou.com/notesep.

Machine learning tools have significantly aided automatic piano music transcription; however, this domain has focused primarily on accurately predicting the pitches and timings of played notes. To produce sheet music for the piano, notes must be separated into two staves, one for each hand, and good sheet music often contains fingering annotations to guide the player when sight-reading or learning fast or complex pieces. We propose 8 statistical approaches for combined hand and fingering annotation of transcribed piano notes, including baseline hidden Markov models, rule-based methods, a synthesis of existing approaches, and N-gram language models. Furthermore, we develop a pipeline for complete transcription from piano audio to fingering-annotated sheet music. Evaluations with the PIG dataset demonstrate that our Synthesis model achieves a hand separation accuracy of 90.8% and a joint hand and finger annotation accuracy of 56.6%. These approaches serve as a new baseline for further research into this problem, while our pipeline demonstrates the feasibility of a combined system for automated note transcription, hand separation, and fingering annotation.

These notes develop the mathematical foundations and construction of a Fourier-Bessel wavelet family inspired by the disk harmonics of Shaqfa et al.[9]. We begin with the relevant properties of Bessel and modified Bessel functions and introduce the wavelet properties required for the construction. We then derive the Fourier-Bessel disk harmonics as solutions to the Helmholtz equation on the unit disk subject to a Neumann boundary condition. Building on this basis, we construct a wavelet family by applying a Gaussian spatial envelope and introducing a zero-mean correction for the zeroth angular order. We derive the corresponding normalisation constants for $L^2$-based applications and discuss $L^1$-based normalisation for frequency-domain peak consistency. Finally, we derive a closed-form Fourier-domain representation of the resulting wavelets. The main motivation is the approximately linear spacing, which converges to $π$ between consecutive radial eigenvalues. Rather than replacing the conventional dyadic organisation of wavelet families, this construction lays out the foundation to explore whether a more uniform radial frequency allocation can be useful for applications in which broad and balanced frequency coverage is desirable.

Quantization schemes based on randomized rotations have recently received renewed attention, including the roles of MMSE and unbiased reconstruction scalings. In this note, we point out the connection to classical results in statistical signal processing and communication theory. Specifically, the two reconstruction scales used in the EDEN line of work admit a natural interpretation as finite-dimensional, realization-dependent counterparts of the Wiener and unbiased coefficients in the classical CDEF formulation. At finite blocklength, the CDEF +1 relation holds pointwise for each rotation realization as an exact geometric (Pythagorean) identity, but does not hold after averaging the distortions over the rotation. The classical SNR relation $\sf{SNR}_{\rm MMSE}=\sf{SNR}_{\rm MMSE,U}+1$ is recovered as $d\to\infty$: once the overall scale is handled separately, the empirical coordinate statistics of a randomly rotated vector approach their i.i.d. Gaussian counterparts, and the rotation-dependent quantities concentrate. Importantly, EDEN goes beyond this classical correspondence: for every finite $d$, its Haar-rotation formulation guarantees exact conditional unbiasedness, a stronger property than the second-order notion of unbiasedness in CDEF. We further comment on two distinct roles random rotations play in quantization: one is approximate Gaussianization of the coordinates; the other is decorrelation of reconstruction errors across quantization branches.

Social media fact-checking has long been challenged by evidence-level and aggregation-level conflicts, where erroneous evidence mimics authoritative news sources. To capture this challenge and support conflict verification tasks, we present ContraNote, a large-scale real-world dataset curated from X's Community Notes system. It includes 33,686 posts for evaluating evidence-level conflict resolution, and 54,474 instances for evaluating aggregation-level prioritization. Additionally, we propose CoVer, a factual adjudication framework with three-stage pipelines: evidence schema normalization, factual consensus and support verification. This prioritizes evidence over noise to prevent it from compromising the final verdict. Technical evaluations show that CoVer achieves strong performance compared with state-of-the-art baselines across ContraNote (86.0% Acc., 68.0% mac. F1, 64.5 bal. Acc. on Conflict; and 88.5% Acc., 88.5 mac. F1 and 89.2 bal. Acc. on Prioritization), CONFACT-HumC (88.4% Acc.) and CONFACT-ModC (89.4% Acc.).

Ambient AI scribes draft clinical notes under the reassurance that a clinician signs every note. We audited three commercial AI scribes on the same 142 consultations: 565 notes from recorded UK primary-care and US ambulatory encounters plus authored scenarios. Twelve discovery passes proposed 13,678 candidate errors; the 5,898 clearing an importance filter went to an adversarial panel of two models from different families, each told to refute what it could, and 618 survived. One note in three (31.3% [27.0, 35.6]) carries a verified failure, concentrated in allergy and medication information, invented patient identity, and history written up as examination on telephone consultations that can contain none. No product was given a patient record; setting aside the two classes a record would have prefilled, invented identity and dates, the rate is 24.8% [20.8, 29.0]. One failure mode did not fit our scheme, drawn from published scribe-error taxonomies: a treatment the clinician retracts, recorded as delivered care. Two clinicians adjudicated blind, disjoint samples: a physician author upheld 20 of 21 findings (95.2% [77.3, 99.2]) and an independent clinician, not an author, 12 of 12 ([75.8, 100]); both judged every sampled refusal genuine. A failure rate depends on the instrument as much as the scribes. With model, evidence and settings fixed, the review instruction alone moves the share of candidates verified from 9.3% to 79.0%, and the reviewing family moves it too: alone at that instruction the gentler flags 54.8% of notes against 27.8%. Between 28% and 97% of sampled notes carry a failure depending on the standard. Published audits disagree among themselves by a margin instrument differences alone can produce: omission is 54-86% of their errors against our 23.1%. We release all 618 findings with transcript-side evidence, every prompt and model version, and the re-runnable pipeline.

Recurrent, attention-free sequence models share a structural weakness: a fading state cannot perform exact recall of something seen once, far in the past. We add to the Kathleen trunk a second memory layer -- a "notebook": a fixed-key holographic (HRR) associative store with a learned local write gate, a self-gating raw read, and write-triggered forgetting -- 25K parameters that attach to the logits of any trunk. (1) Mechanism: on a controlled needle-in-haystack task the notebook reaches 80-82% one-shot recall at 4x the training length, where the bare trunk scores ~4% and a parameter-matched attention head scores 100% inside its training length and 0% beyond it. Addressing is length-invariant by construction; the untrained memory alone recalls at 90% accuracy identically at 512, 2048 and 4096 bytes. Because the store is a linear superposition, two capabilities follow from arithmetic alone: selective unlearning (one subtraction erases one fact to chance, retained facts unharmed) and per-token attribution (counterfactual erasure names the source fact of every correct byte, 100% provenance). (2) Real text: on WikiText-2 bytes the notebook improves prediction of repeated rare words by +0.15-0.27 bits/byte, the gain growing with the distance between mentions and holding zero-shot at 4x training length; write-triggered forgetting eliminates memory pollution at 8x length (first-mention cost +0.33 -> -0.004). (3) Scope and scale: a parameter-matched attention head does generalize on natural-text repetition, so the notebook's claim is exact recall at O(L); on a WikiText-103 ladder (8 to 512 MB) the zero-shot repeat gain rises monotonically. All experiments are pre-registered, seeds reported, and reproducible on a single free-tier GPU.

How a document's arrangement is written down, its notation, is a training variable that no dataset card records. The field has established that text-extraction choices change model behaviour, and has never once measured the notation of what those choices put into the corpus. We define clean-window survival, a deterministic count of how much of a stream still demands the boundary inference, and measure notation on three fronts. What corpora carry: a census of thirteen public corpora, where survival falls to 0.153 in a vision-converted PDF slice against 0.889 in C4; the scarce resource is not unmarked text but long unmarked text; a pre-registered supply test finds what remains institutional, not consumer. Our own pre-registered prediction failed: converters do not fabricate structure on prose, and that null forced the reliability mechanism that survives it. What readers use: across five base models spanning 0.6B to 8.2B and two pipelines, deleting a structural announcement makes the following prose measurably harder to predict, while swapping its notation moves nothing. That zero does not make notation unimportant; it relocates the variable: the operative cue is the announcement, not the sigil. What writers impose: a bounded null. Base models do not impose the marked register above the authored baseline, and handed prose with every announcement deleted they do not put one back, at a rate indistinguishable from zero against an authored reference of zero. We ship the format those measurements imply: the pure frame, paragraphs in authored order, every announcement deleted into a reversible sidecar, mixed against the marked copy over announcement presence rather than notation. Choose format operators by the capability they train, not by the fidelity they preserve, and record extractor identity and survival on data cards.

Inline notes and collected commentaries are important forms of scholarly communication that evolved within the Confucian exegetical tradition, yet have received little computational attention. Drawing on traditional Chinese exegetics and philology, this paper formulates collected commentary compilation as an NLP task and proposes a computational framework that preserves the contextual dependency of inline notes while enabling their automatic compilation and exegetical knowledge organization. It combines two-step prompt chaining for identifying the associated main-text segments and exegetical functions of annotations with cross-source mention clustering for integrating commentary across editions, achieving a CoNLL F1 score above 97% in a case study on the Classic of Mountains. Our framework lays the foundation for the large-scale organization of historical exegetical knowledge, thereby supporting a broad range of downstream philological and NLP tasks.

Humans distill experience into reusable abstractions, e.g., strategies and cautionary reminders, and apply them to gradually solve problems more effectively. We study whether Large Language Models (LLMs) can similarly benefit from such experiential abstractions. From LLMs' solution traces on the MATH training set, a stronger teacher or the LLMs themselves extract natural-language abstractions into a retrievable library. We explore two usage modes: (1) inference-time retrieval and (2) reinforcement learning (RL) with abstraction-augmented training prompts. Experiential abstractions improve LLM performance on mathematical and logical reasoning benchmarks. Self-extracted abstractions match teacher-extracted ones, and our abstraction usage framework can transfer to other datasets and models. These findings suggest LLMs can extract and apply experiential abstractions much as humans leverage distilled experience.

Jupyter Notebooks have become widely adopted in data science, as they allow the sharing of reproducible computational analysis. They are, however, accessible only to people who understand computer code. To reach the broader audience of scientists interested in data analysis and computation, but unfamiliar with code, we introduce Plainbook, notebooks centered on natural language rather than code. Plainbook is based on two principles: promote the natural language descriptions, and verify the values. In plainbook, the natural language descriptions are preserved, rather than the resulting code; the code is generated automatically from the cell descriptions. As natural language is read top to bottom, Plainbook adopts a linear execution semantics, in which cells are guaranteed to be executed in the order in which they appear; there is no "hidden state" or out-of-order execution as in Jupyter. To allow users who may not understand code to verify the correctness of the computation, we have built into Plainbook verification mechanisms centered on values and value inspection. These include mechanisms that focus on individual cells, akin to unit tests, as well as global mechanisms. Both the linear execution semantics, and the verification mechanisms, are underpinned by a snapshot kernel that caches execution states and makes execution and verification efficient.

Community Notes, a bridging-based crowd-sourced fact-checking system, has emerged as a new mechanism for moderating misleading information on social media and has been adopted by major platforms including X, Facebook, Instagram, Threads, and TikTok. Since its introduction, there has been an open question about what role AI could play in scaling and optimizing the system. Recently, X extended its Community Notes system by introducing Collaborative Notes: notes initially drafted by an LLM and iteratively refined based on feedback from human contributors. In this work, we systematically analyze the complete corpus of 19,146 collaborative notes and 211,850 instances of human feedback. First, we develop a taxonomy of human suggestions for improving AI-generated note drafts and find that suggestions involving factual corrections and additional context are most likely to be incorporated, while subjective policy judgments rarely are. Second, we examine changes in helpfulness across versions of collaborative notes and find that human feedback leads to more helpful notes, with the greatest impact coming from suggestions that challenge the main claim in the previous draft, particularly when submitted by more active contributors. Finally, we find that although collaborative notes improve through human feedback, they reach helpful status and are shown on the platform at lower rates than human-only or AI-only notes, with limited human participation emerging as a key bottleneck. Nevertheless, rather than serving as a weaker substitute, collaborative notes tend to play a complementary role, predominantly targeting posts that do not attract human-only or AI-only notes. Our analysis provides an initial description of efforts to use AI to improve crowdsourced content moderation in a real-world moderation system and outlines pathways for future improvements to such features.

Symbolic music alignment links notes in a symbolic performance to their counterparts in a score. While existing alignment encoding formats provide unique correspondences between these notes, there are various musical practices and forms such as practice repetitions in rehearsal and improvised realizations in basso continuo that require a more flexible approach to encoding their alignments. In this paper, we propose a minimal, backward-compatible extension to the Match file format to support such non-unique and semantically complex alignments. We introduce two virtual pointer notes - virtual score notes and virtual performance notes - which allow to encode multiple links between performance and score notes. In addition we expand the Match file's 'section' line to include semantically meaningful annotations of performance regions beyond score-indicated musical repetitions. We further demonstrate the utility of these extensions through two representative use-cases in piano rehearsal and basso continuo.

Jupyter Notebooks are an increasingly popular coding environment used across many domains, especially in Python-based data science and scientific computing. Originally used for prototyping and interactive exploration, notebooks are increasingly used to develop more complex programs, leading to a rapid rise in buggy notebooks on platforms like GitHub. To address this trend, we present JupOtter, a bug detection system designed specifically for Jupyter Notebooks. JupOtter features three novel contributions: (1) a notebook-specific tokenization strategy that preserves cell structure, (2) a cell-level bug prediction technique, and (3) a new labeled dataset, OtterDataset, containing over 21,000 notebooks annotated for fine-grained cell-level bug detection. JupOtter achieves cell-level bug detection F1 scores that surpass static analyzers and large language models in two out of three evaluation datasets.

Automatic Music Transcription (AMT) models have achieved a high level of success in polyphonic transcription of various instruments. Velocity, typically a measure of note intensity, is less commonly predicted in these models due to the absence of velocity labels in available datasets and lack of a proper definition for instruments other than piano. We present a methodology and model for velocity prediction in Automatic Guitar Transcription (AGT) which uses virtual instruments to generate synthetic training data with velocity labels. We first pretrain a model on this synthetic data. These weights are then transferred to a different model and trained on real guitar audio, allowing the model to retain the working velocity prediction while also achieving high performance and generalisability from the real training data. The velocity prediction is shown to outperform a baseline model which does not use the pretrained velocity weights, when evaluated on synthetic data. In addition, using the pretrained velocity weights offers a small improvement in note transcription, though the magnitude of this improvement is limited and not always significant depending on the testing data. Overall the model achieves results comparable to the state of the art in guitar transcription, while also successfully predicting velocity.

Large language models (LLMs) can make clinical decision support more accessible by interpreting free-text documentation, but their direct use as diagnostic engines is limited by sensitivity to prompts, information order, and plausible but incorrect outputs. Structured machine-learning models offer more stable risk prediction, yet they require tabular inputs that are difficult to integrate with narrative clinical workflows. We present ClaMPAPP (Clinical Language-assisted Machine-learning Pipeline for Appendicitis), a hybrid system that uses an LLM as an interface rather than as the final decision-maker. ClaMPAPP extracts schema-constrained clinical features from note-like narratives, applies deterministic plausibility checks, and passes validated features to an XGBoost classifier trained on clinical, laboratory, and ultrasound variables. We evaluated ClaMPAPP on two independent pediatric appendicitis cohorts from German hospitals and compared it with end-to-end LLM baselines, including open-source and proprietary models. To preserve ground truth while testing free-text input, narratives were generated from structured electronic health records through template rendering and constrained LLM rewriting, with additional sentence-order permutation to assess positional robustness. ClaMPAPP achieved the strongest overall diagnostic performance in both internal and external validation while minimizing missed appendicitis cases, the key safety concern in acute triage. End-to-end LLMs showed unstable sensitivity-specificity trade-offs and greater degradation under narrative reordering. These results support an LLM-as-interface, ML-as-predictor design that separates natural-language usability from predictive inference and provides a more auditable pathway for clinical decision support.

Prefix caching reuses prefill only across an exactly shared prefix, so one changed field invalidates the entire downstream cache. Yet overwriting the field's own key/value vectors and reusing the rest leaves the model acting on the old value. The reason, established causally across four model families: at prefill the model has already written the field-conditioned conclusion onto downstream notes; the field's own key/value drives under 1% of the decision. Read as a notebook of memoized conclusions, two capabilities follow. (1) It is editable. A salient erratum amends the notes; and with chain-of-thought, editing the field alone recovers the decision (1.00 at 8B, ~1% compute), while without CoT it is ignored. (2) It is composable. The notes are position-portable, so a precompiled skill can be RoPE-repositioned and spliced into any context, indistinguishable from full recompute (logit cosine 0.90-0.999, twelve models) at O(L) rather than O(L^2) time-to-first-token. A unified edit+compose agent stays decision-identical to recompute at up to 14.9x lower latency. The approach applies to any per-token attention KV cache, validated across scale, quantization, Mixture-of-Experts, and multimodal caches, and extends to several attention variants through small adapters. Because the erratum is append-only, it composes with production prefix caching: in an online vLLM benchmark it keeps the prefix cache-aligned (98.5% hit-rate), cutting p90 time-to-first-token by 53-398x.

Scientific discovery workflows rely heavily on lab notes, where researchers record observations, interpret uncertain results, and plan follow-up experiments. Unlike polished publications, lab notes preserve evolving scientific reasoning, tacit scientific knowledge, and author uncertainty, giving AI agents access to the process of science. However, most prior work on scientific text focuses on papers, protocols, or structured databases, leaving informal laboratory notes underexplored as inputs to AI agents for science. This gap matters because tacit knowledge in lab notes is not written as a clean set of instructions: validated observations, tentative judgments, and possible experimental next steps often appear in the same passage. If these signals are conflated, an AI agent may mistake uncertain scientific judgments for confirmed conclusions or executable actions. To this end, we present Notes2Skills, a two-stage framework for turning lab notebooks into verifiable skills for scientific AI agents while preserving the author's certainty. Across three wet-lab sessions and seven original downstream configurations, Notes2Skills is the only tested configuration that avoids both observed regime-level failures: over-acting on uncertain notes and missing firm directives. We show that certainty preservation is a key missing piece between lab notebooks and reliable agent skills, opening a path toward safer AI co-scientist systems.

Lampson's confinement problem asks how to prevent a program that processes confidential information from leaking it to a third party. We introduce the strategic confinement problem, which arises when the communicating parties are strategic agents with shared coordination resources. In this setting, residual communication capacity can be concentrated on low-entropy, high-impact predicates of the confidential data. Consequently, bounds on information leakage need not induce corresponding bounds on worst-case harm: a channel with negligible capacity may still suffice to select damaging outcomes. We argue that systems of learnt strategic agents naturally instantiate this problem because they do not admit complete behavioural specifications, their learnt conventions generally cannot be predicted or reproduced by an external observer, and sufficiently capable agents can construct covert communication schemes that are difficult to detect or eliminate. Our contribution is therefore not a new theory of communication, but a reinterpretation of confinement in the presence of strategic agents. Classical confinement bounds what information may flow; strategic confinement highlights that this need not bound what strategic agents can jointly achieve.

We study finite-sample generalization for a client-sampled distributed optimization scheme with matrix-valued parameters and orthogonalized momentum updates. The central quantity is the gap between the population and empirical objectives at the returned model when only a subset of clients participates in each round. Under independent heterogeneous client data, unequal local sample counts, and fixed aggregation weights, we derive a finite-round upper-tail guarantee from a coupled-neighbor stability recursion and a weighted concentration step. The bound keeps the client-selection counts through the amplification factor $Y_i(\mathcal C)$; in the uniform full-participation full-batch regime, it yields $\widetilde{\mathcal O}(n^{-1}+n^{-1/2})$ scaling whenever the horizon-dependent amplification terms are controlled. The matrix-orthogonalization rule is required to be Lipschitz along paired trajectories, a condition satisfied by regularized polar-type maps and normalized finite-step Newton--Schulz orthogonalizers. For the unregularized matrix sign, the same argument requires coupled spectral separation, whereas Gaussian smoothing gives a finite-round smoothed variant. A one-dimensional counterexample shows why a gap, smoothing, or regularity condition is necessary.

This tech note describes the architecture and execution results of the LPDDR5X-PIM simulator, developed by Samsung Electronics. Based on the latest research and internal specifications, the simulator provides a high-fidelity model of both the hardware data paths and the software control layers of the LPDDR5X-PIM block. This integrated hardware-software simulation approach enables precise evaluation of system performance and energy efficiency while maximizing PIM resource utilization. We have refined existing simulation frameworks to align with actual hardware implementation, ensuring consistent behavioral accuracy. Further technical details regarding the specific architecture and circuit design of the LPDDR5X-PIM will be disclosed in future publications

Large language models in Agentic AI systems consume tool schemas and execution results and emit tool invocations as structured data. The default language for that exchange, JSON, was designed for application-to-application interchange rather than token efficiency, so its structural elements impose substantial token overhead. Recent work proposes token-optimized alternatives such as TOON (Token-Oriented Object Notation) and TRON (Token Reduced Object Notation) as more compact replacements, but these formats have been evaluated only on isolated comprehension or generation tasks. Whether their token reductions hold inside end-to-end agentic loops therefore remains an open question. We evaluate TOON and TRON on four agentic benchmarks (BFCL, MCPToolBenchPP, MCP-Universe, StableToolBench) and five open-weight LLMs, decoupling input compression from output compression to measure comprehension and generation independently. TRON reduces tokens by up to 27% with accuracy within 14pp of the JSON baseline. TOON achieves up to 18% reduction at a similar 9pp accuracy cost, but additionally cascades on multi-turn parsing failures and collapses parallel tool-call output for most models. The code is available at: https://github.com/lkutschka/notation-matters

Item-to-Item (I2I) retrieval is a fundamental part of modern content platforms, supporting critical industrial workflows from recommendation engines to content auditing. While multimodal embedding methods have advanced general retrieval, they often falter in I2I scenarios due to the challenges of balancing global content representation with fine-grained local retrieval, the systemic inefficiency of decoupled embedding-and-ranking pipelines, and the inherent trade-offs between model precision and serving latency. To solve these issues, we propose \textbf{UniNote}, a unified embedding model designed for industrial I2I retrieval. Tailored retrieval strategies are introduced to support representation learning over complex, multimodal content at varying granularities. To operationalize these strategies, UniNote employs a two-stage training paradigm: the first stage leverages contrastive SFT to establish robust base embeddings, while the second stage refines ranking quality through a reinforcement learning (RL) process that aligns the model with content relevance. Our results show that UniNote achieves SOTA performance across diverse I2I tasks. Deployed at Xiaohongshu and integrated with Matryoshka Representation Learning (MRL), UniNote achieved significant improvements in retrieval quality and cost efficiency in large-scale applications.

Wasserstein Policy Optimization (WPO) is a recently proposed reinforcement learning algorithm that leverages Wasserstein gradient flows to optimize stochastic policies in continuous action spaces. Despite its empirical success, the theoretical convergence properties of WPO in environments with continuous state and action spaces have yet to be fully established. In this note, we argue that WPO within the framework of entropy-regularised Markov Decision Processes converges linearly. This is done by leveraging recent advances in mean-field analysis for convergence of gradient flows using log-Sobole inequalities. Assuming existence of sufficiently regular solution to the gradient flow equation we demonstrate monotonic energy dissipation along the flow and establish a local log-Sobolev inequality. Ultimately, these properties allow us to argue that the value function should converge linearly to the global optimum.

A large amount of musical heritage has been digitised by memory institutions: libraries, museums, and archives. Nevertheless, the field of Optical Music Recognition (OMR) has struggled with making this music machine-readable, despite advances in deep learning, mostly because no datasets for training systems in realistic conditions were available. The MusiCorpus dataset aims to remedy this situation by providing 1,309 pages of historical sheet music, primarily handwritten, with MusicXML transcriptions and symbol annotations. It is the largest dataset of handwritten music to date and the first dataset containing a realistic and representative sample of musical document collections from memory institutions, suitable for training and evaluating both end-to-end and object detection-based OMR systems and comparing their performance.

The Föllmer process is a Brownian motion conditioned to have a pre-specified distribution at time 1. This process can be interpreted as an ``augmented'' time-compressed version of the reverse stochastic differential equation (SDE) corresponding to the denoising diffusion probabilistic model (DDPM). While this fact has been indirectly used to analyze DDPM sampling errors via discretization of the reverse SDE, the connection between direct discretization of the Föllmer process and the DDPM sampler has not yet been fully explored. This paper clarifies this point while surveying relevant results from the literature. We show that discretized Föllmer processes give natural hyper-parameter settings of the DDPM sampler while accommodating a broader class of variance schedules than discretized reverse SDEs. Moreover, this allows us to systematically recover state-of-the-art results on DDPM sampling error bounds, along with slight improvements.

Large language models (LLMs) can generate or synthesize clinical text for a wide range of applications, from improving clinical documentation to augmenting clinical text analytics. Yet evaluations typically focus on a narrow aspect -- such as similarity or utility comparisons -- even though these aspects are complementary and best viewed in parallel. In this study, we aim to conduct a systematic evaluation of LLM-generated clinical text, which includes intrinsic, extrinsic, and factuality evaluations of synthetic clinical notes rephrased from MIMIC databases at million-note scale. Our analysis demonstrates that synthetic notes preserve core clinical information and predictive utility for coarse-grained tasks despite substantial linguistic changes, but lose fine-grained details for task like ICD coding. We show this loss of detail can be substantially mitigated by rephrasing notes by chunks rather than by the whole note, but at the cost of reduced factual precision under incomplete context. Through fact-checking and error analysis, we further find that synthesis errors are dominated by misinterpretation of clinical context, alongside temporal confusion, measurement errors, and fabricated claims. Finally, we show that the synthetic notes -- despite their task-agnostic nature -- can effectively augment task-specific training for rare ICD codes.

$L_1$-Approximating polynomials, i.e., polynomials that approximate indicator functions in $L_1$-norm under certain distributions, are widely used in computational learning theory. We study the existence of \textit{non-negative} $L_1$-approximating polynomials with respect to Gaussian distributions. This is a stronger requirement than $L_1$-approximation but weaker than sandwiching polynomials (which themselves have many applications). These non-negative approximating polynomials have recently found uses in smoothed learning from positive-only examples. In this short note, we prove that every class of sets with Gaussian surface area (GSA) at most $Γ$ under the standard Gaussian admits degree-$k$ non-negative polynomials that $\eps$-approximate its indicator functions in $L_1$-norm, for $k=\tilde{O}(Γ^2/\varepsilon^2)$. Equivalently, finite GSA implies $L_1$-approximation with the stronger pointwise guarantee that the approximating polynomial has range contained in $[0,\infty)$. Up to a constant-factor, this matches the degree of the best currently known Gaussian $L_1$-approximation degree bound without the non-negativity constraint.

EigenDecomposition (ED) is at the heart of many computer vision algorithms and applications. One crucial bottleneck limiting its usage is the expensive computation cost, particularly for a mini-batch of matrices in deep neural networks. Our previous work proposed a dedicated QR-based ED algorithm for batched small matrices (dim${<}32$). This short paper targets the limitation and proposes a batch-efficient Divide-and-Conquer based ED algorithm for larger matrices. The numerical test shows that for a mini-batch of matrices whose dimensions are smaller than $64$, our method can be much faster than the Pytorch SVD function.

In Orabona and Pál [2016], we introduced the shifted KT potentials, to remove the $\ln \ln T$ factor in the parameter-free learning with expert bound. In this short technical note, I show that this is equivalent to changing the prior in the Krichevsky--Trofimov algorithm. Then, I show how to use the same idea to remove the $\ln \ln T$ factor in the data-independent bound for the Squint algorithm.

Omnimodal Notation Processing (ONP) represents a unique frontier for omnimodal AI due to the rigorous, multi-dimensional alignment required across auditory, visual, and symbolic domains. Current research remains fragmented, focusing on isolated transcription tasks that fail to bridge the gap between superficial pattern recognition and the underlying musical logic. This landscape is further complicated by severe notation biases toward Western staff and the inherent unreliability of "LLM-as-a-judge" metrics, which often mask structural reasoning failures with systemic hallucinations. To establish a more rigorous standard, we introduce ONOTE, a multi-format benchmark that utilizes a deterministic pipeline--grounded in canonical pitch projection--to eliminate subjective scoring biases across diverse notation systems. Our evaluation of leading omnimodal models exposes a fundamental disconnect between perceptual accuracy and music-theoretic comprehension, providing a necessary framework for diagnosing reasoning vulnerabilities in complex, rule-constrained domains.

This note clarifies the relationship between the recent TurboQuant work and the earlier DRIVE (NeurIPS 2021) and EDEN (ICML 2022) schemes. DRIVE is a 1-bit quantizer that EDEN extended to any $b>0$ bits per coordinate; we refer to them collectively as EDEN. First, TurboQuant$_{\text{mse}}$ is a special case of EDEN obtained by fixing EDEN's scalar scale parameter to $S=1$. EDEN supports both biased and unbiased quantization, each optimized by a different $S$ (chosen via methods described in the EDEN works). The fixed choice $S=1$ used by TurboQuant is generally suboptimal, although the optimal $S$ for biased EDEN converges to $1$ as the dimension grows; accordingly TurboQuant$_{\text{mse}}$ approaches EDEN's behavior for large $d$. Second, TurboQuant$_{\text{prod}}$ combines a biased $(b-1)$-bit EDEN step with an unbiased 1-bit QJL quantization of the residual. It is suboptimal in three ways: (1) its $(b-1)$-bit step uses the suboptimal $S=1$; (2) its 1-bit unbiased residual quantization has worse MSE than (unbiased) 1-bit EDEN; (3) chaining a biased $(b-1)$-bit step with a 1-bit unbiased residual step is inferior to unbiasedly quantizing the input directly with $b$-bit EDEN. Third, some of the analysis in the TurboQuant work mirrors that of the EDEN works: both exploit the connection between random rotations and the shifted Beta distribution, use the Lloyd-Max algorithm, and note that Randomized Hadamard Transforms can replace uniform random rotations. Experiments support these claims: biased EDEN (with optimized $S$) is more accurate than TurboQuant$_{\text{mse}}$, and unbiased EDEN is markedly more accurate than TurboQuant$_{\text{prod}}$, often by more than a bit (e.g., 2-bit EDEN beats 3-bit TurboQuant$_{\text{prod}}$). We also repeat all accuracy experiments from the TurboQuant paper, showing that EDEN outperforms it in every setup we have tried.

Background: Clinical notes contain extensive duplicated text from templates, copy-paste, and auto-populated fields ("note bloat"), diluting clinical signal, limiting longitudinal context, and increasing large language model (LLM) costs. Methods: TRACE removes note bloat using note-level EHR metadata to identify templated and copied content, with frequency-based de-duplication when metadata are unavailable. We evaluated TRACE using blinded physician span review and gold-standard templated-text annotations across four cohorts spanning liver transplant, obstetrics, and inpatient populations at multiple health systems (5.3M notes). We compared zero-shot LLMs and embedding-based classifiers using original and TRACE-processed notes for 20 information extraction tasks and prediction of 5-year survival, postpartum hemorrhage, and 30-day readmission. Results: Only 0.3-6.6% of removed text was flagged as author-generated; TRACE captured 86% of annotated templated characters. Information extraction F1 differences averaged by cohort ranged from -0.009 to +0.004; task-specific prediction F1 differences ranged from -0.011 to +0.018. Among 1,000 randomly sampled Stanford Health Care patients, TRACE reduced chart text by 47.3% (742.7M characters), averaging 220,167 fewer tokens per patient. Using 2024 encounter volumes at a large tertiary academic center and one query per encounter, projected three-year net savings ranged from $1.00M to$13.58M across evaluated model pricing schemes, including initial and annual TRACE processing costs. Conclusion: TRACE substantially reduces clinical note redundancy while preserving information extraction and prediction performance. Underused EHR metadata can reduce LLM inference costs, expand usable longitudinal context, and support scalable clinical AI.

In high-stakes domains such as healthcare, privacy concerns severely limit the use of real-world training data. Differentially private (DP) synthetic data offers a promising alternative with formal privacy guarantees, but achieving strong utility remains challenging for clinical note generation due to domain specificity and long-form text complexity. We present Term2Note, a method for synthesising full-length clinical notes under DP constraints. By structurally separating content and form, Term2Note generates section-wise note content conditioned on medical terms, with terms and notes privatised under separate DP constraints, and applies a DP quality maximiser to improve outputs. Experiments demonstrate that Term2Note produces synthetic notes with statistical properties closely aligned with real clinical notes, and that downstream models trained on these notes achieve performance comparable to those trained on real clinical data. Compared to existing DP text generation baselines, Term2Note substantially improves both fidelity and utility, without relying on label distribution assumptions, highlighting its effectiveness as a practical privacy-preserving alternative to real clinical notes.