Sub Specie Aeternitatis: Fourier Transforms from the Theory of Heat to Musical Signals

J. B. Fourier in his \emph{Théorie Analytique de la Chaleur} of 1822 introduced, amongst other things, two ideas that have made a fundamental impact in fields as diverse as Mathematical Physics, Electrical Engineering, Computer Science, and Music. The first one of these, a method to find the coefficients for a trigonometric series describing an arbitrary function, was very early on picked up by G. Ohm and H. Helmholtz as the foundation for a theory of \emph{musical tones}. The second one, which is described by Fourier's double integral, became the basis for treating certain kinds of infinity in discontinuous functions, as shown by A. De Morgan in his 1842 \emph{The Differential and Integral Calculus}. Both make up the fundamental basis for what is now commonly known as the \emph{Fourier theorem}. With the help of P. A. M. Dirac's insights into the nature of these infinities, we can have a compact description of the frequency spectrum of a function of time, or conversely of a waveform corresponding to a given function of frequency. This paper, using solely primary sources, takes us from the physics of heat propagation to the modern theory of musical signals. It concludes with some considerations on the inherent duality of time and frequency emerging from Fourier's theorem.

MAEB: Massive Audio Embedding Benchmark

We introduce the Massive Audio Embedding Benchmark (MAEB), a large-scale benchmark covering 30 tasks across speech, music, environmental sounds, and cross-modal audio-text reasoning in 100+ languages. We evaluate 50+ models and find that no single model dominates across all tasks: contrastive audio-text models excel at environmental sound classification (e.g., ESC50) but score near random on multilingual speech tasks (e.g., SIB-FLEURS), while speech-pretrained models show the opposite pattern. Clustering remains challenging for all models, with even the best-performing model achieving only modest results. We observe that models excelling on acoustic understanding often perform poorly on linguistic tasks, and vice versa. We also show that the performance of audio encoders on MAEB correlates highly with their performance when used in audio large language models. MAEB is derived from MAEB+, a collection of 98 tasks. MAEB is designed to maintain task diversity while reducing evaluation cost, and it integrates into the MTEB ecosystem for unified evaluation across text, image, and audio modalities. We release MAEB and all 98 tasks along with code and a leaderboard at https://github.com/embeddings-benchmark/mteb.

Spectral Convolution on Orbifolds for Geometric Deep Learning

Geometric deep learning (GDL) deals with supervised learning on data domains that go beyond Euclidean structure, such as data with graph or manifold structure. Due to the demand that arises from application-related data, there is a need to identify further topological and geometric structures with which these use cases can be made accessible to machine learning. There are various techniques, such as spectral convolution, that form the basic building blocks for some convolutional neural network-like architectures on non-Euclidean data. In this paper, the concept of spectral convolution on orbifolds is introduced. This provides a building block for making learning on orbifold structured data accessible using GDL. The theory discussed is illustrated using an example from music theory.

Evaluating Disentangled Representations for Controllable Music Generation

Recent approaches in music generation rely on disentangled representations, often labeled as structure and timbre or local and global, to enable controllable synthesis. Yet the underlying properties of these embeddings remain underexplored. In this work, we evaluate such disentangled representations in a set of music audio models for controllable generation using a probing-based framework that goes beyond standard downstream tasks. The selected models reflect diverse unsupervised disentanglement strategies, including inductive biases, data augmentations, adversarial objectives, and staged training procedures. We further isolate specific strategies to analyze their effect. Our analysis spans four key axes: informativeness, equivariance, invariance, and disentanglement, which are assessed across datasets, tasks, and controlled transformations. Our findings reveal inconsistencies between intended and actual semantics of the embeddings, suggesting that current strategies fall short of producing truly disentangled representations, and prompting a re-examination of how controllability is approached in music generation.

Climber-Pilot: A Non-Myopic Generative Recommendation Model Towards Better Instruction-Following

Generative retrieval has emerged as a promising paradigm in recommender systems, offering superior sequence modeling capabilities over traditional dual-tower architectures. However, in large-scale industrial scenarios, such models often suffer from inherent myopia: due to single-step inference and strict latency constraints, they tend to collapse diverse user intents into locally optimal predictions, failing to capture long-horizon and multi-item consumption patterns. Moreover, real-world retrieval systems must follow explicit retrieval instructions, such as category-level control and policy constraints. Incorporating such instruction-following behavior into generative retrieval remains challenging, as existing conditioning or post-hoc filtering approaches often compromise relevance or efficiency. In this work, we present Climber-Pilot, a unified generative retrieval framework to address both limitations. First, we introduce Time-Aware Multi-Item Prediction (TAMIP), a novel training paradigm designed to mitigate inherent myopia in generative retrieval. By distilling long-horizon, multi-item foresight into model parameters through time-aware masking, TAMIP alleviates locally optimal predictions while preserving efficient single-step inference. Second, to support flexible instruction-following retrieval, we propose Condition-Guided Sparse Attention (CGSA), which incorporates business constraints directly into the generative process via sparse attention, without introducing additional inference steps. Extensive offline experiments and online A/B testing at NetEase Cloud Music, one of the largest music streaming platforms, demonstrate that Climber-Pilot significantly outperforms state-of-the-art baselines, achieving a 4.24\% lift of the core business metric.

NarraScore: Bridging Visual Narrative and Musical Dynamics via Hierarchical Affective Control

Synthesizing coherent soundtracks for long-form videos remains a formidable challenge, currently stalled by three critical impediments: computational scalability, temporal coherence, and, most critically, a pervasive semantic blindness to evolving narrative logic. To bridge these gaps, we propose NarraScore, a hierarchical framework predicated on the core insight that emotion serves as a high-density compression of narrative logic. Uniquely, we repurpose frozen Vision-Language Models (VLMs) as continuous affective sensors, distilling high-dimensional visual streams into dense, narrative-aware Valence-Arousal trajectories. Mechanistically, NarraScore employs a Dual-Branch Injection strategy to reconcile global structure with local dynamism: a \textit{Global Semantic Anchor} ensures stylistic stability, while a surgical \textit{Token-Level Affective Adapter} modulates local tension via direct element-wise residual injection. This minimalist design bypasses the bottlenecks of dense attention and architectural cloning, effectively mitigating the overfitting risks associated with data scarcity. Experiments demonstrate that NarraScore achieves state-of-the-art consistency and narrative alignment with negligible computational overhead, establishing a fully autonomous paradigm for long-video soundtrack generation.

TADA! Tuning Audio Diffusion Models through Activation Steering

Audio diffusion models can synthesize high-fidelity music from text, yet their internal mechanisms for representing high-level concepts remain poorly understood. In this work, we use activation patching to demonstrate that distinct semantic musical concepts, such as the presence of specific instruments, vocals, or genre characteristics, are controlled by a small, shared subset of attention layers in state-of-the-art audio diffusion architectures. Next, we demonstrate that applying Contrastive Activation Addition and Sparse Autoencoders in these layers enables more precise control over the generated audio, indicating a direct benefit of the specialization phenomenon. By steering activations of the identified layers, we can alter specific musical elements with high precision, such as modulating tempo or changing a track's mood.

MOSS-Audio-Tokenizer: Scaling Audio Tokenizers for Future Audio Foundation Models

Discrete audio tokenizers are fundamental to empowering large language models with native audio processing and generation capabilities. Despite recent progress, existing approaches often rely on pretrained encoders, semantic distillation, or heterogeneous CNN-based architectures. These designs introduce fixed inductive biases that limit reconstruction fidelity and hinder effective scaling. In this paper, we argue that discrete audio tokenization should be learned fully end-to-end using a homogeneous and scalable architecture. To this end, we first propose CAT (Causal Audio Tokenizer with Transformer), a purely Transformer-based architecture that jointly optimizes the encoder, quantizer, and decoder from scratch for high-fidelity reconstruction. Building on the CAT architecture, we develop MOSS-Audio-Tokenizer, a large-scale audio tokenizer featuring 1.6 billion parameters, pre-trained on 3 million hours of diverse, general audio data. We show that this simple, fully end-to-end approach built from homogeneous, causal Transformer blocks scales gracefully and supports high-fidelity reconstruction across diverse audio domains. Across speech, sound, and music, MOSS-Audio-Tokenizer consistently outperforms prior codecs over a wide range of bitrates, while exhibiting predictable improvements with increased scale. Notably, leveraging the discrete tokens from our model, we develop the first purely autoregressive TTS model that surpasses prior non-autoregressive and cascaded systems. Furthermore, MOSS-Audio-Tokenizer enables competitive ASR performance without auxiliary encoders. Our findings position the CAT architecture as a unified, scalable interface for the next generation of native audio foundation models.

Musical Metamerism with Time--Frequency Scattering

The concept of metamerism originates from colorimetry, where it describes a sensation of visual similarity between two colored lights despite significant differences in spectral content. Likewise, we propose to call ``musical metamerism'' the sensation of auditory similarity which is elicited by two music fragments which differ in terms of underlying waveforms. In this technical report, we describe a method to generate musical metamers from any audio recording. Our method is based on joint time--frequency scattering in Kymatio, an open-source software in Python which enables GPU computing and automatic differentiation. The advantage of our method is that it does not require any manual preprocessing, such as transcription, beat tracking, or source separation. We provide a mathematical description of JTFS as well as some excerpts from the Kymatio source code. Lastly, we review the prior work on JTFS and draw connections with closely related algorithms, such as spectrotemporal receptive fields (STRF), modulation power spectra (MPS), and Gabor filterbank (GBFB).

IncompeBench: A Permissively Licensed, Fine-Grained Benchmark for Music Information Retrieval

Multimodal Information Retrieval has made significant progress in recent years, leveraging the increasingly strong multimodal abilities of deep pre-trained models to represent information across modalities. Music Information Retrieval (MIR), in particular, has considerably increased in quality, with neural representations of music even making its way into everyday life products. However, there is a lack of high-quality benchmarks for evaluating music retrieval performance. To address this issue, we introduce \textbf{IncompeBench}, a carefully annotated benchmark comprising $1,574$ permissively licensed, high-quality music snippets, $500$ diverse queries, and over $125,000$ individual relevance judgements. These annotations were created through the use of a multi-stage pipeline, resulting in high agreement between human annotators and the generated data. The resulting datasets are publicly available at https://huggingface.co/datasets/mixedbread-ai/incompebench-strict and https://huggingface.co/datasets/mixedbread-ai/incompebench-lenient with the prompts available at https://github.com/mixedbread-ai/incompebench-programs.