Unveiling Hidden Convexity in Deep Learning: a Sparse Signal Processing Perspective

Deep neural networks (DNNs), particularly those using Rectified Linear Unit (ReLU) activation functions, have achieved remarkable success across diverse machine learning tasks, including image recognition, audio processing, and language modeling. Despite this success, the non-convex nature of DNN loss functions complicates optimization and limits theoretical understanding. In this paper, we highlight how recently developed convex equivalences of ReLU NNs and their connections to sparse signal processing models can address the challenges of training and understanding NNs. Recent research has uncovered several hidden convexities in the loss landscapes of certain NN architectures, notably two-layer ReLU networks and other deeper or varied architectures. This paper seeks to provide an accessible and educational overview that bridges recent advances in the mathematics of deep learning with traditional signal processing, encouraging broader signal processing applications.

Variable-Length Audio Fingerprinting

Audio fingerprinting converts audio to much lower-dimensional representations, allowing distorted recordings to still be recognized as their originals through similar fingerprints. Existing deep learning approaches rigidly fingerprint fixed-length audio segments, thereby neglecting temporal dynamics during segmentation. To address limitations due to this rigidity, we propose Variable-Length Audio FingerPrinting (VLAFP), a novel method that supports variable-length fingerprinting. To the best of our knowledge, VLAFP is the first deep audio fingerprinting model capable of processing audio of variable length, for both training and testing. Our experiments show that VLAFP outperforms existing state-of-the-arts in live audio identification and audio retrieval across three real-world datasets.

Combi-CAM: A Novel Multi-Layer Approach for Explainable Image Geolocalization

Planet-scale photo geolocalization involves the intricate task of estimating the geographic location depicted in an image purely based on its visual features. While deep learning models, particularly convolutional neural networks (CNNs), have significantly advanced this field, understanding the reasoning behind their predictions remains challenging. In this paper, we present Combi-CAM, a novel method that enhances the explainability of CNN-based geolocalization models by combining gradient-weighted class activation maps obtained from several layers of the network architecture, rather than using only information from the deepest layer as is typically done. This approach provides a more detailed understanding of how different image features contribute to the model's decisions, offering deeper insights than the traditional approaches.

Deep Neural Regression Collapse

Neural Collapse is a phenomenon that helps identify sparse and low rank structures in deep classifiers. Recent work has extended the definition of neural collapse to regression problems, albeit only measuring the phenomenon at the last layer. In this paper, we establish that Neural Regression Collapse (NRC) also occurs below the last layer across different types of models. We show that in the collapsed layers of neural regression models, features lie in a subspace that corresponds to the target dimension, the feature covariance aligns with the target covariance, the input subspace of the layer weights aligns with the feature subspace, and the linear prediction error of the features is close to the overall prediction error of the model. In addition to establishing Deep NRC, we also show that models that exhibit Deep NRC learn the intrinsic dimension of low rank targets and explore the necessity of weight decay in inducing Deep NRC. This paper provides a more complete picture of the simple structure learned by deep networks in the context of regression.

Decentralized End-to-End Multi-AAV Pursuit Using Predictive Spatio-Temporal Observation via Deep Reinforcement Learning

Decentralized cooperative pursuit in cluttered environments is challenging for autonomous aerial swarms, especially under partial and noisy perception. Existing methods often rely on abstracted geometric features or privileged ground-truth states, and therefore sidestep perceptual uncertainty in real-world settings. We propose a decentralized end-to-end multi-agent reinforcement learning (MARL) framework that maps raw LiDAR observations directly to continuous control commands. Central to the framework is the Predictive Spatio-Temporal Observation (PSTO), an egocentric grid representation that aligns obstacle geometry with predictive adversarial intent and teammate motion in a unified, fixed-resolution projection. Built on PSTO, a single decentralized policy enables agents to navigate static obstacles, intercept dynamic targets, and maintain cooperative encirclement. Simulations demonstrate that the proposed method achieves superior capture efficiency and competitive success rates compared to state-of-the-art learning-based approaches relying on privileged obstacle information. Furthermore, the unified policy scales seamlessly across different team sizes without retraining. Finally, fully autonomous outdoor experiments validate the framework on a quadrotor swarm relying on only onboard sensing and computing.

Forecasting with Guidance: Representation-Level Supervision for Time Series Forecasting

Nowadays, time series forecasting is predominantly approached through the end-to-end training of deep learning architectures using error-based objectives. While this is effective at minimizing average loss, it encourages the encoder to discard informative yet extreme patterns. This results in smooth predictions and temporal representations that poorly capture salient dynamics. To address this issue, we propose ReGuider, a plug-in method that can be seamlessly integrated into any forecasting architecture. ReGuider leverages pretrained time series foundation models as semantic teachers. During training, the input sequence is processed together by the target forecasting model and the pretrained model. Rather than using the pretrained model's outputs directly, we extract its intermediate embeddings, which are rich in temporal and semantic information, and align them with the target model's encoder embeddings through representation-level supervision. This alignment process enables the encoder to learn more expressive temporal representations, thereby improving the accuracy of downstream forecasting. Extensive experimentation across diverse datasets and architectures demonstrates that our ReGuider consistently improves forecasting performance, confirming its effectiveness and versatility.

SumRank: Aligning Summarization Models for Long-Document Listwise Reranking

Large Language Models (LLMs) have demonstrated superior performance in listwise passage reranking task. However, directly applying them to rank long-form documents introduces both effectiveness and efficiency issues due to the substantially increased context length. To address this challenge, we propose a pointwise summarization model SumRank, aligned with downstream listwise reranking, to compress long-form documents into concise rank-aligned summaries before the final listwise reranking stage. To obtain our summarization model SumRank, we introduce a three-stage training pipeline comprising cold-start Supervised Fine-Tuning (SFT), specialized RL data construction, and rank-driven alignment via Reinforcement Learning. This paradigm aligns the SumRank with downstream ranking objectives to preserve relevance signals. We conduct extensive experiments on five benchmark datasets from the TREC Deep Learning tracks (TREC DL 19-23). Results show that our lightweight SumRank model achieves state-of-the-art (SOTA) ranking performance while significantly improving efficiency by reducing both summarization overhead and reranking complexity.

ArrayDPS-Refine: Generative Refinement of Discriminative Multi-Channel Speech Enhancement

Multi-channel speech enhancement aims to recover clean speech from noisy multi-channel recordings. Most deep learning methods employ discriminative training, which can lead to non-linear distortions from regression-based objectives, especially under challenging environmental noise conditions. Inspired by ArrayDPS for unsupervised multi-channel source separation, we introduce ArrayDPS-Refine, a method designed to enhance the outputs of discriminative models using a clean speech diffusion prior. ArrayDPS-Refine is training-free, generative, and array-agnostic. It first estimates the noise spatial covariance matrix (SCM) from the enhanced speech produced by a discriminative model, then uses this estimated noise SCM for diffusion posterior sampling. This approach allows direct refinement of any discriminative model's output without retraining. Our results show that ArrayDPS-Refine consistently improves the performance of various discriminative models, including state-of-the-art waveform and STFT domain models. Audio demos are provided at https://xzwy.github.io/ArrayDPSRefineDemo/.

Kirchhoff-Inspired Neural Networks for Evolving High-Order Perception

Deep learning architectures are fundamentally inspired by neuroscience, particularly the structure of the brain's sensory pathways, and have achieved remarkable success in learning informative data representations. Although these architectures mimic the communication mechanisms of biological neurons, their strategies for information encoding and transmission are fundamentally distinct. Biological systems depend on dynamic fluctuations in membrane potential; by contrast, conventional deep networks optimize weights and biases by adjusting the strengths of inter-neural connections, lacking a systematic mechanism to jointly characterize the interplay among signal intensity, coupling structure, and state evolution. To tackle this limitation, we propose the Kirchhoff-Inspired Neural Network (KINN), a state-variable-based network architecture constructed based on Kirchhoff's current law. KINN derives numerically stable state updates from fundamental ordinary differential equations, enabling the explicit decoupling and encoding of higher-order evolutionary components within a single layer while preserving physical consistency, interpretability, and end-to-end trainability. Extensive experiments on partial differential equation (PDE) solving and ImageNet image classification validate that KINN outperforms state-of-the-art existing methods.

MolEvolve: LLM-Guided Evolutionary Search for Interpretable Molecular Optimization

Despite deep learning's success in chemistry, its impact is hindered by a lack of interpretability and an inability to resolve activity cliffs, where minor structural nuances trigger drastic property shifts. Current representation learning, bound by the similarity principle, often fails to capture these structural-activity discontinuities. To address this, we introduce MolEvolve, an evolutionary framework that reformulates molecular discovery as an autonomous, look-ahead planning problem. Unlike traditional methods that depend on human-engineered features or rigid prior knowledge, MolEvolve leverages a Large Language Model (LLM) to actively explore and evolve a library of executable chemical symbolic operations. By utilizing the LLM to cold start and an Monte Carlo Tree Search (MCTS) engine for test-time planning with external tools (e.g. RDKit), the system self-discovers optimal trajectories autonomously. This process evolves transparent reasoning chains that translate complex structural transformations into actionable, human-readable chemical insights. Experimental results demonstrate that MolEvolve's autonomous search not only evolves transparent, human-readable chemical insights, but also outperforms baselines in both property prediction and molecule optimization tasks.