On the Expressive Power of Transformers for Maxout Networks and Continuous Piecewise Linear Functions

Transformer networks have achieved remarkable empirical success across a wide range of applications, yet their theoretical expressive power remains insufficiently understood. In this paper, we study the expressive capabilities of Transformer architectures. We first establish an explicit approximation of maxout networks by Transformer networks while preserving comparable model complexity. As a consequence, Transformers inherit the universal approximation capability of ReLU networks under similar complexity constraints. Building on this connection, we develop a framework to analyze the approximation of continuous piecewise linear functions by Transformers and quantitatively characterize their expressivity via the number of linear regions, which grows exponentially with depth. Our analysis establishes a theoretical bridge between approximation theory for standard feedforward neural networks and Transformer architectures. It also yields structural insights into Transformers: self-attention layers implement max-type operations, while feedforward layers realize token-wise affine transformations.

Long-range Modeling and Processing of Multimodal Event Sequences

Temporal point processes (TPPs) have emerged as powerful tools for modeling asynchronous event sequences. While recent advances have extended TPPs to handle textual information, existing approaches are limited in their ability to generate rich, multimodal content and reason about event dynamics. A key challenge is that incorporating multimodal data dramatically increases sequence length, hindering the ability of attention-based models to generate coherent, long-form textual descriptions that require long-range understanding. In this paper, we propose a novel framework that extends LLM-based TPPs to the visual modality, positioning text generation as a core capability alongside time and type prediction. Our approach addresses the long-context problem through an adaptive sequence compression mechanism based on temporal similarity, which reduces sequence length while preserving essential patterns. We employ a two-stage paradigm of pre-training on compressed sequences followed by supervised fine-tuning for downstream tasks. Extensive experiments, including on the challenging DanmakuTPP-QA benchmark, demonstrate that our method outperforms state-of-the-art baselines in both predictive accuracy and the quality of its generated textual analyses.

Diving into Kronecker Adapters: Component Design Matters

Kronecker adapters have emerged as a promising approach for fine-tuning large-scale models, enabling high-rank updates through tunable component structures. However, existing work largely treats the component structure as a fixed or heuristic design choice, leaving the dimensions and number of Kronecker components underexplored. In this paper, we identify component structure as a key factor governing the capacity of Kronecker adapters. We perform a fine-grained analysis of both the dimensions and number of Kronecker components. In particular, we show that the alignment between Kronecker adapters and full fine-tuning depends on component configurations. Guided by these insights, we propose Component Designed Kronecker Adapters (CDKA). We further provide parameter-budget-aware configuration guidelines and a tailored training stabilization strategy for practical deployment. Experiments across various natural language processing tasks demonstrate the effectiveness of CDKA. Code is available at https://github.com/rainstonee/CDKA.

A Tilted Seesaw: Revisiting Autoencoder Trade-off for Controllable Diffusion

In latent diffusion models, the autoencoder (AE) is typically expected to balance two capabilities: faithful reconstruction and a generation-friendly latent space (e.g., low gFID). In recent ImageNet-scale AE studies, we observe a systematic bias toward generative metrics in handling this trade-off: reconstruction metrics are increasingly under-reported, and ablation-based AE selection often favors the best-gFID configuration even when reconstruction fidelity degrades. We theoretically analyze why this gFID-dominant preference can appear unproblematic for ImageNet generation, yet becomes risky when scaling to controllable diffusion: AEs can induce condition drift, which limits achievable condition alignment. Meanwhile, we find that reconstruction fidelity, especially instance-level measures, better indicates controllability. We empirically validate the impact of tilted autoencoder evaluation on controllability by studying several recent ImageNet AEs. Using a multi-dimensional condition-drift evaluation protocol reflecting controllable generation tasks, we find that gFID is only weakly predictive of condition preservation, whereas reconstruction-oriented metrics are substantially more aligned. ControlNet experiments further confirm that controllability tracks condition preservation rather than gFID. Overall, our results expose a gap between ImageNet-centric AE evaluation and the requirements of scalable controllable diffusion, offering practical guidance for more reliable benchmarking and model selection.

Fair Bayesian Data Selection via Generalized Discrepancy Measures

Fairness concerns are increasingly critical as machine learning models are deployed in high-stakes applications. While existing fairness-aware methods typically intervene at the model level, they often suffer from high computational costs, limited scalability, and poor generalization. To address these challenges, we propose a Bayesian data selection framework that ensures fairness by aligning group-specific posterior distributions of model parameters and sample weights with a shared central distribution. Our framework supports flexible alignment via various distributional discrepancy measures, including Wasserstein distance, maximum mean discrepancy, and $f$-divergence, allowing geometry-aware control without imposing explicit fairness constraints. This data-centric approach mitigates group-specific biases in training data and improves fairness in downstream tasks, with theoretical guarantees. Experiments on benchmark datasets show that our method consistently outperforms existing data selection and model-based fairness methods in both fairness and accuracy.

Negative Binomial Variational Autoencoders for Overdispersed Latent Modeling

Biological neurons communicate through spike trains, discrete, irregular bursts of activity that exhibit variability far beyond the modeling capacity of conventional variational autoencoders (VAEs). Recent work, such as the Poisson-VAE, makes a biologically inspired move by modeling spike counts using the Poisson distribution. However, they impose a rigid constraint: equal mean and variance, which fails to reflect the true stochastic nature of neural activity. In this work, we challenge this constraint and introduce NegBio-VAE, a principled extension of the VAE framework that models spike counts using the negative binomial distribution. This shift grants explicit control over dispersion, unlocking a broader and more accurate family of neural representations. We further develop two ELBO optimization schemes and two differentiable reparameterization strategies tailored to the negative binomial setting. By introducing one additional dispersion parameter, NegBio-VAE generalizes the Poisson latent model to a negative binomial formulation. Empirical results demonstrate this minor yet impactful change leads to significant gains in reconstruction fidelity, highlighting the importance of explicitly modeling overdispersion in spike-like activations.

AU-Blendshape for Fine-grained Stylized 3D Facial Expression Manipulation

While 3D facial animation has made impressive progress, challenges still exist in realizing fine-grained stylized 3D facial expression manipulation due to the lack of appropriate datasets. In this paper, we introduce the AUBlendSet, a 3D facial dataset based on AU-Blendshape representation for fine-grained facial expression manipulation across identities. AUBlendSet is a blendshape data collection based on 32 standard facial action units (AUs) across 500 identities, along with an additional set of facial postures annotated with detailed AUs. Based on AUBlendSet, we propose AUBlendNet to learn AU-Blendshape basis vectors for different character styles. AUBlendNet predicts, in parallel, the AU-Blendshape basis vectors of the corresponding style for a given identity mesh, thereby achieving stylized 3D emotional facial manipulation. We comprehensively validate the effectiveness of AUBlendSet and AUBlendNet through tasks such as stylized facial expression manipulation, speech-driven emotional facial animation, and emotion recognition data augmentation. Through a series of qualitative and quantitative experiments, we demonstrate the potential and importance of AUBlendSet and AUBlendNet in 3D facial animation tasks. To the best of our knowledge, AUBlendSet is the first dataset, and AUBlendNet is the first network for continuous 3D facial expression manipulation for any identity through facial AUs. Our source code is available at https://github.com/wslh852/AUBlendNet.git.

Wav2Sem: Plug-and-Play Audio Semantic Decoupling for 3D Speech-Driven Facial Animation

In 3D speech-driven facial animation generation, existing methods commonly employ pre-trained self-supervised audio models as encoders. However, due to the prevalence of phonetically similar syllables with distinct lip shapes in language, these near-homophone syllables tend to exhibit significant coupling in self-supervised audio feature spaces, leading to the averaging effect in subsequent lip motion generation. To address this issue, this paper proposes a plug-and-play semantic decorrelation module-Wav2Sem. This module extracts semantic features corresponding to the entire audio sequence, leveraging the added semantic information to decorrelate audio encodings within the feature space, thereby achieving more expressive audio features. Extensive experiments across multiple Speech-driven models indicate that the Wav2Sem module effectively decouples audio features, significantly alleviating the averaging effect of phonetically similar syllables in lip shape generation, thereby enhancing the precision and naturalness of facial animations. Our source code is available at https://github.com/wslh852/Wav2Sem.git.

PM-KVQ: Progressive Mixed-precision KV Cache Quantization for Long-CoT LLMs

Recently, significant progress has been made in developing reasoning-capable Large Language Models (LLMs) through long Chain-of-Thought (CoT) techniques. However, this long-CoT reasoning process imposes substantial memory overhead due to the large Key-Value (KV) Cache memory overhead. Post-training KV Cache quantization has emerged as a promising compression technique and has been extensively studied in short-context scenarios. However, directly applying existing methods to long-CoT LLMs causes significant performance degradation due to the following two reasons: (1) Large cumulative error: Existing methods fail to adequately leverage available memory, and they directly quantize the KV Cache during each decoding step, leading to large cumulative quantization error. (2) Short-context calibration: Due to Rotary Positional Embedding (RoPE), the use of short-context data during calibration fails to account for the distribution of less frequent channels in the Key Cache, resulting in performance loss. We propose Progressive Mixed-Precision KV Cache Quantization (PM-KVQ) for long-CoT LLMs to address the above issues in two folds: (1) To reduce cumulative error, we design a progressive quantization strategy to gradually lower the bit-width of KV Cache in each block. Then, we propose block-wise memory allocation to assign a higher bit-width to more sensitive transformer blocks. (2) To increase the calibration length without additional overhead, we propose a new calibration strategy with positional interpolation that leverages short calibration data with positional interpolation to approximate the data distribution of long-context data. Extensive experiments on 7B-70B long-CoT LLMs show that PM-KVQ improves reasoning benchmark performance by up to 8% over SOTA baselines under the same memory budget. Our code is available at https://github.com/thu-nics/PM-KVQ.

DanmakuTPPBench: A Multi-modal Benchmark for Temporal Point Process Modeling and Understanding

We introduce DanmakuTPPBench, a comprehensive benchmark designed to advance multi-modal Temporal Point Process (TPP) modeling in the era of Large Language Models (LLMs). While TPPs have been widely studied for modeling temporal event sequences, existing datasets are predominantly unimodal, hindering progress in models that require joint reasoning over temporal, textual, and visual information. To address this gap, DanmakuTPPBench comprises two complementary components: (1) DanmakuTPP-Events, a novel dataset derived from the Bilibili video platform, where user-generated bullet comments (Danmaku) naturally form multi-modal events annotated with precise timestamps, rich textual content, and corresponding video frames; (2) DanmakuTPP-QA, a challenging question-answering dataset constructed via a novel multi-agent pipeline powered by state-of-the-art LLMs and multi-modal LLMs (MLLMs), targeting complex temporal-textual-visual reasoning. We conduct extensive evaluations using both classical TPP models and recent MLLMs, revealing significant performance gaps and limitations in current methods' ability to model multi-modal event dynamics. Our benchmark establishes strong baselines and calls for further integration of TPP modeling into the multi-modal language modeling landscape. The code and dataset have been released at https://github.com/FRENKIE-CHIANG/DanmakuTPPBench