Spoken Language Understanding

In this paper, we examine the impact and significance of bias terms in Implicit Neural Representations (INRs). While bias terms are known to enhance nonlinear capacity by shifting activations in typical neural networks, we discover their functionality differs markedly in neural representation networks. Our analysis reveals that INR performance neither scales with increased number of bias terms nor shows substantial improvement through bias term gradient propagation. We demonstrate that bias terms in INRs primarily serve to eliminate \textit{spatial aliasing} caused by symmetry from both coordinates and activation functions, with input-layer bias terms yielding the most significant benefits. These findings challenge the conventional practice of implementing full-bias INR architecture. We propose using freezing bias terms exclusively in input layers, which consistently outperforms fully biased networks in signal fitting tasks. Furthermore, we introduce Feature-Biased INRs~(Feat-Bias), which initialize input-layer bias with high-level features extracted from pre-trained models. This feature-biasing approach effectively addresses the limited performance in INR post-processing tasks due to neural parameter uninterpretability, achieving superior accuracy while reducing parameter count and improving reconstruction quality.

The rapid advancement of Large Language Models (LLMs) has spurred significant progress in Large Speech-Language Models (LSLMs), enhancing their capabilities in both speech understanding and generation. While existing LSLMs often concentrate on augmenting speech generation or tackling a diverse array of short-speech tasks, the efficient processing of long-form speech remains a critical yet underexplored challenge. This gap is primarily attributed to the scarcity of long-speech training datasets and the high computational costs associated with long sequences. To address these limitations, we introduce FastLongSpeech, a novel framework designed to extend LSLM capabilities for efficient long-speech processing without necessitating dedicated long-speech training data. FastLongSpeech incorporates an iterative fusion strategy that can compress excessively long-speech sequences into manageable lengths. To adapt LSLMs for long-speech inputs, it introduces a dynamic compression training approach, which exposes the model to short-speech sequences at varying compression ratios, thereby transferring the capabilities of LSLMs to long-speech tasks. To assess the long-speech capabilities of LSLMs, we develop a long-speech understanding benchmark called LongSpeech-Eval. Experiments show that our method exhibits strong performance in both long-speech and short-speech tasks, while greatly improving inference efficiency.

Partial observability is a notorious challenge in reinforcement learning (RL), due to the need to learn complex, history-dependent policies. Recent empirical successes have used *privileged expert distillation* -- which leverages availability of latent state information during training (e.g., from a simulator) to learn and imitate the optimal latent, Markovian policy -- to disentangle the task of ''learning to see'' from ''learning to act''. While expert distillation is more computationally efficient than RL without latent state information, it also has well-documented failure modes. In this paper -- through a simple but instructive theoretical model called the *perturbed Block MDP*, and controlled experiments on challenging simulated locomotion tasks -- we investigate the algorithmic trade-off between privileged expert distillation and standard RL without privileged information. Our main findings are: **(1)** The trade-off empirically hinges on the *stochasticity* of the latent dynamics, as theoretically predicted by contrasting *approximate decodability* with *belief contraction* in the perturbed Block MDP; and **(2)** The optimal latent policy is not always the best latent policy to distill. Our results suggest new guidelines for effectively exploiting privileged information, potentially advancing the efficiency of policy learning across many practical partially observable domains.

Differential Transformer has recently gained significant attention for its impressive empirical performance, often attributed to its ability to perform noise canceled attention. However, precisely how differential attention achieves its empirical benefits remains poorly understood. Moreover, Differential Transformer architecture demands large-scale training from scratch, hindering utilization of open pretrained weights. In this work, we conduct an in-depth investigation of Differential Transformer, uncovering three key factors behind its success: (1) enhanced expressivity via negative attention, (2) reduced redundancy among attention heads, and (3) improved learning dynamics. Based on these findings, we propose DEX, a novel method to efficiently integrate the advantages of differential attention into pretrained language models. By reusing the softmax attention scores and adding a lightweight differential operation on the output value matrix, DEX effectively incorporates the key advantages of differential attention while remaining lightweight in both training and inference. Evaluations confirm that DEX substantially improves the pretrained LLMs across diverse benchmarks, achieving significant performance gains with minimal adaptation data (< 0.01%).

Transformers have proven highly effective across various applications, especially in handling sequential data such as natural languages and time series. However, transformer models often lack clear interpretability, and the success of transformers has not been well understood in theory. In this paper, we study the capability and interpretability of transformers in learning a family of classic statistical models, namely random walks on circles. We theoretically demonstrate that, after training with gradient descent, a one-layer transformer model can achieve optimal accuracy in predicting random walks. Importantly, our analysis reveals that the trained model is interpretable: the trained softmax attention serves as a token selector, focusing on the direct parent state; subsequently, the value matrix executes a one-step probability transition to predict the location of the next state based on this parent state. We also show that certain edge cases not covered by our theory are indeed failure cases, demonstrating that our theoretical conditions are tight. By investigating these success and failure cases, it is revealed that gradient descent with small initialization may fail or struggle to converge to a good solution in certain simple tasks even beyond random walks. Experiments are conducted to support our theoretical findings.

Effective robotic autonomy in unknown environments demands proactive exploration and precise understanding of both geometry and semantics. In this paper, we propose ActiveSGM, an active semantic mapping framework designed to predict the informativeness of potential observations before execution. Built upon a 3D Gaussian Splatting (3DGS) mapping backbone, our approach employs semantic and geometric uncertainty quantification, coupled with a sparse semantic representation, to guide exploration. By enabling robots to strategically select the most beneficial viewpoints, ActiveSGM efficiently enhances mapping completeness, accuracy, and robustness to noisy semantic data, ultimately supporting more adaptive scene exploration. Our experiments on the Replica and Matterport3D datasets highlight the effectiveness of ActiveSGM in active semantic mapping tasks.

The study of Neural Tangent Kernels (NTKs) in deep learning has drawn increasing attention in recent years. NTKs typically actively change during training and are related to feature learning. In parallel, recent work on Gradient Descent (GD) has found a phenomenon called Edge of Stability (EoS), in which the largest eigenvalue of the NTK oscillates around a value inversely proportional to the step size. However, although follow-up works have explored the underlying mechanism of such eigenvalue behavior in depth, the understanding of the behavior of the NTK *eigenvectors* during EoS is still missing. This paper examines the dynamics of NTK eigenvectors during EoS in detail. Across different architectures, we observe that larger learning rates cause the leading eigenvectors of the final NTK, as well as the full NTK matrix, to have greater alignment with the training target. We then study the underlying mechanism of this phenomenon and provide a theoretical analysis for a two-layer linear network. Our study enhances the understanding of GD training dynamics in deep learning.

Despite its widespread adoption, Adam's advantage over Stochastic Gradient Descent (SGD) lacks a comprehensive theoretical explanation. This paper investigates Adam's sensitivity to rotations of the parameter space. We observe that Adam's performance in training transformers degrades under random rotations of the parameter space, indicating a crucial sensitivity to the choice of basis in practice. This reveals that conventional rotation-invariant assumptions are insufficient to capture Adam's advantages theoretically. To better understand the rotation-dependent properties that benefit Adam, we also identify structured rotations that preserve or even enhance its empirical performance. We then examine the rotation-dependent assumptions in the literature and find that they fall short in explaining Adam's behavior across various rotation types. In contrast, we verify the orthogonality of the update as a promising indicator of Adam’s basis sensitivity, suggesting it may be the key quantity for developing rotation-dependent theoretical frameworks that better explain its empirical success.

Adam is a popular and widely used adaptive gradient method in deep learning, which has also received tremendous focus in theoretical research. However, most existing theoretical work primarily analyzes its full-batch version, which differs fundamentally from the stochastic variant used in practice. Unlike SGD, stochastic Adam does not converge to its full-batch counterpart even with infinitesimal learning rates. We present the first theoretical characterization of how batch size affects Adam's generalization, analyzing two-layer over-parameterized CNNs on image data. Our results reveal that while both Adam and AdamW with proper weight decay $\lambda$ converge to poor test error solutions, their mini-batch variants can achieve near-zero test error. We further prove Adam has a strictly smaller effective weight decay bound than AdamW, theoretically explaining why Adam requires more sensitive $\lambda$ tuning. Extensive experiments validate our findings, demonstrating the critical role of batch size and weight decay in Adam's generalization performance.

Sparse neural networks promise efficiency, yet training them effectively remains a fundamental challenge. Despite advances in pruning methods that create sparse architectures, understanding why some sparse structures are better trainable than others with the same level of sparsity remains poorly understood. Aiming to develop a systematic approach to this fundamental problem, we propose a novel theoretical framework based on the theory of graph limits, particularly graphons, that characterizes sparse neural networks in the infinite-width regime. Our key insight is that connectivity patterns of sparse neural networks induced by pruning methods converge to specific graphons as networks' width tends to infinity, which encodes implicit structural biases of different pruning methods. We postulate the *Graphon Limit Hypothesis* and provide empirical evidence to support it. Leveraging this graphon representation, we derive a *Graphon Neural Tangent Kernel (Graphon NTK)* to study the training dynamics of sparse networks in the infinite width limit. Graphon NTK provides a general framework for the theoretical analysis of sparse networks. We empirically show that the spectral analysis of Graphon NTK correlates with observed training dynamics of sparse networks, explaining the varying convergence behaviours of different pruning methods. Our framework provides theoretical insights into the impact of connectivity patterns on the trainability of various sparse network architectures.

As both model and dataset sizes continue to scale rapidly, conventional pretraining strategies with fixed compute budgets—such as cosine learning rate schedules—are increasingly inadequate for large-scale training. Recent alternatives, including warmup-stable-decay (WSD) schedules and weight averaging, offer greater flexibility. However, WSD relies on explicit decay phases to track progress, while weight averaging addresses this limitation at the cost of additional memory. In search of a more principled and scalable alternative, we revisit the Schedule-Free (SF) method [Defazio et al., 2024], which has shown strong empirical performance across diverse settings. We show that SF-AdamW effectively navigates the "river" structure of the loss landscape without decay phases or auxiliary averaging, making it particularly suitable for continuously scaling training workloads. To understand this behavior, we conduct a theoretical and empirical analysis of SF dynamics, revealing that it implicitly performs weight averaging without memory overhead. Guided by this analysis, we propose a refined variant of SF that improves robustness to momentum and performs better under large batch sizes, addressing key limitations of the original method. Together, these results establish SF as a practical, scalable, and theoretically grounded approach for language model training.

Large language models are known to memorize parts of their training data, posing risk of copyright violations. To systematically examine this risk, we pretrain language models (1B/3B/8B) from scratch on 83B tokens, mixing web-scale data with public domain books used to simulate copyrighted content at controlled frequencies at lengths at least ten times longer than prior work. We thereby identified the offset effect, a phenomenon characterized by two key findings: (1) verbatim memorization is most strongly triggered by short prefixes drawn from the beginning of the context window, with memorization decreasing counterintuitively as prefix length increases; and (2) a sharp decline in verbatim recall when prefix begins offset from the initial tokens of the context window. We attribute this to positional fragility: models rely disproportionately on the earliest tokens in their context window as retrieval anchors, making them sensitive to even slight shifts. We further observe that when the model fails to retrieve memorized content, it often produces degenerated text. Leveraging these findings, we show that shifting sensitive data deeper into the context window suppresses both extractable memorization and degeneration. Our results suggest that positional offset is a critical and previously overlooked axis for evaluating memorization risks, since prior work implicitly assumed uniformity by probing only from the beginning of documents or training sequences.

The success of modern multimodal representation learning relies on internet-scale datasets. Due to the low quality of a large fraction of raw web data, data curation has become a critical step in the training pipeline. Filtering using a trained model (i.e., teacher-based filtering) has emerged as a successful solution, leveraging a pre-trained model to compute quality scores. To explain the empirical success of teacher-based filtering, we characterize the performance of filtered contrastive learning under the standard bimodal data generation model. Denoting $\eta\in(0,1]$ as the fraction of data with correctly matched modalities among $n$ paired samples, we utilize a linear contrastive learning setup to show a provable benefit of data filtering: $(i)$ the error without filtering is upper and lower bounded by $\frac{1}{\eta \sqrt{n}}$, and $(ii)$ the error with teacher-based filtering is upper bounded by $\frac{1}{\sqrt{\eta n}}$ in the large $\eta$ regime, and by $\frac{1}{\sqrt{n}}$ in the small $\eta$ regime.

Despite the growing success of transform-based tensor models such as the t-product, their underlying geometric principles remain poorly understood. Classical differential geometry, built on real-valued function spaces, is not well suited to capture the algebraic and spectral structure induced by transform-based tensor operations. In this work, we take an initial step toward a geometric framework for tensors equipped with tube-wise multiplication via orthogonal transforms. We introduce the notion of smooth t-manifolds, defined as topological spaces locally modeled on structured tensor modules over a commutative t-scalar ring. This formulation enables transform-consistent definitions of geometric objects, including metrics, gradients, Laplacians, and geodesics, thereby bridging discrete and continuous tensor settings within a unified algebraic-geometric perspective. On this basis, we develop a statistical procedure for testing whether tensor data lie near a low-dimensional t-manifold, and provide nonasymptotic guarantees for manifold fitting under noise. We further establish approximation bounds for tensor neural networks that learn smooth functions over t-manifolds, with generalization rates determined by intrinsic geometric complexity. This framework offers a theoretical foundation for geometry-aware learning in structured tensor spaces and supports the development of models that align with transform-based tensor representations.