Jianqiao Zheng

Xunzhuo Liu, Huamin Chen, Samzong Lu et al.

As large language models (LLMs) diversify across modalities, capabilities, and cost profiles, the problem of intelligent request routing: selecting the right model for each query at inference time, has become a critical systems challenge. We present vLLM Semantic Router, a signal-driven decision routing framework for Mixture-of-Modality (MoM) model deployments. The architecture follows two complementary Shannon-inspired views. In the information-theoretic regime, signal extraction reduces the entropy of "which model?" by distilling routing-relevant information from raw queries. In the Boolean-algebraic regime, the decision engine composes functionally complete routing policies from signal conditions. The central innovation is composable signal orchestration: thirteen heterogeneous signal types, spanning sub-millisecond heuristics and neural classifiers for semantics, safety, and modality, are composed through configurable Boolean decision rules into deployment-specific routing policies, so that fundamentally different scenarios (multi-cloud enterprise, privacy-regulated, cost-optimized) are expressed as different configurations over the same architecture. Matched decisions drive semantic model routing via thirteen selection algorithms, while per-decision plugin chains enforce safety constraints including a three-stage HaluGate hallucination detection pipeline and a lightweight episodic memory system with ReflectionGate for personalized multi-turn context. A typed neural-symbolic DSL specifies these routing policies and compiles them to multiple deployment targets, enabling configuration-first adaptation without code changes. Together, these components show that composable signal orchestration enables a single framework to serve diverse deployment scenarios with differentiated cost, privacy, and safety policies.

Xueqian Li, Jianqiao Zheng, Francesco Ferroni et al.

Neural Scene Flow Prior (NSFP) is of significant interest to the vision community due to its inherent robustness to out-of-distribution (OOD) effects and its ability to deal with dense lidar points. The approach utilizes a coordinate neural network to estimate scene flow at runtime, without any training. However, it is up to 100 times slower than current state-of-the-art learning methods. In other applications such as image, video, and radiance function reconstruction innovations in speeding up the runtime performance of coordinate networks have centered upon architectural changes. In this paper, we demonstrate that scene flow is different -- with the dominant computational bottleneck stemming from the loss function itself (i.e., Chamfer distance). Further, we rediscover the distance transform (DT) as an efficient, correspondence-free loss function that dramatically speeds up the runtime optimization. Our fast neural scene flow (FNSF) approach reports for the first time real-time performance comparable to learning methods, without any training or OOD bias on two of the largest open autonomous driving (AV) lidar datasets Waymo Open and Argoverse.

Jianqiao Zheng, Sameera Ramasinghe, Xueqian Li et al.

It is well noted that coordinate-based MLPs benefit -- in terms of preserving high-frequency information -- through the encoding of coordinate positions as an array of Fourier features. Hitherto, the rationale for the effectiveness of these positional encodings has been mainly studied through a Fourier lens. In this paper, we strive to broaden this understanding by showing that alternative non-Fourier embedding functions can indeed be used for positional encoding. Moreover, we show that their performance is entirely determined by a trade-off between the stable rank of the embedded matrix and the distance preservation between embedded coordinates. We further establish that the now ubiquitous Fourier feature mapping of position is a special case that fulfills these conditions. Consequently, we present a more general theory to analyze positional encoding in terms of shifted basis functions. In addition, we argue that employing a more complex positional encoding -- that scales exponentially with the number of modes -- requires only a linear (rather than deep) coordinate function to achieve comparable performance. Counter-intuitively, we demonstrate that trading positional embedding complexity for network deepness is orders of magnitude faster than current state-of-the-art; despite the additional embedding complexity. To this end, we develop the necessary theoretical formulae and empirically verify that our theoretical claims hold in practice.

Jianqiao Zheng, Hemanth Saratchandran, Simon Lucey

Implicit Neural Representations (INRs) have revolutionized continuous signal modeling, yet they struggle to recover fine-grained details within finite training budgets. While empirical techniques, such as positional encoding (PE), sinusoidal activations (SIREN), and batch normalization (BN), effectively mitigate this, their theoretical justifications are predominantly post hoc, focusing on the global NTK spectrum only after modifications are applied. In this work, we reverse this paradigm by introducing a structural diagnostic framework. By performing a layer-wise decomposition of the NTK, we mathematically identify the ``Inlet Rank Collapse'': a phenomenon where the low-dimensional input coordinates fail to span the high-dimensional embedding space, creating a fundamental rank deficiency at the first layer that acts as an expressive bottleneck for the entire network. This framework provides a unified perspective to re-interpret PE, SIREN, and BN as different forms of rank restoration. Guided by this diagnosis, we derive a Rank-Expanding Initialization, a minimalist remedy that ensures the representation rank scales with the layer width without architectural modifications or computational overhead. Our results demonstrate that this principled remedy enables standard MLPs to achieve high-fidelity reconstructions, proving that the key to empowering INRs lies in the structural optimization of the initial rank propagation to effectively populate the latent space.

Jianqiao Zheng, Sameera Ramasinghe, Simon Lucey

It is well noted that coordinate based MLPs benefit -- in terms of preserving high-frequency information -- through the encoding of coordinate positions as an array of Fourier features. Hitherto, the rationale for the effectiveness of these positional encodings has been solely studied through a Fourier lens. In this paper, we strive to broaden this understanding by showing that alternative non-Fourier embedding functions can indeed be used for positional encoding. Moreover, we show that their performance is entirely determined by a trade-off between the stable rank of the embedded matrix and the distance preservation between embedded coordinates. We further establish that the now ubiquitous Fourier feature mapping of position is a special case that fulfills these conditions. Consequently, we present a more general theory to analyze positional encoding in terms of shifted basis functions. To this end, we develop the necessary theoretical formulae and empirically verify that our theoretical claims hold in practice. Codes available at https://github.com/osiriszjq/Rethinking-positional-encoding.

Jianqiao Zheng, Xueqian Li, Simon Lucey

The training of vision transformer (ViT) networks on small-scale datasets poses a significant challenge. By contrast, convolutional neural networks (CNNs) have an architectural inductive bias enabling them to perform well on such problems. In this paper, we argue that the architectural bias inherent to CNNs can be reinterpreted as an initialization bias within ViT. This insight is significant as it empowers ViTs to perform equally well on small-scale problems while maintaining their flexibility for large-scale applications. Our inspiration for this ``structured'' initialization stems from our empirical observation that random impulse filters can achieve comparable performance to learned filters within CNNs. Our approach achieves state-of-the-art performance for data-efficient ViT learning across numerous benchmarks including CIFAR-10, CIFAR-100, and SVHN.

Jianqiao Zheng, Xueqian Li, Simon Lucey

Training vision transformer networks on small datasets poses challenges. In contrast, convolutional neural networks (CNNs) can achieve state-of-the-art performance by leveraging their architectural inductive bias. In this paper, we investigate whether this inductive bias can be reinterpreted as an initialization bias within a vision transformer network. Our approach is motivated by the finding that random impulse filters can achieve almost comparable performance to learned filters in CNNs. We introduce a novel initialization strategy for transformer networks that can achieve comparable performance to CNNs on small datasets while preserving its architectural flexibility.

Yiping Ji, James Martens, Jianqiao Zheng et al.

Transformers have achieved remarkable success across a wide range of applications, a feat often attributed to their scalability. Yet training them without skip (residual) connections remains notoriously difficult. While skips stabilize optimization, they also disrupt the hierarchical structure of representations, raising the long-standing question of whether transformers can be trained efficiently without them. In this work, we address this problem by analyzing the Jacobian of a skipless transformer block, showing why skips improve conditioning and revealing that their stabilization benefits can be recovered through a principled initialization strategy. Building on this insight, we introduce the first method that enables stable and efficient training of skipless transformers without altering the standard architecture. We validate our approach on Vision Transformers (ViTs) in both supervised and self-supervised settings, demonstrating that skipless ViTs trained with our initialization overcome the usual optimization barriers, learn richer hierarchical representations, and outperform strong baselines, that incorporate skip connections, on dense prediction benchmarks. These results show that skip connections are not a fundamental requirement for training ViTs and open new avenues for hierarchical representation learning in vision models.

Hemanth Saratchandran, Jianqiao Zheng, Yiping Ji et al.

This paper questions whether the strong performance of softmax attention in transformers stems from producing a probability distribution over inputs. Instead, we argue that softmax's effectiveness lies in its implicit regularization of the Frobenius norm of the attention matrix, which stabilizes training. Motivated by this, we explore alternative activations, specifically polynomials, that achieve a similar regularization effect. Our theoretical analysis shows that certain polynomials can serve as effective substitutes for softmax, achieving strong performance across transformer applications despite violating softmax's typical properties of positivity, normalization, and sparsity. Extensive experiments support these findings, offering a new perspective on attention mechanisms.

Jianqiao Zheng, Cameron Gordon, Yiping Ji et al.

Task-agnostic tabular foundation models such as TabPFN have achieved impressive performance on tabular learning tasks, yet the origins of their inductive biases remain poorly understood. In this work, we study TabPFN through the lens of signal reconstruction and provide the first frequency-based analysis of its in-context learning behavior. We show that TabPFN possesses a broader effective frequency capacity than standard ReLU-MLPs, even without hyperparameter tuning. Moreover, unlike MLPs whose spectra evolve primarily over training epochs, we find that TabPFN's spectral capacity adapts directly to the number of samples provided in-context, a phenomenon we term Spectral Adaptivity. We further demonstrate that positional encoding modulates TabPFN's frequency response, mirroring classical results in implicit neural representations. Finally, we show that these properties enable TabPFN to perform training-free and hyperparameter-free image denoising, illustrating its potential as a task-agnostic implicit model. Our analysis provides new insight into the structure and inductive biases of tabular foundation models and highlights their promise for broader signal reconstruction tasks.

Jianqiao Zheng, Xueqian Li, Sameera Ramasinghe et al.

End-to-end trained per-point embeddings are an essential ingredient of any state-of-the-art 3D point cloud processing such as detection or alignment. Methods like PointNet, or the more recent point cloud transformer -- and its variants -- all employ learned per-point embeddings. Despite impressive performance, such approaches are sensitive to out-of-distribution (OOD) noise and outliers. In this paper, we explore the role of an analytical per-point embedding based on the criterion of bandwidth. The concept of bandwidth enables us to draw connections with an alternate per-point embedding -- positional embedding, particularly random Fourier features. We present compelling robust results across downstream tasks such as point cloud classification and registration with several categories of OOD noise.