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Let $F=\mathbb{F}_q$ and let $K=\mathbb{F}_{q^m}$ be a finite extension. An additive left group code is a left $FG$-submodule of the group algebra $KG$. In this paper, we introduce projector additive left group codes and restricted projector additive left group codes as additive counterparts of idempotent group codes in the classical theory of group codes. More precisely, they are defined, respectively, as images of $FG$-linear projectors on $KG$ and as images of left $FG$-submodules under such projectors. This perspective is motivated by the fact that idempotent elements of $KG$ do not yield a sufficiently general and natural algebraic framework for the study of additive left group codes. Projector additive left group codes are a particular class of projective left $FG$-submodules of $KG$. Consequently, in the semisimple case every additive left group code arises in this way, whereas in the non-semisimple case the projector construction captures precisely the direct summands of $KG$ as left $FG$-modules, and hence a natural subclass of projective left $FG$-submodules. We further relate trace-Euclidean and trace-Hermitian duality to adjoint projectors, establish criteria for the LC

We propose LAPIG, a language guided projector image generation method with surface adaptation and stylization. LAPIG consists of a projector-camera system and a target textured projection surface. LAPIG takes the user text prompt as input and aims to transform the surface style using the projector. LAPIG's key challenge is that due to the projector's physical brightness limitation and the surface texture, the viewer's perceived projection may suffer from color saturation and artifacts in both dark and bright regions, such that even with the state-of-the-art projector compensation techniques, the viewer may see clear surface texture-related artifacts. Therefore, how to generate a projector image that follows the user's instruction while also displaying minimum surface artifacts is an open problem. To address this issue, we propose projection surface adaptation (PSA) that can generate compensable surface stylization. We first train two networks to simulate the projector compensation and project-and-capture processes, this allows us to find a satisfactory projector image without real project-and-capture and utilize gradient descent for fast convergence. Then, we design content and sat

Recent advances in LLM-based ASR connect frozen speech encoders with Large Language Models (LLMs) via lightweight projectors. While effective in monolingual settings, a single projector struggles to capture the diverse acoustic-to-semantic mappings required for multilingual ASR. To address this, we propose SMEAR-MoE, a stabilized Mixture-of-Experts projector that ensures dense gradient flow to all experts, preventing expert collapse while enabling cross-lingual sharing. We systematically compare monolithic, static multi-projector, and dynamic MoE designs across four Indic languages (Hindi, Marathi, Tamil, Telugu). Our SMEAR-MoE achieves strong performance, delivering upto a 7.6% relative WER reduction over the single-projector baseline, while maintaining comparable runtime efficiency. Analysis of expert routing further shows linguistically meaningful specialization, with related languages sharing experts. These results demonstrate that stable multi-expert projectors are key to scalable and robust multilingual ASR.

Conventional multi-projector calibration requires projecting and capturing structured light patterns for each projector sequentially, causing calibration time and effort to increase linearly with the number of projectors. This scalability bottleneck has long limited the deployment of large-scale projection mapping systems. We present a new calibration framework that breaks this limitation by embedding cameras into the surface of the calibration target. The embedded cameras directly capture the incoming projection light, enabling the separation of simultaneously projected structured light patterns from multiple projectors according to their incident directions. Our method establishes correspondences between the optical centers of the embedded cameras and the projector pixels, allowing the intrinsic and extrinsic parameters of all projectors to be simultaneously estimated. We further introduce a correction technique for small misalignments between the calibration board and camera optical centers. As a result, our system achieves calibration accuracy comparable to conventional methods while reducing the required number of projection-capture cycles from linear to nearly constant with r

Integrating pretrained speech encoders with large language models (LLMs) is promising for ASR, but performance and data efficiency depend on the speech-language interface. A common choice is a learned projector that maps encoder features into the LLM embedding space, whereas an alternative is to expose discrete phoneme sequences to the LLM. Using the same encoder and LLM backbones, we compare phoneme-based and vanilla projector-based interfaces in high-resource English and low-resource Tatar. We also propose a BPE-phoneme interface that groups frequent local phoneme patterns while preserving explicit word-boundary cues for phoneme-to-grapheme generation. On LibriSpeech, the phoneme-based interface is competitive with the vanilla projector, and the BPE-phoneme interface yields further gains. On Tatar, the phoneme-based interface substantially outperforms the vanilla projector. We further find that phoneme supervision yields a phoneme-informed hybrid interface that is stronger than the vanilla projector.

Projector compensation seeks to correct geometric and photometric distortions that occur when images are projected onto nonplanar or textured surfaces. However, most existing methods are highly setup-dependent, requiring fine-tuning or retraining whenever the surface, lighting, or projector-camera pose changes. Progress has been limited by two key challenges: (1) the absence of large, diverse training datasets and (2) existing geometric correction models are typically constrained by specific spatial setups; without further retraining or fine-tuning, they often fail to generalize directly to novel geometric configurations. We introduce SIComp, the first Setup-Independent framework for full projector Compensation, capable of generalizing to unseen setups without fine-tuning or retraining. To enable this, we construct a large-scale real-world dataset spanning 277 distinct projector-camera setups. SIComp adopts a co-adaptive design that decouples geometry and photometry: A carefully tailored optical flow module performs online geometric correction, while a novel photometric network handles photometric compensation. To further enhance robustness under varying illumination, we integrate

The Transformer's quadratic complexity with input length imposes an unsustainable computational load on large language models (LLMs). In contrast, the Selective Scan Structured State-Space Model, or Mamba, addresses this computational challenge effectively. This paper explores a query-based cross-modal projector designed to bolster Mamba's efficiency for vision-language modeling by compressing visual tokens based on input through the cross-attention mechanism. This innovative projector also removes the need for manually designing the 2D scan order of original image features when converting them into an input sequence for Mamba LLM. Experimental results across various vision-language understanding benchmarks show that the proposed cross-modal projector enhances Mamba-based multimodal LLMs, boosting both performance and throughput.

We introduce a novel class of projectors for 3D cone beam tomographic reconstruction. Analytical formulas are derived to compute the relationship between the volume of a voxel projected onto a detector pixel and its contribution to the line integral of attenuation recorded by that pixel. Based on these formulas, we construct a near-exact projector and backprojector, particularly suited for algebraic reconstruction techniques and hierarchical reconstruction approaches with nonuniform voxel grids. Unlike traditional projectors, which assume a uniform grid with fixed voxel sizes, our method enables local refinement of voxels, allowing for adaptive grid resolution and improved reconstruction quality in regions of interest. We have implemented this cutting voxel projector along with a relaxed, speed-optimized version and compared them to two established projectors: a ray-tracing projector based on Siddon's algorithm and a TT footprint projector. Our results demonstrate that the cutting voxel projector achieves higher accuracy than the TT projector, especially for large cone beam angles. Furthermore, the relaxed version of the cutting voxel projector offers a significant speed advantage,

We define the computational task of detecting projectors in finite dimensional associative algebras with a combinatorial basis, labelled by representation theory data, using combinatorial central elements in the algebra. In the first example, the projectors belong to the centre of a symmetric group algebra and are labelled by Young diagrams with a fixed number of boxes $n$. We describe a quantum algorithm for the task based on quantum phase estimation (QPE) and obtain estimates of the complexity as a function of $n$. We compare to a classical algorithm related to the projector identification problem by the AdS/CFT correspondence. This gives a concrete proof of concept for classical/quantum comparisons of the complexity of a detection task, based in holographic correspondences. A second example involves projectors labelled by triples of Young diagrams, all having $n$ boxes, with non-vanishing Kronecker coefficient. The task takes as input the projector, and consists of identifying the triple of Young diagrams. In both of the above cases the standard QPE complexities are polynomial in $n$. A third example of quantum projector detection involves projectors labelled by a triple of Youn

Conventionally, during the knowledge distillation process (e.g. feature distillation), an additional projector is often required to perform feature transformation due to the dimension mismatch between the teacher and the student networks. Interestingly, we discovered that even if the student and the teacher have the same feature dimensions, adding a projector still helps to improve the distillation performance. In addition, projectors even improve logit distillation if we add them to the architecture too. Inspired by these surprising findings and the general lack of understanding of the projectors in the knowledge distillation process from existing literature, this paper investigates the implicit role that projectors play but so far have been overlooked. Our empirical study shows that the student with a projector (1) obtains a better trade-off between the training accuracy and the testing accuracy compared to the student without a projector when it has the same feature dimensions as the teacher, (2) better preserves its similarity to the teacher beyond shallow and numeric resemblance, from the view of Centered Kernel Alignment (CKA), and (3) avoids being over-confident as the teach

An ideal projector on the space of polynomials $\mathbb{C} [\mathbf{x}]=\mathbb{C} [x_{1},\ldots ,x_{d}]$ is a projector whose kernel is an ideal in $\mathbb{C}[ \mathbf{x}]$. The question of characterization of ideal projectors that are limits of Lagrange projector was posed by Carl de Boor. In this paper we make a contribution to this problem. Every ideal projector $P$ can be written as a sum of ideal projector $\sum P^{(k)}$ $\ $such that $\cap \ker P^{(k)}$ is a primary decomposition of the ideal $\ker P$. We show that $P$ is a limit of Lagrange projectors if and only if each $P^{(k)}$ is. As an application we construct an ideal projector $P$ whose kernel is a symmetric ideal, yet $P$ is not a limit of Lagrange projectors.

Intrinsic projector calibration is essential in projection mapping (PM) applications, especially in dynamic PM. However, due to the shallow depth-of-field (DOF) of a projector, more work is needed to ensure accurate calibration. We aim to estimate the intrinsic parameters of a projector while avoiding the limitation of shallow DOF. As the core of our technique, we present a practical calibration device that requires a minimal working volume directly in front of the projector lens regardless of the projector's focusing distance and aperture size. The device consists of a flat-bed scanner and pinhole-array masks. For calibration, a projector projects a series of structured light patterns in the device. The pinholes directionally decompose the structured light, and only the projected rays that pass through the pinholes hit the scanner plane. For each pinhole, we extract a ray passing through the optical center of the projector. Consequently, we regard the projector as a pinhole projector that projects the extracted rays only, and we calibrate the projector by applying the standard camera calibration technique, which assumes a pinhole camera model. Using a proof-of-concept prototype, w

We construct and study a lift of Jones-Wenzl projectors to the setting of Khovanov spectra, and provide a realization of such lifted projectors via a Cooper-Krushkal-like sequence of maps. We also give a polynomial action on the 3-strand spectral projector allowing a complete computation of the 3-colored Khovanov spectrum of the unknot, proving a conjecture of Lobb-Orson-Schütz. As a byproduct, we disprove a conjecture of Lawson-Lipshitz-Sarkar on the topological Hochschild homology of tangle spectra.

For a Riemannian manifold with a cylindrical end, consider a Dirac-type operator that is asymptotically product type with the generalized Atiyah-Patodi-Singer boundary condition on any finite portion of the cylinder. In the present work we consider the problem of constructing the Calderon projector in this setting and studying the adiabatic limit of it along the cylindrical end. As a consequence, we extend a result of Nicolaescu on adiabatic limits of Cauchy data spaces. The proof leverages resolvent and its estimates in the framework of the b-calculus needed for the construction of the Calderon projector corresponding to our Dirac-type operator.

Full projector compensation is a practical task of projector-camera systems. It aims to find a projector input image, named compensation image, such that when projected it cancels the geometric and photometric distortions due to the physical environment and hardware. State-of-the-art methods use deep learning to address this problem and show promising performance for low-resolution setups. However, directly applying deep learning to high-resolution setups is impractical due to the long training time and high memory cost. To address this issue, this paper proposes a practical full compensation solution. Firstly, we design an attention-based grid refinement network to improve geometric correction quality. Secondly, we integrate a novel sampling scheme into an end-to-end compensation network to alleviate computation and introduce attention blocks to preserve key features. Finally, we construct a benchmark dataset for high-resolution projector full compensation. In experiments, our method demonstrates clear advantages in both efficiency and quality.

In Multimodal Large Language Models (MLLMs), a visual projector plays a crucial role in bridging pre-trained vision encoders with LLMs, enabling profound visual understanding while harnessing the LLMs' robust capabilities. Despite the importance of the visual projector, it has been relatively less explored. In this study, we first identify two essential projector properties: (i) flexibility in managing the number of visual tokens, crucial for MLLMs' overall efficiency, and (ii) preservation of local context from visual features, vital for spatial understanding. Based on these findings, we propose a novel projector design that is both flexible and locality-enhanced, effectively satisfying the two desirable properties. Additionally, we present comprehensive strategies to effectively utilize multiple and multifaceted instruction datasets. Through extensive experiments, we examine the impact of individual design choices. Finally, our proposed MLLM, Honeybee, remarkably outperforms previous state-of-the-art methods across various benchmarks, including MME, MMBench, SEED-Bench, and LLaVA-Bench, achieving significantly higher efficiency. Code and models are available at https://github.com

In knowledge distillation, previous feature distillation methods mainly focus on the design of loss functions and the selection of the distilled layers, while the effect of the feature projector between the student and the teacher remains under-explored. In this paper, we first discuss a plausible mechanism of the projector with empirical evidence and then propose a new feature distillation method based on a projector ensemble for further performance improvement. We observe that the student network benefits from a projector even if the feature dimensions of the student and the teacher are the same. Training a student backbone without a projector can be considered as a multi-task learning process, namely achieving discriminative feature extraction for classification and feature matching between the student and the teacher for distillation at the same time. We hypothesize and empirically verify that without a projector, the student network tends to overfit the teacher's feature distributions despite having different architecture and weights initialization. This leads to degradation on the quality of the student's deep features that are eventually used in classification. Adding a proj

We present a method of defining projectors in the virtual Temperley-Lieb algebra, that generalizes the Jones-Wenzl projectors in Temperley-Lieb algebra. We show that the projectors have similar properties with the Jones-Wenzl projectors, and contain an extra property which is associated with the virtual generator elements, that is, the product of a projector with a virtual generator is unchanged. We also show the uniqueness of the projector $f_n$ in terms of its axiomatic properties in the virtual Temperley-Lieba algebra $VTL_n(d)$. Finally, we find the coefficients of $f_n$ and give an explicit formula for the projector $f_n$.

This paper proposes a novel framework integrating the principles of active stereo in standard passive camera systems without a physical pattern projector. We virtually project a pattern over the left and right images according to the sparse measurements obtained from a depth sensor. Any such devices can be seamlessly plugged into our framework, allowing for the deployment of a virtual active stereo setup in any possible environment, overcoming the limitation of pattern projectors, such as limited working range or environmental conditions. Experiments on indoor/outdoor datasets, featuring both long and close-range, support the seamless effectiveness of our approach, boosting the accuracy of both stereo algorithms and deep networks.

A lighting-based multispectral imaging system using an RGB camera and a projector is one of the most practical and low-cost systems to acquire multispectral observations for estimating the scene's spectral reflectance information. However, existing projector-based systems assume that the spectral power distribution (SPD) of each projector primary is known, which requires additional equipment such as a spectrometer to measure the SPD. In this paper, we present a method for jointly estimating the spectral reflectance and the SPD of each projector primary. In addition to adopting a common spectral reflectance basis model, we model the projector's SPD by a low-dimensional model using basis functions obtained by a newly collected projector's SPD database. Then, the spectral reflectances and the projector's SPDs are alternatively estimated based on the basis models. We experimentally show the performance of our joint estimation using a different number of projected illuminations and investigate the potential of the spectral reflectance estimation using a projector with unknown SPD.