Daily Papers

Multimodal large language models (MLLMs) are increasingly expected to act on visual information, yet the same scene may require different actions under different task contexts. How reliably can a model turn the same visual evidence into the action required by the current context? To answer this question, we introduce ROSE (Reference-conditioned Oddity and Symbolic Execution), a controlled benchmark that holds the visual scene fixed while varying region constraints and required symbolic outputs. Through coupled counting and coordinate-action tasks, ROSE tests whether models can infer an implicit majority reference and act on the resulting fine-grained visual evidence under changing contexts. Across nine recent MLLMs, performance drops by as much as 44.5 percentage points from counting-oriented tasks to region-conditioned action, despite 98.8\% human performance. The gap persists on paired scenes and regions for which the same model returns the correct count, while global-click and matched local controls show that coordinate grounding explains only part of the loss, revealing a distinct, model-dependent bottleneck in turning shared visual evidence into context-specific actions.

Large language models (LLMs), despite strong performance on complex mathematical problems, exhibit systematic limitations in counting tasks. This issue arises from architectural limits of transformers, where counting is performed across layers, leading to degraded precision for larger counting problems due to depth constraints. To address this limitation, we propose a simple test-time strategy inspired by System-2 cognitive processes that decomposes large counting tasks into smaller, independent sub-problems that the model can reliably solve. We evaluate this approach using observational and causal mediation analyses to understand the underlying mechanism of this System-2-like strategy. Our mechanistic analysis identifies key components: latent counts are computed and stored in the final item representations of each part, transferred to intermediate steps via dedicated attention heads, and aggregated in the final stage to produce the total count. Experimental results demonstrate that this strategy enables LLMs to surpass architectural limitations and achieve high accuracy on large-scale counting tasks. This work provides mechanistic insight into System-2 counting in LLMs and presents a generalizable approach for improving and understanding their reasoning behavior.

We propose the use of dilated filters to construct an aggregation module in a multicolumn convolutional neural network for perspective-free counting. Counting is a common problem in computer vision (e.g. traffic on the street or pedestrians in a crowd). Modern approaches to the counting problem involve the production of a density map via regression whose integral is equal to the number of objects in the image. However, objects in the image can occur at different scales (e.g. due to perspective effects) which can make it difficult for a learning agent to learn the proper density map. While the use of multiple columns to extract multiscale information from images has been shown before, our approach aggregates the multiscale information gathered by the multicolumn convolutional neural network to improve performance. Our experiments show that our proposed network outperforms the state-of-the-art on many benchmark datasets, and also that using our aggregation module in combination with a higher number of columns is beneficial for multiscale counting.

Object counting is a foundational vision task with over a decade of dedicated research, yet state-of-the-art models still fail systematically in the mixed-object setting that dominates real-world applications such as industrial inspection and product sorting. We show that this gap is strongly driven by limitations in existing training and evaluation data: real counting datasets are prohibitively expensive to annotate and suffer from labeling noise, while existing synthetic alternatives lack diversity and realism. We address this with MixCount, a dataset and benchmark for mixed-object counting designed to target the failure modes of current counting models. To overcome the high cost of constructing and labeling such data, we develop an automatic generation pipeline that synthesizes images, fine-grained textual descriptions, and pixel-perfect counting annotations at scale, eliminating the labeling ambiguity that plagues prior datasets. Evaluating state-of-the-art counting models on MixCount exposes severe degradation in the mixed-object setting. More importantly, training these models on our synthesized data yields substantial gains on real-world benchmarks, reducing MAE by 20.14% on FSC-147 and by 18.3% on PairTally. These results establish MixCount as both a benchmark and a training dataset for fine-grained counting, and demonstrate that our pipeline, which produces effectively unlimited labeled data, helps address a long-standing bottleneck in counting models.

Complex numerical time series analysis often demands multi-step reasoning capabilities beyond current models' reach. Tasks like medical diagnosis and weather forecasting require sequential reasoning processes - including counterfactual analysis, logical deduction, knowledge application, and multi-modal contextual integration - that existing time series models cannot explicitly perform. While recent research has shown large language models (LLMs) can achieve sophisticated Chain-of-Thought (CoT) reasoning through reinforcement learning (RL), these advances have primarily focused on mathematical and coding domains, with LLMs still demonstrating poor performance on time series tasks. We introduce Chain Of thought for Understanding Numerical Time Series (COUNTS), the first framework that trains LLMs to perform CoT reasoning across diverse time series tasks using RL with verifiable rewards. Our approach employs a Residual Vector-Quantized VAE to create high-fidelity discrete tokens that seamlessly integrate into a pre-trained LLM's vocabulary. COUNTS undergoes a two-stage training process: first, supervised fine-tuning on time series analysis tasks to master our novel representations, followed by Group Relative Policy Optimization training on verifiable problems using prompting strategies that encourage explicit reasoning steps before producing final answers. Our experiments demonstrate that this RL-driven approach with intermediate CoT reasoning significantly enhances LLM performance across various time series analysis tasks, opening new possibilities for complex temporal data reasoning.

We address a persistent challenge in text-to-image models: accurately generating a specified number of objects. Current models, which learn from image-text pairs, inherently struggle with counting, as training data cannot depict every possible number of objects for any given object. To solve this, we propose optimizing the generated image based on a counting loss derived from a counting model that aggregates an object\'s potential. Employing an out-of-the-box counting model is challenging for two reasons: first, the model requires a scaling hyperparameter for the potential aggregation that varies depending on the viewpoint of the objects, and second, classifier guidance techniques require modified models that operate on noisy intermediate diffusion steps. To address these challenges, we propose an iterated online training mode that improves the accuracy of inferred images while altering the text conditioning embedding and dynamically adjusting hyperparameters. Our method offers three key advantages: (i) it can consider non-derivable counting techniques based on detection models, (ii) it is a zero-shot plug-and-play solution facilitating rapid changes to the counting techniques and image generation methods, and (iii) the optimized counting token can be reused to generate accurate images without additional optimization. We evaluate the generation of various objects and show significant improvements in accuracy. The project page is available at https://ozzafar.github.io/count_token.

Object counting remains fragmented across domain-specific datasets and task formulations, despite rapid progress in generalist vision models. Existing counting models are often tailored to scenarios such as crowds, vehicles, cells, crops, or remote-sensing objects, and thus struggle to generalize across categories, visual domains, object scales, and density distributions. In this paper, we study text-guided object counting across domains, where a model takes an image and a natural-language query as input and returns an instance-grounded set of target points whose cardinality gives the count. This formulation unifies category-conditioned counting with interpretable spatial localization. To support this setting, we construct CLOC, a Cross-domain Large-scale Object Counting dataset that reorganizes diverse public data sources into a unified benchmark. CLOC covers six visual domains: General Scene, Remote Sensing, Histopathology, Cellular Microscopy, Agriculture, and Microbiology, with about 220K images, 619 categories, and 15M object instances. Based on CLOC, we propose Count Anything, a generalist model for text-guided object counting. Unlike density-map-based methods, which dominate counting models, Count Anything adopts discrete instance points and performs dual-granularity instance enumeration. A Region-level Sparse Counter provides object-level anchors for large and sparse targets, while a Pixel-level Dense Counter handles small, crowded, and weakly bounded targets via dense point prediction. A point-centric supervision strategy enables learning from heterogeneous annotations, and Complementary Count Fusion combines both counters in a parameter-free manner. Extensive experiments show that Count Anything achieves strong accuracy and multi-domain generalization, outperforming existing open-world counting methods. Code is available at: https://github.com/Mengqi-Lei/count-anything.

Systematic under-counting effects are observed in data collected across many disciplines, e.g., epidemiology and ecology. Under-counted tensor completion (UC-TC) is well-motivated for many data analytics tasks, e.g., inferring the case numbers of infectious diseases at unobserved locations from under-counted case numbers in neighboring regions. However, existing methods for similar problems often lack supports in theory, making it hard to understand the underlying principles and conditions beyond empirical successes. In this work, a low-rank Poisson tensor model with an expressive unknown nonlinear side information extractor is proposed for under-counted multi-aspect data. A joint low-rank tensor completion and neural network learning algorithm is designed to recover the model. Moreover, the UC-TC formulation is supported by theoretical analysis showing that the fully counted entries of the tensor and each entry's under-counting probability can be provably recovered from partial observations -- under reasonable conditions. To our best knowledge, the result is the first to offer theoretical supports for under-counted multi-aspect data completion. Simulations and real-data experiments corroborate the theoretical claims.

Open-world object counting remains brittle: despite rapid advances in vision-language models (VLMs), reliably counting the objects a user intends is far from solved. We argue that a central reason is that counting granularity is left implicit; users may refer to a specific identity, an attribute, an instance type, a category, or an abstract concept, yet most methods treat "what to count" as a single, category-level matching problem. In this work, we redefine open-world counting as multi-grained counting, where visual exemplars specify target appearance and fine-grained text, with optional negative prompts, specifies the intended semantic granularity across five explicit levels. Making granularity explicit, however, exposes a critical data bottleneck: existing counting datasets lack the multi-category scenes, controlled distractors, and instance-level annotations needed to verify fine-grained prompt semantics. To address this, we propose the first fully automatic data-scaling pipeline that integrates controllable 3D synthesis with consistent image editing and VLM-based filtering, and use it to construct KubriCount, the largest and most comprehensively annotated counting dataset to date, supporting both training and multi-grained evaluation. Systematic benchmarking reveals that both multimodal large language models and specialist counting models exhibit severe prompt-following failures under fine-grained distinctions. Motivated by these findings, we train HieraCount, a multi-grained counting model that jointly leverages text and visual exemplars as complementary target specifications. HieraCount substantially improves multi-grained counting accuracy and generalizes robustly to challenging real-world scenarios. The project page is available here: https://verg-avesta.github.io/KubriCount/.

Video understanding requires models to continuously track and update world state during playback. While existing benchmarks have advanced video understanding evaluation across multiple dimensions, the observation of how models maintain world state remains insufficient. We propose VCBench, a streaming counting benchmark that repositions counting as a minimal probe for diagnosing world state maintenance capability. We decompose this capability into object counting and event counting, forming 8 fine-grained subcategories. Object counting covers tracking currently visible objects and cumulative unique identities, while event counting covers detecting instantaneous actions and tracking complete activity cycles. VCBench contains 406 videos with frame-by-frame annotations of 10,071 event occurrence moments and object state change moments, generating 1,000 streaming QA pairs with 4,576 query points along timelines. By observing state maintenance trajectories through streaming multi-point queries, we design three complementary metrics to diagnose numerical precision, trajectory consistency, and temporal awareness. Evaluation on mainstream video-language models shows that current models still exhibit significant deficiencies in spatial-temporal state maintenance, particularly struggling with tasks like periodic event counting. VCBench provides a diagnostic framework for measuring and improving state maintenance in video understanding systems. Our code and data are available at https://github.com/buaaplay/VCBench.

Object counting is pivotal for understanding the composition of scenes. Previously, this task was dominated by class-specific methods, which have gradually evolved into more adaptable class-agnostic strategies. However, these strategies come with their own set of limitations, such as the need for manual exemplar input and multiple passes for multiple categories, resulting in significant inefficiencies. This paper introduces a new, more practical approach enabling simultaneous counting of multiple object categories using an open vocabulary framework. Our solution, OmniCount, stands out by using semantic and geometric insights from pre-trained models to count multiple categories of objects as specified by users, all without additional training. OmniCount distinguishes itself by generating precise object masks and leveraging point prompts via the Segment Anything Model for efficient counting. To evaluate OmniCount, we created the OmniCount-191 benchmark, a first-of-its-kind dataset with multi-label object counts, including points, bounding boxes, and VQA annotations. Our comprehensive evaluation in OmniCount-191, alongside other leading benchmarks, demonstrates OmniCount's exceptional performance, significantly outpacing existing solutions and heralding a new era in object counting technology.

Most counting questions in visual question answering (VQA) datasets are simple and require no more than object detection. Here, we study algorithms for complex counting questions that involve relationships between objects, attribute identification, reasoning, and more. To do this, we created TallyQA, the world's largest dataset for open-ended counting. We propose a new algorithm for counting that uses relation networks with region proposals. Our method lets relation networks be efficiently used with high-resolution imagery. It yields state-of-the-art results compared to baseline and recent systems on both TallyQA and the HowMany-QA benchmark.

The flexibility and accuracy of methods for automatically counting objects in images and videos are limited by the way the object can be specified. While existing methods allow users to describe the target object with text and visual examples, the visual examples must be manually annotated inside the image, and there is no way to specify what not to count. To address these gaps, we introduce novel capabilities that expand how the target object can be specified. Specifically, we extend the prompt to enable what not to count to be described with text and/or visual examples, introduce the concept of `pseudo-exemplars' that automate the annotation of visual examples at inference, and extend counting models to accept visual examples from both natural and synthetic external images. We also use our new counting model, CountGD++, as a vision expert agent for an LLM. Together, these contributions expand the prompt flexibility of multi-modal open-world counting and lead to significant improvements in accuracy, efficiency, and generalization across multiple datasets. Code is available at https://github.com/niki-amini-naieni/CountGDPlusPlus.

Scaling laws predict loss from compute but not how capabilities interact. We measure the coupling between reasoning and truthfulness across 63 base models from 16 families and find a regime change invisible to loss curves: below a family-dependent critical scale N_c, capabilities anticorrelate; above it, they cooperate. N_c approx 3.5B parameters [2.9B, 13.4B] (bootstrap 95% CI), but model size is not the only variable that determines phase. Architecture, data curation, and training recipe each shift N_c independently: curated training eliminated the coupling dip between Qwen generations (0.025 to 0.830 at matched scale), Gemma-4 at 4B achieves coupling 0.871, characteristic of 13B+ standard-trained models, through distillation and architectural innovation, and Phi at 1B matches web-trained coupling at 10B through data curation alone. Width normalization eliminates the anticorrelation across all tested families, supporting an output-projection bottleneck. Internally, 38 of 40 models show zero competing attention heads. A sparse-regression ODE cross-predicts held-out Llama-2 at 5.6% error. The diagnostic requires no model internals -- only public benchmark scores across a model family. The cooperative regime extends to the frontier (r = +0.72, 34 models, 10 labs). Code, data, and an open-source activation-steering tool for any open-weight model are released alongside an interactive dashboard that diagnoses any model's coupling phase, suggests concrete interventions (data curation, width, benchmark rotation), and provides ODE scaling predictions, frontier diagnostics, and eigenstructure analysis: https://zehenlabs.com/cape/.

We show that crowd counting can be viewed as a decomposable point querying process. This formulation enables arbitrary points as input and jointly reasons whether the points are crowd and where they locate. The querying processing, however, raises an underlying problem on the number of necessary querying points. Too few imply underestimation; too many increase computational overhead. To address this dilemma, we introduce a decomposable structure, i.e., the point-query quadtree, and propose a new counting model, termed Point quEry Transformer (PET). PET implements decomposable point querying via data-dependent quadtree splitting, where each querying point could split into four new points when necessary, thus enabling dynamic processing of sparse and dense regions. Such a querying process yields an intuitive, universal modeling of crowd as both the input and output are interpretable and steerable. We demonstrate the applications of PET on a number of crowd-related tasks, including fully-supervised crowd counting and localization, partial annotation learning, and point annotation refinement, and also report state-of-the-art performance. For the first time, we show that a single counting model can address multiple crowd-related tasks across different learning paradigms. Code is available at https://github.com/cxliu0/PET.

We propose a novel framework for interactive class-agnostic object counting, where a human user can interactively provide feedback to improve the accuracy of a counter. Our framework consists of two main components: a user-friendly visualizer to gather feedback and an efficient mechanism to incorporate it. In each iteration, we produce a density map to show the current prediction result, and we segment it into non-overlapping regions with an easily verifiable number of objects. The user can provide feedback by selecting a region with obvious counting errors and specifying the range for the estimated number of objects within it. To improve the counting result, we develop a novel adaptation loss to force the visual counter to output the predicted count within the user-specified range. For effective and efficient adaptation, we propose a refinement module that can be used with any density-based visual counter, and only the parameters in the refinement module will be updated during adaptation. Our experiments on two challenging class-agnostic object counting benchmarks, FSCD-LVIS and FSC-147, show that our method can reduce the mean absolute error of multiple state-of-the-art visual counters by roughly 30% to 40% with minimal user input. Our project can be found at https://yifehuang97.github.io/ICACountProjectPage/.

Perspective distortions and crowd variations make crowd counting a challenging task in computer vision. To tackle it, many previous works have used multi-scale architecture in deep neural networks (DNNs). Multi-scale branches can be either directly merged (e.g. by concatenation) or merged through the guidance of proxies (e.g. attentions) in the DNNs. Despite their prevalence, these combination methods are not sophisticated enough to deal with the per-pixel performance discrepancy over multi-scale density maps. In this work, we redesign the multi-scale neural network by introducing a hierarchical mixture of density experts, which hierarchically merges multi-scale density maps for crowd counting. Within the hierarchical structure, an expert competition and collaboration scheme is presented to encourage contributions from all scales; pixel-wise soft gating nets are introduced to provide pixel-wise soft weights for scale combinations in different hierarchies. The network is optimized using both the crowd density map and the local counting map, where the latter is obtained by local integration on the former. Optimizing both can be problematic because of their potential conflicts. We introduce a new relative local counting loss based on relative count differences among hard-predicted local regions in an image, which proves to be complementary to the conventional absolute error loss on the density map. Experiments show that our method achieves the state-of-the-art performance on five public datasets, i.e. ShanghaiTech, UCF_CC_50, JHU-CROWD++, NWPU-Crowd and Trancos.

Existing works on visual counting primarily focus on one specific category at a time, such as people, animals, and cells. In this paper, we are interested in counting everything, that is to count objects from any category given only a few annotated instances from that category. To this end, we pose counting as a few-shot regression task. To tackle this task, we present a novel method that takes a query image together with a few exemplar objects from the query image and predicts a density map for the presence of all objects of interest in the query image. We also present a novel adaptation strategy to adapt our network to any novel visual category at test time, using only a few exemplar objects from the novel category. We also introduce a dataset of 147 object categories containing over 6000 images that are suitable for the few-shot counting task. The images are annotated with two types of annotation, dots and bounding boxes, and they can be used for developing few-shot counting models. Experiments on this dataset shows that our method outperforms several state-of-the-art object detectors and few-shot counting approaches. Our code and dataset can be found at https://github.com/cvlab-stonybrook/LearningToCountEverything.

Class-agnostic counting methods enumerate objects of an arbitrary class, providing tremendous utility in many fields. Prior works have limited usefulness as they require either a set of examples of the type to be counted or that the query image contains only a single type of object. A significant factor in these shortcomings is the lack of a dataset to properly address counting in settings with more than one kind of object present. To address these issues, we propose the first Multi-class, Class-Agnostic Counting dataset (MCAC) and A Blind Counter (ABC123), a method that can count multiple types of objects simultaneously without using examples of type during training or inference. ABC123 introduces a new paradigm where instead of requiring exemplars to guide the enumeration, examples are found after the counting stage to help a user understand the generated outputs. We show that ABC123 outperforms contemporary methods on MCAC without needing human in-the-loop annotations. We also show that this performance transfers to FSC-147, the standard class-agnostic counting dataset. MCAC is available at MCAC.active.vision and ABC123 is available at ABC123.active.vision.

Recently, the problem of inaccurate learning targets in crowd counting draws increasing attention. Inspired by a few pioneering work, we solve this problem by trying to predict the indices of pre-defined interval bins of counts instead of the count values themselves. However, an inappropriate interval setting might make the count error contributions from different intervals extremely imbalanced, leading to inferior counting performance. Therefore, we propose a novel count interval partition criterion called Uniform Error Partition (UEP), which always keeps the expected counting error contributions equal for all intervals to minimize the prediction risk. Then to mitigate the inevitably introduced discretization errors in the count quantization process, we propose another criterion called Mean Count Proxies (MCP). The MCP criterion selects the best count proxy for each interval to represent its count value during inference, making the overall expected discretization error of an image nearly negligible. As far as we are aware, this work is the first to delve into such a classification task and ends up with a promising solution for count interval partition. Following the above two theoretically demonstrated criterions, we propose a simple yet effective model termed Uniform Error Partition Network (UEPNet), which achieves state-of-the-art performance on several challenging datasets. The codes will be available at: https://github.com/TencentYoutuResearch/CrowdCounting-UEPNet.

Generative modeling is widely regarded as one of the most essential problems in today's AI community, with text-to-image generation having gained unprecedented real-world impacts. Among various approaches, diffusion models have achieved remarkable success and have become the de facto solution for text-to-image generation. However, despite their impressive performance, these models exhibit fundamental limitations in adhering to numerical constraints in user instructions, frequently generating images with an incorrect number of objects. While several prior works have mentioned this issue, a comprehensive and rigorous evaluation of this limitation remains lacking. To address this gap, we introduce T2ICountBench, a novel benchmark designed to rigorously evaluate the counting ability of state-of-the-art text-to-image diffusion models. Our benchmark encompasses a diverse set of generative models, including both open-source and private systems. It explicitly isolates counting performance from other capabilities, provides structured difficulty levels, and incorporates human evaluations to ensure high reliability. Extensive evaluations with T2ICountBench reveal that all state-of-the-art diffusion models fail to generate the correct number of objects, with accuracy dropping significantly as the number of objects increases. Additionally, an exploratory study on prompt refinement demonstrates that such simple interventions generally do not improve counting accuracy. Our findings highlight the inherent challenges in numerical understanding within diffusion models and point to promising directions for future improvements.

Accurate plant counting provides valuable information for agriculture such as crop yield prediction, plant density assessment, and phenotype quantification. Vision-based approaches are currently the mainstream solution. Prior art typically uses a detection or a regression model to count a specific plant. However, plants have biodiversity, and new cultivars are increasingly bred each year. It is almost impossible to exhaust and build all species-dependent counting models. Inspired by class-agnostic counting (CAC) in computer vision, we argue that it is time to rethink the problem formulation of plant counting, from what plants to count to how to count plants. In contrast to most daily objects with spatial and temporal invariance, plants are dynamic, changing with time and space. Their non-rigid structure often leads to worse performance than counting rigid instances like heads and cars such that current CAC and open-world detection models are suboptimal to count plants. In this work, we inherit the vein of the TasselNet plant counting model and introduce a new extension, TasselNetV4, shifting from species-specific counting to cross-species counting. TasselNetV4 marries the local counting idea of TasselNet with the extract-and-match paradigm in CAC. It builds upon a plain vision transformer and incorporates novel multi-branch box-aware local counters used to enhance cross-scale robustness. Two challenging datasets, PAC-105 and PAC-Somalia, are harvested. Extensive experiments against state-of-the-art CAC models show that TasselNetV4 achieves not only superior counting performance but also high efficiency.Our results indicate that TasselNetV4 emerges to be a vision foundation model for cross-scene, cross-scale, and cross-species plant counting.

In this paper, we consider the problem of generalised visual object counting, with the goal of developing a computational model for counting the number of objects from arbitrary semantic categories, using arbitrary number of "exemplars", i.e. zero-shot or few-shot counting. To this end, we make the following four contributions: (1) We introduce a novel transformer-based architecture for generalised visual object counting, termed as Counting Transformer (CounTR), which explicitly capture the similarity between image patches or with given "exemplars" with the attention mechanism;(2) We adopt a two-stage training regime, that first pre-trains the model with self-supervised learning, and followed by supervised fine-tuning;(3) We propose a simple, scalable pipeline for synthesizing training images with a large number of instances or that from different semantic categories, explicitly forcing the model to make use of the given "exemplars";(4) We conduct thorough ablation studies on the large-scale counting benchmark, e.g. FSC-147, and demonstrate state-of-the-art performance on both zero and few-shot settings.

Even for simple arithmetic tasks like integer addition, it is challenging for Transformers to generalize to longer sequences than those encountered during training. To tackle this problem, we propose position coupling, a simple yet effective method that directly embeds the structure of the tasks into the positional encoding of a (decoder-only) Transformer. Taking a departure from the vanilla absolute position mechanism assigning unique position IDs to each of the tokens, we assign the same position IDs to two or more "relevant" tokens; for integer addition tasks, we regard digits of the same significance as in the same position. On the empirical side, we show that with the proposed position coupling, our models trained on 1 to 30-digit additions can generalize up to 200-digit additions (6.67x of the trained length). On the theoretical side, we prove that a 1-layer Transformer with coupled positions can solve the addition task involving exponentially many digits, whereas any 1-layer Transformer without positional information cannot entirely solve it. We also demonstrate that position coupling can be applied to other algorithmic tasks such as Nx2 multiplication and a two-dimensional task.

The goal of this paper is to improve the generality and accuracy of open-vocabulary object counting in images. To improve the generality, we repurpose an open-vocabulary detection foundation model (GroundingDINO) for the counting task, and also extend its capabilities by introducing modules to enable specifying the target object to count by visual exemplars. In turn, these new capabilities - being able to specify the target object by multi-modalites (text and exemplars) - lead to an improvement in counting accuracy. We make three contributions: First, we introduce the first open-world counting model, CountGD, where the prompt can be specified by a text description or visual exemplars or both; Second, we show that the performance of the model significantly improves the state of the art on multiple counting benchmarks - when using text only, CountGD is comparable to or outperforms all previous text-only works, and when using both text and visual exemplars, we outperform all previous models; Third, we carry out a preliminary study into different interactions between the text and visual exemplar prompts, including the cases where they reinforce each other and where one restricts the other. The code and an app to test the model are available at https://www.robots.ox.ac.uk/~vgg/research/countgd/.

We extend the simply-typed guarded lambda-calculus with discrete probabilities and endow it with a program logic for reasoning about relational properties of guarded probabilistic computations. This provides a framework for programming and reasoning about infinite stochastic processes like Markov chains. We demonstrate the logic sound by interpreting its judgements in the topos of trees and by using probabilistic couplings for the semantics of relational assertions over distributions on discrete types. The program logic is designed to support syntax-directed proofs in the style of relational refinement types, but retains the expressiveness of higher-order logic extended with discrete distributions, and the ability to reason relationally about expressions that have different types or syntactic structure. In addition, our proof system leverages a well-known theorem from the coupling literature to justify better proof rules for relational reasoning about probabilistic expressions. We illustrate these benefits with a broad range of examples that were beyond the scope of previous systems, including shift couplings and lump couplings between random walks.

Modifications to test-time sampling have emerged as an important extension to diffusion algorithms, with the goal of biasing the generative process to achieve a given objective without having to retrain the entire diffusion model. However, generating jointly correlated samples from multiple pre-trained diffusion models while simultaneously enforcing task-specific constraints without costly retraining has remained challenging. To this end, we propose Projected Coupled Diffusion (PCD), a novel test-time framework for constrained joint generation. PCD introduces a coupled guidance term into the generative dynamics to encourage coordination between diffusion models and incorporates a projection step at each diffusion step to enforce hard constraints. Empirically, we demonstrate the effectiveness of PCD in application scenarios of image-pair generation, object manipulation, and multi-robot motion planning. Our results show improved coupling effects and guaranteed constraint satisfaction without incurring excessive computational costs.

In this paper, we propose two modified neural networks based on dual path multi-scale fusion networks (SFANet) and SegNet for accurate and efficient crowd counting. Inspired by SFANet, the first model, which is named M-SFANet, is attached with atrous spatial pyramid pooling (ASPP) and context-aware module (CAN). The encoder of M-SFANet is enhanced with ASPP containing parallel atrous convolutional layers with different sampling rates and hence able to extract multi-scale features of the target object and incorporate larger context. To further deal with scale variation throughout an input image, we leverage the CAN module which adaptively encodes the scales of the contextual information. The combination yields an effective model for counting in both dense and sparse crowd scenes. Based on the SFANet decoder structure, M-SFANet's decoder has dual paths, for density map and attention map generation. The second model is called M-SegNet, which is produced by replacing the bilinear upsampling in SFANet with max unpooling that is used in SegNet. This change provides a faster model while providing competitive counting performance. Designed for high-speed surveillance applications, M-SegNet has no additional multi-scale-aware module in order to not increase the complexity. Both models are encoder-decoder based architectures and are end-to-end trainable. We conduct extensive experiments on five crowd counting datasets and one vehicle counting dataset to show that these modifications yield algorithms that could improve state-of-the-art crowd counting methods. Codes are available at https://github.com/Pongpisit-Thanasutives/Variations-of-SFANet-for-Crowd-Counting.

Despite progress in video understanding, current MLLMs struggle with counting tasks. Existing benchmarks are limited by short videos, close-set queries, lack of clue annotations, and weak multimodal coverage. In this paper, we introduce CG-AV-Counting, a manually-annotated clue-grounded counting benchmark with 1,027 multimodal questions and 5,845 annotated clues over 497 long videos. It supports both black-box and white-box evaluation, serving as a comprehensive testbed for both end-to-end and reasoning-based counting. To explore ways to improve model's counting capability, we propose AV-Reasoner, a model trained with GRPO and curriculum learning to generalize counting ability from related tasks. AV-Reasoner achieves state-of-the-art results across multiple benchmarks, demonstrating the effectiveness of reinforcement learning. However, experiments show that on out-of-domain benchmarks, reasoning in the language space fails to bring performance gains. The code and benchmark have been realeased on https://av-reasoner.github.io.

Most crowd counting methods directly regress blockwise density maps using Mean Squared Error (MSE) losses. This practice has two key limitations: (1) it fails to account for the extreme spatial sparsity of annotations -- over 95% of 8x8 blocks are empty across standard benchmarks, so supervision signals in informative regions are diluted by the predominant zeros; (2) MSE corresponds to a Gaussian error model that poorly matches discrete, non-negative count data. To address these issues, we introduce ZIP, a scalable crowd counting framework that models blockwise counts with a Zero-Inflated Poisson likelihood: a zero-inflation term learns the probability a block is structurally empty (handling excess zeros), while the Poisson component captures expected counts when people are present (respecting discreteness). We provide a generalization analysis showing a tighter risk bound for ZIP than MSE-based losses and DMCount provided that the training resolution is moderately large. To assess the scalability of ZIP, we instantiate it on backbones spanning over 100x in parameters/compute. Experiments on ShanghaiTech A & B, UCF-QNRF, and NWPU-Crowd demonstrate that ZIP consistently surpasses state-of-the-art methods across all model scales.

Object counting methods typically rely on manually annotated datasets. The cost of creating such datasets has restricted the versatility of these networks to count objects from specific classes (such as humans or penguins), and counting objects from diverse categories remains a challenge. The availability of robust text-to-image latent diffusion models (LDMs) raises the question of whether these models can be utilized to generate counting datasets. However, LDMs struggle to create images with an exact number of objects based solely on text prompts but they can be used to offer a dependable sorting signal by adding and removing objects within an image. Leveraging this data, we initially introduce an unsupervised sorting methodology to learn object-related features that are subsequently refined and anchored for counting purposes using counting data generated by LDMs. Further, we present a density classifier-guided method for dividing an image into patches containing objects that can be reliably counted. Consequently, we can generate counting data for any type of object and count them in an unsupervised manner. Our approach outperforms other unsupervised and few-shot alternatives and is not restricted to specific object classes for which counting data is available. Code to be released upon acceptance.

We propose YOLO-Count, a differentiable open-vocabulary object counting model that tackles both general counting challenges and enables precise quantity control for text-to-image (T2I) generation. A core contribution is the 'cardinality' map, a novel regression target that accounts for variations in object size and spatial distribution. Leveraging representation alignment and a hybrid strong-weak supervision scheme, YOLO-Count bridges the gap between open-vocabulary counting and T2I generation control. Its fully differentiable architecture facilitates gradient-based optimization, enabling accurate object count estimation and fine-grained guidance for generative models. Extensive experiments demonstrate that YOLO-Count achieves state-of-the-art counting accuracy while providing robust and effective quantity control for T2I systems.

Large language models often fail at simple counting tasks, even when the items to count are explicitly present in the prompt. We investigate whether this failure occurs because transformers do not represent counts internally, or because they cannot convert those representations into the correct output tokens. Across three model families, Pythia, Qwen3, and Mistral, ranging from 0.4B to 14B parameters, we find strong evidence for the second explanation. Linear probes recover the correct count from intermediate layers with near-perfect accuracy (R^2>0.99), showing that the information is present. However, the internal directions that encode counts are nearly orthogonal to the output-head rows for digit tokens (|cos|leq0.032). In other words, the model stores the count in a form that the digit logits do not naturally read out. We localize this failure with two interventions. Updating only the digit rows of the output head (36,864 parameters) substantially improves constrained next-token digit prediction (60.7 to 100.0% across four tasks), but it does not fix autoregressive generation. By contrast, a small LoRA intervention on attention Q/V weights (7.67M parameters) improves upstream routing and achieves 83.1% +/- 7.2% in true greedy autoregressive generation. Logit-lens measurements confirm the mechanism: the correct digit's vocabulary rank drops from 55,980 to 1, a 50,000x improvement. Additional norm, logit-lens, and cross-task analyses show that the bottleneck generalizes across character counting, addition, and list length, while remaining absent from broader multi-step reasoning benchmarks, including MMLU, GSM8K, and DROP. These results identify counting failure as a geometric readout bottleneck rather than a failure of internal representation: the model knows the count but the output pathway is geometrically misaligned with the tokens needed to express it.

Recently, most handwritten mathematical expression recognition (HMER) methods adopt the encoder-decoder networks, which directly predict the markup sequences from formula images with the attention mechanism. However, such methods may fail to accurately read formulas with complicated structure or generate long markup sequences, as the attention results are often inaccurate due to the large variance of writing styles or spatial layouts. To alleviate this problem, we propose an unconventional network for HMER named Counting-Aware Network (CAN), which jointly optimizes two tasks: HMER and symbol counting. Specifically, we design a weakly-supervised counting module that can predict the number of each symbol class without the symbol-level position annotations, and then plug it into a typical attention-based encoder-decoder model for HMER. Experiments on the benchmark datasets for HMER validate that both joint optimization and counting results are beneficial for correcting the prediction errors of encoder-decoder models, and CAN consistently outperforms the state-of-the-art methods. In particular, compared with an encoder-decoder model for HMER, the extra time cost caused by the proposed counting module is marginal. The source code is available at https://github.com/LBH1024/CAN.

Time series play a fundamental role in many domains, capturing a plethora of information about the underlying data-generating processes. When a process generates multiple synchronized signals we are faced with multidimensional time series. In this context a fundamental problem is that of motif mining, where we seek patterns repeating twice with minor variations, spanning some of the dimensions. State of the art exact solutions for this problem run in time quadratic in the length of the input time series. We provide a scalable method to find the top-k motifs in multidimensional time series with probabilistic guarantees on the quality of the results. Our algorithm runs in time subquadratic in the length of the input, and returns the exact solution with probability at least 1-δ, where δ is a user-defined parameter. The algorithm is designed to be adaptive to the input distribution, self-tuning its parameters while respecting user-defined limits on the memory to use. Our theoretical analysis is complemented by an extensive experimental evaluation, showing that our algorithm is orders of magnitude faster than the state of the art.

We introduce a novel method for representation learning that uses an artificial supervision signal based on counting visual primitives. This supervision signal is obtained from an equivariance relation, which does not require any manual annotation. We relate transformations of images to transformations of the representations. More specifically, we look for the representation that satisfies such relation rather than the transformations that match a given representation. In this paper, we use two image transformations in the context of counting: scaling and tiling. The first transformation exploits the fact that the number of visual primitives should be invariant to scale. The second transformation allows us to equate the total number of visual primitives in each tile to that in the whole image. These two transformations are combined in one constraint and used to train a neural network with a contrastive loss. The proposed task produces representations that perform on par or exceed the state of the art in transfer learning benchmarks.

In crowd counting, each training image contains multiple people, where each person is annotated by a dot. Existing crowd counting methods need to use a Gaussian to smooth each annotated dot or to estimate the likelihood of every pixel given the annotated point. In this paper, we show that imposing Gaussians to annotations hurts generalization performance. Instead, we propose to use Distribution Matching for crowd COUNTing (DM-Count). In DM-Count, we use Optimal Transport (OT) to measure the similarity between the normalized predicted density map and the normalized ground truth density map. To stabilize OT computation, we include a Total Variation loss in our model. We show that the generalization error bound of DM-Count is tighter than that of the Gaussian smoothed methods. In terms of Mean Absolute Error, DM-Count outperforms the previous state-of-the-art methods by a large margin on two large-scale counting datasets, UCF-QNRF and NWPU, and achieves the state-of-the-art results on the ShanghaiTech and UCF-CC50 datasets. DM-Count reduced the error of the state-of-the-art published result by approximately 16%. Code is available at https://github.com/cvlab-stonybrook/DM-Count.

The dynamic imbalance of the fore-background is a major challenge in video object counting, which is usually caused by the sparsity of target objects. This remains understudied in existing works and often leads to severe under-/over-prediction errors. To tackle this issue in video object counting, we propose a density-embedded Efficient Masked Autoencoder Counting (E-MAC) framework in this paper. To empower the model's representation ability on density regression, we develop a new Density-Embedded Masked mOdeling (DEMO) method, which first takes the density map as an auxiliary modality to perform multimodal self-representation learning for image and density map. Although DEMO contributes to effective cross-modal regression guidance, it also brings in redundant background information, making it difficult to focus on the foreground regions. To handle this dilemma, we propose an efficient spatial adaptive masking derived from density maps to boost efficiency. Meanwhile, we employ an optical flow-based temporal collaborative fusion strategy to effectively capture the dynamic variations across frames, aligning features to derive multi-frame density residuals. The counting accuracy of the current frame is boosted by harnessing the information from adjacent frames. In addition, considering that most existing datasets are limited to human-centric scenarios, we first propose a large video bird counting dataset, DroneBird, in natural scenarios for migratory bird protection. Extensive experiments on three crowd datasets and our DroneBird validate our superiority against the counterparts. The code and dataset are available.

We develop a discipline-agnostic emergence calculus that treats theories as fixed points of idempotent operators acting on descriptions. We show that, once processes are composable but access to the underlying system is mediated by a bounded observational interface, a canonical toolkit of six closure-changing primitives (P1--P6) is unavoidable. The framework unifies order-theoretic closure operators with dynamics-induced endomaps E_{τ,f} built from a Markov kernel, a coarse-graining lens, and a time scale τ. We introduce a computable total-variation idempotence defect for E_{τ,f}; small retention error implies approximate idempotence and yields stable "objects" packaged at the chosen τ within a fixed lens. For directionality, we define an arrow-of-time functional as the path-space KL divergence between forward and time-reversed trajectories and prove it is monotone under coarse-graining (data processing); we also formalize a protocol-trap audit showing that protocol holonomy alone cannot sustain asymmetry without a genuine affinity in the lifted dynamics. Finally, we prove a finite forcing-style counting lemma: relative to a partition-based theory, definable predicate extensions are exponentially rare, giving a clean anti-saturation mechanism for strict ladder climbing.

Vision--language models (VLMs) have achieved impressive performance on complex multimodal reasoning tasks, yet they still fail on simple grounding skills such as object counting. Existing evaluations mostly assess only final outputs, offering limited insight into where these failures arise inside the model. In this work, we present an empirical study of VLM counting behavior through both behavioral and mechanistic analysis. We introduce COUNTINGTRICKS, a controlled evaluation suite of simple shape-based counting cases designed to expose vulnerabilities under different patchification layouts and adversarial prompting conditions. Using attention analysis and component-wise probing, we show that count-relevant visual evidence is strongest in the modality projection stage but degrades substantially in later language layers, where models become more susceptible to text priors. Motivated by this finding, we further evaluate Modality Attention Share (MAS), a lightweight intervention that encourages a minimum budget of visual attention during answer generation. Our results suggest that counting failures in VLMs stem not only from visual perception limits, but also from the underuse of visual evidence during language-stage reasoning. Code and dataset will be released at https://github.com/leduy99/-CVPRW26-Modality-Attention-Share.

Task Arithmetic is a model merging technique that enables the combination of multiple models' capabilities into a single model through simple arithmetic in the weight space, without the need for additional fine-tuning or access to the original training data. However, the factors that determine the success of Task Arithmetic remain unclear. In this paper, we examine Task Arithmetic for multi-task learning by framing it as a one-shot Federated Learning problem. We demonstrate that Task Arithmetic is mathematically equivalent to the commonly used algorithm in Federated Learning, called Federated Averaging (FedAvg). By leveraging well-established theoretical results from FedAvg, we identify two key factors that impact the performance of Task Arithmetic: data heterogeneity and training heterogeneity. To mitigate these challenges, we adapt several algorithms from Federated Learning to improve the effectiveness of Task Arithmetic. Our experiments demonstrate that applying these algorithms can often significantly boost performance of the merged model compared to the original Task Arithmetic approach. This work bridges Task Arithmetic and Federated Learning, offering new theoretical perspectives on Task Arithmetic and improved practical methodologies for model merging.

Predictive multiplicity refers to the phenomenon in which classification tasks may admit multiple competing models that achieve almost-equally-optimal performance, yet generate conflicting outputs for individual samples. This presents significant concerns, as it can potentially result in systemic exclusion, inexplicable discrimination, and unfairness in practical applications. Measuring and mitigating predictive multiplicity, however, is computationally challenging due to the need to explore all such almost-equally-optimal models, known as the Rashomon set, in potentially huge hypothesis spaces. To address this challenge, we propose a novel framework that utilizes dropout techniques for exploring models in the Rashomon set. We provide rigorous theoretical derivations to connect the dropout parameters to properties of the Rashomon set, and empirically evaluate our framework through extensive experimentation. Numerical results show that our technique consistently outperforms baselines in terms of the effectiveness of predictive multiplicity metric estimation, with runtime speedup up to 20times sim 5000times. With efficient Rashomon set exploration and metric estimation, mitigation of predictive multiplicity is then achieved through dropout ensemble and model selection.

Large Language Model (LLM) multi-agent systems are increasingly deployed as interacting agent societies, yet scaling these systems often yields diminishing or unstable returns, the causes of which remain poorly understood. We present the first large-scale empirical study of coordination dynamics in LLM-based multi-agent systems, introducing an atomic event-level formulation that reconstructs reasoning as cascades of coordination. Analyzing over 1.5 Million interactions across tasks, topologies, and scales, we uncover three coupled laws: coordination follows heavy-tailed cascades, concentrates via preferential attachment into intellectual elites, and produces increasingly frequent extreme events as system size grows. We show that these effects are coupled through a single structural mechanism: an integration bottleneck, in which coordination expansion scales with system size while consolidation does not, producing large but weakly integrated reasoning processes. To test this mechanism, we introduce Deficit-Triggered Integration (DTI), which selectively increases integration under imbalance. DTI improves performance precisely where coordination fails, without suppressing large-scale reasoning. Together, our results establish quantitative laws of collective cognition and identify coordination structure as a fundamental, previously unmeasured axis for understanding and improving scalable multi-agent intelligence.

Polypharmacy, most often defined as the simultaneous consumption of five or more drugs at once, is a prevalent phenomenon in the older population. Some of these polypharmacies, deemed inappropriate, may be associated with adverse health outcomes such as death or hospitalization. Considering the combinatorial nature of the problem as well as the size of claims database and the cost to compute an exact association measure for a given drug combination, it is impossible to investigate every possible combination of drugs. Therefore, we propose to optimize the search for potentially inappropriate polypharmacies (PIPs). To this end, we propose the OptimNeuralTS strategy, based on Neural Thompson Sampling and differential evolution, to efficiently mine claims datasets and build a predictive model of the association between drug combinations and health outcomes. We benchmark our method using two datasets generated by an internally developed simulator of polypharmacy data containing 500 drugs and 100 000 distinct combinations. Empirically, our method can detect up to 72% of PIPs while maintaining an average precision score of 99% using 30 000 time steps.

Prediction problems often admit competing models that perform almost equally well. This effect challenges key assumptions in machine learning when competing models assign conflicting predictions. In this paper, we define predictive multiplicity as the ability of a prediction problem to admit competing models with conflicting predictions. We introduce formal measures to evaluate the severity of predictive multiplicity and develop integer programming tools to compute them exactly for linear classification problems. We apply our tools to measure predictive multiplicity in recidivism prediction problems. Our results show that real-world datasets may admit competing models that assign wildly conflicting predictions, and motivate the need to measure and report predictive multiplicity in model development.

Diffusion models have shown remarkable progress in photorealistic image synthesis, yet they remain unreliable for generating scenes with a precise number of object instances, particularly in complex and high-density settings. We present CountLoop, a training-free framework that provides diffusion models with accurate instance control through iterative structured feedback. The approach alternates between image generation and multimodal agent evaluation, where a language-guided planner and critic assess object counts, spatial arrangements, and attribute consistency. This feedback is then used to refine layouts and guide subsequent generations. To further improve separation between objects, especially in occluded scenes, we introduce instance-driven attention masking and compositional generation techniques. Experiments on COCO Count, T2I CompBench, and two new high-instance benchmarks show that CountLoop achieves counting accuracy of up to 98% while maintaining spatial fidelity and visual quality, outperforming layout-based and gradient-guided baselines with a score of 0.97.

Transformers, the backbone of modern large language models (LLMs), face inherent architectural limitations that impede their reasoning capabilities. Unlike recurrent networks, Transformers lack recurrent connections, confining them to constant-depth computation. This restriction places them in the complexity class TC^0, making them theoretically incapable of solving tasks that demand increasingly deep reasoning as input length grows. Counting, a fundamental component of many reasoning tasks, also requires reasoning depth to grow linearly to be performed inductively. While previous studies have established the upper limits of counting ability in Transformer-based expert models (i.e., models specifically trained for counting tasks), these findings do not directly extend to general-purpose LLMs due to differences in reasoning mechanisms. Recent work has highlighted how Chain of Thought (CoT) reasoning can help alleviate some of the architectural limitations of Transformers in counting tasks. However, little attention has been paid to the role of tokenization in these models. Unlike expert models that often use character-level tokenization, LLMs typically rely on byte-level (BPE) tokenizers, which fundamentally alters the way reasoning is processed. Our work investigates the impact of tokenization on the counting abilities of LLMs, uncovering substantial performance variations based on input tokenization differences. We provide both theoretical and experimental analyses, offering insights into how tokenization choices can undermine models' theoretical computability, thereby inspiring the design of new tokenization methods to enhance reasoning in LLMs.

Sonification -- the mapping of data to non-speech audio -- offers an underexplored channel for representing complex dynamical systems. We treat El Niño-Southern Oscillation (ENSO), a canonical example of low-dimensional climate chaos, as a test case for culturally-situated sonification evaluated through complex systems diagnostics. Using parameter-mapping sonification of the Niño 3.4 sea surface temperature anomaly index (1870--2024), we encode ENSO variability into two traditional Javanese gamelan pentatonic systems (pelog and slendro) across four composition strategies, then analyze the resulting audio as trajectories in a two-dimensional acoustic phase space. Recurrence-based diagnostics, convex hull geometry, and coupling analysis reveal that the sonification pipeline preserves key dynamical signatures: alternating modes produce the highest trajectory recurrence rates, echoing ENSO's quasi-periodicity; layered polyphonic modes explore the broadest phase space regions; and the two scale families induce qualitatively distinct coupling regimes between spectral brightness and energy -- predominantly anti-phase in pelog but near-independent in slendro. Phase space trajectory analysis provides a rigorous geometric framework for comparing sonification designs within a complex systems context. Perceptual validation remains necessary; we contribute the dynamical systems methodology for evaluating such mappings.

Learning and decision making in the brain are key processes critical to survival, and yet are processes implemented by non-ideal biological building blocks which can impose significant error. We explore quantitatively how the brain might cope with this inherent source of error by taking advantage of two ubiquitous mechanisms, redundancy and synchronization. In particular we consider a neural process whose goal is to learn a decision function by implementing a nonlinear gradient dynamics. The dynamics, however, are assumed to be corrupted by perturbations modeling the error which might be incurred due to limitations of the biology, intrinsic neuronal noise, and imperfect measurements. We show that error, and the associated uncertainty surrounding a learned solution, can be controlled in large part by trading off synchronization strength among multiple redundant neural systems against the noise amplitude. The impact of the coupling between such redundant systems is quantified by the spectrum of the network Laplacian, and we discuss the role of network topology in synchronization and in reducing the effect of noise. A range of situations in which the mechanisms we model arise in brain science are discussed, and we draw attention to experimental evidence suggesting that cortical circuits capable of implementing the computations of interest here can be found on several scales. Finally, simulations comparing theoretical bounds to the relevant empirical quantities show that the theoretical estimates we derive can be tight.

The problem of robotic synchronisation and coordination is a long-standing one. Combining autonomous, computerised systems with unpredictable real-world conditions can have consequences ranging from poor performance to collisions and damage. This paper proposes using coupled oscillators to create a drone swarm that is decentralised and self organising. This allows for greater flexibility and adaptiveness than a hard-coded swarm, with more resilience and scalability than a centralised system. Our method allows for a variable number of drones to spontaneously form a swarm and react to changing swarm conditions. Additionally, this method includes provisions to prevent communication interference between drones, and signal processing techniques to ensure a smooth and cohesive swarm.

Large vision-language models (VLMs) are shown to learn rich joint image-text representations enabling high performances in relevant downstream tasks. However, they fail to showcase their quantitative understanding of objects, and they lack good counting-aware representation. This paper conducts a reproducibility study of 'Teaching CLIP to Count to Ten' (Paiss et al., 2023), which presents a method to finetune a CLIP model (Radford et al., 2021) to improve zero-shot counting accuracy in an image while maintaining the performance for zero-shot classification by introducing a counting-contrastive loss term. We improve the model's performance on a smaller subset of their training data with lower computational resources. We verify these claims by reproducing their study with our own code. The implementation can be found at https://github.com/SforAiDl/CountCLIP.