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In this paper, we consider the Santa Claus problem in the CONGEST model. This NP-hard problem can be modeled as a bipartite graph of children and gifts where an edge indicates that a child desires a gift. Notably, each gift can have a different value. The goal is to assign the gifts to the children such that the least happy child is as happy as possible. Even though this is a well-studied problem in the sequential setting, we obtain the first results the distributed setting. In particular, we show that the complexity of computing an $\mathcal{O}(\log n/\log \log n)$-approximation is $\hat Θ(\sqrt n+D)$ rounds, where our $\widetildeΩ(\sqrt n+D)$-round lower bound is even stronger and holds for any approximation.

The prevailing post-training paradigm for Large Reasoning Models (LRMs) - Supervised Fine-Tuning (SFT) followed by Reinforcement Learning (RL) - suffers from an intrinsic optimization mismatch: the rigid supervision inherent in SFT induces distributional collapse, thereby exhausting the exploration space necessary for subsequent RL. In this paper, we reformulate SFT to reconcile post-training objectives and propose Gibbs Initialization with Finite Temperature (GIFT). We characterize standard SFT as a degenerate zero-temperature limit that suppresses base priors. Conversely, GIFT incorporates supervision as a finite-temperature energy potential, establishing a distributional bridge that promotes objective consistency throughout the post-training pipeline. Our experiments demonstrate that GIFT significantly outperforms standard SFT and other competitive baselines when utilized for RL initialization, providing a mathematically principled pathway to preserve exploration and align the two post-training stages. Our code is available at https://github.com/zzy1127/GIFT.

Financial portfolio trading is naturally formulated as a reinforcement learning problem, where an agent sequentially rebalances assets under changing market conditions to balance return, risk, and transaction costs. Yet in non-stationary markets, raw OHLCV states and short-horizon return rewards often provide an under-specified learning interface, motivating large language models as a way to inject financial knowledge into state and reward design while constraining open-ended generation. To this end, we propose GIFT, an LLM-guided framework for state-reward interface design in PPO-based financial reinforcement learning. Rather than using the LLM to make trading decisions, GIFT uses Factor-guided State Enhancement to generate state features from financial-factor primitives, Risk-rule-guided Reward Shaping to generate auxiliary rewards from portfolio-risk rules, and Diagnostic-guided Refinement to revise candidate interfaces using PPO rollout diagnostics. After refinement, GIFT fixes the selected state-reward interface before evaluation, with no further LLM queries or interface updates at test time. Comprehensive rolling-window experiments across diverse market regimes and portfolio

A promising paradigm for adapting instruction-tuned language models is to learn task-specific updates on a pretrained base model and subsequently merge them into the instruction-tuned model. However, existing approaches typically treat the instruction-tuned model as a passive target that is only involved at the final merging stage, without guiding the training process. We propose GIFT (Guided Fine-Tuning and Transfer), a simple and efficient framework that incorporates guidance from the instruction model into task adaptation. GIFT fine-tunes a low-rank adapter on the pretrained base model using confidence signals derived from the instruction-tuned model. The learned adapter is then merged into the instruction-tuned model, yielding task-specialized models that preserve general instruction-following behavior. We evaluate GIFT on mathematical and knowledge-intensive benchmarks across multiple model families and scales. Results show that GIFT consistently outperforms direct fine-tuning and representative transfer-based baselines, while maintaining robust generalization and favorable test-time scaling behavior.

Gradient communication is a primary scaling bottleneck in large language model (LLM) pretraining. Communicating gradients in low-precision formats, such as FP8 and NVFP4, can significantly reduce the communication volume. Existing methods quantize gradients via linear or nonlinear mappings in Euclidean space, often degrading model performance because highly anisotropic gradients incur direction-dependent distortion. We present GIFT, a geometry-informed gradient scaling method that performs low-precision communication in geometry-aware coordinates. By transforming gradients into a near-isotropic space before quantization, GIFT makes low-precision representations substantially more faithful to their high-precision counterparts. GIFT only changes the coordinate system used for low-precision gradient communication and does not change the optimizer, training recipe, communication collective, or low-precision format. We also develop a simplified geometry-aware transformation algorithm with low-rank approximation and selective application to balance the computation overhead and communication reduction. We examine the empirical convergence of GIFT using Llama-300M and Llama-600M models. Ou

Video Large Language Models (VLMs) have achieved remarkable success in video understanding, but the significant computational cost from processing dense frames severely limits their practical application. Existing methods alleviate this by selecting keyframes, but their greedy decision-making, combined with a decoupled evaluation of relevance and diversity, often falls into local optima and results in erroneously selecting irrelevant noise frames. To address these challenges, we propose GIFT: Global Irreplaceability Frame Targeting, a novel training-free framework that selects frames by assessing their intrinsic irreplaceability. Specifically, we first introduce Directed Diversity to quantify a frame's uniqueness conditioned on relevance, which allows us to formulate a unified irreplaceability score. Subsequently, our Budget-Aware Refinement strategy employs a adaptive iterative process that first secures a core set of frames with the highest irreplaceability, and then shifts its priority to building crucial temporal context around these selections as the budget expands. Extensive experiments demonstrate that GIFT achieves a maximum average improvement of 12.5% across long-form vid

As Large Reasoning Models (LRMs) are increasingly deployed, auditing their chain-of-thought (CoT) traces for safety becomes critical. Recent work has reported that monitorability--the degree to which CoT faithfully and informatively reflects internal computation--can appear as a "free gift" during the early stages of Reinforcement Learning with Verifiable Rewards (RLVR). We make this observation concrete through a systematic evaluation across model families and training domains. Our results show that this effect is not universal: monitorability improvements are strongly data-dependent. In particular, we demonstrate the critical role of data diversity and instruction-following data during RLVR training. We further show that monitorability is orthogonal to capability--improvements in reasoning performance do not imply increased transparency. Through mechanistic analysis, we attribute monitorability gains primarily to response distribution sharpening (entropy reduction) and increased attention to the prompt, rather than stronger causal reliance on reasoning traces. We also reveal how monitorability dynamics vary with controlled training and evaluation difficulty. Together, these findi

Robots learn reward functions from user demonstrations, but these rewards often fail to generalize to new environments. This failure occurs because learned rewards latch onto spurious correlations in training data rather than the underlying human intent that demonstrations represent. Existing methods leverage visual or semantic similarity to improve robustness, yet these surface-level cues often diverge from what humans actually care about. We present Generalizing Intent for Flexible Test-Time Rewards (GIFT), a framework that grounds reward generalization in human intent rather than surface cues. GIFT leverages language models to infer high-level intent from user demonstrations by contrasting preferred with non-preferred behaviors. At deployment, GIFT maps novel test states to behaviorally equivalent training states via intent-conditioned similarity, enabling learned rewards to generalize across distribution shifts without retraining. We evaluate GIFT on tabletop manipulation tasks with new objects and layouts. Across four simulated tasks with over 50 unseen objects, GIFT consistently outperforms visual and semantic similarity baselines in test-time pairwise win rate and state-alig

This paper examines how gifting spreads among viewers on Twitch, one of the largest live streaming platforms worldwide. Twitch users can give gift subscriptions to other viewers in the chat room, with the majority of gifters opting for community gifting, which is gifting to randomly selected viewers. We identify the random nature of gift-receiving in our data as a natural experiment setting. We investigate whether gift recipients pay it forward, considering various gift types that may either promote or deter the spread of gifting. Our findings reveal that Twitch viewers who receive gift subscriptions are generally more likely to pay it forward than non-recipients, and the positive impact of gift-receiving becomes stronger when the recipient is the sole beneficiary of the giver's gifting behavior. However, we found that gifts from frequent gifters discourage recipients from paying it forward, and gifts from anonymous gifters do not influence the likelihood of viewers becoming future gifters. This research contributes to the existing literature on the spread of online prosocial behavior by providing robust evidence and suggests practical strategies for promoting online gifting.

Generating executable CAD programs from images requires alignment between visual geometry and symbolic program representations, a capability that current methods fail to learn reliably as design complexity increases. Existing fine-tuning approaches rely on either limited supervised datasets or expensive post-training pipelines, resulting in brittle systems that restrict progress in generative CAD design. We argue that the primary bottleneck lies not in model or algorithmic capacity, but in the scarcity of diverse training examples that align visual geometry with program syntax. This limitation is especially acute because the collection of diverse and verified engineering datasets is both expensive and difficult to scale, constraining the development of robust generative CAD models. We introduce Geometric Inference Feedback Tuning (GIFT), a data augmentation framework that leverages geometric feedback to turn test-time compute into a bootstrapped set of high-quality training samples. GIFT combines two mechanisms: Soft-Rejection Sampling (GIFT-REJECT), which retains diverse high-fidelity programs beyond exact ground-truth matches, and Failure-Driven Augmentation (GIFT-FAIL), which co

Deep reinforcement learning policies achieve strong performance in complex continuous control environments with nonlinear contact forces. However, these policies often produce chaotic state dynamics, with trivially small changes to the initial conditions significantly impacting the long-term behaviour of the control system. This high sensitivity to initial conditions limits the application of Deep RL to real-world control systems where performance and stability guarantees are often required. To address this issue, we propose Global stabilisation via Intrinsic Fine Tuning (GIFT), a general-purpose training framework which directly optimises the global stability of existing high-performing deep RL policies using a custom reward function. We demonstrate that GIFT increase the stability of the control interaction while maintaining comparable task performance, thereby improving the suitability of deep RL policies for real-world control systems.

Digital gift-giving has become a key means of maintaining social relationships, but most existing research has focused on gifting within global e-commerce or social media platforms. The emergence of messenger-based gifting in East Asia, where Korea, Japan, and China each have distinct and deeply rooted gifting traditions, remains underexplored. This study examines how in-app gifting services on the most widely used messaging platforms in South Korea (KakaoTalk), Japan (LINE), and China (WeChat) reflect and reshape culturally embedded gifting practices. Through semi-structured interviews with 26 university students, we found that KakaoTalk facilitates frequent, informal exchanges aligned with Korea's emphasis on broad social ties; LINE supports selective and carefully presented gifts, reflecting Japanese norms of formality and sincerity; and WeChat's Hongbao feature enables playful, communal monetary exchanges largely detached from traditional, obligation-driven gifting. Drawing on these findings, we propose the Channel-Oriented Gifting Cycle model, which extends classical gift-exchange theory by showing that the choice of gifting platform is not merely logistical but a culturally m

The holiday gift exchange game is a familiar social institution with nontrivial strategic structure. We provide a formal treatment of the game's mechanics, defining the state space, action sets, and the recursive structure of stealing chains; we prove termination and derive an algorithm for counting distinct game trajectories, which grow far faster than the space of possible final allocations. Beyond the base mechanics, we introduce a decorated model incorporating partial information, social costs, and adaptive strategies grounded in discrete choice theory and the frustration-aggression literature. A full factorial simulation of 240,000 games yields three findings of note: implicit social costs are the dominant regulator of aggression, reducing stealing by 27--48\% and outweighing both uncertainty and strategic sophistication; partial information, contrary to expectation, slightly increases stealing through asymmetric uncertainty; correlated valuations amplify every behavioral effect, so that consensus about gift quality, rather than the features themselves, is what intensifies competition. The first-player advantage is robust across all conditions.

Reducing wealth inequality is a global challenge, and the problems of capitalism stem from the enclosure of the commons and the breakdown of the community. According to previous studies by Polanyi, Karatani, and Graeber, economic modes can be divided into capitalist market economy (enclosure and exchange), power economy (de-enclosure and redistribution), gift economy (obligation to return and reciprocity), and concession economy (de-obligation to return). The concession economy reflects Graeber's baseline communism (from each according to their abilities, to each according to their needs) and Deguchi's We-turn philosophy (the "I" as an individual has a "fundamental incapability" and the subject of physical action, responsibility, and freedom is "We" as a multi-agent system, including the "I"). In this study, we constructed novel network models for these four modes and compared their properties (cluster coefficient, graph density, reciprocity, assortativity, centrality, and Gini coefficient). From the calculation results, it became clear that the market economy leads to inequality; the power economy mitigates inequality but cannot eliminate it; the gift and concession economies lead

Point tracking is becoming a powerful solver for motion estimation and video editing. Compared to classical feature matching, point tracking methods have the key advantage of robustly tracking points under complex camera motion trajectories and over extended periods. However, despite certain improvements in methodologies, current point tracking methods still struggle to track any position in video frames, especially in areas that are texture-less or weakly textured. In this work, we first introduce metrics for evaluating the texture intensity of a 3D object. Using these metrics, we classify the 3D models in ShapeNet into three levels of texture intensity and create GIFT, a challenging synthetic benchmark comprising 1800 indoor video sequences with rich annotations. Unlike existing datasets that assign ground truth points arbitrarily, GIFT precisely anchors ground truth on classified target objects, ensuring that each video corresponds to a specific texture intensity level. Furthermore, we comprehensively evaluate current methods on GIFT to assess their performance across different texture intensity levels and analyze the impact of texture on point tracking.

Pre-trained Vision-Language Models (VLMs) require Continual Learning (CL) to efficiently update their knowledge and adapt to various downstream tasks without retraining from scratch. However, for VLMs, in addition to the loss of knowledge previously learned from downstream tasks, pre-training knowledge is also corrupted during continual fine-tuning. This issue is exacerbated by the unavailability of original pre-training data, leaving VLM's generalization ability degrading. In this paper, we propose GIFT, a novel continual fine-tuning approach that utilizes synthetic data to overcome catastrophic forgetting in VLMs. Taking advantage of recent advances in text-to-image synthesis, we employ a pre-trained diffusion model to recreate both pre-training and learned downstream task data. In this way, the VLM can revisit previous knowledge through distillation on matching diffusion-generated images and corresponding text prompts. Leveraging the broad distribution and high alignment between synthetic image-text pairs in VLM's feature space, we propose a contrastive distillation loss along with an image-text alignment constraint. To further combat in-distribution overfitting and enhance dist

Diffusion models have recently shown strong potential in language modeling, offering faster generation compared to traditional autoregressive approaches. However, applying supervised fine-tuning (SFT) to diffusion models remains challenging, as they lack precise probability estimates at each denoising step. While the diffusion mechanism enables the model to reason over entire sequences, it also makes the generation process less predictable and often inconsistent. This highlights the importance of controlling key tokens that guide the direction of generation. To address this issue, we propose GIFT, an importance-aware finetuning method for diffusion language models, where tokens are assigned different importance weights based on their entropy. Derived from diffusion theory, GIFT delivers substantial gains: across diverse settings including different mainstream training datasets ranging from 1k to 10k in size, utilizing LoRA or full parameter fine-tuning, and training on base or instruct models, GIFT consistently achieves superior overall performance compared to standard SFT on four widely used reasoning benchmarks (Sudoku, Countdown, GSM8K, and MATH-500).

Robotic manipulation of unfamiliar objects in new environments is challenging due to limited generalisation capabilities. We propose a new skill transfer framework, GIFT (Geometry-Induced Functional Transfer), which enables a robot to transfer complex object manipulation skills and constraints from a single human demonstration. Our approach addresses the challenge of skill acquisition and task execution by deriving geometric representations from demonstrations focusing on object-centric interactions. By leveraging the Functional Maps (FMC) framework, we efficiently map interaction functions between objects and their environments, allowing the robot to replicate task operations across objects of similar topologies or categories, even when they have significantly different shapes. Additionally, our method incorporates screw interpolation (ScLERP) for generating smooth, geometrically-aware robot paths to ensure the transferred skills adhere to the demonstrated task constraints. We validate the effectiveness and adaptability of our approach through extensive experiments, demonstrating successful skill transfer and task execution in diverse real-world environments without requiring addi