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Continuous-time approximation of Stochastic Gradient Descent (SGD) is a crucial tool to study its escaping behaviors from stationary points. However, existing stochastic differential equation (SDE) models fail to fully capture these behaviors, even for simple quadratic objectives. Built on a novel stochastic backward error analysis framework, we derive the Hessian-Aware Stochastic Modified Equation (HA-SME), an SDE that incorporates Hessian information of the objective function into both its drift and diffusion terms. Our analysis shows that HA-SME matches the order-best approximation error guarantee among existing SDE models in the literature, while achieving a significantly reduced dependence on the smoothness parameter of the objective. Further, for quadratic objectives, under mild conditions, HA-SME is proved to be the first SDE model that recovers exactly the SGD dynamics in the distributional sense. Consequently, when the local landscape near a stationary point can be approximated by quadratics, HA-SME is expected to accurately predict the local escaping behaviors of SGD.

Vision-Language Models seamlessly discriminate among arbitrary semantic categories, yet they still suffer from poor generalization when presented with challenging examples. For this reason, Episodic Test-Time Adaptation (TTA) strategies have recently emerged as powerful techniques to adapt VLMs in the presence of a single unlabeled image. The recent literature on TTA is dominated by the paradigm of prompt tuning by Marginal Entropy Minimization, which, relying on online backpropagation, inevitably slows down inference while increasing memory. In this work, we theoretically investigate the properties of this approach and unveil that a surprisingly strong TTA method lies dormant and hidden within it. We term this approach ZERO (TTA with "zero" temperature), whose design is both incredibly effective and frustratingly simple: augment N times, predict, retain the most confident predictions, and marginalize after setting the Softmax temperature to zero. Remarkably, ZERO requires a single batched forward pass through the vision encoder only and no backward passes. We thoroughly evaluate our approach following the experimental protocol established in the literature and show that ZERO largely surpasses or compares favorably w.r.t. the state-of-the-art while being almost 10x faster and 13x more memory-friendly than standard Test-Time Prompt Tuning. Thanks to its simplicity and comparatively negligible computation, ZERO can serve as a strong baseline for future work in this field. The code is available at //github.com/FarinaMatteo/zero.

Novel Instance Detection and Segmentation (NIDS) aims at detecting and segmenting novel object instances given a few examples of each instance. We propose a unified framework (NIDS-Net) comprising object proposal generation, embedding creation for both instance templates and proposal regions, and embedding matching for instance label assignment. Leveraging recent advancements in large vision methods, we utilize the Grounding DINO and Segment Anything Model (SAM) to obtain object proposals with accurate bounding boxes and masks. Central to our approach is the generation of high-quality instance embeddings. We utilize foreground feature averages of patch embeddings from the DINOv2 ViT backbone, followed by refinement through a weight adapter mechanism that we introduce. We show experimentally that our weight adapter can adjust the embeddings locally within their feature space and effectively limit overfitting. This methodology enables a straightforward matching strategy, resulting in significant performance gains. Our framework surpasses current state-of-the-art methods, demonstrating notable improvements of 22.3, 46.2, 10.3, and 24.0 in average precision (AP) across four detection datasets. In instance segmentation tasks on seven core datasets of the BOP challenge, our method outperforms the top RGB methods by 3.6 AP and remains competitive with the best RGB-D method. Code is available at: //github.com/YoungSean/NIDS-Net

We revisit the fundamental Boolean Matrix Multiplication (BMM) problem. With the invention of algebraic fast matrix multiplication over 50 years ago, it also became known that BMM can be solved in truly subcubic $O(n^\omega)$ time, where $\omega<3$; much work has gone into bringing $\omega$ closer to $2$. Since then, a parallel line of work has sought comparably fast combinatorial algorithms but with limited success. The naive $O(n^3)$-time algorithm was initially improved by a $\log^2{n}$ factor [Arlazarov et al.; RAS'70], then by $\log^{2.25}{n}$ [Bansal and Williams; FOCS'09], then by $\log^3{n}$ [Chan; SODA'15], and finally by $\log^4{n}$ [Yu; ICALP'15]. We design a combinatorial algorithm for BMM running in time $n^3 / 2^{\Omega(\sqrt[7]{\log n})}$ -- a speed-up over cubic time that is stronger than any poly-log factor. This comes tantalizingly close to refuting the conjecture from the 90s that truly subcubic combinatorial algorithms for BMM are impossible. This popular conjecture is the basis for dozens of fine-grained hardness results. Our main technical contribution is a new regularity decomposition theorem for Boolean matrices (or equivalently, bipartite graphs) under a notion of regularity that was recently introduced and analyzed analytically in the context of communication complexity [Kelley, Lovett, Meka; arXiv'23], and is related to a similar notion from the recent work on $3$-term arithmetic progression free sets [Kelley, Meka; FOCS'23].

This paper addresses the challenge of selecting explanations for XAI (Explainable AI)-based Intelligent Decision Support Systems (IDSSs). IDSSs have shown promise in improving user decisions through XAI-generated explanations along with AI predictions, and the development of XAI made it possible to generate a variety of such explanations. However, how IDSSs should select explanations to enhance user decision-making remains an open question. This paper proposes X-Selector, a method for selectively presenting XAI explanations. It enables IDSSs to strategically guide users to an AI-suggested decision by predicting the impact of different combinations of explanations on a user's decision and selecting the combination that is expected to minimize the discrepancy between an AI suggestion and a user decision. We compared the efficacy of X-Selector with two naive strategies (all possible explanations and explanations only for the most likely prediction) and two baselines (no explanation and no AI support). The results suggest the potential of X-Selector to guide users to AI-suggested decisions and improve task performance under the condition of a high AI accuracy.

This paper presents a novel approach for signal reconstruction using Spiking Neural Networks (SNN) based on the principles of Cognitive Informatics and Cognitive Computing. The proposed SNN leverages the Discrete Fourier Transform (DFT) to represent and reconstruct arbitrary time series signals. By employing N spiking neurons, the SNN captures the frequency components of the input signal, with each neuron assigned a unique frequency. The relationship between the magnitude and phase of the spiking neurons and the DFT coefficients is explored, enabling the reconstruction of the original signal. Additionally, the paper discusses the encoding of impulse delays and the phase differences between adjacent frequency components. This research contributes to the field of signal processing and provides insights into the application of SNN for cognitive signal analysis and reconstruction.

The study of behavioral diversity in Multi-Agent Reinforcement Learning (MARL) is a nascent yet promising field. In this context, the present work deals with the question of how to control the diversity of a multi-agent system. With no existing approaches to control diversity to a set value, current solutions focus on blindly promoting it via intrinsic rewards or additional loss functions, effectively changing the learning objective and lacking a principled measure for it. To address this, we introduce Diversity Control (DiCo), a method able to control diversity to an exact value of a given metric by representing policies as the sum of a parameter-shared component and dynamically scaled per-agent components. By applying constraints directly to the policy architecture, DiCo leaves the learning objective unchanged, enabling its applicability to any actor-critic MARL algorithm. We theoretically prove that DiCo achieves the desired diversity, and we provide several experiments, both in cooperative and competitive tasks, that show how DiCo can be employed as a novel paradigm to increase performance and sample efficiency in MARL. Multimedia results are available on the paper's website: //sites.google.com/view/dico-marl.

Federated Class Incremental Learning (FCIL) is a critical yet largely underexplored issue that deals with the dynamic incorporation of new classes within federated learning (FL). Existing methods often employ generative adversarial networks (GANs) to produce synthetic images to address privacy concerns in FL. However, GANs exhibit inherent instability and high sensitivity, compromising the effectiveness of these methods. In this paper, we introduce a novel data-free federated class incremental learning framework with diffusion-based generative memory (DFedDGM) to mitigate catastrophic forgetting by generating stable, high-quality images through diffusion models. We design a new balanced sampler to help train the diffusion models to alleviate the common non-IID problem in FL, and introduce an entropy-based sample filtering technique from an information theory perspective to enhance the quality of generative samples. Finally, we integrate knowledge distillation with a feature-based regularization term for better knowledge transfer. Our framework does not incur additional communication costs compared to the baseline FedAvg method. Extensive experiments across multiple datasets demonstrate that our method significantly outperforms existing baselines, e.g., over a 4% improvement in average accuracy on the Tiny-ImageNet dataset.

State-of-the-art sequential reasoning in Large Language Models (LLMs) has expanded the capabilities of Copilots beyond conversational tasks to complex function calling, managing thousands of API calls. However, the tendency of compositional prompting to segment tasks into multiple steps, each requiring a round-trip to the GPT APIs, leads to increased system latency and costs. Although recent advancements in parallel function calling have improved tool execution per API call, they may necessitate more detailed in-context instructions and task breakdown at the prompt level, resulting in higher engineering and production costs. Inspired by the hardware design principles of multiply-add (MAD) operations, which fuse multiple arithmetic operations into a single task from the compiler's perspective, we propose LLM-Tool Compiler, which selectively fuses similar types of tool operations under a single function at runtime, presenting them as a unified task to the LLM. This selective fusion inherently enhances parallelization and efficiency. Benchmarked on a large-scale Copilot platform, LLM-Tool Compiler achieves up to four times more parallel calls than existing methods, reducing token costs and latency by up to 40% and 12%, respectively.

In this paper, we propose a novel Feature Decomposition and Reconstruction Learning (FDRL) method for effective facial expression recognition. We view the expression information as the combination of the shared information (expression similarities) across different expressions and the unique information (expression-specific variations) for each expression. More specifically, FDRL mainly consists of two crucial networks: a Feature Decomposition Network (FDN) and a Feature Reconstruction Network (FRN). In particular, FDN first decomposes the basic features extracted from a backbone network into a set of facial action-aware latent features to model expression similarities. Then, FRN captures the intra-feature and inter-feature relationships for latent features to characterize expression-specific variations, and reconstructs the expression feature. To this end, two modules including an intra-feature relation modeling module and an inter-feature relation modeling module are developed in FRN. Experimental results on both the in-the-lab databases (including CK+, MMI, and Oulu-CASIA) and the in-the-wild databases (including RAF-DB and SFEW) show that the proposed FDRL method consistently achieves higher recognition accuracy than several state-of-the-art methods. This clearly highlights the benefit of feature decomposition and reconstruction for classifying expressions.