The controllable generation of diffusion models aims to steer the model to generate samples that optimize some given objective functions. It is desirable for a variety of applications including image generation, molecule generation, and DNA/sequence generation. Reinforcement Learning (RL) based fine-tuning of the base model is a popular approach but it can overfit the reward function while requiring significant resources. We frame controllable generation as a problem of finding a distribution that optimizes a KL-regularized objective function. We present SLCD -- Supervised Learning based Controllable Diffusion, which iteratively generates online data and trains a small classifier to guide the generation of the diffusion model. Similar to the standard classifier-guided diffusion, SLCD's key computation primitive is classification and does not involve any complex concepts from RL or control. Via a reduction to no-regret online learning analysis, we show that under KL divergence, the output from SLCD provably converges to the optimal solution of the KL-regularized objective. Further, we empirically demonstrate that SLCD can generate high quality samples with nearly the same inference time as the base model in both image generation with continuous diffusion and biological sequence generation with discrete diffusion. Our code is available at https://github.com/Owen-Oertell/slcd

The relationship between inverse reinforcement learning (IRL) and inverse optimization (IO) for Markov decision processes (MDPs) has been relatively underexplored in the literature, despite addressing the same problem. In this work, we revisit the relationship between the IO framework for MDPs, IRL, and apprenticeship learning (AL). We incorporate prior beliefs on the structure of the cost function into the IRL and AL problems, and demonstrate that the convex-analytic view of the AL formalism (Kamoutsi et al., 2021) emerges as a relaxation of our framework. Notably, the AL formalism is a special case in our framework when the regularization term is absent. Focusing on the suboptimal expert setting, we formulate the AL problem as a regularized min-max problem. The regularizer plays a key role in addressing the ill-posedness of IRL by guiding the search for plausible cost functions. To solve the resulting regularized-convex-concave-min-max problem, we use stochastic mirror descent (SMD) and establish convergence bounds for the proposed method. Numerical experiments highlight the critical role of regularization in learning cost vectors and apprentice policies.

Replay-based continual learning (CL) methods assume that models trained on a small subset can also effectively minimize the empirical risk of the complete dataset. These methods maintain a memory buffer that stores a sampled subset of data from previous tasks to consolidate past knowledge. However, this assumption is not guaranteed in practice due to the limited capacity of the memory buffer and the heuristic criteria used for buffer data selection. To address this issue, we propose a new dataset distillation framework tailored for CL, which maintains a learnable memory buffer to distill the global information from the current task data and accumulated knowledge preserved in the previous memory buffer. Moreover, to avoid the computational overhead and overfitting risks associated with parameterizing the entire buffer during distillation, we introduce a lightweight distillation module that can achieve global information distillation solely by generating learnable soft labels for the memory buffer data. Extensive experiments show that, our method can achieve competitive results and effectively mitigates forgetting across various datasets. The source code will be publicly available.

The optimization of neural networks under weight decay remains poorly understood from a theoretical standpoint. While weight decay is standard practice in modern training procedures, most theoretical analyses focus on unregularized settings. In this work, we investigate the loss landscape of the $\ell_2$-regularized training loss for two-layer ReLU networks. We show that the landscape becomes benign -- i.e., free of spurious local minima -- under large overparametrization, specifically when the network width $m$ satisfies $m \gtrsim \min(n^d, 2^n)$, where $n$ is the number of data points and $d$ the input dimension. More precisely in this regime, almost all constant activation regions contain a global minimum and no spurious local minima. We further show that this level of overparametrization is not only sufficient but also necessary via the example of orthogonal data. Finally, we demonstrate that such loss landscape results primarily hold relevance in the large initialization regime. In contrast, for small initializations -- corresponding to the feature learning regime -- optimization can still converge to spurious local minima, despite the global benignity of the landscape.

Scaling foundation model training with Distributed Data Parallel (DDP) methods is bandwidth-limited. Existing infrequent communication methods like Local SGD were designed to synchronize only model parameters and cannot be trivially applied to adaptive optimizers due to additional optimizer states. Current approaches extending Local SGD either lack convergence guarantees or require synchronizing all optimizer states, tripling communication costs. We propose Desynced Low Communication Adaptive Optimizers (DES-LOC), a family of optimizers assigning independent synchronization periods to parameters and momenta, enabling lower communication costs while preserving convergence. Through extensive experiments on language models of up to 1.7B, we show that DES-LOC can communicate 170x less than DDP and 2x less than the previous state-of-the-art Local ADAM. Furthermore, unlike previous heuristic approaches, DES-LOC is suited for practical training scenarios prone to system failures. DES-LOC offers a scalable, bandwidth-efficient, and fault-tolerant solution for foundation model training.

Optimization is an important module of modern machine learning applications. Tremendous efforts have been made to accelerate optimization algorithms. A common formulation is achieving a lower loss at a given time. This enables a differentiable framework with respect to the algorithm hyperparameters. In contrast, its dual, minimizing the time to reach a target loss, is believed to be non-differentiable, as the time is not differentiable. As a result, it usually serves as a conceptual framework or is optimized using zeroth-order methods. To address this limitation, we propose a differentiable stopping time and theoretically justify it based on differential equations. An efficient algorithm is designed to backpropagate through it. As a result, the proposed differentiable stopping time enables a new differentiable formulation for accelerating algorithms. We further discuss its applications, such as online hyperparameter tuning and learning to optimize. Our proposed methods show superior performance in comprehensive experiments across various problems, which confirms their effectiveness.

Parameter-Efficient Fine-Tuning (PEFT) methods achieve performance comparable to Full Fine-Tuning (FFT) while requiring significantly fewer computing resources, making it the go-to choice for researchers. We find that although PEFT can achieve competitive results on some benchmarks, its performance falls short of FFT in complex tasks, such as reasoning and instruction-based fine-tuning. In this paper, we compare the characteristics of PEFT and FFT in terms of representational capacity and robustness based on optimization theory. We theoretically demonstrate that PEFT is a strict subset of FFT. By providing theoretical upper bounds for PEFT, we show that the limited parameter space constrains the model's representational ability, making it more susceptible to perturbations. Experiments on 15 datasets encompassing classification, generation, reasoning, instruction fine-tuning tasks and 11 adversarial test sets validate our theories. We hope that these results spark further research beyond the realms of well established PEFT. The source code is in the anonymous Github repository\footnote{https://github.com/misonsky/PEFTEval}.

Recent 3D Gaussian Splatting (3DGS) techniques for Visual Simultaneous Localization and Mapping (SLAM) have significantly progressed in tracking and high-fidelity mapping. However, their sequential optimization framework and sensitivity to dynamic objects limit real-time performance and robustness in real-world scenarios. We present UP-SLAM, a real-time RGB-D SLAM system for dynamic environments that decouples tracking and mapping through a parallelized framework. A probabilistic octree is employed to manage Gaussian primitives adaptively, enabling efficient initialization and pruning without hand-crafted thresholds. To robustly filter dynamic regions during tracking, we propose a training-free uncertainty estimator that fuses multi-modal residuals to estimate per-pixel motion uncertainty, achieving open-set dynamic object handling without reliance on semantic labels. Furthermore, a temporal encoder is designed to enhance rendering quality. Concurrently, low-dimensional features are efficiently transformed via a shallow multilayer perceptron to construct DINO features, which are then employed to enrich the Gaussian field and improve the robustness of uncertainty prediction. Extensive experiments on multiple challenging datasets suggest that UP-SLAM outperforms state-of-the-art methods in both localization accuracy (by 59.8%) and rendering quality (by 4.57 dB PSNR), while maintaining real-time performance and producing reusable, artifact-free static maps in dynamic environments.The project: https://aczheng-cai.github.io/up_slam.github.io/

With the advent of 6G communications, intelligent communication systems face multiple challenges, including constrained perception and response capabilities, limited scalability, and low adaptability in dynamic environments. This tutorial provides a systematic introduction to the principles, design, and applications of Large Artificial Intelligence Models (LAMs) and Agentic AI technologies in intelligent communication systems, aiming to offer researchers a comprehensive overview of cutting-edge technologies and practical guidance. First, we outline the background of 6G communications, review the technological evolution from LAMs to Agentic AI, and clarify the tutorial's motivation and main contributions. Subsequently, we present a comprehensive review of the key components required for constructing LAMs. We further categorize LAMs and analyze their applicability, covering Large Language Models (LLMs), Large Vision Models (LVMs), Large Multimodal Models (LMMs), Large Reasoning Models (LRMs), and lightweight LAMs. Next, we propose a LAM-centric design paradigm tailored for communications, encompassing dataset construction and both internal and external learning approaches. Building upon this, we develop an LAM-based Agentic AI system for intelligent communications, clarifying its core components such as planners, knowledge bases, tools, and memory modules, as well as its interaction mechanisms. We also introduce a multi-agent framework with data retrieval, collaborative planning, and reflective evaluation for 6G. Subsequently, we provide a detailed overview of the applications of LAMs and Agentic AI in communication scenarios. Finally, we summarize the research challenges and future directions in current studies, aiming to support the development of efficient, secure, and sustainable next-generation intelligent communication systems.

Novel techniques in evolutionary optimization, simulation and machine learning allow for a broad analysis of domains like fluid dynamics, in which computation is expensive and flow behavior is complex. Under the term of full domain analysis we understand the ability to efficiently determine the full space of solutions in a problem domain, and analyze the behavior of those solutions in an accessible and interactive manner. The goal of full domain analysis is to deepen our understanding of domains by generating many examples of flow, their diversification, optimization and analysis. We define a formal model for full domain analysis, its current state of the art, and requirements of subcomponents. Finally, an example is given to show what we can learn by using full domain analysis. Full domain analysis, rooted in optimization and machine learning, can be a helpful tool in understanding complex systems in computational physics and beyond.