Daily Papers

PRefLexOR (Preference-based Recursive Language Modeling for Exploratory Optimization of Reasoning) combines preference optimization with concepts from Reinforcement Learning to enable models to self-teach through iterative reasoning improvements. We propose a recursive learning approach that engages the model in multi-step reasoning, revisiting, and refining intermediate steps before producing a final output in training and inference phases. Through multiple training stages, the model first learns to align its reasoning with accurate decision paths by optimizing the log odds between preferred and non-preferred responses. During this process, PRefLexOR builds a dynamic knowledge graph by generating questions from random text chunks and retrieval-augmentation to contextualize relevant details from the entire training corpus. In the second stage, preference optimization enhances model performance by using rejection sampling to fine-tune reasoning quality by continually producing in-situ training data while masking the reasoning steps. Recursive optimization within a thinking token framework introduces iterative feedback loops, where the model refines reasoning, achieving deeper coherence, consistency, and adaptability. Implemented in small language models with only 3 billion parameters, we should that even tiny models can iteratively teach themselves to reason with greater depth and reflectivity. Our implementation is straightforward and can be incorporated into any existing pretrained LLM. We focus our examples on applications in biological materials science and demonstrate the method in a variety of case studies that range from in-domain to cross-domain applications. Using reasoning strategies that include thinking and reflection modalities we build a multi-agent recursive self-improving inference approach to successively improve responses via repeated sampling in inference time.

Camouflaged object detection is an emerging and challenging computer vision task that requires identifying and segmenting objects that blend seamlessly into their environments due to high similarity in color, texture, and size. This task is further complicated by low-light conditions, partial occlusion, small object size, intricate background patterns, and multiple objects. While many sophisticated methods have been proposed for this task, current methods still struggle to precisely detect camouflaged objects in complex scenarios, especially with small and multiple objects, indicating room for improvement. We propose a Multi-Scale Recursive Network that extracts multi-scale features via a Pyramid Vision Transformer backbone and combines them via specialized Attention-Based Scale Integration Units, enabling selective feature merging. For more precise object detection, our decoder recursively refines features by incorporating Multi-Granularity Fusion Units. A novel recursive-feedback decoding strategy is developed to enhance global context understanding, helping the model overcome the challenges in this task. By jointly leveraging multi-scale learning and recursive feature optimization, our proposed method achieves performance gains, successfully detecting small and multiple camouflaged objects. Our model achieves state-of-the-art results on two benchmark datasets for camouflaged object detection and ranks second on the remaining two. Our codes, model weights, and results are available at https://github.com/linaagh98/MSRNet{https://github.com/linaagh98/MSRNet}.

Diffusion models achieve remarkable generation quality but suffer from computational intensive sampling due to suboptimal step discretization. While existing works focus on optimizing denoising directions, we address the principled design of stepsize schedules. This paper proposes Optimal Stepsize Distillation, a dynamic programming framework that extracts theoretically optimal schedules by distilling knowledge from reference trajectories. By reformulating stepsize optimization as recursive error minimization, our method guarantees global discretization bounds through optimal substructure exploitation. Crucially, the distilled schedules demonstrate strong robustness across architectures, ODE solvers, and noise schedules. Experiments show 10x accelerated text-to-image generation while preserving 99.4% performance on GenEval. Our code is available at https://github.com/bebebe666/OptimalSteps.

The OpenAI o1-series models have demonstrated that leveraging long-form Chain of Thought (CoT) can substantially enhance performance. However, the recursive thinking capabilities of Large Language Models (LLMs) remain limited, particularly in the absence of expert-curated data for distillation. In this paper, we propose AvR: Alignment via Refinement, a novel method aimed at unlocking the potential of LLMs for recursive reasoning through long-form CoT. AvR introduces a refinement process that integrates criticism and improvement actions, guided by differentiable learning techniques to optimize refinement-aware rewards. As a result, the synthesized multi-round data can be organized as a long refinement thought, further enabling test-time scaling. Experimental results show that AvR significantly outperforms conventional preference optimization methods. Notably, with only 3k synthetic samples, our method boosts the performance of the LLaMA-3-8B-Instruct model by over 20\% in win rate on AlpacaEval 2.0. Our code is available at Github (https://github.com/Banner-Z/AvR.git).

Recurrent neural networks (RNNs) are widely used throughout neuroscience as models of local neural activity. Many properties of single RNNs are well characterized theoretically, but experimental neuroscience has moved in the direction of studying multiple interacting areas, and RNN theory needs to be likewise extended. We take a constructive approach towards this problem, leveraging tools from nonlinear control theory and machine learning to characterize when combinations of stable RNNs will themselves be stable. Importantly, we derive conditions which allow for massive feedback connections between interacting RNNs. We parameterize these conditions for easy optimization using gradient-based techniques, and show that stability-constrained "networks of networks" can perform well on challenging sequential-processing benchmark tasks. Altogether, our results provide a principled approach towards understanding distributed, modular function in the brain.

We consider the optimization problem of the form min_{x in R^d} f(x) triangleq E_{xi} [F(x; xi)], where the component F(x;xi) is L-mean-squared Lipschitz but possibly nonconvex and nonsmooth. The recently proposed gradient-free method requires at most O( L^4 d^{3/2} epsilon^{-4} + Delta L^3 d^{3/2} delta^{-1} epsilon^{-4}) stochastic zeroth-order oracle complexity to find a (delta,epsilon)-Goldstein stationary point of objective function, where Delta = f(x_0) - inf_{x in R^d} f(x) and x_0 is the initial point of the algorithm. This paper proposes a more efficient algorithm using stochastic recursive gradient estimators, which improves the complexity to O(L^3 d^{3/2} epsilon^{-3}+ Delta L^2 d^{3/2} delta^{-1} epsilon^{-3}).

Despite the success of neural-based combinatorial optimization methods for end-to-end heuristic learning, out-of-distribution generalization remains a challenge. In this paper, we present a novel formulation of Combinatorial Optimization Problems (COPs) as Markov Decision Processes (MDPs) that effectively leverages common symmetries of COPs to improve out-of-distribution robustness. Starting from a direct MDP formulation of a constructive method, we introduce a generic way to reduce the state space, based on Bisimulation Quotienting (BQ) in MDPs. Then, for COPs with a recursive nature, we specialize the bisimulation and show how the reduced state exploits the symmetries of these problems and facilitates MDP solving. Our approach is principled and we prove that an optimal policy for the proposed BQ-MDP actually solves the associated COPs. We illustrate our approach on five classical problems: the Euclidean and Asymmetric Traveling Salesman, Capacitated Vehicle Routing, Orienteering and Knapsack Problems. Furthermore, for each problem, we introduce a simple attention-based policy network for the BQ-MDPs, which we train by imitation of (near) optimal solutions of small instances from a single distribution. We obtain new state-of-the-art results for the five COPs on both synthetic and realistic benchmarks. Notably, in contrast to most existing neural approaches, our learned policies show excellent generalization performance to much larger instances than seen during training, without any additional search procedure.

We present a neat yet effective recursive operation on vision transformers that can improve parameter utilization without involving additional parameters. This is achieved by sharing weights across the depth of transformer networks. The proposed method can obtain a substantial gain (~2%) simply using naive recursive operation, requires no special or sophisticated knowledge for designing principles of networks, and introduces minimal computational overhead to the training procedure. To reduce the additional computation caused by recursive operation while maintaining the superior accuracy, we propose an approximating method through multiple sliced group self-attentions across recursive layers which can reduce the cost consumption by 10~30% with minimal performance loss. We call our model Sliced Recursive Transformer (SReT), a novel and parameter-efficient vision transformer design that is compatible with a broad range of other designs for efficient ViT architectures. Our best model establishes significant improvement on ImageNet-1K over state-of-the-art methods while containing fewer parameters. The proposed weight sharing mechanism by sliced recursion structure allows us to build a transformer with more than 100 or even 1000 shared layers with ease while keeping a compact size (13~15M), to avoid optimization difficulties when the model is too large. The flexible scalability has shown great potential for scaling up models and constructing extremely deep vision transformers. Code is available at https://github.com/szq0214/SReT.

Recent advances in vision transformers (ViTs) have demonstrated the advantage of global modeling capabilities, prompting widespread integration of large-kernel convolutions for enlarging the effective receptive field (ERF). However, the quadratic scaling of parameter count and computational complexity (FLOPs) with respect to kernel size poses significant efficiency and optimization challenges. This paper introduces RecConv, a recursive decomposition strategy that efficiently constructs multi-frequency representations using small-kernel convolutions. RecConv establishes a linear relationship between parameter growth and decomposing levels which determines the effective kernel size ktimes 2^ell for a base kernel k and ell levels of decomposition, while maintaining constant FLOPs regardless of the ERF expansion. Specifically, RecConv achieves a parameter expansion of only ell+2 times and a maximum FLOPs increase of 5/3 times, compared to the exponential growth (4^ell) of standard and depthwise convolutions. RecNeXt-M3 outperforms RepViT-M1.1 by 1.9 AP^{box} on COCO with similar FLOPs. This innovation provides a promising avenue towards designing efficient and compact networks across various modalities. Codes and models can be found at https://github.com/suous/RecNeXt.

Nonconvex optimization is central in solving many machine learning problems, in which block-wise structure is commonly encountered. In this work, we propose cyclic block coordinate methods for nonconvex optimization problems with non-asymptotic gradient norm guarantees. Our convergence analysis is based on a gradient Lipschitz condition with respect to a Mahalanobis norm, inspired by a recent progress on cyclic block coordinate methods. In deterministic settings, our convergence guarantee matches the guarantee of (full-gradient) gradient descent, but with the gradient Lipschitz constant being defined w.r.t.~a Mahalanobis norm. In stochastic settings, we use recursive variance reduction to decrease the per-iteration cost and match the arithmetic operation complexity of current optimal stochastic full-gradient methods, with a unified analysis for both finite-sum and infinite-sum cases. We prove a faster linear convergence result when a Polyak-{\L}ojasiewicz (P{\L}) condition holds. To our knowledge, this work is the first to provide non-asymptotic convergence guarantees -- variance-reduced or not -- for a cyclic block coordinate method in general composite (smooth + nonsmooth) nonconvex settings. Our experimental results demonstrate the efficacy of the proposed cyclic scheme in training deep neural nets.

Controllable music generation remains a significant challenge, with existing methods often requiring model retraining or introducing audible artifacts. We introduce MusicRFM, a framework that adapts Recursive Feature Machines (RFMs) to enable fine-grained, interpretable control over frozen, pre-trained music models by directly steering their internal activations. RFMs analyze a model's internal gradients to produce interpretable "concept directions", or specific axes in the activation space that correspond to musical attributes like notes or chords. We first train lightweight RFM probes to discover these directions within MusicGen's hidden states; then, during inference, we inject them back into the model to guide the generation process in real-time without per-step optimization. We present advanced mechanisms for this control, including dynamic, time-varying schedules and methods for the simultaneous enforcement of multiple musical properties. Our method successfully navigates the trade-off between control and generation quality: we can increase the accuracy of generating a target musical note from 0.23 to 0.82, while text prompt adherence remains within approximately 0.02 of the unsteered baseline, demonstrating effective control with minimal impact on prompt fidelity. We release code to encourage further exploration on RFMs in the music domain.

The rapid advancement of large language models (LLMs) has significantly enhanced the capabilities of AI-driven agents across various tasks. However, existing agentic systems, whether based on fixed pipeline algorithms or pre-defined meta-learning frameworks, cannot search the whole agent design space due to the restriction of human-designed components, and thus might miss the globally optimal agent design. In this paper, we introduce G\"odel Agent, a self-evolving framework inspired by the G\"odel machine, enabling agents to recursively improve themselves without relying on predefined routines or fixed optimization algorithms. G\"odel Agent leverages LLMs to dynamically modify its own logic and behavior, guided solely by high-level objectives through prompting. Experimental results on mathematical reasoning and complex agent tasks demonstrate that implementation of G\"odel Agent can achieve continuous self-improvement, surpassing manually crafted agents in performance, efficiency, and generalizability.

The pursuit of automated scientific discovery has fueled progress from symbolic logic to modern AI, forging new frontiers in reasoning and pattern recognition. Transformers function as potential systems, where every possible relationship remains latent potentiality until tasks impose constraints, akin to measurement. Yet, refining their sampling requires more than probabilistic selection: solutions must conform to specific structures or rules, ensuring consistency and the invocation of general principles. We present Graph-PReFLexOR (Graph-based Preference-based Recursive Language Modeling for Exploratory Optimization of Reasoning), a framework that combines graph reasoning with symbolic abstraction to dynamically expand domain knowledge. Inspired by reinforcement learning, Graph-PReFLexOR defines reasoning as a structured mapping, where tasks yield knowledge graphs, abstract patterns, and ultimately, final answers. Inspired by category theory, it encodes concepts as nodes and their relationships as edges, supporting hierarchical inference and adaptive learning through isomorphic representations. Demonstrations include hypothesis generation, materials design, and creative reasoning, such as discovering relationships between mythological concepts like 'thin places' with materials science. We propose a 'knowledge garden growth' strategy that integrates insights across domains, promoting interdisciplinary connections. Results with a 3-billion-parameter Graph-PReFLexOR model show superior reasoning depth and adaptability, underscoring the potential for transparent, multidisciplinary AI-driven discovery. It lays the groundwork for general autonomous reasoning solutions.

Efficient detectors for edge devices are often optimized for parameters or speed count metrics, which remain in weak correlation with the energy of detectors. However, some vision applications of convolutional neural networks, such as always-on surveillance cameras, are critical for energy constraints. This paper aims to serve as a baseline by designing detectors to reach tradeoffs between energy and performance from two perspectives: 1) We extensively analyze various CNNs to identify low-energy architectures, including selecting activation functions, convolutions operators, and feature fusion structures on necks. These underappreciated details in past work seriously affect the energy consumption of detectors; 2) To break through the dilemmatic energy-performance problem, we propose a balanced detector driven by energy using discovered low-energy components named FemtoDet. In addition to the novel construction, we improve FemtoDet by considering convolutions and training strategy optimizations. Specifically, we develop a new instance boundary enhancement (IBE) module for convolution optimization to overcome the contradiction between the limited capacity of CNNs and detection tasks in diverse spatial representations, and propose a recursive warm-restart (RecWR) for optimizing training strategy to escape the sub-optimization of light-weight detectors by considering the data shift produced in popular augmentations. As a result, FemtoDet with only 68.77k parameters achieves a competitive score of 46.3 AP50 on PASCAL VOC and 1.11 W & 64.47 FPS on Qualcomm Snapdragon 865 CPU platforms. Extensive experiments on COCO and TJU-DHD datasets indicate that the proposed method achieves competitive results in diverse scenes.

Large language models (LLMs) are susceptible to persuasion, which can pose risks when models are faced with an adversarial interlocutor. We take a first step towards defending models against persuasion while also arguing that defense against adversarial (i.e. negative) persuasion is only half of the equation: models should also be able to accept beneficial (i.e. positive) persuasion to improve their answers. We show that optimizing models for only one side results in poor performance on the other. In order to balance positive and negative persuasion, we introduce Persuasion-Balanced Training (or PBT), which leverages multi-agent recursive dialogue trees to create data and trains models via preference optimization to accept persuasion when appropriate. PBT consistently improves resistance to misinformation and resilience to being challenged while also resulting in the best overall performance on holistic data containing both positive and negative persuasion. Crucially, we show that PBT models are better teammates in multi-agent debates. We find that without PBT, pairs of stronger and weaker models have unstable performance, with the order in which the models present their answers determining whether the team obtains the stronger or weaker model's performance. PBT leads to better and more stable results and less order dependence, with the stronger model consistently pulling the weaker one up.

Training deep neural networks--and more recently, large models--demands efficient and scalable optimizers. Adaptive gradient algorithms like Adam, AdamW, and their variants have been central to this task. Despite the development of numerous variance reduction algorithms in the past decade aimed at accelerating stochastic optimization in both convex and nonconvex settings, variance reduction has not found widespread success in training deep neural networks or large language models. Consequently, it has remained a less favored approach in modern AI. In this paper, to unleash the power of variance reduction for efficient training of large models, we propose a unified optimization framework, MARS (Make vAriance Reduction Shine), which reconciles preconditioned gradient methods with variance reduction via a scaled stochastic recursive momentum technique. Within our framework, we introduce three instances of MARS that leverage preconditioned gradient updates based on AdamW, Lion, and Shampoo, respectively. We also draw a connection between our algorithms and existing optimizers. Experimental results on training GPT-2 models indicate that MARS consistently outperforms AdamW by a large margin.