Jun He

ByteDance Seed, Jiaze Chen, Tiantian Fan et al. · bytedance

We introduce Seed1.5-Thinking, capable of reasoning through thinking before responding, resulting in improved performance on a wide range of benchmarks. Seed1.5-Thinking achieves 86.7 on AIME 2024, 55.0 on Codeforces and 77.3 on GPQA, demonstrating excellent reasoning abilities in STEM and coding. Beyond reasoning tasks, the method demonstrates notable generalization across diverse domains. For instance, it surpasses DeepSeek R1 by 8% in win rate on non-reasoning tasks, indicating its broader applicability. Compared to other state-of-the-art reasoning models, Seed1.5-Thinking is a Mixture-of-Experts (MoE) model with a relatively small size, featuring 20B activated and 200B total parameters. As part of our effort to assess generalized reasoning, we develop two internal benchmarks, BeyondAIME and Codeforces, both of which will be publicly released to support future research. Model trial link: https://www.volcengine.com/experience/ark.

Jun He, Siang Yew Chong, Xin Yao

The fitness level method is a widely used technique for estimating the mean hitting time of elitist evolutionary algorithms on level-based fitness functions. However, this paper identifies its main limitation: the linear lower bound derived from traditional fitness level partitioning is not tight when applied to many non-level-based fitness functions. A new subset level method is introduced to address this limitation. It selects a subset of non-optimal solutions, partitions them into levels, and then estimates linear bound coefficients based on drift analysis. Explicit expressions are proposed to compute the lower bound on the mean hitting time of elitist evolutionary algorithms. The proposed method is validated using six instances of the knapsack problem. Results show that the new method can be used to quickly estimate the lower bound on the mean hitting time of elitist evolutionary algorithms. This expands the application scope of the fitness level method to non-level-based functions.

Xukun Zhou, Fengxin Li, Ziqiao Peng et al.

Audio-driven 3D face animation is increasingly vital in live streaming and augmented reality applications. While remarkable progress has been observed, most existing approaches are designed for specific individuals with predefined speaking styles, thus neglecting the adaptability to varied speaking styles. To address this limitation, this paper introduces MetaFace, a novel methodology meticulously crafted for speaking style adaptation. Grounded in the novel concept of meta-learning, MetaFace is composed of several key components: the Robust Meta Initialization Stage (RMIS) for fundamental speaking style adaptation, the Dynamic Relation Mining Neural Process (DRMN) for forging connections between observed and unobserved speaking styles, and the Low-rank Matrix Memory Reduction Approach to enhance the efficiency of model optimization as well as learning style details. Leveraging these novel designs, MetaFace not only significantly outperforms robust existing baselines but also establishes a new state-of-the-art, as substantiated by our experimental results.

Jun He, Andrew L. Liu, Yihsu Chen

Designing socially optimal policies in multi-agent environments is a fundamental challenge in both economics and artificial intelligence. This paper studies a general framework for learning Stackelberg equilibria in dynamic and uncertain environments, where a single leader interacts with a population of adaptive followers. Motivated by pressing real-world challenges such as equitable electricity tariff design for consumers with distributed energy resources (such as rooftop solar and energy storage), we formalize a class of Stackelberg Markov games and establish the existence and uniqueness of stationary Stackelberg equilibria under mild continuity and monotonicity conditions. We then extend the framework to incorporate a continuum of agents via mean-field approximation, yielding a tractable Stackelberg-Mean Field Equilibrium (S-MFE) formulation. To address the computational intractability of exact best-response dynamics, we introduce a softmax-based approximation and rigorously bound its error relative to the true Stackelberg equilibrium. Our approach enables scalable and stable learning through policy iteration without requiring full knowledge of follower objectives. We validate the framework on an energy market simulation, where a public utility or a state utility commission sets time-varying rates for a heterogeneous population of prosumers. Our results demonstrate that learned policies can simultaneously achieve economic efficiency, equity across income groups, and stability in energy systems. This work demonstrates how game-theoretic learning frameworks can support data-driven policy design in large-scale strategic environments, with applications to real-world systems like energy markets.

Xukun Zhou, Zhenbo Song, Jun He et al.

Scene Graph Generation is a critical enabler of environmental comprehension for autonomous robotic systems. Most of existing methods, however, are often thwarted by the intricate dynamics of background complexity, which limits their ability to fully decode the inherent topological information of the environment. Additionally, the wealth of contextual information encapsulated within depth cues is often left untapped, rendering existing approaches less effective. To address these shortcomings, we present STDG, an avant-garde Depth-Guided One-Stage Scene Graph Generation methodology. The innovative architecture of STDG is a triad of custom-built modules: The Depth Guided HHA Representation Generation Module, the Depth Guided Semi-Teaching Network Learning Module, and the Depth Guided Scene Graph Generation Module. This trifecta of modules synergistically harnesses depth information, covering all aspects from depth signal generation and depth feature utilization, to the final scene graph prediction. Importantly, this is achieved without imposing additional computational burden during the inference phase. Experimental results confirm that our method significantly enhances the performance of one-stage scene graph generation baselines.

Cong Wang, Jun He, Yu Chen et al.

Although differential evolution (DE) algorithms perform well on a large variety of complicated optimization problems, only a few theoretical studies are focused on the working principle of DE algorithms. To make the first attempt to reveal the function of binomial crossover, this paper aims to answer whether it can reduce the approximation error of evolutionary algorithms. By investigating the expected approximation error and the probability of not finding the optimum, we conduct a case study comparing two evolutionary algorithms with and without binomial crossover on two classical benchmark problems: OneMax and Deceptive. It is proven that using binomial crossover leads to the dominance of transition matrices. As a result, the algorithm with binomial crossover asymptotically outperforms that without crossover on both OneMax and Deceptive, and outperforms on OneMax, however, not on Deceptive. Furthermore, an adaptive parameter strategy is proposed which can strengthen the superiority of binomial crossover on Deceptive.

Yu Chen, Jun He

Known as two cornerstones of problem solving by search, exploitation and exploration are extensively discussed for implementation and application of evolutionary algorithms (EAs). However, only a few researches focus on evaluation and theoretical estimation of exploitation and exploration. Considering that exploitation and exploration are two issues regarding global search and local search, this paper proposes to evaluate them via the success probability and the one-step improvement rate computed in different domains of integration. Then, case studies are performed by analyzing performances of (1+1) random univariate search and (1+1) evolutionary programming on the sphere function and the cheating problem. By rigorous theoretical analysis, we demonstrate that both exploitation and exploration of the investigated elitist EAs degenerate exponentially with the problem dimension $n$. Meanwhile, it is also shown that maximization of exploitation and exploration can be achieved by setting an appropriate value for the standard deviation $σ$ of Gaussian mutation, which is positively related to the distance from the present solution to the center of the promising region.

Jun He, Thomas Jansen, Christine Zarges

Performance analysis of all kinds of randomised search heuristics is a rapidly growing and developing field. Run time and solution quality are two popular measures of the performance of these algorithms. The focus of this paper is on the solution quality an optimisation heuristic achieves, not on the time it takes to reach this goal, setting it far apart from runtime analysis. We contribute to its further development by introducing a novel analytical framework, called unlimited budget analysis, to derive the expected fitness value after arbitrary computational steps. It has its roots in the very recently introduced approximation error analysis and bears some similarity to fixed budget analysis. We present the framework, apply it to simple mutation-based algorithms, covering both, local and global search. We provide analytical results for a number of pseudo-Boolean functions for unlimited budget analysis and compare them to results derived within the fixed budget framework for the same algorithms and functions. There are also results of experiments to compare bounds obtained in the two different frameworks with the actual observed performance. The study show that unlimited budget analysis may lead to the same or more general estimation beyond fixed budget.

Cong Wang, Yu Chen, Jun He et al.

When globally optimal solutions of complicated optimization problems cannot be located by evolutionary algorithms (EAs) in polynomial expected running time, the hitting time/running time analysis is not flexible enough to accommodate the requirement of theoretical study, because sometimes we have no idea on what approximation ratio is available in polynomial expected running time. Thus, it is necessary to propose an alternative routine for the theoretical analysis of EAs. To bridge the gap between theoretical analysis and algorithm implementation, in this paper we perform an error analysis where expected approximation error is estimated to evaluate performances of randomized search heuristics (RSHs). Based on the Markov chain model of RSHs, the multi-step transition matrix can be computed by diagonalizing the one-step transition matrix, and a general framework for estimation of expected approximation errors is proposed. Case studies indicate that the error analysis works well for both uni- and multi-modal benchmark problems. It leads to precise estimations of approximation error instead of asymptotic results on fitness values, which demonstrates its competitiveness to fixed budget analysis.

Yu Chen, Jun He

The average convergence rate (ACR) measures how fast the approximation error of an evolutionary algorithm converges to zero per generation. It is defined as the geometric average of the reduction rate of the approximation error over consecutive generations. This paper makes a theoretical analysis of the ACR in continuous optimization. The obtained results are summarized as follows. According to the limit property, the ACR is classified into two categories: (1) linear ACR whose limit inferior value is larger than a positive and (2) sublinear ACR whose value converges to zero. Then, it is proven that the ACR is linear for evolutionary programming using positive landscape-adaptive mutation, but sublinear for that using landscape-invariant or zero landscape-adaptive mutation. The relationship between the ACR and the decision space dimension is also classified into two categories: (1) polynomial ACR whose value is larger than the reciprocal of a polynomial function of the dimension for any generation, and (2) exponential ACR whose value is less than the reciprocal of an exponential function of the dimension for an exponential long period. It is proven that for easy problems such as linear functions, the ACR of the (1+1) adaptive random univariate search is polynomial. But for hard functions such as the deceptive function, the ACR of both the (1+1) adaptive random univariate search and evolutionary programming is exponential.

Jun He, Yu Chen, Yuren Zhou

In the empirical study of evolutionary algorithms, the solution quality is evaluated by either the fitness value or approximation error. The latter measures the fitness difference between an approximation solution and the optimal solution. Since the approximation error analysis is more convenient than the direct estimation of the fitness value, this paper focuses on approximation error analysis. However, it is straightforward to extend all related results from the approximation error to the fitness value. Although the evaluation of solution quality plays an essential role in practice, few rigorous analyses have been conducted on this topic. This paper aims at establishing a novel theoretical framework of approximation error analysis of evolutionary algorithms for discrete optimization. This framework is divided into two parts. The first part is about exact expressions of the approximation error. Two methods, Jordan form and Schur's triangularization, are presented to obtain an exact expression. The second part is about upper bounds on approximation error. Two methods, convergence rate and auxiliary matrix iteration, are proposed to estimate the upper bound. The applicability of this framework is demonstrated through several examples.

Tao Xu, Jun He

Solving constrained optimization problems by multi-objective evolutionary algorithms has scored tremendous achievements in the last decade. Standard multi-objective schemes usually aim at minimizing the objective function and also the degree of constraint violation simultaneously. This paper proposes a new multi-objective method for solving constrained optimization problems. The new method keeps two standard objectives: the original objective function and the sum of degrees of constraint violation. But besides them, four more objectives are added. One is based on the feasible rule. The other three come from the penalty functions. This paper conducts an initial experimental study on thirteen benchmark functions. A simplified version of CMODE is applied to solving multi-objective optimization problems. Our initial experimental results confirm our expectation that adding more helper functions could be useful. The performance of SMODE with more helper functions (four or six) is better than that with only two helper functions.

Jun He, Guangming Lin

In evolutionary optimization, it is important to understand how fast evolutionary algorithms converge to the optimum per generation, or their convergence rate. This paper proposes a new measure of the convergence rate, called average convergence rate. It is a normalised geometric mean of the reduction ratio of the fitness difference per generation. The calculation of the average convergence rate is very simple and it is applicable for most evolutionary algorithms on both continuous and discrete optimization. A theoretical study of the average convergence rate is conducted for discrete optimization. Lower bounds on the average convergence rate are derived. The limit of the average convergence rate is analysed and then the asymptotic average convergence rate is proposed.

Jun He, Yong Wang, Yuren Zhou

Multi-objective optimisation is regarded as one of the most promising ways for dealing with constrained optimisation problems in evolutionary optimisation. This paper presents a theoretical investigation of a multi-objective optimisation evolutionary algorithm for solving the 0-1 knapsack problem. Two initialisation methods are considered in the algorithm: local search initialisation and greedy search initialisation. Then the solution quality of the algorithm is analysed in terms of the approximation ratio.

Xinsheng Lai, Yuren Zhou, Jun He et al.

Some experimental investigations have shown that evolutionary algorithms (EAs) are efficient for the minimum label spanning tree (MLST) problem. However, we know little about that in theory. As one step towards this issue, we theoretically analyze the performances of the (1+1) EA, a simple version of EAs, and a multi-objective evolutionary algorithm called GSEMO on the MLST problem. We reveal that for the MLST$_{b}$ problem the (1+1) EA and GSEMO achieve a $\frac{b+1}{2}$-approximation ratio in expected polynomial times of $n$ the number of nodes and $k$ the number of labels. We also show that GSEMO achieves a $(2ln(n))$-approximation ratio for the MLST problem in expected polynomial time of $n$ and $k$. At the same time, we show that the (1+1) EA and GSEMO outperform local search algorithms on three instances of the MLST problem. We also construct an instance on which GSEMO outperforms the (1+1) EA.

Jun He, Feidun He, Hongbin Dong

The 0-1 knapsack problem is a well-known combinatorial optimisation problem. Approximation algorithms have been designed for solving it and they return provably good solutions within polynomial time. On the other hand, genetic algorithms are well suited for solving the knapsack problem and they find reasonably good solutions quickly. A naturally arising question is whether genetic algorithms are able to find solutions as good as approximation algorithms do. This paper presents a novel multi-objective optimisation genetic algorithm for solving the 0-1 knapsack problem. Experiment results show that the new algorithm outperforms its rivals, the greedy algorithm, mixed strategy genetic algorithm, and greedy algorithm + mixed strategy genetic algorithm.

Jun He, Feidun He, Xin Yao

The convergence, convergence rate and expected hitting time play fundamental roles in the analysis of randomised search heuristics. This paper presents a unified Markov chain approach to studying them. Using the approach, the sufficient and necessary conditions of convergence in distribution are established. Then the average convergence rate is introduced to randomised search heuristics and its lower and upper bounds are derived. Finally, novel average drift analysis and backward drift analysis are proposed for bounding the expected hitting time. A computational study is also conducted to investigate the convergence, convergence rate and expected hitting time. The theoretical study belongs to a prior and general study while the computational study belongs to a posterior and case study.

Jun He, Xin Yao

This paper aims to study how the population size affects the computation time of evolutionary algorithms in a rigorous way. The computation time of an evolutionary algorithm can be measured by either the expected number of generations (hitting time) or the expected number of fitness evaluations (running time) to find an optimal solution. Population scalability is the ratio of the expected hitting time between a benchmark algorithm and an algorithm using a larger population size. Average drift analysis is presented for comparing the expected hitting time of two algorithms and estimating lower and upper bounds on population scalability. Several intuitive beliefs are rigorously analysed. It is prove that (1) using a population sometimes increases rather than decreases the expected hitting time; (2) using a population cannot shorten the expected running time of any elitist evolutionary algorithm on unimodal functions in terms of the time-fitness landscape, but this is not true in terms of the distance-based fitness landscape; (3) using a population cannot always reduce the expected running time on fully-deceptive functions, which depends on the benchmark algorithm using elitist selection or random selection.

Boris Mitavskiy, Elio Tuci, Chris Cannings et al.

The classical Geiringer theorem addresses the limiting frequency of occurrence of various alleles after repeated application of crossover. It has been adopted to the setting of evolutionary algorithms and, a lot more recently, reinforcement learning and Monte-Carlo tree search methodology to cope with a rather challenging question of action evaluation at the chance nodes. The theorem motivates novel dynamic parallel algorithms that are explicitly described in the current paper for the first time. The algorithms involve independent agents traversing a dynamically constructed directed graph that possibly has loops. A rather elegant and profound category-theoretic model of cognition in biological neural networks developed by a well-known French mathematician, professor Andree Ehresmann jointly with a neurosurgeon, Jan Paul Vanbremeersch over the last thirty years provides a hint at the connection between such algorithms and Hebbian learning.

Boris Mitavskiy, Jun He

Hybrid and mixed strategy EAs have become rather popular for tackling various complex and NP-hard optimization problems. While empirical evidence suggests that such algorithms are successful in practice, rather little theoretical support for their success is available, not mentioning a solid mathematical foundation that would provide guidance towards an efficient design of this type of EAs. In the current paper we develop a rigorous mathematical framework that suggests such designs based on generalized schema theory, fitness levels and drift analysis. An example-application for tackling one of the classical NP-hard problems, the "single-machine scheduling problem" is presented.

Jun He, Wei Hou, Hongbin Dong et al.

In pure strategy meta-heuristics, only one search strategy is applied for all time. In mixed strategy meta-heuristics, each time one search strategy is chosen from a strategy pool with a probability and then is applied. An example is classical genetic algorithms, where either a mutation or crossover operator is chosen with a probability each time. The aim of this paper is to compare the performance between mixed strategy and pure strategy meta-heuristic algorithms. First an experimental study is implemented and results demonstrate that mixed strategy evolutionary algorithms may outperform pure strategy evolutionary algorithms on the 0-1 knapsack problem in up to 77.8% instances. Then Complementary Strategy Theorem is rigorously proven for applying mixed strategy at the population level. The theorem asserts that given two meta-heuristic algorithms where one uses pure strategy 1 and another uses pure strategy 2, the condition of pure strategy 2 being complementary to pure strategy 1 is sufficient and necessary if there exists a mixed strategy meta-heuristics derived from these two pure strategies and its expected number of generations to find an optimal solution is no more than that of using pure strategy 1 for any initial population, and less than that of using pure strategy 1 for some initial population.

Simon T. Powers, Jun He

Network intrusion detection is the problem of detecting unauthorised use of, or access to, computer systems over a network. Two broad approaches exist to tackle this problem: anomaly detection and misuse detection. An anomaly detection system is trained only on examples of normal connections, and thus has the potential to detect novel attacks. However, many anomaly detection systems simply report the anomalous activity, rather than analysing it further in order to report higher-level information that is of more use to a security officer. On the other hand, misuse detection systems recognise known attack patterns, thereby allowing them to provide more detailed information about an intrusion. However, such systems cannot detect novel attacks. A hybrid system is presented in this paper with the aim of combining the advantages of both approaches. Specifically, anomalous network connections are initially detected using an artificial immune system. Connections that are flagged as anomalous are then categorised using a Kohonen Self Organising Map, allowing higher-level information, in the form of cluster membership, to be extracted. Experimental results on the KDD 1999 Cup dataset show a low false positive rate and a detection and classification rate for Denial-of-Service and User-to-Root attacks that is higher than those in a sample of other works.

Jun He, Tianshi Chen, Xin Yao

The hardness of fitness functions is an important research topic in the field of evolutionary computation. In theory, the study can help understanding the ability of evolutionary algorithms. In practice, the study may provide a guideline to the design of benchmarks. The aim of this paper is to answer the following research questions: Given a fitness function class, which functions are the easiest with respect to an evolutionary algorithm? Which are the hardest? How are these functions constructed? The paper provides theoretical answers to these questions. The easiest and hardest fitness functions are constructed for an elitist (1+1) evolutionary algorithm to maximise a class of fitness functions with the same optima. It is demonstrated that the unimodal functions are the easiest and deceptive functions are the hardest in terms of the time-fitness landscape. The paper also reveals that the easiest fitness function to one algorithm may become the hardest to another algorithm, and vice versa.

Boris Mitavskiy, Jun He

Nowadays hybrid evolutionary algorithms, i.e, heuristic search algorithms combining several mutation operators some of which are meant to implement stochastically a well known technique designed for the specific problem in question while some others playing the role of random search, have become rather popular for tackling various NP-hard optimization problems. While empirical studies demonstrate that hybrid evolutionary algorithms are frequently successful at finding solutions having fitness sufficiently close to the optimal, many fewer articles address the computational complexity in a mathematically rigorous fashion. This paper is devoted to a mathematically motivated design and analysis of a parameterized family of evolutionary algorithms which provides a polynomial time approximation scheme for one of the well-known NP-hard combinatorial optimization problems, namely the "single machine scheduling problem without precedence constraints". The authors hope that the techniques and ideas developed in this article may be applied in many other situations.