fengling.eth

Feng Ling

I am curious about the interesting things that emerge from complex systems, like intelligence from neural networks, consensus and utility from public blockchains, viral spreading from social networks and mobility patterns from urban systems, and I am also interested in improving them.

Principal scientist at the Institute of Advanced Intelligence and Computing, A*STAR Singapore, and adjunct associate professor in physics at the National University of Singapore.

A glowing network of nodes and links spreading across a landscape that changes from smooth sand on the left, through green hills, to jagged dark rock on the right.

0 · Self-organized criticality

Evolution to the edge of ergodicity

The EvoSK model running live: 128 agents, memory α = 0.75. Each step the least fit agent (outlined) is replaced by a newcomer with a random temperature between 0 and 2. Started hot, the mean temperature ⟨T⟩ falls into the edge window (shaded, measured at α = 0.75) and stays there, with no tuning.

Ecosystems, economies and societies are made of many different agents that learn and pursue their own goals. They are quite unlike the sandpiles of classic self-organized criticality. To ask how such systems organise themselves, we built a minimal model called EvoSK. Its agents learn by reinforcement on a rugged spin-glass landscape, and again and again the least fit agent is replaced by a newcomer with a random exploration temperature.

Without any tuning, the population evolves to the edge of ergodicity breaking of its own learning dynamics. There it shows scale-free avalanches of change, and it reaches a collective reward higher than any fixed, hand-tuned temperature can give. These three findings all follow from one condition: the cascade of changes set off by each replacement branches marginally, with a branching ratio of one. An exact rule of the evolution, that every arrival must eventually die, the well-adapted included, is what pushes the population onto that condition.

1 · Intelligence

Intelligence at the critical point

My research on AI looks at the complexity science and dynamics of deep learning models. The biological brain has been found to work best in a state between order and chaos, which raises a question: do artificial neural networks follow the same principle? Drawing on dynamical systems and spin glasses, I study how networks reach their best performance and generalisation at the “edge of chaos”, the boundary between ordered and chaotic phases.

Trained networks show brain-like signatures of criticality, namely 1/f noise and a critical branching mechanism. We developed a theory in which the edge of chaos, determined by the Jacobian norm, coincides with peak information transfer (Optimal Machine Intelligence at the Edge of Chaos). Training can be steered to the edge by setting the weight decay, and the stability of a trained network can also predict how well it generalises, which earned 9th place in a NeurIPS 2020 competition.

Most recently, in overtrained LSTMs we found multiple descents of the test loss. Each descent is associated with a phase transition of the network, and the global optimum sits on the first edge of chaos (see the movie below). Together, these studies bridge physics and AI.

Order–chaos transitions in a neural network. Every frame shows all training epochs of an LSTM at once; each descent of the test loss goes with a phase transition of the network. Movie 1 of Wei et al., “Multiple descents in deep learning as a sequence of order–chaos transitions”, Physica A 697, 131754 (2026). No sound.

2 · Consensus

Self-organisation in public blockchains

Channel structure of Bitcoin's Lightning Network.
Channel structure of Bitcoin’s Lightning Network. Ren et al., ICPADS 2018. Tap to enlarge.

Public blockchains (often mistaken for cryptocurrencies) are, in a sense, an inevitable evolution of techno-social phenomena, and they will likely revolutionise key aspects of our social and economic life. Like many social phenomena, they emerge from a large number of people. Unlike most of them, they spread exponentially fast, thanks to the underlying technology: the internet, mathematics (hashing, zero-knowledge proofs and so on) and our ever-growing need for consensus and truth.

One aspect I have been looking into is how blockchain ecosystems organise themselves: the evolution of transaction networks, decentralised social networks, and the optimal construction of layer 2s like the Lightning Network.

On a more personal note, I am a (somewhat) active member of the blockchain community, as you might tell from my ENS name, fengling.eth. I take part in proof-of-work and proof-of-stake networks, vote in community governance, and report bugs.

Will decentralisation last, or will we keep cycling between decentralisation and centralisation (合久必分,分久必合), as human civilisations always have? This may be the first time in history that things are different.

3 · Networks

Spreading and resilience on networks

Map of the X (Twitter) follower network in Singapore in 2024; large hubs include The Straits Times, CNA and TODAY.
Structure of the X (Twitter) network in Singapore, 2024. Jeremy Oon and Feng Ling. Tap to enlarge.

Spreading events, from infectious disease over human contact networks to information over online social media, can switch between limited local spread and widespread global impact, much like a phase transition. I apply complexity theory to social media and other social networks to understand how such spreading works.

My work has looked at how influence travels beyond direct contacts, which we described as an induced percolation phenomenon; how the local structure of a network can identify and quantify its most influential spreaders; and how a mechanistic model of viral spreading on an empirical network can predict popularity. When people are overloaded with information, a message spreads unlike a disease and has a finite epidemic threshold. For epidemics, too little resource for treatment in the early stage makes the outbreak size jump abruptly.

The same tools describe how networks hold together. Community structure in interdependent networks can hide an extreme risk: weakening the communities can abruptly drive the whole system into a fragile state. Other work shows that how predictable a network's structure is can be read from how well it compresses, and recovers with machine learning the order in which a network's links formed. Current work maps the structure of the X (Twitter) network in Singapore.

›9 more papersShow fewer

4 · Econophysics

Collective behaviour in financial markets

Toy herding market, for illustration (not the model of our paper). Each day, traders who share a strategy form groups, and each group buys, sells or waits as one. Independent traders' orders largely cancel and price changes stay Gaussian. When strategies are shared, whole groups trade at once, the price jumps, and large changes become far more common than the Gaussian predicts: fat tails.

A financial market is made of many traders whose decisions interact, and its prices share universal statistical features: returns with fat tails, and volatility with long-term memory. With an agent-based model we showed that fat tails arise when traders share similar technical trading strategies. Extending the model to a stochastic one, we linked the long-term memory of returns to the way investors evaluate their investments over different time horizons, in agreement with empirical data.

Related work adds adaptive confidence to the traders, which raises price volatility; quantifies systemic risk in networks of banks and assets, where collective failure can change discontinuously; and follows the time-evolving network of venture-capital investment in China.

›1 more paperShow fewer

5 · Mobility

Urban systems

Map of Singapore planning areas coloured by the change in mobility patterns during the pandemic.
Mobility pattern changes during the pandemic in Singapore. Mepparambath et al., Transp. Res. Interdiscip. Perspect. 21, 100883 (2023). Tap to enlarge.

The movements of millions of people in a city add up to regular, law-like patterns of flow. I study these patterns with transit, flight and travel-survey data, mostly from Singapore.

With transit data from before, during and after the COVID-19 pandemic, we found that three classic theories of human mobility, the gravity model, the radiation model and the visitation law, all stayed valid, with the visitation law the best throughout and the gravity model improving during and after the pandemic. At the global scale, an airport's passenger volume follows its place in the flight network, best measured by PageRank weighted by the number of airlines; Asian airports carry more traffic than their connectivity predicts. For transport simulations, we built a generative model that creates synthetic itineraries for every private-vehicle user, keeping the statistics of the travel survey while protecting privacy.

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