mathematics Thief & Chef "through the window of differential equations, mathematics sees the light in the real world" / "通过微分方程的窗子,数学家看到现实世界的光" (Jiang Zehan)

Seattle
Joined June 2008
“This Is Not How Mathematicians Are Trained” 数学家不是这样训练的 1, "Solving the forward problem (positive time) and the inverse problem (negative time) together has always been a desire of mathematicians, but they’ve never known where to begin. Neural networks, however, tackle this problem naturally" (将正时间的正问题与负时间的反问题同时求解,一直是数学家的梦想,但他们始终不知道从何入手。而神经网络却能自然地处理这个问题) 2. “Variables, coefficients, even coordinates, are changing. Everything is in flux. This is not how mathematicians are trained. It would be impossible for mathematicians to come up with such a design” (变量、系数,甚至坐标都在变化,一切都处于变动之中。数学家不是这样的训练。这样的设计,不可能出自数学家之手) 3. “Mathematicians tread carefully around composite functions with more than two layers, wary of the many pitfalls, yet neural networks solve them effortlessly, almost nonchalantly.” (数学家在处理超过两层的复合函数时格外谨慎,警惕其中诸多陷阱, 而神经网络却几乎漫不经心地轻松应对) 4. “Neural networks have stacked covers, mathematically speaking, whereas the Numerical Manifold Method typically uses only 3 to 4. In contrast, neural networks stack hundreds or even thousands of such covers. I never imagined anyone would take it that far”. (神经网络在数学上拥有堆叠的覆盖层,而数值流形通常只有三到四层覆盖。相比之下,神经网络则堆叠了上百乃至上千层。我从未想过有人会将其推进到这种程度). That was what Gen-Hua Shi (石根华) told me after returning from a two-week vacation in early June 2024.. see rest of the story, click the link open.substack.com/pub/deepma…
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Multi-LLM collaboration is only as good as the team you hire 💼 With 2M+ open models, who joins the team? We study strategic model selection: 9 strategies, from stated diversity to item response theory & idiosyncrasy signals, to LLM recruiters that interview candidates 🧵👇
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Build specialized harnesses, folks. This is a banger paper from Google Cloud AI Research on self-evolving agent harnesses. (bookmark it) They introduce OO-Harness, which raises AutomationBench from 61.6% to 77.4% with the same Gemini 3.5 Flash executor. It also beats Meta-Harness on all three benchmarks they test. More details below. Instead of evolving one global harness for every task, an evolution agent builds a class hierarchy of specialized harnesses from execution records. The design has three parts. > Subclasses inherit the base harness and override only the methods a task cluster needs > Design lessons record which changes helped and which ones failed > A router reads the task and the base run, then picks a subclass or keeps the base result On Workspace-Bench, the score goes from 25.5% to 39.5%, and on Toolathlon-GYM strict pass goes from 31.2% to 37.5%. Spending extra inference on best-of-K sampling or self-refinement does not reliably help. Inheritance also improves results. On Workspace-Bench, harnesses built as subclasses score 4.96 points higher than the same evolved code copied into flat classes. arxiv.org/abs/2610.28380 Chat with Paper: academy.dair.ai/papers/objec…
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Solid mathematical ideas almost always outperform contrived engineering tricks. For years deep learning has been dominated by increasingly complex architectural hacks: CNN blocks, attention layers, channel mixers, residual pathways, normalization stacks. Every few years a new architecture is announced as if it were a revolution. One of the most famous examples was Kaiming He and Residual Networks (ResNet). At the time he was paraded around the AI world like a celebrity because residual connections supposedly “solved” deep learning. But these were largely engineering patches. Now something much more interesting appeared. A new architecture called CliffordNet returns to mathematics — specifically Clifford Algebra, developed in the 19th century by William Kingdon Clifford. Instead of stacking arbitrary modules, the model is built around the geometric product uv = u·v + u∧v A single algebraic operation that simultaneously captures inner product structure and geometric interactions. In other words: the math already contains the interaction mechanism. No attention blocks. No mixer layers. No architectural spaghetti. The result: • 77.82% accuracy on CIFAR-100 with only 1.4M parameters • roughly 8× fewer parameters than ResNet-18 And with strict O(N) complexity. The paper even suggests that once geometric interactions are modeled correctly, feed-forward networks become largely redundant. A good reminder for the AI community. Engineering tricks can dominate for years. But eventually mathematics shows up and deletes half the architecture. Paper: arxiv.org/pdf/2601.06793?utm… 19th century geometry just walked into computer vision.
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1/8 New paper with Ivan Ilin: "Local Work, Global Progress: A Convergence Theory of AI Agent Collaboration". We all know that teams of LLM agents can tackle big tasks. However, their collaboration protocols lack guarantees. We model collaboration as block optimization and, under suitable assumptions, prove convergence. arxiv.org/abs/2610.28286
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#DeepManifoldInterpretation Misalignment is a model or computational error, and its root causes are inherited by design, mathematically: 1. Inverse learning 2. Propertyless and full-rank relational structure 3. Data complexity and numerical approximation The difficulty is that these are also what make AI extraordinarily powerful. We therefore face a double-edged problem: the mathematical sources of capability are also inherited sources of misalignment.
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📈 As models get stronger, data becomes saturated. How can we still extract useful learning signals from saturated data in RL? We study interventions on data, rollouts, rewards & advantages 🧵👇
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What should a student ask to learn the most from its teacher? We train a model to ask better questions—without reference answers, correctness rewards, or per-question student updates. Meet Ask-to-Distill (A2D). 👇 arxiv.org/abs/2610.27450
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SAEs have become the dominant approach in mechanistic interpretability. But what if a good old statistical method from decades ago could do just as well, at a fraction of the cost? In our latest work, we revisited Independent Component Analysis (ICA) and discovered something surprising: a bug in the evaluation code of an influential early SAE paper had significantly underestimated ICA's interpretability! After correcting it, we found ICA to be remarkably competitive with SAEs. Many of my academic friends from the good old days probably remember me as the tensor decomposition and spectral methods person. So this feels a little like going back to my roots. :) Sometimes, old mathematical tools still have surprises in store! But there's another motivation behind this work that I care about even more. I've always wished mechanistic interpretability could be more actionable. Understanding what happens inside a neural network is fascinating, but what comes next? Can we use that understanding to actually intervene, steer behavior, and improve the model? With ICA Lens, we take steps in that direction, from discovering and annotating interpretable features to using them to understand new hidden states and steer model behavior. Interpretability shouldn't end with understanding. It should empower us to act. And we'd love for the community to try it! ICA Lens is open-source, lightweight, and requires no training of another sparse dictionary. 🌹 Try it yourself: pip install icalens pypi.org/project/icalens/ Curious to hear what the mechanistic interpretability community thinks!
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Is this machine playing? 🏀🪁🛝 We left Eko, an embodied coding agent, on an island for 30 hours with no task or goal, studying it like ethologists study a new species Eko explored, built, climbed, made games, and learned completely new techniques (1/9) machineplaying.org
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シャノンは通信の送り手と受け手の間のコードブック共有を前提に通信理論を築き,通信の意味論的側面を切り捨てました。では学習済みVAEのエンコーダとデコーダは同じコードブックを共有しているのか?再構成が完璧でも,標準的な学習指標では判定できないことを証明しました alphaxiv.org/abs/2610.14012
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Excited to introduce DiscoveryRSI! One model that recursively learns to discover valuable hypotheses, and gets sharper with every research round. Let's RSI Discovery! 📄 Paper: arxiv.org/abs/2610.23839 💻 Code: github.com/Gen-Verse/Discove… #RSI #AIforScience #AIAgents #ScientificDiscovery
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#DeepManifoldInterpretation paper: Trajectory Planning without Trajectory Data: A Manifold-Guided Approach Interesting work, but isn't manifold learning an overcomplicated approach to collision avoidance? Given sufficient collision and collision-free observations, we can reconstruct obstacle boundaries or configuration-space constraints directly, then plan paths using classical geometric or topological methods. What advantage does learning a state manifold and integrating an ODE offer over this simpler approach? @SilongYong, @liu_anji, @JimmyDai218776, @GuanyaShi, @du_yilun, @xie_yaqi
Can generative models plan trajectories without ever training on trajectory data? Introducing Ariadne 🧵: trajectory generation from state-only data without learning from trajectories. #NeurIPS2026
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#DeepManifoldInterpretation Paper: Inverse IFEval: Can LLMs Unlearn Stubborn Training Conventions to Follow Real Instructions? Cognitive ability in LLMs is largely an **illusion** emerging from learned patterns in training data, rather than cognition in the human sense. Through training, learning progressively converges toward ** stochastic fixed-point classes **. Cognitive inertia may therefore be a manifestation of stochastic fixed-point class persistence: training reinforces particular response classes, while inference-time boundary conditions are sometimes insufficient to shift the stochastic solution into the instructed class. Importantly, such inertia also depends on training dynamics: how response classes are progressively formed, reinforced, and stabilized. We need to understand the training conditions under which this inertia develops, and how to control its degree. The goal is not to eliminate inertia entirely, but to balance fixed-point stability with adaptability to new boundary conditions.
A few papers & benchmarks on LLM failure to follow instructions 🧵 I. Can LLMs Unlearn Stubborn Training Conventions? “LLMs often exhibit cognitive inertia, struggling when tasked with instructions that explicitly deviate from their training norms” arxiv.org/abs/2509.04292 1/
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#DeepManifoldInterpretation Paper: RSI-Anything: Unlocking Recursive Self-Improvement with World Models Very impressive work! I'm surprised to see JEPA pushed this far toward agentic RSI. One fundamental mathematical question remains: actions involve time, yet neural networks do not have an intrinsic time dimension, as we pointed out in our 2024 Deep Manifold Part 1 paper. How does JEPA account for temporal dynamics beyond discrete state transitions? @Charles_Y_Wu
Introducing RSI-Anything: Unlocking Recursive Self-Improvement with World Models 🚀 Can AI learn to improve itself by predicting the consequences of its actions? Built on JEPA-Anything, RSI-Anything uses world models to guide action selection and learning. Feedback improves the policy or workflow and, when needed, the world model. Validated updates carry forward to shape the next round of experience. Across code, GUI interaction, laboratory planning, and reaction optimization: • Code-repair success: 26.3% → 31.2%, with the coder fixed • GUI agent task: 39.4% fewer actions, with higher completion • Lab-planning scores: 21.80% → 46.01% over five policy versions • Mean best observed reaction yield: 96.15% vs. 82.16% for Bayesian optimization, under the same 40-experiment budget 📄 Paper: arxiv.org/abs/2610.13912 💻 Code: github.com/Gen-Verse/RSI-Any… Watch the video below 👇 #RSI #WorldModels #RSI #AIAgents #AIforScience #JEPA
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#DeepManifoldInterpretation Quite interesting. This paper takes almost the reverse approach to ours: it uses social and economic mechanisms to develop collective AI intelligence, while we use AI to understand and simulate social behavior. We view agents as a connected discontinuous system (agent pack), and develop mathematics to reconstruct its network mappings and adaptive interactions. This paper explores how AI can operate like a society; we explore how AI can help us understand how society operates. @ZhentingQi, @Huangyu58589918, @ao_qu18465, @hanzheng_7, @Kevin_GuoweiXu, @Weirui_Ye, @pliang279, @hima_lakkaraju, @ShamKakade6, @du_yilun
Leonard Read's pencil story: no one knows how to make a pencil from scratch, yet millions are made without a central manager. Each worker knows only their part. Incentives, not central control, coordinate their efforts. Current multi-agent AI seems to work the opposite way. A central manager does everything: assigns roles, writes the workflow, and decides who acts next. As agents increase and tasks get harder, that manager might become the bottleneck: it should understand every agent and every task, and adaptation becomes inefficient. So how can a group of machine agents organize themselves into something none of them could achieve alone? Further, how can that society of agents keep improving itself over time? In Economy of Minds (EoM), we show that simple local incentives can drive global self-coordination and self-improvement for modern LLM agents. We let agents live in a minimal economy: they compete for work, earn by helping others succeed, and go broke when they don't. Workflows, specialists, and improvement naturally emerge, with no one in charge. Across 5 domains (math reasoning, financial research, scientific research, accelerator design, and distributed-system optimization), limited agents grow into strong societies. The whole idea in a 90-second cartoon👇
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