Physics of Intelligence: A Physics-Based Approach to Understanding AI and the Brain

Dr. Hidenori Tanaka’s “Physics of Intelligence” project (also called the Physics of Artificial Intelligence) is an ambitious research initiative aiming to apply concepts from physics – such as symmetry, conservation laws, and phase transitions – to the study of intelligence in neural networks. Launched in the early 2020s and evolving through collaborations between industry and academia, this program treats artificial intelligence as a phenomenon to be understood with the same rigor as a natural sciencenews.harvard.edu. By integrating physics, neuroscience, computer science, and psychology, the project seeks fundamental laws of intelligence that could make AI systems more interpretable, trustworthy, and energy-efficientntt-research.comnews.harvard.edu. Below, we delve into the core hypotheses, methods, collaborations, findings, and broader impacts of this cutting-edge initiative, clearly distinguishing speculative visions from empirical results.

Core Scientific Hypotheses and Principles

At the heart of the Physics of Intelligence project is the hypothesis that principles from physics can explain and predict the behavior of learning systems (both artificial and biological). In particular, Tanaka’s team proposes that key phenomena in deep neural networks – such as how they learn, generalize, and exhibit emergent abilities – can be elucidated by analogies to physical laws:

• Symmetry and Conservation in Learning Dynamics: Just as symmetry in physics leads to conserved quantities (via Noether’s theorem), neural network architectures contain symmetries that impose invariants on the training dynamicsai.stanford.eduai.stanford.edu. For example, modern networks often have translation symmetries (adding a constant bias to certain weights doesn’t change the loss), scale symmetries (scaling weights before a normalization layer), or rescaling symmetries between layers. Tanaka et al. showed that under gradient flow (continuous idealized training), each such symmetry yields a conserved quantity – a combination of parameters that remains constant during learningai.stanford.eduai.stanford.edu. This is directly analogous to Noether’s theorem linking symmetry to conserved energy or momentum in physical systems. Concretely, for a network with translation symmetry, the sum of those parameters stays fixed; with scale symmetry, the overall weight norm is fixed; with rescaling symmetry, the difference of two weight norms is fixedai.stanford.eduai.stanford.edu. These conservation laws constrain the trajectory of learning to specific geometric surfaces (e.g. a hyperplane for translation symmetry, a spherical surface for scale symmetry, or a hyperboloid for rescaling) as illustrated in Figure 1 below. Importantly, these invariants help simplify the high-dimensional “black box” of training into tractable directions of analysisar5iv.labs.arxiv.orgar5iv.labs.arxiv.org. Just as in physics, ideal conservation laws are broken by real-world effects (analogous to friction or external forces) – here, finite learning rates, stochastic noise, weight decay, and other optimizer tricks violate the perfect conservationai.stanford.eduai.stanford.edu. A major hypothesis of the project is that understanding how these approximate conservation laws break can reveal the “forces” driving neural networks to generalize.

Figure 1:* Geometric interpretation of a conservation law in neural network training (rescaling symmetry case). Due to a symmetry in the model, the learning trajectory is constrained to a surface (here a hyperbola) defined by a constant difference between two groups of weight norms. The heatmap color (red to blue) indicates the conserved quantity’s value, and black lines show its level sets. Such physics-inspired invariants restrict how a network’s parameters evolvear5iv.labs.arxiv.orgar5iv.labs.arxiv.org.*

• Emergence and Phase Transitions in Learning: Another core idea is that “emergent” abilities in AI can be studied like phase transitions or percolation in physics. As AI models scale up or get more data, they often display sudden jumps in capability – for example, a language model might abruptly learn to do arithmetic once it passes a certain size. Tanaka’s team draws an analogy to how matter can abruptly change phase (like water freezing) when an underlying parameter crosses a threshold. In a 2024 study, they define emergence in neural networks as the moment when a model acquires a general underlying structure that causes a sharp rise in performance on specific tasksarxiv.orgarxiv.org. They built a controllable experimental setup using a formal language task: a Transformer is trained on strings generated by a context-sensitive grammar. They observed that once the model internalized the grammar’s structure, its accuracy on related “narrow” tasks suddenly jumped – a clear emergent behaviorarxiv.org. By analogy with percolation theory, they modeled the learning process as a graph that gradually “connects” pieces of knowledge. The onset of emergence corresponds to a phase transition in this graph’s connectivityarxiv.org. This percolation model of emergence provided a quantitative prediction for when the performance jump will occur as training data or structure variesarxiv.org. Such results support the hypothesis that seemingly mysterious leaps in AI ability can be demystified by phase transition models, lending a physicist’s understanding to questions of generalization and capability growth.
• Noether’s Learning Dynamics and Symmetry Breaking: While perfect symmetry yields conservation, broken symmetry can be even more illuminating in learning. In their NeurIPS 2021 paper “Noether’s Learning Dynamics”, Tanaka and collaborators extended Noether’s theorem to realistic neural network training, which includes kinetic symmetry breaking (KSB)openreview.netopenreview.net. They formulated the learning process in Lagrangian mechanics terms: treating the loss function as analogous to potential energy and the training rule (like stochastic gradient descent) as analogous to kinetic energyopenreview.net. In this view, adding certain mechanisms (like normalization layers or momentum) explicitly breaks symmetries in the “kinetic energy” of learning. This broken symmetry is not a bug but a feature: the theory predicts it can introduce beneficial forces in parameter space. Indeed, they found that normalization layers induce a form of symmetry breaking that acts like an adaptive optimizer (similar to RMSProp) built into the dynamicsopenreview.netopenreview.net. In other words, what looks like a mere architectural tweak (batch normalization) has a physics analog: it breaks a conservation law in a way that makes learning more efficient and stable, much as friction can help a system settle to equilibrium. The broader hypothesis is that by systematically identifying when and how training violates ideal symmetries – through weight decay, noise, etc. – one can derive exact equations for the broken conservation laws that govern real neural networksar5iv.labs.arxiv.orgar5iv.labs.arxiv.org. This yields analytic predictions for phenomena like parameter norm growth or decay under various training regimesar5iv.labs.arxiv.orgar5iv.labs.arxiv.org. Such insights ground the often heuristic practice of deep learning in a firmer theoretical framework, akin to how breaking of physical symmetries (e.g. in crystal defects or particle masses) leads to deeper understanding in physics.
• “Laws of AI” as a Scientific Goal: Underlying all these hypotheses is a unifying vision: just as physics produced laws like F = ma or E = mc², there may exist concise laws governing intelligence and learningntt-research.com. The Physics of Intelligence project explicitly seeks general principles that apply across different substrates – whether silicon neural nets or biological brains. For instance, a conjectured law of generalization might relate a network’s architecture and training conditions to its ability to transfer knowledge, analogous to a conservation law or equation of state. While such laws are still speculative, Tanaka often emphasizes that AI’s rapid advances present an opportunity much like past scientific revolutions: AI is “a new subject of study for the science of intelligence” that could yield new physicsnews.harvard.edu. This outlook is partly philosophical – treating intelligence itself as a natural phenomenon – and partly pragmatic, aiming to tame AI’s complexity so that engineers can design systems with predictable and safe behavior. The project’s hypotheses push beyond viewing neural networks as only engineering artifacts, instead regarding them as objects of scientific inquiry governed by emergent laws.

In summary, the core scientific stance of the project is that intelligence can be understood through the lens of physics. Symmetries in networks lead to constraints just like in physical systemsai.stanford.eduai.stanford.edu; sudden learning behaviors can be mapped to phase transitionsarxiv.org; and introducing certain architectural elements is akin to adding forces or breaking invariances in a physical systemopenreview.net. These hypotheses have driven a series of theoretical models and experiments over 2020–2025, described next. While the notion of “laws of AI” remains aspirational, the work to date provides concrete examples (conservation laws, percolation thresholds, etc.) where physics-style reasoning yields testable predictions about neural networks’ behavior. Such predictions begin to bridge the gap between the black box complexity of deep learning and the transparent explanations scientists seek.

Techniques: Experimental and Mathematical Approaches

To investigate these hypotheses, Tanaka’s Physics of Intelligence group employs a blend of theoretical physics methods, analytical modeling, and controlled experimental simulations. Their approach is highly interdisciplinary: they treat neural networks as experimental subjects (much like one would study an organism or a physical system) and use mathematical tools from physics to derive insights. Key techniques include:

• Continuous Dynamical Systems Analysis: One hallmark of the project is recasting discrete training processes (like iterative weight updates in SGD) into continuous-time equations that can be analyzed with calculus and differential equationsai.stanford.eduai.stanford.edu. By taking the gradient flow limit (infinitesimal learning rate), the team writes down ordinary differential equations (ODEs) for weight evolutionai.stanford.edu. In this formulation, training resembles a particle moving in a force field defined by the loss function. Classic physics tools can then be applied: for example, identifying conserved quantities via inner products of the ODE with symmetry generatorsai.stanford.edu, or using modified equation analysis from numerical analysis to account for finite step sizesai.stanford.edu. In practice, they developed “modified gradient flow” equations that include correction terms for finite learning rates and momentum, improving the match between theory and actual training trajectoriesai.stanford.eduai.stanford.edu. This continuous modeling lets them solve for certain weight combinations exactly (e.g., how a particular norm decays over time) and to visualize training as trajectories in a potential landscapeai.stanford.eduai.stanford.edu. Such analysis revealed, for instance, how adding momentum in SGD introduces an effective inertia and rescales time without changing the path (akin to adding mass to a particle)ai.stanford.edu. It also showed that gradient noise due to mini-batches has a special low-rank structure that does not perturb the symmetry-constrained directions of motionai.stanford.eduai.stanford.edu – a nontrivial insight into why certain parameter combinations remain predictable despite stochastic training. This continuous dynamics approach is a powerful theoretical technique to derive closed-form expressions for learning curves under various conditionsar5iv.labs.arxiv.orgar5iv.labs.arxiv.org. While these calculations often rely on idealizations (infinitesimal steps, infinite data, etc.), the group validates them on real networks (e.g., a VGG-16 on ImageNet) to ensure they capture real behaviorar5iv.labs.arxiv.orgar5iv.labs.arxiv.org. The ability to predict aspects of training dynamics analytically is a significant step toward a mechanistic understanding of deep learning, analogous to solving equations of motion in physics rather than just numerically simulating them.
• Synthetic “Model Systems” for Experiments: In parallel with mathematical analysis, the team conducts experiments on simplified or synthetic tasks to isolate phenomena of interest. This is akin to a physicist designing a clean experiment to reveal a specific effect. For example, to study emergent abilities and phase transitions, they constructed a context-free and context-sensitive grammar task for Transformersarxiv.org. By training networks on strings generated from a known grammar, they can measure exactly when the network grasps the underlying rules. This level of control is impossible with a massive language model trained on the entire internet, but in the synthetic setup, they observed clear phase-transition-like behavior (a sudden jump in performance once the grammar was learned)arxiv.org. Another example is the use of formal languages and logical tasks to probe compositional generalization: in one 2024 study, the group examined how Transformers learn concepts and rules by training them on synthetic data where the ground-truth compositional structure is knownsites.google.comsites.google.com. By tracking internal representations during training on these tasks, they identified distinct “algorithmic phases” – regimes in which the model appears to use one strategy vs. anothersites.google.com. They even observed switching dynamics suggesting competition between strategies until one dominates (much like phases competing in a physical system). Furthermore, the team built toy models of neural networks (sometimes as simple as a single-neuron or one-dimensional system) to derive intuition. The “ghost mechanism” study (2025) is a good example: they crafted a minimal recurrent network task (a “delayed activation” toy problem) that produces an abrupt learning curve – long plateaus then sudden improvementar5iv.labs.arxiv.orgar5iv.labs.arxiv.org. By analyzing this one-dimensional system, they discovered a “ghost” fixed point causing the delay (related to ghost states in dynamical systems theory)ar5iv.labs.arxiv.orgar5iv.labs.arxiv.org. This insight then guided them to identify similar ghost effects in larger recurrent neural nets, along with methods to mitigate the plateaus (like lowering confidence of outputs or increasing model redundancy)ar5iv.labs.arxiv.orgar5iv.labs.arxiv.org. In summary, *the group uses simplified experimental setups – from formal languages to few-neuron models – to uncover mechanisms that would be hidden in more complex tasks. These controlled experiments yield phenomena (emergence, ghost instabilities, etc.) that can be quantitatively measured and then linked back to theoretical models (like percolation graphs or bifurcation analysis). It’s a marriage of simulation and theory reminiscent of early computational physics or systems biology: the simulation “experiments” generate data to be explained, and the physics-based theory provides the explanatory frameworkarxiv.orgar5iv.labs.arxiv.org.
• Mathematical Modeling & Proofs: Many results of the Physics of Intelligence project come in the form of mathematical derivations or proofs, borrowing techniques from statistical mechanics, linear algebra, and beyond. For instance, in the Noether’s Learning Dynamics work, the team proved a generalized Noether theorem for learning: under kinetic symmetry breaking, the usual conservation law acquires an extra term (a “Noether charge motion”) that they derived explicitlyopenreview.netopenreview.net. They then applied this theorem to derive an exact correspondence between a network with batch normalization and a form of the RMSProp update ruleopenreview.netopenreview.net – an analytical insight bridging architecture and optimization. In the Synaptic Flow pruning algorithm (NeurIPS 2020), Tanaka et al. first mathematically formulated a conservation law for network connectivity at initializationpapers.nips.cc. They showed that naive weight pruning methods break a “flow conservation” across layers, leading to entire layers dying (layer-collapse)papers.nips.cc. By enforcing a conservation of total synaptic strength through the network, they derived a new pruning criterion (SynFlow) that provably avoids layer-collapsepapers.nips.cc. This was a theoretical contribution that immediately yielded a practical algorithm – one that prunes networks without any training data, yet achieves competitive performance by preserving an invariant quantity through the sparsification processpapers.nips.cc. The team also uses tools like Hessian eigenvalue analysis and mode connectivity to explore loss landscapes. In one 2023 paper, they examined how fine-tuning changes a model’s internal representations by studying the connectivity of minima in weight space (mode connectivity), providing a mechanistic view of why fine-tuning sometimes drastically shifts behaviorsites.google.com. Additionally, they employ techniques from information theory and statistics: e.g., analyzing shattering of representations in transformer models when knowledge is editedsites.google.com, or using percolation theory equations to predict threshold pointsarxiv.org. Many of these models are backed by rigorous proofs or derivations in appendices of their papers, underscoring the emphasis on theoretical soundness.
• Neuroscience and Psychology Experiments: A distinctive aspect of the Physics of Intelligence program is that it doesn’t study AI in isolation – it actively seeks parallels in biological intelligence. The team has collaborated with neuroscientists to test AI-driven hypotheses about brains. For example, Tanaka co-authored a Neuron 2023 paper analyzing how the retina encodes natural scenessites.google.com. They used deep learning models to infer the “code” of retinal neurons and discovered interpretable computations, bridging from deep learning to mechanistic understanding in neurosciencesites.google.comsites.google.com. In another collaborative effort, members of his group (including former colleagues now at Yale and Princeton) studied behavioral sequences in animals: a 2022 PLoS Computational Biology paper introduced a “lexical” method to identify action sequences in animal behavior, akin to parsing sentencessites.google.com. Here the physics of intelligence approach – looking for structure and rules in complex sequences – was applied to biological data, showing the versatility of their techniques. Moreover, the group is interested in psychological applications; their site mentions exploring AI + psychology for education and psychiatrysites.google.com. While details are sparse, this likely involves using insights from AI learning dynamics to model human learning or mental processes, or vice versa. The interdisciplinary experiments are facilitated by the project’s residence at Harvard’s Center for Brain Science, where computational neuroscientists and cognitive scientists interact with the team. By designing experiments that compare artificial neural networks and real neural circuits, the project aims to find common principles of intelligence. This is still an emerging area, but it aligns with the project’s foundational claim that natural and artificial intelligence share underlying scientific principlesntt-research.comntt-research.com. If true, this could lead to AI models that not only mimic performance but also mimic mechanisms of human cognition, potentially offering better interpretability and robustness.

In summary, the Physics of Intelligence initiative employs a toolkit reminiscent of a scientific field rather than pure engineering: analytical equations, controlled experiments, toy models, and cross-species comparisons. This dual emphasis on theory and empirical validation is critical. Many of their predictions (e.g., conserved quantities, emergent thresholds) have been validated on actual neural networks or in simulationai.stanford.eduarxiv.org, lending credibility to the approach. At the same time, some techniques are largely theoretical (e.g., Lagrangian formulations) and still need more empirical corroboration in large-scale AI systems. The combination of approaches – from pencil-and-paper math to GPU-powered training runs – exemplifies the interdisciplinary spirit of the project. By treating neural networks like physical systems for experimentation, Tanaka’s group can derive insights that purely empirical deep learning or purely abstract theory might miss. This strategy has begun to yield a library of techniques and results (conservation laws, phase models, pruning algorithms, etc.) that pave the way toward a more scientific understanding of AI.

Collaborators, Institutions, and Programs

The Physics of Intelligence project is fundamentally a collaborative and multi-institutional effort, spanning a network of research labs and academic centers. Key players and partnerships from 2020–2025 include:

• NTT Research (PHI Lab and Physics of AI Group): The project originated within NTT Research’s Physics & Informatics (PHI) Lab in Silicon Valley. Dr. Hidenori Tanaka joined NTT’s PHI Lab in 2020 as a Senior Research Scientist and led its Intelligent Systems Groupsites.google.comsites.google.com. The PHI Lab’s mission was to explore new computing paradigms by fusing physics and information (for example, the lab is known for optical computing and the Coherent Ising Machine). Early on, NTT PHI Lab recognized that understanding the “black box” of AI was crucial for building next-gen, energy-efficient systemsntt-research.com. This vision had strong support from NTT’s leadership. By 2021, NTT Research entered a joint research agreement with Harvard’s Center for Brain Science to collaborate on natural and artificial intelligencenews.harvard.edu. In April 2025, NTT formally spun off the Physics of Artificial Intelligence (PAI) Group as an independent research group, elevating Tanaka to Group Headntt-research.com. The Physics of AI Group (within NTT Research) now continues the work with a focused mandate: to enhance understanding, trust, and control of advanced AIntt-research.com. NTT framed this as transitioning from foundational studies to a broader pursuit of human-AI collaborationntt-research.com. The PAI Group builds on the “Physics of Intelligence” vision developed over the past five years and retains close ties to academia. NTT’s support has been not just financial but strategic: their Upgrade 2024/2025 summits highlighted Physics of Intelligence for trustworthy and green AI as a pillar of innovationunite.aiunite.ai. NTT Research’s CEO, Kazuhiro Gomi, often emphasizes that AI’s rise is akin to inventions like the steam engine – a new force driving physics research – and that NTT sees this as an opportunity to foster “trustworthy and green AI” through basic science collaborationsnews.harvard.edu. In terms of personnel, Maya Okawa (visiting scientist) and Ekdeep Singh Lubana (postdoctoral fellow) are part of the core NTT team with Tanakantt-research.com. The PHI Lab as a whole has partnered with many institutions (Caltech, Cornell, MIT, etc. ntt-research.com), and some of those collaborations (e.g., with MIT and Stanford) feed directly into the Physics of Intelligence project’s research on AI. Notably, NTT Research Foundation provided a philanthropic gift to Harvard (see below), and NTT’s PHI/PAI groups facilitate the industry side of the research with funding, computational resources, and translation of findings into potential applications (such as the bias removal algorithm being recognized by NIST, or exploring optical hardware to cut AI’s energy usentt-research.com).
• Harvard University – Center for Brain Science (CBS): Since 2022, Dr. Tanaka has been an Associate at Harvard’s Center for Brain Science (CBS)sites.google.com, where his group is physically based. The Harvard CBS provides an academic environment for the project, embedding it among neuroscientists and cognitive scientists. A significant development was the establishment of the CBS-NTT Program in Physics of Intelligence in 2024, enabled by a gift of up to $1.7M from the NTT Research Foundationnews.harvard.eduthecrimson.com. This program funds postdoctoral fellowships and joint research activities in the physics of intelligence, effectively formalizing the collaboration between Harvard and NTT. It supports two postdoc researchers at a time, plus seminars, travel, and other collaborative eventsnews.harvard.edu. Harvard faculty (like Prof. Venkatesh Murthy, CBS director) have embraced this as a way to “develop ideas around the Physics of Intelligence” in an interdisciplinary settingnews.harvard.edu. The Harvard side of the collaboration is interested in how this physics-driven approach can enhance neuroscience: CBS researchers study neural circuits, computation in the brain, development, and disordersnews.harvard.edu, and they see value in the fresh theoretical approaches brought by Tanaka’s team. For instance, neuroscientists can use AI both as a tool and as a model of brains; the Physics of Intelligence program provides a formal framework to do this, potentially leading to new insights in brain science as wellthecrimson.comthecrimson.com. Some key collaborators at Harvard include cognitive scientist Tomás Lozano-Pérez Ullman (who co-authored work on neural text generation with Tanakasites.google.com) and others in psychology and neuroscience departments who are part of Tanaka’s extended group (e.g., Eric Bigelow, a PhD student in Psychology, co-advised projects bridging human cognition and AI text modelssites.google.com). The CBS-NTT program also supports alignment with the broader Harvard community, for example by hosting talks (Tanaka gave seminars at Harvard’s math and ML groups in 2022sites.google.com) and integrating with student training. Harvard undergrads and grads (such as Kento Nishi and Corey Francisco Park, who co-authored papers on in-context learningsites.google.comsites.google.com) have worked in the group. This provides a pipeline of young researchers from a variety of fields into the physics-of-AI endeavor. In essence, Harvard CBS provides the academic hub where the natural science of intelligence is explored, ensuring the project is grounded in biological reality and cognitive science as well as in theory.
• MIT and IAIFI: Dr. Tanaka became an Affiliate of the MIT Institute for Artificial Intelligence and Fundamental Interactions (IAIFI) in 2024sites.google.com. IAIFI is an NSF-funded institute focused on the intersection of AI and physics (originally emphasizing using AI for physics and vice versa). Being an affiliate suggests active collaboration or co-supervision of fellows. Indeed, one of Tanaka’s group members, Dr. Sam Bright-Thonney, is an IAIFI Postdoctoral Fellow in physics at MIT working with the groupsites.google.com. Through IAIFI, the project connects to a network of physicists thinking about AI from first principles. This likely facilitates joint workshops, idea exchange, and possibly joint appointments of researchers. MIT’s strengths in both theoretical physics and computer science make it an ideal partner. The IAIFI affiliation indicates that Tanaka’s approaches (like symmetry in deep learning) resonated with the fundamental questions IAIFI tackles (such as: what are the fundamentals of learning, or how can physics insights improve AI?). Moreover, collaborators such as Mikail Khona (a physics PhD student at MIT in Tanaka’s groupsites.google.com) and Max Aalto (an EECS PhD at MIT in the groupsites.google.com) foster cross-pollination between Harvard/NTT and MIT. The IAIFI and MIT connections also bring in expertise from physics heavyweights – for instance, Prof. Max Tegmark or others at MIT who are known for physics approaches to AI could be informal collaborators, though not explicitly listed. Additionally, Tanaka’s group joining the ML Alignment & Theory Scholars (MATS) program as a mentor in late 2024sites.google.com shows engagement with the broader AI alignment community, which often has ties to MIT and Harvard via initiatives like the Center for Brains, Minds & Machines. In short, MIT IAIFI provides another institutional pillar, emphasizing the fundamental interactions part of the project – connecting AI with the laws of nature.
• University of Tokyo – Institute for Physics of Intelligence: In 2023, Tanaka became a Visiting Researcher at the Institute for Physics of Intelligence (IPI) at the University of Tokyosites.google.com. The very name of this institute mirrors the “Physics of Intelligence” concept, suggesting a parallel initiative in Japan. This likely resulted in exchange of ideas and possibly joint workshops or student visits between Cambridge, MA and Tokyo. Ziyin Liu, a University of Tokyo physics PhD student, was co-advised by Tanaka on a publication about loss landscapes in self-supervised learningsites.google.comsites.google.com, reflecting this collaboration. The University of Tokyo IPI focuses on understanding intelligence through physics and math (founded by Prof. Masaki Aono and others), so Tanaka’s involvement there helps globalize the project’s reach. It also ties into NTT’s roots in Japan – showing that while Tanaka’s group sits at Harvard/NTT in the US, it maintains strong links to Japanese research efforts. The exchange of ideas is two-way: for example, co-authors like Dr. Makoto Ueda (University of Tokyo) worked with Tanaka’s group on understanding loss landscapessites.google.com. Through IPI, the project gains access to a broader talent pool and complementary perspectives from the Japanese scientific community.
• Other Key Collaborators: The project is inherently collaborative, and many individuals have contributed. A few notable ones:
  • Prof. Surya Ganguli (Stanford University): Tanaka was a postdoc with Surya Ganguli and co-authored several foundational papers with him (including the synaptic flow pruningpapers.nips.cc and Noether’s dynamics work). Ganguli, a Stanford physicist/neuroscientist, remains a close collaborator – the 2025 NTT press release explicitly states plans to continue collaborating with Surya Ganguli on the projectntt-research.com. Ganguli’s lab brings expertise in theoretical neuroscience and deep learning theory, likely collaborating on projects like the ghost dynamics (which had many Stanford co-authorsar5iv.labs.arxiv.org) and mechanistic mode connectivity. This Stanford-Harvard-NTT triangle has been very productive, blending Ganguli’s theoretical savvy with Tanaka’s cross-domain approach.
  • Dr. Daniel Kunin: Kunin was a Stanford PhD student who co-led the “Neural Mechanics” and “Noether’s dynamics” papersai.stanford.edu. He was a driving force in those early theoretical works and worked with Tanaka at NTT PHI Lab. Kunin is listed as a former member of Tanaka’s group (now finishing PhD at Stanford)sites.google.com. His contribution is central to the symmetry/conservation law line of research. The continuity of collaboration is evident: Tanaka and Kunin published multiple papers in 2020–2021, establishing much of the theoretical foundationsites.google.comsites.google.com.
  • Dr. Gautam Reddy and Dr. Logan Wright: Both were colleagues of Tanaka in the NTT PHI Lab’s Intelligent Systems group and are now professors (Reddy at Princeton, Wright at Yale). They contributed to early interdisciplinary projects – for instance, Reddy is co-author on the animal behavior sequences papersites.google.com. The 2025 press release mentions collaboration with Gautam Reddy (Princeton) as ongoingntt-research.com. This indicates that even after leaving NTT, Reddy remains part of the physics-of-intelligence endeavor, perhaps focusing on links to biological physics and behavior.
  • Dr. Kenji Kawaguchi (NTT & RIKEN): Kawaguchi co-authored the percolation model of emergence paperarxiv.org, bringing expertise in theoretical ML (Kawaguchi is known for work on optimization theory). This collaboration (including Robert Dick from University of Michiganarxiv.org) shows the project’s network extending to specialists in different subfields like formal theory of deep learning and even hardware (Dick’s background is in computer engineering).
  • Interdisciplinary Students: A number of PhD students from various universities have been part of the project (often as visiting researchers or co-advised). For example, Ekdeep Lubana (U. Michigan) has co-authored many papers on in-context learning and emergencesites.google.comsites.google.com and is now a postdoc at NTT; Yongyi Yang (Michigan), Bhavya Vasudeva (USC), Rahul Ramesh (UPenn), Bo Zhao (UCSD) all contributed to publications in 2023–2024 dealing with transformers’ capabilitiessites.google.comsites.google.com. Their diverse home institutions highlight the collaborative web Tanaka’s group has spun – an extended “lab” that crosses university boundaries. This also reflects the CBS-NTT fellowship program’s role in bringing in fresh talent from different fields (e.g., a psychology student working alongside a physics student).

In essence, the Physics of Intelligence project thrives on a consortium of academia and industry: NTT Research provides a platform and funding, Harvard provides an interdisciplinary scientific environment, MIT IAIFI and others provide intellectual cross-fertilization, and a host of collaborators bring expertise from theoretical physics to neuroscience. The formal CBS-NTT Program at Harvardnews.harvard.edu and the new NTT PAI Groupntt-research.com ensure that this collaboration is sustained through joint appointments and funding streams. Such a structure is somewhat novel – it is neither a purely academic lab nor a siloed corporate lab, but a hybrid. This allows the project to pursue long-term fundamental questions (something academia excels at) while keeping an eye on real-world impact and applications (the forte of industry labs). It also encourages students and postdocs to move fluidly between academic and industrial research settings. The result is a global effort (U.S., Japan, etc.) with a shared vision.

One can see the influence of this collaborative network in the direction of research: for instance, the emphasis on trustworthy AI and green AI comes partly from NTT’s priorities (and their clients’ needs), whereas the push to unify with neuroscience comes from the Harvard side and Tanaka’s own physics/neuro background. By having stakeholders like NTT’s CEO explicitly mention goals of unbiased, trustworthy, and green AInews.harvard.edu, the project aligns its scientific questions with broader societal and technological priorities, as discussed next.

Publications, Communications, and Key Results (2020–2025)

Over the past few years, Tanaka’s team has produced a rich body of academic papers, blog articles, and talks that articulate the vision and report results of the Physics of Intelligence initiative. Here we review some of the prominent outputs and their significance:

• Foundational Papers (2020–2021): The groundwork was laid with a series of theoretical papers:
  • NeurIPS 2020: “Pruning neural networks without any data by iteratively conserving synaptic flow” – Introduced the SynFlow algorithmpapers.nips.cc. This paper’s vision: even at initialization, a network has a “flow of synaptic strengths” that should be conserved when pruning to avoid losing capacitypapers.nips.cc. It verified (experimentally and theoretically) a conservation law that explained failures of prior methods and demonstrated a new pruning technique that achieved up to 99.99% sparsity without training datapapers.nips.cc. This was one of the earliest concrete successes of the physics-of-AI approach (conservation law → algorithm).
  • ICLR 2021: “Neural Mechanics: Symmetry and Broken Conservation Laws in Deep Learning Dynamics” – A highly cited work by Kunin, Tanaka, et al., accompanied by a Stanford AI Lab Blog post explaining it in accessible termsai.stanford.edu. This paper systematically identified symmetries in common network architectures (translation invariance in softmax weights, scale invariance in batchnorm, etc.) and derived the associated gradient constraints and conservation lawsai.stanford.eduai.stanford.edu. It then extended the theory to modified gradient flow for finite learning rates, providing exact formulas for how those conserved quantities evolve when the ideal is brokenai.stanford.eduai.stanford.edu. The key result was showing that even state-of-the-art networks on real data respect these physics-derived dynamics to a large degreear5iv.labs.arxiv.orgar5iv.labs.arxiv.org (and deviations can be predicted by their continuous models). The SAIL blog article drew parallels to classical mechanics and highlighted how “each symmetry of a network architecture has a corresponding ‘conserved quantity’ through training”ai.stanford.edu. This helped seed the idea that understanding learning dynamics is like discovering the laws of motion for neural networks.
  • NeurIPS 2021: “Noether’s Learning Dynamics: Role of Symmetry Breaking in Neural Networks” – This follow-up (Tanaka & Kunin) pushed the envelope by incorporating Kinetic Symmetry Breaking (KSB)openreview.net. It framed gradient descent in a Lagrangian mechanics picture and derived Noether’s Learning Dynamics (NLD), an equation describing the motion of the conserved quantities when symmetries are brokenopenreview.netopenreview.net. The paper applied NLD to show how normalization layers act as an implicit optimizer, analytically linking a design choice to an optimization benefitopenreview.netopenreview.net. An NTT blog summary called it “The Role of Kinetic Symmetry Breaking in Deep Learning” and emphasized how this theoretical framework can identify geometric design principles for neural network trainingopenreview.netopenreview.net. Together, the Neural Mechanics and NLD papers form a one-two punch: the former identifies conservation laws; the latter explains what happens when you break them on purpose for better learning. These works garnered attention in the ML theory community and are empirically supported by experiments on networks like ResNets and VGGsai.stanford.eduar5iv.labs.arxiv.org.
• Interdisciplinary Papers (2022–2023): As the program grew, outputs diversified:
  • NeurIPS 2022: Papers like “Beyond BatchNorm: Towards a Unified Understanding of Normalization in Deep Learning”sites.google.com attempted to demystify why tricks like BatchNorm, LayerNorm, etc. work, using a unifying theoretical lens. This likely drew on the symmetry concepts to show commonalities between normalization methods (though details are beyond our scope here).
  • PLoS Comp Bio 2022: “A lexical approach for identifying behavioural action sequences”sites.google.com – an application of AI methods to neuroscience data (zebrafish or rodent behavior), showing the project’s expanding reach to natural intelligence.
  • Neuron 2023: “Interpreting the retinal neural code for natural scenes: from computations to neurons”sites.google.com – This high-profile neuroscience paper used deep learning models and theory to crack the code of vision in the retina, exemplifying the two-way street of the collaboration (AI helping neuroscience). Tanaka was a co-author and theoretical co-first author, highlighting his group’s role in the theory behind the analyses.
  • Neural Computation 2023: “Rethinking the limiting dynamics of SGD: modified loss, phase space oscillations and anomalous diffusion”sites.google.com – Another theoretical work (with Ganguli’s lab) that studied SGD’s behavior as a dynamical system, finding phenomena like oscillatory modes and diffusion in the weight trajectory. This connects with the idea of understanding training at a fundamental level (possibly identifying regimes where training dynamics resemble physical processes like diffusion).
  • NeurIPS 2023: “CORNN: Convex Optimization of Recurrent Neural Networks for rapid inference of neural dynamics”sites.google.com – This paper (Dinc et al.) introduces a method to optimally configure recurrent nets to emulate neural dynamics quickly, potentially useful for brain-machine interfaces. It shows the practical offshoots of understanding neural mechanics: if you know the dynamics, you can design networks to meet them. It’s an interesting blend of convex optimization and neuroscience, again reflecting the interdisciplinary nature of the lab.
• Emergent Behavior and In-Context Learning (2023–2025): A major thrust in the past two years has been investigating emergent abilities and in-context learning in large models (especially Transformers). Some notable outputs:
  • ICLR 2024: “Dynamics of Concept Learning and Compositional Generalization”sites.google.com – Studied how networks acquire abstract concepts and compositional skills over training, using synthetic tasks. They likely identified distinct stages or sudden improvements, contributing to understanding grokking (where test performance jumps after a delay).
  • ICLR 2024: “In-Context Learning Dynamics with Random Binary Sequences”sites.google.com – Focused on how Transformers can learn to do tasks within their forward pass (in-context learning) without gradient updates. By using random sequences tasks, they analyzed what mechanisms allow models to learn from prompts. This is very relevant to understanding how large language models can perform new tasks just from examples in a prompt – a currently mysterious capability. The team’s work provides algorithmic phase interpretations: e.g., showing that in-context learning might switch from a “memorization phase” to a “generalization phase” depending on prompt diversitysites.google.com.
  • NeurIPS 2024 (to appear): “Emergence of Hidden Capabilities: Exploring Learning Dynamics in Concept Space”sites.google.com – Likely an extension of emergence studies, possibly identifying when hidden skills surface during training.
  • ICML 2024: Two papers on reasoning in Transformerssites.google.comsites.google.com – one on stepwise reasoning in a graph navigation task, another on effects of fine-tuning on procedural tasks. These works try to open the black box of reasoning processes in AI: e.g., how a Transformer’s internal states evolve when doing multi-step inference, and how fine-tuning alters that.
  • ICLR 2025: As per the site’s news, 5 works were accepted at ICLR 2025sites.google.com, indicating a significant volume of contributions. Among these is likely the “Percolation model of emergence” (which was on arXiv Aug 2024 and would align with ICLR’25 timing). Indeed, the arXiv for “A Percolation Model of Emergence: Analyzing Transformers on a Formal Language” shows it was updated in Sep 2024arxiv.orgarxiv.org – presumably now accepted to ICLR 2025. This paper is particularly noteworthy: it formalizes the emergence concept and confirms it empirically with controlled tasksarxiv.orgarxiv.org, as discussed earlier. It also stands out as bridging to questions of AI governance, noting that understanding emergence is crucial for risk management of AIarxiv.org.
  • Another ICLR 2025 work likely from the list is “Competition Dynamics Shape Algorithmic Phases of In-Context Learning”sites.google.com. The title suggests they found that as a model tries to learn in-context, different “algorithms” (perhaps pattern-matching vs reasoning) compete, and the dominant one shifts in phases. This is a deep insight for interpretability of LLMs and connects to the physics idea of phase transitions or phase competition in a system.
  The common thread in these recent papers is demystifying emergent and higher-order behaviors of AI (like in-context learning, reasoning, compositionality) using simplified tasks and theoretical analogies. These are exactly the behaviors that have captured public attention (e.g., how GPT-4 suddenly can do multi-step math) and also worry experts (unpredictable emergence of capabilities). By publishing in top venues (NeurIPS, ICLR, ICML) and writing accessible summaries (e.g., Stanford blog, Twitter threads by team members), Tanaka’s team is actively disseminating their findings to both specialists and the broader AI community. For instance, the team often posts Twitter highlight threads (the site links a tweet for the NeurIPS 2021 papersites.google.com and others), indicating a conscious effort to communicate results widely.
• Talks and Media: The project has been covered in press releases and talks targeted to broader audiences:
  • Harvard Gazette (Apr 2024): Announcement of the Harvard–NTT program gave a concise summary of the project’s goals: using physics to tackle fundamental questions in intelligence, bridging multiple disciplinesnews.harvard.edu, and addressing urgent problems like unbiased, trustworthy, green AInews.harvard.edu. It included quotes framing AI as potentially launching a new field in physics, much as historic inventions didnews.harvard.edu.
  • Harvard Crimson (Apr 2024): The student newspaper’s piece reinforced that narrative, noting that Harvard was chosen after a “bidding process” among institutions because its approach aligned with NTT’s visionthecrimson.com. It highlighted the interdisciplinary hiring (bringing in new PhDs from varied fields) and quoted Tanaka on the need for people from diverse backgrounds to build this new fieldthecrimson.com. Tellingly, Murthy (CBS director) admitted “this is new for all of us… How do you explain intelligent behavior in equations or physics terms?”thecrimson.com – capturing the excitement and uncertainty of this venture.
  • NTT Upgrade 2025 Summit (Mar 2025): Tanaka’s group was featured in NTT’s annual R&D event, with a talk titled “Physics of Intelligence for Trustworthy and Green AI”. In a Unite.AI article covering that event, Tanaka is quoted reflecting on profound questions: “Mathematically, how can you think of the concept of creativity? … kindness? These concepts would have remained abstract if not for AI… now, if we want to make AI kind, we have to tell it in the language of mathematics what kindness is.”unite.ai. This quote exemplifies the philosophical angle of the project – using AI as a testbed to formalize fuzzy concepts (creativity, kindness) that physics and math traditionally sidestep. The talk and article also reiterated the black box problem and how applying scientific methods from physics can demystify AI’s learning processesunite.ai. The Unite.AI piece did a nice job contextualizing Physics of AI as a response to real incidents and concerns (self-driving car failures, biased hiring algorithms) that motivate the need for trust and safetyunite.aiunite.ai. It effectively communicated to a general audience why merging physics, psychology, neuroscience, and AI is a timely pursuit to ensure AI benefits society.
  • YouTube and Conference Talks: Hidenori Tanaka has also given talks at various venues explaining pieces of this research. For example, at Stanford Symsys (2023) he talked about “Physics of intelligence for trustworthy and green AI”neuroscience.stanford.eduyoutube.com (the title suggests aligning with the key impact themes). On YouTube, one can find his presentation “3 Mechanisms Underlying Emergent Abilities in Generative Models”youtube.com – likely a summary of recent findings on emergence, perhaps given at a workshop or symposium. These talks are important for disseminating the project’s vision beyond written papers, allowing interactive discussion with both experts in AI and in other fields (physics, cognitive science).
  • Media Recognition: The press release in April 2025 about the launch of the NTT Physics of AI Group was picked up by outlets like Yahoo Finance, BusinessWire, and tech blogsfinance.yahoo.comlinkedin.com. Forbes even published an article “The Laws of Automation: NTT details ‘Physics of AI’” – indicating mainstream interest in the idea of laws governing AI. In that coverage, NTT’s framing of “AI as a new force in physics” and the focus on understanding AI’s black box for trust were echoed. The Forbes piece (by Adrian Bridgwater) likely discussed how this group’s creation formalizes a trend of applying scientific rigor to AI, and might have mentioned the bias-removal and pruning contributions as examples of early wins.

In reviewing these communications, it’s clear the team is actively shaping the narrative that AI can and should be studied like a natural phenomenon. They underscore both vision (grand questions about intelligence, even kindness, in mathematical terms) and results (like algorithms that reduce bias or predict training outcomes). Speculative ideas – such as finding a unifying theory of intelligence or encoding ethics into AI equations – are openly discussed in talks and press, but always alongside empirical progress that builds confidence (e.g., “we have found exact conserved quantities,” “we created a bias fix that NIST noted”ntt-research.comntt-research.com). By maintaining this balance, Tanaka’s team has managed to legitimize a field that could otherwise sound highly speculative.

One concrete outcome highlighted in press materials is a “bias-removal algorithm for large language models (LLMs) recognized by NIST”ntt-research.com. Although details aren’t given in the press release, this presumably refers to a method developed by the group to identify and remove latent biases in an LLM’s outputs. NIST (the U.S. National Institute of Standards and Technology) has been working on AI bias standards, so recognition from them means the method offered both scientific insight and practical utility. It might be linked to one of the group’s works on knowledge editing or representation shattering in transformerssites.google.com, where altering internal representations can mitigate undesired outputs. This example shows how a line of theoretical inquiry (e.g., understanding model internals as physical systems) can yield a tool for a pressing real-world problem (AI fairness).

In summary, the project’s outputs from 2020–2025 span theoretical breakthroughs, practical algorithms, cross-disciplinary studies, and public-facing communications. The academic papers form the backbone, presenting peer-reviewed evidence of the approach’s validity. The blog posts and press articles translate those findings for broader consumption and link them to the bigger picture (AI safety, ethics, efficiency). The talks and conferences help build a community and influence how other researchers think about AI (for instance, inspiring others to consider physics analogies or to use synthetic tasks to probe their models). Collectively, these outputs have started to outline the “physics of intelligence” paradigm: we see its foundational principles (invariance, dynamics, emergence), its methodologies (analytical and experimental), and glimpses of its impact (bias reduction, explanation of black-box behavior).

Broader Technological and Philosophical Impact

One of the most important aspects of the Physics of Intelligence initiative is its potential impact on how we trust, interpret, and efficiently implement AI systems. By uncovering fundamental principles of intelligence, the project aims to address key societal and technical challenges of modern AI:

• Interpretability and Understanding (“Demystifying the Black Box”): AI models, especially deep neural networks, have long been criticized as opaque “black boxes.” By applying physics-style analysis, Tanaka’s team is chipping away at that opacity. If we know, for example, that certain combinations of weights follow a conserved quantity or a simple dynamical law, we have a handle on the model’s internal state that is both interpretable and predictiveai.stanford.eduar5iv.labs.arxiv.org. This contributes to mechanistic interpretability – understanding how a network’s parameters and activations lead to its outputs. For instance, discovering an analogy between batch normalization and an adaptive optimizeropenreview.net interprets the role of that layer in a human-understandable way (it’s as if the network is tuning its learning rate for each feature). Similarly, identifying phases in a model’s learning (say a “memorization phase” vs “generalization phase” in in-context learning) means we can, in principle, detect which phase a model is in by observing certain metrics or internal signalssites.google.com. That helps practitioners know whether a model is likely to generalize or just reciting memorized data. In the long run, the hope is to achieve trust through understanding: if the behavior of an AI can be explained by a set of scientific principles (like we explain an airplane’s flight with aerodynamics), users and regulators can trust the AI more. This aligns with NTT’s stated goal of building trust that leads to a harmonious fusion of human and AIntt-research.comntt-research.com. Rather than just saying “the network weights did something,” physics of intelligence might let us say “the network made that decision because it’s conserving X and has entered Y regime of operation.” Such explanations could be audited and debated much like scientific theories, thereby increasing transparency.
• Ethics, Alignment, and Trustworthiness: On a philosophical level, Tanaka’s musings about defining concepts like “kindness” mathematicallyunite.ai speak to the AI alignment problem – how to ensure AI goals align with human values. The approach here is novel: instead of treating ethics as an external set of rules to impose on AI, embed ethical principles into the fundamental understanding of the AI’s operation. The PAI group’s mission explicitly mentions integrating ethics from within, rather than through patchwork fine-tuningntt-research.com. This could mean designing training dynamics that inherently conserve or optimize for fairness metrics, or identifying symmetry principles that correspond to fairness (e.g., requiring that swapping demographic identifiers is a symmetry of the loss, which would enforce unbiased behavior as a conserved “charge”). The bias-removal algorithm recognized by NIST is a concrete outcome on this front – it suggests the team found a systematic way to adjust a model to remove biasesntt-research.com, likely informed by understanding of the model’s internal geometry or conservation laws. In addition, trustworthiness comes from predictability: if emergent behaviors can be predicted (via percolation models or phase diagramsarxiv.org), AI developers can anticipate and mitigate undesirable behaviors before deploying the model. This proactive stance could inform AI governance; for example, if we know scaling data by a factor will suddenly make the model capable of some dangerous task, we can decide to withhold that scaling. The team’s work is already interfacing with risk considerations – note they mention “enable risk regulation frameworks for AI” when understanding emergencearxiv.org. Philosophically, this project suggests that to trust AI, we must first understand its laws, similar to how we trust bridges because we understand physics, not just because we tested the bridge a bunch of times. If successful, it could shift AI safety from a reactive, empirical field to a principled, scientific one.
• Energy Efficiency and Green AI: Modern AI models, especially large ones, consume enormous energy in training and inference. The Physics of Intelligence project addresses this in two ways. First, by pruning and optimizing networks – the SynFlow algorithm is an example of striving for sparsity without performance loss, which directly translates to faster, energy-saving inferencepapers.nips.ccpapers.nips.cc. If you can prune 99% of a model’s weights using a physics-informed criterion and still solve the task, you’ve made that model dramatically greener. This technique doesn’t rely on data, so it could be applied at initialization to large models to cut down their size before the costly training even begins. Second, by seeking biologically inspired efficiency. Human brains operate on ~20 watts, while a large AI might use megawatts in a data center. Tanaka’s group, especially via NTT PHI Lab, is aware of this vast gapntt-research.com. The press release notes that other PHI Lab groups are working on optical computing and novel hardware (like thin-film lithium niobate photonics) to reduce AI’s energy consumption, and that the Physics of AI group will look to leverage similarities between brains and neural networks in pursuit of efficiencyntt-research.comntt-research.com. This suggests the group might study features like sparse firing, analog computation, or event-driven processing in brains to inform new architectures that use energy more sparingly. Already, by connecting with neuroscientists, they might identify which computations the brain performs exactly (which might hint at what’s unnecessary in current AI models). On the hardware side, if the team’s theoretical insights yield simpler models or new algorithms, those can be implemented in low-power analog or photonic hardware being developed by PHI Lab. In broad terms, a scientific understanding of AI could reveal redundancies or more efficient pathways that engineers alone might miss. A simple example: if a conservation law implies some weights are effectively unused (conserved in a way that doesn’t affect output), those weights could be pruned or quantized to lower precision, saving energy. By the rhetoric in NTT and Harvard press, “green AI” is a major promised outcomenews.harvard.eduunite.ai.
• Fusion of Human and AI Collaboration: The project often mentions creating a “harmonious coexistence” or “fusion” of human and AIntt-research.comntt-research.com. This goes beyond just trust – it imagines AI systems that can integrate into human workflows and society in a seamless, predictable way. A physics of intelligence could provide a common language for human cognition and AI cognition. For example, if both brains and networks are described by similar equations or principles, one could design interfaces where they meet optimally (think brain-computer interfaces guided by theory, or AI assistants that truly understand human mental models). While this is a speculative long-term impact, it aligns with philosophical questions: What is the nature of intelligence? Is an AI’s problem-solving fundamentally similar to a human’s? If yes, we might use that to make AI decisions more relatable or to enhance human intelligence (by learning from the efficient strategies of algorithms). Tanaka’s quote about everyone being willing to talk about AI and learning from each such conversationunite.ai hints at the idea that AI is a unifying subject – if scientifically understood, it could tie together insights from psychology (how humans think) and computer science (how machines think) into one framework. The philosophical payoff would be enormous: a theory of intelligence could reshape how we view our own minds (just as understanding thermodynamics reshaped our view of heat and life processes in the 19th century).
• Limitations and Responsible Innovation: It’s worth noting that while the aspirations are high, the team is careful to validate and not over-claim. They distinguish speculation from supported findings. For instance, they do not yet have a single equation that explains “intelligent behavior” fully – Murthy’s question “How do you explain intelligent behavior in equations?” remains partially openthecrimson.com. The project’s impact so far has been more about frameworks and pieces of the puzzle (like explaining one aspect of training or one emergent feature) rather than a grand unified theory. However, even these pieces have practical implications (SynFlow for efficiency, bias removal for fairness). By continuing to chip away, they could gradually build a comprehensive picture. An important philosophical stance here is humility in the face of complexity – they approach intelligence with the assumption it can be understood (not mystical), but also with respect for its complexity (hence borrowing approaches from fields that handle complexity, like statistical physics). In doing so, they contribute to an AI narrative that is less hyperbolic and more scientific: rather than “just trust the deep net” or conversely “AI is incomprehensible and dangerous,” they offer a middle ground of studying AI like we study any complex natural system. This attitude could influence regulators and the public to demand more explainable and principled AI. It moves the conversation from fearing an alien mind to figuring out its “source code” in nature’s language.

To summarize the broader impact: Physics of Intelligence is pioneering a path to make AI understood, safe, and efficient by treating it as an object of scientific inquiry. If successful, this could transform AI development from an artisanal engineering endeavor into a rigorous discipline grounded in laws and principles. That, in turn, means AI systems might come with guarantees (like how bridges come with stress tolerances), biases might be identifiable and correctable a priori, and new AI designs might be discovered by reasoning (instead of trial-and-error). Such a transformation is inherently philosophical too, as it forces us to ask: What does it mean for a machine to “understand” or “decide”? Can those processes be described in the language of physics and math? The Tanaka team is betting that the answer is yes – and that pursuing these questions will not only yield better AI, but also deeper insights into intelligence itself, including our own.

Visual Overview of the Physics of Intelligence Approach

Figure 2:* Conceptual flowchart of the Physics of Intelligence approach. The project combines physics-inspired approaches (left oval) – such as applying symmetry analysis (Noether’s theorem) and designing controlled experiments – to derive scientific findings and principles about learning (center oval), including conserved quantities during training, emergent phase transitions in ability, and analogies between neural network behavior and algorithms. These findings in turn inform outcomes and impacts (right oval): more interpretable AI models (with known invariants and dynamics), trustworthy systems that embed ethical principles and are predictable, and energy-efficient algorithms optimized by understanding which computations are essential. In essence, the flowchart shows how foundational science is leveraged to achieve practical AI goals.*

The diagram above provides a high-level summary: the input is a set of interdisciplinary scientific techniques; the output is a set of improvements in AI technology and understanding. This visual underscores that Tanaka’s team doesn’t view AI development as separate from science – rather, AI progress can be driven by scientific inquiry, and reciprocally, AI is a new domain to discover scientific laws. Each arrow (→) in the flowchart can be thought of as research translating into impact: e.g., finding a conservation law (middle) leads to a pruning algorithm that makes AI more efficient (right), or using a physics experiment approach (left) leads to discovering emergent behavior rules (middle) that make AI more interpretable (right).

Summary Table: Goals, Methods, Collaborators, and Outcomes

Finally, we consolidate the key aspects of Dr. Hidenori Tanaka’s Physics of Intelligence project in the table below, summarizing its driving goals, the methodologies employed, the major collaborators/institutions involved, and the expected outcomes and impacts:

Goals (Scientific and Societal)	Methodologies (Techniques & Approaches)	Key Collaborators & Institutions	Expected Outcomes (Vision & Results)
– Uncover fundamental laws of learning and intelligence (analogous to physical laws)ntt-research.com. – Understand and align AI’s emergent abilities with human valuessites.google.com. – Develop mathematical descriptions of AI generalization and decision-makingsites.google.com. – Integrate insights from AI and human cognition to aid education and mental healthsites.google.com. – Address urgent needs for unbiased, trustworthy, and “green” AI systemsnews.harvard.edu.	– Theoretical physics tools applied to neural networks (symmetry analysis, Noether’s theorem, Lagrangian dynamics) to derive invariant quantities and dynamicsai.stanford.eduai.stanford.edu. – Continuous dynamical modeling of learning (gradient flow ODEs, modified equations for SGD) to solve training behavior analyticallyar5iv.labs.arxiv.orgar5iv.labs.arxiv.org. – Controlled experimental setups (synthetic tasks, formal languages, toy models) to observe phase transitions, abrupt learning, and test hypotheses under clean conditionsarxiv.orgarxiv.org. – Interdisciplinary data analysis, linking AI models to neuroscience/psychology experiments (e.g. comparing network representations to brain data) to find common principles.sites.google.comsites.google.com. – Algorithm design via theory: using derived principles to create new methods (e.g. SynFlow pruning conserving synaptic flowpapers.nips.cc, bias removal via identified geometry).	– NTT Research – PHI Lab & Physics of AI (PAI) Group: Industry research lab funding and driving the project; led by H. Tanaka (Group Head) with core team (M. Okawa, E.S. Lubana)ntt-research.comntt-research.com. Provides computational resources and translation to applications (energy-efficient hardware, etc.). – Harvard University – Center for Brain Science (CBS): Academic host of the CBS-NTT Physics of Intelligence Programnews.harvard.edu. Director Venkatesh Murthy and others collaborate, bringing neuroscience and psychology expertise. Joint program funds postdocs and fosters cross-pollination on campus. – MIT – IAIFI (Institute for AI and Fundamental Interactions): Collaboration via affiliate role and IAIFI postdocssites.google.comsites.google.com. Connects to MIT physics/AI researchers and resources; contributes theoretical physics perspectives (e.g. quantum analogies, fundamental math). – University of Tokyo – Institute for Physics of Intelligence: International partnership with similar goalssites.google.com. Facilitates exchange of researchers (e.g. Z. Liu, M. Ueda co-authors) and globalizes the research agenda. – Stanford University (Ganguli Lab) & Princeton University (Reddy): Key academic collaboratorsntt-research.com. Ganguli’s lab co-develops theory (symmetry, dynamics), Reddy and others link to biological physics and behavior. Also includes students from Michigan, USC, Yale, etc. working within Tanaka’s group, reflecting a broad academic network.	– Scientific breakthroughs in understanding AI: e.g. identification of conserved quantities in deep learningai.stanford.edu, phase transition models of emergent skillsarxiv.org, and general theoretical frameworks that unify architecture and optimizationopenreview.net. – Practical algorithms and tools: data-agnostic network pruning (SynFlow) for efficient modelspapers.nips.cc; methods to mitigate bias in language models (one recognized by NIST for its impact)ntt-research.com; techniques for mechanistic interpretability (diagnosing “algorithmic phases” within a model) that help debug and improve AIsites.google.com. – Improved AI trust and safety: Ability to predict and control AI behavior, reducing “black box” surprises. For example, embedding ethical constraints as symmetries or invariants in training (a speculative yet desired outcome) so that AI systems are aligned by design rather than retrofittedntt-research.com. Greater transparency through physics-style explainability builds human trust in AI decisionsntt-research.com. – Energy-efficient AI systems: Leaner models via principled pruning and architecture insights; inspiration from brain efficiency to guide new hardware (optical/neuromorphic) and algorithms. The “green AI” goal is AI that achieves more with less computational powernews.harvard.eduntt-research.com, guided by scientific understanding of which computations are necessary. – Cross-disciplinary knowledge: A unifying theory of intelligence that informs neuroscience (e.g. explaining neural coding with deep learning modelssites.google.com) and vice versa. Training a new generation of researchers fluent in both physics and AI, capable of further breakthroughs. Ultimately, a conceptual bridge between human and machine intelligence that could transform technology and cognitive science.

In the table above, each element underscores how the Physics of Intelligence project is not just about theory for theory’s sake, but tightly interweaves its scientific pursuits with real-world outcomes. The goals drive the choice of methods (e.g., to achieve trustworthy AI, they examine symmetries related to fairness); the collaborations provide the breadth of expertise needed; and the outcomes are both measurable (algorithms, papers) and aspirational (a future of more human-compatible AI).

In conclusion, Dr. Hidenori Tanaka’s Physics of Intelligence project represents a bold and comprehensive effort to scientifically decode the nature of intelligence – in machines and organisms – using the language of physics. In the past few years, it has made substantial strides: formulating exact analogies between neural network training and physical lawsai.stanford.eduai.stanford.edu, revealing why and when AI systems undergo phase changes in capabilityarxiv.org, and delivering tools that improve AI’s efficiency and fairness (SynFlow, bias mitigation)papers.nips.ccntt-research.com. It has also built an ecosystem of collaboration spanning industry and academia, which is accelerating progress in this nascent fieldnews.harvard.eduntt-research.com. Many of the ideas are still taking shape – the quest to fully explain “intelligent behavior in equations” continues, and some implications remain speculative. However, the distinctive approach of treating AI as a natural phenomenon is already yielding fresh insights that neither standard deep learning research nor traditional neuroscience alone could achieve. By clearly distinguishing what is known (e.g., specific conservation laws, empirically observed emergent thresholds) versus what is conjectured (e.g., eventual unification of AI and cognitive science under physics), the project maintains scientific rigor while pushing the boundaries of our understanding.

Moving forward, the Physics of Intelligence initiative is poised to influence not only how we build AI, but also how we conceptualize intelligence itself – potentially leading to AI that is more interpretable, more aligned with human values, and more energy efficient, because it would be designed on a foundation of scientific principles rather than trial-and-error. In a time when AI is becoming ever more powerful (and sometimes unpredictable), this convergence of physics and AI offers a path toward “upgrading reality” with AI that we can truly trust and harmonize withunite.aintt-research.com. The coming years will reveal how far this physics-of-AI paradigm can go, but its early successes already suggest that understanding intelligence through physics is not only possible but deeply rewarding – yielding insights that are as intellectually fascinating as they are practically important.