Freezing chaos without synaptic plasticity

Chaos is ubiquitous in high-dimensional neural dynamics. A strong chaotic fluctuation may be harmful to information processing. A traditional way to mitigate this issue is to introduce Hebbian plasticity, which can stabilize the dynamics. Here, we introduce another distinct way without synaptic plasticity. An Onsager reaction term due to the feedback of the neuron itself is added to the vanilla recurrent dynamics, making the driving force a gradient form. The original unstable fixed points supporting the chaotic fluctuation can then be approached by further decreasing the kinetic energy of the dynamics. We show that this freezing effect also holds in more biologically realistic networks, such as those composed of excitatory and inhibitory neurons. The gradient dynamics are also useful for computational tasks such as recalling or predicting external time-dependent stimuli.

PEP-GS: Perceptually-Enhanced Precise Structured 3D Gaussians for View-Adaptive Rendering

Recent advances in structured 3D Gaussians for view-adaptive rendering, particularly through methods like Scaffold-GS, have demonstrated promising results in neural scene representation. However, existing approaches still face challenges in perceptual consistency and precise view-dependent effects. We present PEP-GS, a novel framework that enhances structured 3D Gaussians through three key innovations: (1) a Local-Enhanced Multi-head Self-Attention (LEMSA) mechanism that replaces spherical harmonics for more accurate view-dependent color decoding, and (2) Kolmogorov-Arnold Networks (KAN) that optimize Gaussian opacity and covariance functions for enhanced interpretability and splatting precision. (3) a Neural Laplacian Pyramid Decomposition (NLPD) that improves perceptual similarity across views. Our comprehensive evaluation across multiple datasets indicates that, compared to the current state-of-the-art methods, these improvements are particularly evident in challenging scenarios such as view-dependent effects, specular reflections, fine-scale details and false geometry generation.

How high dimensional neural dynamics are confined in phase space

High dimensional dynamics play a vital role in brain function, ecological systems, and neuro-inspired machine learning. Where and how these dynamics are confined in the phase space remains challenging to solve. Here, we provide an analytic argument that the confinement region is an M-shape when the neural dynamics show a diversity, with two sharp boundaries and a flat low-density region in between. Despite increasing synaptic strengths in a neural circuit, the shape remains qualitatively the same, while the left boundary is continuously pushed away. However, in deep chaotic regions, an arch-shaped confinement gradually emerges. Our theory is supported by numerical simulations on finite-sized networks. This analytic theory opens up a geometric route towards addressing fundamental questions about high dimensional non-equilibrium dynamics.

Spin glass model of in-context learning

Large language models show a surprising in-context learning ability -- being able to use a prompt to form a prediction for a query, yet without additional training, in stark contrast to old-fashioned supervised learning. Providing a mechanistic interpretation and linking the empirical phenomenon to physics are thus challenging and remain unsolved. We study a simple yet expressive transformer with linear attention, and map this structure to a spin glass model with real-valued spins, where the couplings and fields explain the intrinsic disorder in data. The spin glass model explains how the weight parameters interact with each other during pre-training, and most importantly why an unseen function can be predicted by providing only a prompt yet without training. Our theory reveals that for single instance learning, increasing the task diversity leads to the emergence of the in-context learning, by allowing the Boltzmann distribution to converge to a unique correct solution of weight parameters. Therefore the pre-trained transformer displays a prediction power in a novel prompt setting. The proposed spin glass model thus establishes a foundation to understand the empirical success of large language models.

Nonequilbrium physics of generative diffusion models

Generative diffusion models apply the concept of Langevin dynamics in physics to machine leaning, attracting a lot of interest from industrial application, but a complete picture about inherent mechanisms is still lacking. In this paper, we provide a transparent physics analysis of the diffusion models, deriving the fluctuation theorem, entropy production, Franz-Parisi potential to understand the intrinsic phase transitions discovered recently. Our analysis is rooted in non-equlibrium physics and concepts from equilibrium physics, i.e., treating both forward and backward dynamics as a Langevin dynamics, and treating the reverse diffusion generative process as a statistical inference, where the time-dependent state variables serve as quenched disorder studied in spin glass theory. This unified principle is expected to guide machine learning practitioners to design better algorithms and theoretical physicists to link the machine learning to non-equilibrium thermodynamics.

Fermi-Bose Machine

Distinct from human cognitive processing, deep neural networks trained by backpropagation can be easily fooled by adversarial examples. To design a semantically meaningful representation learning, we discard backpropagation, and instead, propose a local contrastive learning, where the representation for the inputs bearing the same label shrink (akin to boson) in hidden layers, while those of different labels repel (akin to fermion). This layer-wise learning is local in nature, being biological plausible. A statistical mechanics analysis shows that the target fermion-pair-distance is a key parameter. Moreover, the application of this local contrastive learning to MNIST benchmark dataset demonstrates that the adversarial vulnerability of standard perceptron can be greatly mitigated by tuning the target distance, i.e., controlling the geometric separation of prototype manifolds.

Enhanced Short Text Modeling: Leveraging Large Language Models for Topic Refinement

Crafting effective topic models for brief texts, like tweets and news headlines, is essential for capturing the swift shifts in social dynamics. Traditional topic models, however, often fall short in accurately representing the semantic intricacies of short texts due to their brevity and lack of contextual data. In our study, we harness the advanced capabilities of Large Language Models (LLMs) to introduce a novel approach termed "Topic Refinement". This approach does not directly involve itself in the initial modeling of topics but focuses on improving topics after they have been mined. By employing prompt engineering, we direct LLMs to eliminate off-topic words within a given topic, ensuring that only contextually relevant words are preserved or substituted with ones that fit better semantically. This method emulates human-like scrutiny and improvement of topics, thereby elevating the semantic quality of the topics generated by various models. Our comprehensive evaluation across three unique datasets has shown that our topic refinement approach significantly enhances the semantic coherence of topics.

An optimization-based equilibrium measure describes non-equilibrium steady state dynamics: application to edge of chaos

Understanding neural dynamics is a central topic in machine learning, non-linear physics and neuroscience. However, the dynamics is non-linear, stochastic and particularly non-gradient, i.e., the driving force can not be written as gradient of a potential. These features make analytic studies very challenging. The common tool is to use path integral approach or dynamical mean-field theory, but the drawback is one has to solve the integro-differential or dynamical mean-field equations, which is computationally expensive and has no closed form solutions in general. From the aspect of associated Fokker-Planck equation, the steady state solution is generally unknown. Here, we treat searching for the steady state as an optimization problem, and construct an approximate potential closely related to the speed of the dynamics, and find that searching for the ground state of this potential is equivalent to running a stochastic gradient dynamics. The resultant stationary state follows exactly the canonical Boltzmann measure. Within this framework, the quenched disorder intrinsic in the neural networks can be averaged out by applying the replica method. Our theory reproduces the well-known result of edge-of-chaos, and further the order parameters characterizing the continuous transition are derived, and different scaling behavior with respect to inverse temperature in both sides of the transition is also revealed. Our method opens the door to analytically study the steady state landscape of the deterministic or stochastic high dimensional dynamics.

Spiking mode-based neural networks

Spiking neural networks play an important role in brain-like neuromorphic computations and in studying working mechanisms of neural circuits. One drawback of training a large scale spiking neural network is that an expensive cost of updating all weights is required. Furthermore, after training, all information related to the computational task is hidden into the weight matrix, prohibiting us from a transparent understanding of circuit mechanisms. Therefore, in this work, we address these challenges by proposing a spiking mode-based training protocol. The first advantage is that the weight is interpreted by input and output modes and their associated scores characterizing importance of each decomposition term. The number of modes is thus adjustable, allowing more degrees of freedom for modeling the experimental data. This reduces a sizable training cost because of significantly reduced space complexity for learning. The second advantage is that one can project the high dimensional neural activity in the ambient space onto the mode space which is typically of a low dimension, e.g., a few modes are sufficient to capture the shape of the underlying neural manifolds. We analyze our framework in two computational tasks -- digit classification and selective sensory integration tasks. Our work thus derives a mode-based learning rule for spiking neural networks.

Meta predictive learning model of natural languages

Large language models based on self-attention mechanisms have achieved astonishing performances not only in natural language itself, but also in a variety of tasks of different nature. However, regarding processing language, our human brain may not operate using the same principle. Then, a debate is established on the connection between brain computation and artificial self-supervision adopted in large language models. One of most influential hypothesis in brain computation is the predictive coding framework, which proposes to minimize the prediction error by local learning. However, the role of predictive coding and the associated credit assignment in language processing remains unknown. Here, we propose a mean-field learning model within the predictive coding framework, assuming that the synaptic weight of each connection follows a spike and slab distribution, and only the distribution is trained. This meta predictive learning is successfully validated on classifying handwritten digits where pixels are input to the network in sequence, and on the toy and real language corpus. Our model reveals that most of the connections become deterministic after learning, while the output connections have a higher level of variability. The performance of the resulting network ensemble changes continuously with data load, further improving with more training data, in analogy with the emergent behavior of large language models. Therefore, our model provides a starting point to investigate the physics and biology correspondences of the language processing and the unexpected general intelligence.