The inherent noise of neural systems makes it difficult to construct models which accurately capture experimental measurements of their activity. While much research has been done on how to efficiently model neural activity with descriptive models such as linear-nonlinear-models (LN), Bayesian inference for mechanistic models has received considerably less attention. One reason for this is that these models typically lead to intractable likelihoods and thus make parameter inference difficult. Here, we develop an approximate Bayesian inference scheme for a fully stochastic, biophysically inspired model of glutamate release at the ribbon synapse, a highly specialized synapse found in different sensory systems. The model translates known structural features of the ribbon synapse into a set of stochastically coupled equations. We approximate the posterior distributions by updating a parametric prior distribution via Bayesian updating rules and show that model parameters can be efficiently estimated for synthetic and experimental data from in vivo two-photon experiments in the zebrafish retina. Also, we find that the model captures complex properties of the synaptic release such as the temporal precision and outperforms a standard GLM. Our framework provides a viable path forward for linking mechanistic models of neural activity to measured data.

Neurons in early sensory areas rapidly adapt to changing sensory statistics, both by normalizing the variance of their individual responses and by reducing correlations between their responses. Together, these transformations may be viewed as an adaptive form of statistical whitening. Existing mechanistic models of adaptive whitening exclusively use either synaptic plasticity or gain modulation as the biological substrate for adaptation; however, on their own, each of these models has significant limitations. In this work, we unify these approaches in a normative multi-timescale mechanistic model that adaptively whitens its responses with complementary computational roles for synaptic plasticity and gain modulation. Gains are modified on a fast timescale to adapt to the current statistical context, whereas synapses are modified on a slow timescale to match structural properties of the input statistics that are invariant across contexts. Our model is derived from a novel multi-timescale whitening objective that factorizes the inverse whitening matrix into basis vectors, which correspond to synaptic weights, and a diagonal matrix, which corresponds to neuronal gains. We test our model on synthetic and natural datasets and find that the synapses learn optimal configurations over long timescales that enable adaptive whitening on short timescales using gain modulation.

There are currently two seemingly unrelated frameworks for understanding these patterns. Mechanistic models account for hexagonal firing fields as the result of pattern-forming dynamics in a recurrent neural network with hand-tuned center-surround connectivity. Normative models specify a neural architecture, a learning rule, and a navigational task, and observe that grid-like firing fields emerge due to the constraints of solving this task. Here we provide an analytic theory that unifies the two perspectives by casting the learning dynamics of neural networks trained on navigational tasks as a pattern forming dynamical system. This theory provides insight into the optimal solutions of diverse formulations of the normative task, and shows that symmetries in the representation of space correctly predict the structure of learned firing fields in trained neural networks. Further, our theory proves that a nonnegativity constraint on firing rates induces a symmetry-breaking mechanism which favors hexagonal firing fields. We extend this theory to the case of learning multiple grid maps and demonstrate that optimal solutions consist of a hierarchy of maps with increasing length scales. These results unify previous accounts of grid cell firing and provide a novel framework for predicting the learned representations of recurrent neural networks.

Here, we develop an approximate Bayesian inference scheme for a fully stochastic, biophysically inspired model of glutamate release at the ribbon synapse, a highly specialized synapse found in different sensory systems. The model translates known structural features of the ribbon synapse into a set of stochastically coupled equations.

They include models such as Kepler's laws of planetary motion [1], the SEIR

Neural Information Processing Systems http://nips.cc/

Neural Information Processing Systems http://nips.cc/

Hematotoxicity, drug-induced damage to the blood-forming system, is a frequent side effect of cytotoxic chemotherapy and poses a significant challenge in clinical practice due to its high inter-patient variability and limited predictability. Current mechanistic models often struggle to accurately forecast outcomes for patients with irregular or atypical trajectories. In this study, we develop and compare hybrid mechanistic and data-driven approaches for individualized time series modeling of platelet counts during chemotherapy. We consider hybrid models that combine mechanistic models with neural networks, known as universal differential equations. As a purely data-driven alternative, we utilize a nonlinear autoregressive exogenous model using gated recurrent units as the underlying architecture. These models are evaluated across a range of real patient scenarios, varying in data availability and sparsity, to assess predictive performance. Our findings demonstrate that data-driven methods, when provided with sufficient data, significantly improve prediction accuracy, particularly for high-risk patients with irregular platelet dynamics. This highlights the potential of data-driven approaches in enhancing clinical decision-making. In contrast, hybrid and mechanistic models are superior in scenarios with limited or sparse data. The proposed modeling and comparison framework is generalizable and could be extended to predict other treatment-related toxicities, offering broad applicability in personalized medicine.

The explosion in artificial intelligence (AI) applications is pushing the development of AI-dedicated data centers (AIDCs), creating management challenges that traditional methods and standalone AI solutions struggle to address. While digital twins are beneficial for AI-based design validation and operational optimization, current AI methods for their creation face limitations. Specifically, physical AI (PhyAI) aims to capture the underlying physical laws, which demands extensive, case-specific customization, and generative AI (GenAI) can produce inaccurate or hallucinated results. We propose Fusion Intelligence, a novel framework synergizing GenAI's automation with PhyAI's domain grounding. In this dual-agent collaboration, GenAI interprets natural language prompts to generate tokenized AIDC digital twins. Subsequently, PhyAI optimizes these generated twins by enforcing physical constraints and assimilating real-time data. Case studies demonstrate the advantages of our framework in automating the creation and validation of AIDC digital twins. These twins deliver predictive analytics to support power usage effectiveness (PUE) optimization in the design stage. With operational data collected, the digital twin accuracy is further improved compared with pure physics-based models developed by human experts. Fusion Intelligence offers a promising pathway to accelerate digital transformation. It enables more reliable and efficient AI-driven digital transformation for a broad range of mission-critical infrastructures.