CASE-ID: Constraint-Aware State Estimation and Instability Detection

Deep learning systems lack reliable early-warning indicators for instability during training and deployment. Standard metrics like loss and gradient norms react only after degradation has begun. This paper introduces CASE-ID, a lightweight framework that models neural networks as latent stochastic dynamical systems and detects structural shifts in representation space before performance collapses. Experiments on CIFAR-100 with ResNet-50 show early warnings 120-180 steps before loss-based triggers and a 25-40% reduction in false positives relative to gradient-norm heuristics

Neural networks often experience abrupt instabilities such as distribution shifts, catastrophic forgetting, or gradient explosion. Existing monitoring tools typically detect these events only after they manifest in performance metrics. A proactive approach requires estimating the internal state of the model to detect structural deviations before they propagate. CASE-ID provides this early-warning mechanism by monitoring internal representations through compact statistical descriptors.

Neural networks exhibit structured internal dynamics where activations cluster by class and representation geometry stabilizes as training converges. Instability disrupts these patterns. By treating the network as a dynamical system, we can apply control theory principles to observe "state drift" before "system failure" occurs.

The network is modeled as a latent dynamical system where S_{t+1}=f_{\theta}(S_{t})+\epsilon_{t}. The representation state is approximated as a Gaussian distribution:

3.1 KL Divergence

Instability is quantified via the Kullback-Leibler (KL) Divergence between consecutive states

This measure captures covariance inflation, centroid drift, and representation collapse (volume contraction).  

3.2 Constraint Penalty

A geometric penalty C_{t} captures structural deformations under-weighted by pure probabilistic measures:

The final instability score is I_{t} = D_{t} + C_{t}.  

4. Implementation and Results

Efficiency: Monitoring overhead is <2% (<2ms per step on ResNet-50), making it suitable for production.  

Lead-Time: CASE-ID detects instability median \approx150 steps before loss-based triggers.  

Reliability: The persistence-based detection rule reduces the false positive rate (FPR) by 25-40% compared to gradient-norm monitoring.