Prakul Sunil Hiremath

Prakul Sunil Hiremath, Vruksha Arun Hiremath

Limit order books can transition rapidly from stable to stressed conditions, yet standard early-warning signals such as order flow imbalance and short-term volatility are inherently reactive. We formalise this limitation via a three-regime causal data-generating process (stable $\to$ latent build-up $\to$ stress) in which a latent deterioration phase creates a prediction window prior to observable stress. Under mild assumptions on temporal drift and regime persistence, we establish identifiability of the latent build-up regime and derive guarantees for strictly positive expected lead-time and non-trivial probability of early detection. We propose a trigger-based detector combining MAX aggregation of complementary signal channels, a rising-edge condition, and adaptive thresholding. Across 200 simulations, the method achieves mean lead-time $+18.6 \pm 3.2$ timesteps with perfect precision and moderate coverage, outperforming classical change-point and microstructure baselines. A preliminary application to one week of BTC/USDT order book data shows consistent positive lead-times while baselines remain reactive. Results degrade in low signal-to-noise and short build-up regimes, consistent with theory.

Prakul Sunil Hiremath, Harshit R. Hiremath

We propose Sensitivity-Uncertainty Alignment (SUA), a framework for analyzing failures of large language models under adversarial and ambiguous inputs. We argue that adversarial sensitivity and ambiguity reflect a common issue: misalignment between prediction instability and model uncertainty. A reliable model should express higher uncertainty when its predictions are unstable; failure to do so leads to miscalibration. We define a scalar score, SUA_theta(x), capturing the difference between distributional sensitivity and predictive entropy. We show that minimizing its positive part bounds worst-case perturbed risk and relates to calibration error. We also formalize ambiguity collapse, where models produce overconfident outputs despite multiple valid interpretations. We introduce SUA-TR, a training method combining consistency regularization and entropy alignment, along with an abstention rule for safer inference. Across tasks including question answering and classification, SUA better identifies model failures than entropy or self-consistency alone. The framework is model-agnostic and provides a basis for improving reliability in evolving language models.

Prakul Sunil Hiremath

Edge intelligence is constrained by the energy and latency costs of shuttling data through electronic memory hierarchies. Optical systems offer a fundamentally different computational regime: once an input wavefront is launched into a structured medium, propagation, diffraction, and interference jointly enact a linear transformation whose cost is determined by wave physics rather than by clocked arithmetic. This paper develops a rigorous systems-level treatment of that regime and introduces a hybrid diffractive holographic architecture for image classification. The proposed model couples a Diffractive Optical Neural Network (DONN) with a Holographic Interference-Based Learning (HIBL) operator a formal map from digitally optimized phase distributions to physically realizable, fabrication-compatible interference patterns embeddable in passive optical elements. We express the full inference pipeline as a composition of encoding, phase modulation, free-space propagation, and intensity measurement operators, making explicit which quantities are learned, which are fixed by design, and where nonlinearity enters through photodetection. This operator-theoretic view resolves a persistent gap in the optical-ML literature between learning a transformation and physically realizing it. In physics-informed simulation on MNIST, a three-layer system with approximately 25,000 phase elements achieves 91.2% test accuracy with propagation-limited nanosecond-scale latency. The primary contribution is not a performance claim but a precise computational framework: learned representations can be physically embedded into structured optical media so that inference is executed by wavefront transformation through a passive, fabricated object rather than by sequential electronic multiply accumulate operations.

Prakul Sunil Hiremath

Safety in reinforcement learning (RL) is typically enforced through objective shaping while keeping environment dynamics stationary with respect to observable state-action pairs. Under delayed harm, this can lead to replay: after a washout period, reintroducing the same stimulus under matched observable conditions reproduces a similar harmful cascade. We introduce the Replay Suppression Diagnostic (RSD), a controlled exposure-decay-replay protocol that isolates this failure mode under frozen-policy evaluation. We show that, under stationary observable transition kernels, replay cannot be structurally suppressed without inducing a persistent shift in replay-time action distributions. Motivated by platform-mediated systems, we propose Regret-Aware Policy Optimization (RAPO), which augments the environment with persistent harm-trace and scar fields and applies a bounded, mass-preserving transition reweighting to reduce reachability of historically harmful regions. On graph diffusion tasks (50-1000 nodes), RAPO suppresses replay, reducing re-amplification gain (RAG) from 0.98 to 0.33 on 250-node graphs while retaining 82\% of task return. Disabling transition deformation only during replay restores re-amplification (RAG 0.91), isolating environment-level deformation as the causal mechanism.

Prakul Sunil Hiremath

Model-based reinforcement learning (MBRL) improves sample efficiency by optimizing policies inside imagined rollouts, but long-horizon planning degrades when model errors compound and imagined trajectories drift off the training manifold. We introduce GIRL (Generative Imagination Reinforcement Learning), a latent world-model framework that addresses this failure mode with two key components. First, a cross-modal grounding signal derived from a frozen foundation model (DINOv2) anchors the latent transition prior to a semantically consistent embedding space, penalizing inconsistent or implausible predictions. Second, an uncertainty-adaptive trust-region bottleneck interprets the KL regularizer as the Lagrange multiplier of a constrained optimization problem, restricting imagination drift within a learned region calibrated by Expected Information Gain and a Relative Performance Loss signal. We re-derive a value-gap bound using the Performance Difference Lemma and Integral Probability Metrics, yielding a bound that remains informative as the discount factor approaches one and connects the objective to real-environment regret. Experiments across three benchmark suites, including DeepMind Control, Adroit Hand Manipulation, and Meta-World with visual distractors, show that GIRL reduces latent rollout drift by 38 to 61 percent across tasks relative to DreamerV3, improves asymptotic return, and requires fewer environment interactions on long-horizon tasks. GIRL also outperforms TD-MPC2 on sparse-reward and high-contact settings under standard evaluation metrics. A distilled-prior variant reduces inference overhead and improves computational efficiency relative to the full model.

Prakul Sunil Hiremath

We introduce the Hiremath Early Detection (HED) Score, a principled, measure-theoretic evaluation criterion for quantifying the time-value of information in systems operating over non-stationary stochastic processes subject to abrupt regime transitions. Existing evaluation paradigms, chiefly the ROC/AUC framework and its downstream variants, are temporally agnostic: they assign identical credit to a detection at t + 1 and a detection at t + tau for arbitrarily large tau. This indifference to latency is a fundamental inadequacy in time-critical domains including cyber-physical security, algorithmic surveillance, and epidemiological monitoring. The HED Score resolves this by integrating a baseline-neutral, exponentially decaying kernel over the posterior probability stream of a target regime, beginning precisely at the onset of the regime shift. The resulting scalar simultaneously encodes detection acuity, temporal lead, and pre-transition calibration quality. We prove that the HED Score satisfies three axiomatic requirements: (A1) Temporal Monotonicity, (A2) Invariance to Pre-Attack Bias, and (A3) Sensitivity Decomposability. We further demonstrate that the HED Score admits a natural parametric family indexed by the Hiremath Decay Constant (lambda_H), whose domain-specific calibration constitutes the Hiremath Standard Table. As an empirical vehicle, we present PARD-SSM (Probabilistic Anomaly and Regime Detection via Switching State-Space Models), which couples fractional Stochastic Differential Equations (fSDEs) with a Switching Linear Dynamical System (S-LDS) inference backend. On the NSL-KDD benchmark, PARD-SSM achieves a HED Score of 0.0643, representing a 388.8 percent improvement over a Random Forest baseline (0.0132), with statistical significance confirmed via block-bootstrap resampling (p < 0.001). We propose the HED Score as the successor evaluation standard to ROC/AUC.

Prakul Sunil Hiremath

We develop a semi-parametric state-space model for time-series data with latent regime transitions. Classical Markov-switching models use fixed parametric transition functions, such as logistic or probit links, which restrict flexibility when transitions depend on nonlinear and context-dependent effects. We replace this assumption with learned functions $f_0, f_1 \in \calH$, where $\calH$ is either a reproducing kernel Hilbert space or a spline approximation space, and define transition probabilities as $p_{jk,t} = \sigmoid(f(\bx_{t-1}))$. The transition functions are estimated jointly with emission parameters using a generalized Expectation-Maximization algorithm. The E-step uses the standard forward-backward recursion, while the M-step reduces to a penalized regression problem with weights from smoothed occupation measures. We establish identifiability conditions and provide a consistency argument for the resulting estimators. Experiments on synthetic data show improved recovery of nonlinear transition dynamics compared to parametric baselines. An empirical study on financial time series demonstrates improved regime classification and earlier detection of transition events.

Prakul Sunil Hiremath, PeerAhammad M Bagawan, Sahil Bhekane

Modern adversarial campaigns unfold as sequences of behavioural phases - Reconnaissance, Lateral Movement, Intrusion, and Exfiltration - each often indistinguishable from legitimate traffic when viewed in isolation. Existing intrusion detection systems (IDS) fail to capture this structure: signature-based methods cannot detect zero-day attacks, deep-learning models provide opaque anomaly scores without stage attribution, and standard Kalman Filters cannot model non-stationary multi-modal dynamics. We present PARD-SSM, a probabilistic framework that models network telemetry as a Regime-Dependent Switching Linear Dynamical System with K = 4 hidden regimes. A structured variational approximation reduces inference complexity from exponential to O(TK^2), enabling real-time detection on standard CPU hardware. An online EM algorithm adapts model parameters, while KL-divergence gating suppresses false positives. Evaluated on CICIDS2017 and UNSW-NB15, PARD-SSM achieves F1 scores of 98.2% and 97.1%, with latency less than 1.2 ms per flow. The model also produces predictive alerts approximately 8 minutes before attack onset, a capability absent in prior systems.