Madhava Gaikwad

Madhava Gaikwad

Dense Associative Memory (DAM) generalizes Hopfield networks through higher-order interactions and achieves storage capacity that scales as $O(N^{n-1})$ under suitable pattern separation conditions. Existing dynamical analyses primarily study the thermodynamic limit $N\to\infty$ with randomly sampled patterns and therefore do not provide finite-size guarantees or explicit convergence rates. We develop an algorithmic analysis of DAM retrieval dynamics that yields finite-$N$ guarantees under explicit, verifiable pattern conditions. Under a separation assumption and a bounded-interference condition at high loading, we prove geometric convergence of asynchronous retrieval dynamics, which implies $O(\log N)$ convergence time once the trajectory enters the basin of attraction. We further establish adversarial robustness bounds expressed through an explicit margin condition that quantifies the number of corrupted bits tolerable per sweep, and derive capacity guarantees that scale as $Θ(N^{n-1})$ up to polylogarithmic factors in the worst case, while recovering the classical $Θ(N^{n-1})$ scaling for random pattern ensembles. Finally, we show that DAM retrieval dynamics admit a potential-game interpretation that ensures convergence to pure Nash equilibria under asynchronous updates. Complete proofs are provided in the appendices, together with preliminary experiments that illustrate the predicted convergence, robustness, and capacity scaling behavior.

Madhava Gaikwad

Large language models are exposed to risks of extraction, distillation, and unauthorized fine-tuning. Existing defenses use watermarking or monitoring, but these act after leakage. We design AlignDP, a hybrid privacy lock that blocks knowledge transfer at the data interface. The key idea is to separate rare and non-rare fields. Rare fields are shielded by PAC indistinguishability, giving effective zero-epsilon local DP. Non-rare fields are privatized with RAPPOR, giving unbiased frequency estimates under local DP. A global aggregator enforces composition and budget. This two-tier design hides rare events and adds controlled noise to frequent events. We prove limits of PAC extension to global aggregation, give bounds for RAPPOR estimates, and analyze utility trade-off. A toy simulation confirms feasibility: rare categories remain hidden, frequent categories are recovered with small error.

Madhava Gaikwad

Memory-augmented agents maintain multiple specialized stores, yet most systems retrieve from all stores for every query, increasing cost and introducing irrelevant context. We formulate memory retrieval as a store-routing problem and evaluate it using coverage, exact match, and token efficiency metrics. On downstream question answering, an oracle router achieves higher accuracy while using substantially fewer context tokens compared to uniform retrieval, demonstrating that selective retrieval improves both efficiency and performance. Our results show that routing decisions are a first-class component of memory-augmented agent design and motivate learned routing mechanisms for scalable multi-store systems. We additionally formalize store selection as a cost-sensitive decision problem that trades answer accuracy against retrieval cost, providing a principled interpretation of routing policies.

Madhava Gaikwad

We study reinforcement learning from human feedback under misspecification. Sometimes human feedback is systematically wrong on certain types of inputs, like a broken compass that points the wrong way in specific regions. We prove that when feedback is biased on a fraction alpha of contexts with bias strength epsilon, any learning algorithm needs exponentially many samples exp(n*alpha*epsilon^2) to distinguish between two possible "true" reward functions that differ only on these problematic contexts. However, if you can identify where feedback is unreliable (a "calibration oracle"), you can focus your limited questions there and overcome the exponential barrier with just O(1/(alpha*epsilon^2)) queries. This quantifies why alignment is hard: rare edge cases with subtly biased feedback create an exponentially hard learning problem unless you know where to look. The gap between what we optimize (proxy from human feedback) and what we want (true objective) is fundamentally limited by how common the problematic contexts are (alpha), how wrong the feedback is there (epsilon), and how much the true objectives disagree there (gamma). Murphy's Law for AI alignment: the gap always wins unless you actively route around misspecification.

Madhava Gaikwad

We present Opal, an operator view of reinforcement learning from human feedback (RLHF). Objectives are expressed as ladders of two primitives on a base utility: additive penalties and multiplicative pairwise weights. We describe a simple reduction law with if-and-only-if conditions: such ladders collapse to a normal form on pairwise margins when the reference is fixed, penalties are additive, and weights are independent of intermediate margins. When these assumptions do not hold (reference shift, non-additive gates, score-dependent weights), small examples demonstrate non-reducibility. Building on this view, we introduce GKPO (Generalized Kernel Preference Object), a canonical schema in which many RLHF methods can be represented and, when reducible, mapped back from. GKPO provides a standard JSON serialization, canonicalization and hashing rules, and explicit flags with finite witnesses when assumptions fail. We illustrate these ideas with GKPO examples for DPO, RRHF, and ORPO, along with cross-method conversions (where assumptions permit) and minimal stress tests (SHIFT/GATE/SCORE) that highlight non-reducibility. A lightweight Python reference library accompanies the schema, implementing canonical hashing and adapters for DPO and RRHF.

Madhava Gaikwad

This position paper presents AVEC (Adaptive Verifiable Edge Control), a framework for bootstrapping privacy for local language models by enforcing privacy at the edge with explicit verifiability for delegated queries. AVEC introduces an adaptive budgeting algorithm that allocates per-query differential privacy parameters based on sensitivity, local confidence, and historical usage, and uses verifiable transformation with on-device integrity checks. We formalize guarantees using Rényi differential privacy with odometer-based accounting, and establish utility ceilings, delegation-leakage bounds, and impossibility results for deterministic gating and hash-only certification. Our evaluation is simulation-based by design to study mechanism behavior and accounting; we do not claim deployment readiness or task-level utility with live LLMs. The contribution is a conceptual architecture and theoretical foundation that chart a pathway for empirical follow-up on privately bootstrapping local LLMs.

Madhava Gaikwad, Abhishek Gandhi

We present ANSC, a probabilistic capacity health scoring framework for hyperscale datacenter fabrics. While existing alerting systems detect individual device or link failures, they do not capture the aggregate risk of cascading capacity shortfalls. ANSC provides a color-coded scoring system that indicates the urgency of issues \emph{not solely by current impact, but by the probability of imminent capacity violations}. Our system accounts for both current residual capacity and the probability of additional failures, normalized at datacenter and regional level. We demonstrate that ANSC enables operators to prioritize remediation across more than 400 datacenters and 60 regions, reducing noise and aligning SRE focus on the most critical risks.

Madhava Gaikwad, Ashwini Ramchandra Doke

We present NPO, an alignment-aware learning framework that operationalizes feedback-driven adaptation in human-in-the-loop decision systems. Unlike prior approaches that treat alignment as a static or post-hoc property, NPO introduces a formalization of alignment loss that is measurable, supervisable, and reducible under structured feedback. In parallel, we propose meta-alignment as the fidelity of the monitoring process that governs retraining or override triggers, and show that it is formally reducible to primary alignment via threshold fidelity. Our implementation spans a scalable operational loop involving scenario scoring, threshold tuning, policy validation, and structured feedback ingestion, including "likes", overrides, and abstentions. We provide formal convergence results under stochastic feedback and show that both alignment loss and monitoring fidelity converge additively. Empirically, NPO demonstrates measurable value in hyperscale deployment settings. A simulation-based artifact and ablation studies further illustrate the theoretical principles in action. Together, NPO offers a compact, inspectable architecture for continual alignment monitoring, helping bridge theoretical alignment guarantees with practical reliability in dynamic environments.