Abstract

The rapid proliferation of energy-constrained electronic systems, including IoT nodes, biomedical
implants, and portable devices, has intensified the demand for ultra-low-power and area-efficient analog
circuit design. This thesis presents the design and analysis of advanced ultra-low-power analog building
blocks with a focus on current and voltage references, as well as high-speed comparators, optimized for
energy and area efficiency under wide process, voltage, and temperature variations.
A series of resistorless current and voltage reference architectures are explored, leveraging subthreshold operation and the complementary temperature characteristics of CTAT and PTAT voltages to
achieve robust temperature compensation. A sub-1V current reference generating 593 pA is demonstrated, achieving a temperature coefficient of 378 ppm/◦C over a range of −40◦C to 100◦C, with a line
sensitivity of 0.198%/V across a supply range of 0.8 V to 2.5 V. The design consumes only 3.3 nW at
27◦C and occupies 0.074 mm2
, while maintaining ±0.75% (3σ/µ) process variation, enabling trim-free
operation. Further, an integrated ultra-low-voltage reference operating at 0.5 V generates 90.7 pA and
288 mV current and voltage references, respectively, achieving temperature coefficients of 15.2 ppm/◦C
and 36.8 ppm/◦C. The circuit operates across a wide supply range of 0.5 V to 2.6 V with line sensitivities
of 0.028%/V and 0.154%/V, consuming only 275.26 pW and occupying 0.087 mm2
through the use of
gate leakage-based techniques.
To address line sensitivity and enable operation over extreme temperature ranges, a compact voltage
reference architecture employing only four transistors and a dual-loop regulation scheme is proposed.
The design achieves a reference voltage of 451.6 mV while consuming 37.6 pW, with an ultra-low
line sensitivity of 0.009%/V. It operates over a wide temperature range of −30◦C to 160◦C with a
temperature coefficient of 70.2 ppm/◦C, enabled by threshold voltage modulation and leakage control
techniques.
In addition to reference generation, a 0.3 V bulk-driven rail-to-rail comparator with dynamic transient
enhancement is introduced to overcome the speed limitations of subthreshold operation. The proposed
design achieves a 10× improvement in rise time, with a transient response of 7.56 ns and a bandwidth of
1.07 MHz while consuming only 28 nW of power, demonstrating portability across 65 nm and 180 nm
CMOS technologies.
While the previously presented resistorless architectures demonstrate excellent simulated performance in terms of ultra-low power and compactness, their reliance on device-level characteristics makes
them inherently more susceptible to process variations, potentially impacting yield and long-term reliability. To address these limitations, area-efficient resistance-based current references are investigated
and validated through silicon tape-out measurements. A fabricated design in 0.18 µm CMOS delivers
a 10 nA reference current while consuming 40 nW, achieving a temperature coefficient of 136 ppm/◦C
over −40◦C to 100◦C and a line sensitivity of 1.1%/V across a 1.4 V to 1.9 V supply range, with a compact area of 0.03 mm2
. Furthermore, a low-cost single-point auto-calibration technique is proposed,
enabling compensation of temperature and process variations. The calibrated 1 µA current reference
achieves ±2% accuracy with a temperature coefficient below 150 ppm/◦C over −40◦C to 100◦C, offering performance comparable to conventional trimming methods while significantly reducing calibration
complexity, time, and cost.
Additionally, this thesis presents a fully integrated ultra-low-power and area-efficient RC oscillator based on a resistance amplification technique for compact on-chip timing generation. Implemented
in a 0.18 µm CMOS process, the oscillator synthesizes a large effective resistance using amplified
polysilicon resistor characteristics, significantly reducing silicon area while maintaining frequency stability. Continuous-time offset mitigation techniques are employed to suppress low-frequency noise and
amplifier-induced offsets. The proposed oscillator generates a stable 5 kHz clock from a 1.4 V supply
with ultra-low power consumption, achieving a temperature coefficient of 100 ppm/◦C over −40◦C to
100◦C and a line sensitivity of 1%/V across a 1.4 V to 2 V supply range using single-point calibration.
Overall, the proposed architectures demonstrate significant improvements in power consumption,
area efficiency, temperature stability, and robustness, making them well-suited for next-generation ultralow-power analog and mixed-signal systems.

Abstract

test

Abstract

Modern Optical character recognition (OCR) systems increasingly rely on deep visual sequence
models, yet they are often evaluated mainly through final recognition accuracy. This leaves an important
question underexplored: how do such models learn, stabilize, and exhibit persistent errors over the
course of training? This question is especially relevant for Indic scripts, where visual text recognition is
shaped by complex orthographic structures such as aksharas, modifiers, conjunct-like forms, and dense
character compositions.
This thesis studies the learning behavior of two representative OCR models, CRNN and PARSeq,
using a five-language corpus covering Hindi, Bengali, Tamil, Telugu, and English. The main chapters
present representative analyses, and the same qualitative trends were observed in the remaining languages. The experiments are conducted on cropped printed word images, allowing the analysis to focus
on recognition behavior at the word level. Rather than comparing models only by final CER and WER,
the thesis examines their behavior across four complementary dimensions: training data scale, sequence
length, subword structure, and optimization geometry.
The results show that learning behavior varies meaningfully across model family, data regime, sequence length, and script structure. Under the tested settings, CRNN is more sensitive to reductions in
training data, while PARSeq remains comparatively more stable. Short words are learned faster than
long words, showing that sequence length remains an important source of recognition difficulty. Frequent and structurally simpler subword patterns stabilize earlier than rarer and more compositionally
involved patterns. Loss landscape visualizations further suggest that training moves from sharper and
more irregular regions toward smoother and more stable basins, with fuller data settings reaching such
regions more readily.
Together, these findings show that final recognition scores alone do not fully characterize OCR model
behavior. The analysis can support more informed model selection, especially when data availability,
script complexity, and word length vary across recognition settings. The findings may also inform
dataset design by indicating where additional examples are likely to be useful. By focusing on learning
trajectories, this thesis offers a structured way to evaluate OCR models beyond final accuracy, with
attention to how their behavior changes with data availability, word length, script structure, and training
stability.

Abstract

Random graph theory studies how global structure emerges from simple local rules. The classical
Erd˝os-R´enyi model is the most prominent example: every pair of vertices is connected independently
with the same probability. This model has a remarkably complete theory and displays sharp transitions
for the appearance of components, cycles, a giant component, and connectivity. Nevertheless, many
mathematical and physical networks are not well represented by a completely homogeneous model. In
systems with an underlying geometry, edges are often constrained by spatial locality. Particles interact
mainly with nearby particles, lattice Hamiltonians are often local or quasi-local, communication links
may be restricted by distance, and random walks on such networks inherit the geometry of the ambient
space.
This thesis introduces a new model in which randomness and geometry coexist: the periodic
band random graph. The vertices are placed on the discrete cycle Zn, two vertices are eligible to be
connected only when their cyclic distance is at most a bandwidth parameter m, and each eligible edge
is then retained independently with probability p
The first main result of the thesis is a sharp connectivity threshold for this model. Since each
vertex has exactly 2m admissible neighbours in the deterministic host graph, the probability that a
fixed vertex is isolated is (1 − p)
2m. This suggests that isolated vertices disappear when
pconn(n) ∼
log n
2m
.
We prove that this is the correct sharp threshold: below this scale, isolated vertices persist with high
probability, while above this scale the graph is connected with high probability.
The proof above the threshold is not a purely mean-field argument. In the Erd˝os-R´enyi graph, the
number of possible edges between a set and its complement depends only on the size of the set. In
the band random graph, it also depends on the shape and location of the set along the cycle. Long
intervals have much smaller boundaries than scattered sets of the same size. To overcome this, we
use a geometric block-decomposition argument: large connected pieces are built inside consecutive
intervals, neighbouring pieces are joined across their interfaces, and all small leftover sets are shown to
attach to the resulting connected chain.
We also analyze the graph just below the connectivity threshold. When
p =
log n − c
2m
, c > 0,
the graph is disconnected, but the disconnectedness is caused only by isolated vertices. More precisely,
the number Niso of isolated vertices converges in distribution to a Poisson random variable with mean
e
c
, and with high probability there is a unique giant component C1 satisfying
|C1| = n − Niso.
Thus every non-isolated vertex lies in the giant component. Moreover, unlike in the homogeneous Erd˝os-R´enyi model, this giant component has an explicit geometric structure: it contains an ordered
chain of large connected pieces inside consecutive m-blocks of the cycle, joined across neighbouring
interfaces.
The thesis also studies the random walk on the band random graph. The underlying cycle geometry
creates bottlenecks which persist even after the graph becomes connected. These bottlenecks are
reflected in the spectral gap of the lazy random walk. We show that, in the regime considered here,
the lazy spectral gap has order
γlazy(G) = Θ
m2
n2

and consequently obtain the corresponding mixing-time estimate. Finally, using electrical-network
methods, effective resistance, and explicit flow constructions, we prove that the maximal hitting time
of the simple random walk has order
Hmax(PG) = Θ
max
n
2
m2
, n .
The first term reflects diffusive motion around the cycle with step range m, while the second term
is the natural order of the time needed to hit a specified vertex when the stationary distribution is
close to uniform.
Overall, the thesis shows that the periodic band random graph is a useful model for studying
how independent randomness interacts with deterministic geometry. On the graph-theoretic side,
the model retains part of the Erd˝os-R´enyi connectivity picture: isolated vertices still determine the
sharp connectivity threshold. On the random-walk side, however, the behaviour is controlled by the
one-dimensional band structure, which produces the spectral-gap and hitting-time scales described
above.
The model also suggests a broader spectral direction. If AH denotes the adjacency matrix of the
deterministic host graph C
m
n
, then the adjacency matrix of the sampled graph can be written as
AG = pAH +
p
2mp(1 − p) W,
where W is a centered random band matrix supported on the same band. Thus AG is the sum of a
full-rank deterministic band operator and a random band fluctuation. While this thesis focuses mainly
on connectivity and random walks, the bulk and edge spectra of AG remain largely open and are a
natural direction for future work, connec

Abstract

Classical computers face fundamental barriers when simulating quantum phenomena due to the exponential
growth of quantum state spaces. This limitation motivates quantum simulation, particularly Hamiltonian simulation, as a central application for quantum computers. Simulating quantum dynamics is essential for studying
materials and molecules, and Hamiltonian simulation is an integral subroutine of important quantum algorithms
including ground state preparation, quantum phase estimation, quantum linear systems, and quantum singular value transformation. While various Hamiltonian simulation methods have been developed, those offering
optimal complexity such as qubitization and LCU-based methods require oracular assumptions, complicated
multi-qubit control, and extensive ancilla qubits, making them unsuitable for near and intermediate-term quantum computers. In contrast, hardware-friendly methods such as Trotterization, qDRIFT, and Single-Ancilla
LCU appear more practical, but their performance for concrete physical systems and applications of interest
remains unclear. This thesis provides comprehensive numerical benchmarks comparing Hamiltonian simulation
algorithms for early fault-tolerant quantum computers. We analyze when and why different methods achieve optimal performance based on system structure, precision requirements, and hardware constraints. We benchmark
Single-Ancilla LCU (SA-LCU), first and second-order Trotterization, and qDRIFT across two distinct classes of
quantum systems. For sparse Ising chains with nearest-neighbor interactions, first-order Trotterization achieves
better performance at moderate precision due to tight commutator bounds, while SA-LCU dominates at high
precision owing to its polylogarithmic scaling. For dense quantum chemistry Hamiltonians, SA-LCU consistently achieves the lowest gate counts across nearly all regimes. These results show that no single algorithm
dominates universally, optimal method selection depends on Hamiltonian structure and target precision. We
extend this comparative framework to two applications that use Hamiltonian simulation as a subroutine. First,
we consider the problem of estimating the magnetization of the ground state of the transverse-field Ising Hamiltonian. We vary the transverse-field coupling strength across a quantum phase transition and benchmark the
performance of various Hamiltonian simulation procedures. Our numerical simulations show that SA-LCU outperforms other techniques, requiring shorter circuit depths while using minimal ancilla overhead. Secondly, we
consider the problem of simulating open systems dynamics, an avenue where simulating Hamiltonian dynamics
finds widespread applications. However, most quantum algorithms for this problem require a lot of resources,
rendering them infeasible for early fault-tolerant quantum computers. We develop a collision model framework,
where a single environment qubit repeatedly interacts with the underlying system. This sequence of simple
interactions allows for the simulation of both Markovian and non-Markovian open systems dynamics, while
naturally incorporating near-term Hamiltonian simulation techniques. Our numerical validation shows that
second-order Trotter methods achieve the best asymptotic scaling for long-time evolution, while SA-LCU remains competitive for high-precision, short-time regimes. Our findings offer concrete guidance for the choice of
Hamiltonian simulation method driven by the structure of the system, target precision, and available hardware
resources. In the early fault-tolerant era, no single algorithm dominates universally, and understanding these
trade-offs is essential.

Abstract

This thesis presents a novel approach to domain-specific language model training that significantly
reduces computational costs while maintaining or improving performance on downstream tasks. Our
work aims to addresses the heavy computational costs in current domain adaptation practices; because
of vast corpora available for training models on fields like law and medicine, some popular models like
BioBERT often incur higher computational costs for the domain-specific portion of their training than
the entire cost of training the foundational models they are initialized from. The key contribution of
this work is the development of a domain-adaptive masking strategy that leverages curriculum learn-
ing principles to optimize the continual pre-training process. We hypothesize that much of the training
is redundant, wherein the model effectively spends time relearning lexical and semantic associations
already understood by the foundational language model. To test this hypothesis, rather than employ-
ing the traditional random masking approach used in BERT-based models, we create a concept-based
curriculum that selectively masks tokens corresponding to domain-relevant concepts while filtering out
general-domain knowledge already well-represented in foundational models. We test our approach in
the biomedical domain by further pre-training BERT on a corpus of PubMed Abstracts, mirroring the ar-
chitecture and corpus selection of BioBERT. We evaluate our model against two BioBERT checkpoints
across eight Named Entity Recognition tasks and find that it maintains competitive performance at a
fraction of the computational cost. Specifically, the model outperforms BioBERT-v1.0 on three-fourths
of the evaluated tasks at only two-thirds of the computational cost, and outperforms BioBERT-v1.1 on
half of the tasks at just 9% of its compute cost, while also being trained on a smaller subset of the lat-
ter's training corpus. While we demonstrate the effectiveness of our strategy in the biomedical domain,
our methodology of intelligent sample selection itself is domain-agnostic, and we posit that it may be
adapted to the broader field of transfer learning with minimal modifications. Our findings have signif-
icant implications for resource-constrained environments and suggest a promising direction for scaling
domain-adaptation across various specialized fields.

Abstract

Text-to-speech systems are advancing rapidly, yet reliably evaluating perceptual quality remains a
significant challenge. Human listening tests are expensive, time-consuming, and subject to substantial
inter-rater variability, motivating automatic MOS prediction. Existing approaches face two persistent
limitations: most underexploit the hierarchical layer structure of self-supervised representations, and
models trained on one corpus frequently fail to generalise across acoustic domains.
This thesis presents two complementary frameworks addressing these limitations. The first, QMOS,
extracts hierarchical quality features from a frozen Qwen2-Audio encoder via Grouped Acoustic Pooling (GAP), stratifying its 32 layers into early, mid, and deep groups to capture phonetic, prosodic, and
semantic signals simultaneously. These representations are fused with layer-weighted WavLM-Large
features through cross-attention, with a rater disagreement encoder and a composite objective of heteroscedastic negative log-likelihood and linear concordance correlation providing supplementary supervision. Without system-ID conditioning or listener embeddings, QMOS achieves system-level SRCC of
0.923 and 0.921 on SOMOS and BVCC respectively, with a cross-domain SRCC of 0.702.
The second framework, MDMOS, decomposes perceived quality into four perceptual dimensions:
acoustic fidelity, prosodic naturalness, phonetic intelligibility, and semantic coherence, each modelled
by a dedicated expert head combining layer-grouped WavLM-Large representations with hand-crafted
signal-processing features. A quality-adaptive fusion module dynamically weights expert outputs, while
an ordinal KL loss provides independent per-head supervision preventing head collapse. MDMOS
achieves a system-level SRCC of 0.925 on SOMOS, within the confidence interval of QMOS-B's competing result, and a clearer improvement to 0.944 on BVCC, matching state-of-the-art single-model
baselines without ensembling or listener-dependent modelling.
Ablation studies confirm that explicit correlation alignment is the most critical training component
and that perceptual decomposition captures complementary information not recoverable from a single
scalar predictor. Together, these results demonstrate that exploiting representational hierarchies and
decomposing quality into perceptual dimensions are effective and complementary inductive biases for
robust, generalisable MOS prediction.

Abstract

Sign Language Production (SLP) is a critical technology for bridging the communication gap between the hearing and Deaf communities. However, current systems face a persistent trade-off between
visual realism and semantic scalability. This thesis proposes a multi-modal framework to achieve scalable, fluid, and natural sign language synthesis across 2D and 3D representations.
First, we introduce Sanket Vaani-1K, a curated Indian Sign Language (ISL) dataset spanning over
40 high-utility domains, such as healthcare and banking. We present a 2D production pipeline that utilizes FramePack diffusion-based interpolation to stitch isolated sign units into fluid video, significantly
reducing data requirements compared to end-to-end models.
Transitioning to 3D to overcome 2D limitations like occlusion and depth nuances, we utilize ExAvatar, a Gaussian-based neural renderer driven by optimized SMPL-X body models, which we modified
and optimized for the specific requirements of the sign language use case.
By driving this renderer with person-specific skeletal offsets and high-fidelity facial registration, we
ensure the accurate synthesis of manual and non-manual cues. This is integrated into Gloss-SLQA, a
proof of concept for a sign language question-answering system that enables natural interaction through
a gloss-centric 3D avatar.
Finally, we present SignWeave-3D, which treats sign production as a masked motion infilling task.
By "weaving" isolated 3D motion units with a diffusion transformer, the model synthesizes natural coarticulation. Quantitative evaluations and user studies with the Deaf community demonstrate that our
framework produces significantly more understandable and natural signing than existing state-of-the-art
baselines.

Abstract

Raz [Raz09] proved that multilinear formulas computing the determinant of a
generic n × n matrix must have size n
Ω(log n)
. A natural question this raises is:
which properties of the determinant are actually driving this hardness? The proof
simultaneously exploits several features of the polynomial (the quadratic number
of variables, dense connectivity of the underlying matrix, and various symmetries),
and it is not apparent which of these are genuinely necessary.
This thesis establishes that density is not necessary. We prove the existence
of n × n symbolic matrices with only Θ(n log6 n) nonzero entries, a reduction in
variable count by a factor of n/ log6 n relative to the full matrix, such that any
multilinear formula computing their determinant still requires size n
Ω(log n)
. The
construction is based on rectangle sampling from the complete bipartite graph
Kn,n. The resulting sparse graph G simultaneously possesses a perfect matching
(guaranteeing that the determinant is nonzero) and exhibits diagonal imbalance
under random vertex permutations, a geometric property that turns out to be the
engine behind factor imbalance in Raz's partial derivatives method.
The conclusion is that Raz's technique extends to the sparse setting with no loss
in the quality of the lower bound, and that the key driver of multilinear hardness
for the determinant is an expansion-like combinatorial property of the variable set,
not its size. The analysis relies on concentration inequalities for dependent random
variables, in particular the read-k Chernoff bound due to Gavinsky, Lovett, Saks,
and Srinivasan [GLSS15]. Every result stated for the determinant holds equally
for the permanent.

Abstract

Edge computing has emerged as a key paradigm for supporting latency-aware applications by placing computation closer to end users. At the same time, serverless computing has emerged as a complementary paradigm that enables applications to be decomposed into lightweight functions that can be
dynamically deployed across distributed infrastructure. However, managing serverless applications in
edge environments is challenging due to limited resources, highly dynamic workloads, and constantly
changing network conditions. In such environments, runtime decisions such as function placement and
request routing must continuously balance performance and operational cost. Traditional approaches
for runtime orchestration rely on static rules, heuristics, or optimization-based techniques. While these
methods can provide effective solutions in controlled environments, they often struggle to react quickly
to workload fluctuations and large-scale system dynamics. Learning-based approaches, particularly Reinforcement Learning (RL), offer a promising alternative by enabling systems to adapt their behavior
through interaction with the environment. This thesis presents POSEIDON, a hybrid runtime optimization framework that combines Deep Reinforcement Learning (DRL) with Mixed Integer Linear
Programming (MILP) to optimize serverless function placement and request routing in edge computing environments. In this framework, a DRL agent learns efficient placement strategies under dynamic
workloads, while an optimization solver computes optimal routing decisions based on the placement
configuration. Experimental evaluation demonstrates that the hybrid approach can significantly reduce
decision time while maintaining competitive latency and cost performance compared to traditional optimization methods. Beyond performance evaluation, this thesis also investigates the limitations of
learning-based runtime adaptation. RL models require extensive training and typically operate within
predefined policy spaces, which can restrict their ability to respond to unforeseen system conditions. To
address these limitations, the thesis explores a new direction for self-adaptive systems based on generative artificial intelligence. Specifically, we propose a conceptual architecture that integrates Large
Language Model (LLM) into the runtime adaptation loop using a Monitor, Synthesize, Execute - Knowledge (MSE-K) control framework. In this architecture, the system monitors runtime context and uses
generative models to synthesize adaptation strategies dynamically. This approach aims to enable more
flexible and interpretable runtime decision-making compared to traditional rule-based or RL approaches.
Overall, this thesis contributes to the evolution of runtime decision-making mechanisms in distributed
systems by combining learning-based optimization with emerging generative reasoning techniques. The
results highlight both the potential and the limitations of current approaches and suggest new directions
for building more intelligent and adaptive software systems