arXiv subjects

Ankur Mali

Publications and source records attributed to Ankur Mali.

At least 19 recordsLinked to original sources

arXiv2026

A Human-in-the-Loop Framework for Efficient Prompt Selection in Microscopy Vision-Language Models

Deep-learning pipelines for microscopy image classification often require expensive, labor- and time-intensive expert annotation to produce high-quality ground truth for training. Recent work has shown that prompt tuning of vision-language models (VLMs) can reduce manual annotation by constructing a small prompt set of expert-verified image-caption exemplars that is reused as few-shot context to classify all remaining images at inference time. To further reduce effort, the VLM can draft captions for candidate exemplars, which experts then verify and lightly edit instead of writing text de novo. However, two practical questions remain unaddressed: (1) which unlabeled images should be prioritized for verification, and (2) how many verified exemplars are needed to reach a performance target. In this work, we address these questions by formulating prompt-set construction as a target-driven active learning problem that prioritizes which images to annotate. We study three complementary selection criteria under strict low-resource constraints with small unlabeled pools. Experiments show that our methods reach the target performance with substantially fewer expert-verified images than random selection, achieving 100% test accuracy with as few as 20 annotated images on average. More broadly, our human-in-the-loop framework demonstrates a human-centered use of generative AI in biomedical image analysis, where experts remain actively involved in verifying and refining model output while significantly reducing annotation cost. Code and data will be publicly available.

cs.CV↗

arXiv2026

Curvature-Weighted Capacity Allocation: A Minimum Description Length Framework for Layer-Adaptive Large Language Model Optimization

Layer-wise capacity in large language models is highly non-uniform: some layers contribute disproportionately to loss reduction, whereas others are nearly redundant. Existing layer-scoring methods provide sensitivity estimates but do not give a principled rule for converting those estimates into allocation or pruning decisions under a global hardware budget. We introduce a curvature-aware, MDL-inspired framework built around the layer gain $\zeta_k^2=g_k^\top\widetilde H_{kk}^{-1}g_k$. This quantity equals twice the maximal decrease predicted by the regularized layer-restricted quadratic model and incorporates inverse local curvature; it is therefore a local surrogate for reducible risk, not a universal dominance claim over gradient-norm scores. After normalizing the gains into scores $q_k$, we formulate two convex programs: one allocates expert slots under diminishing returns, and the other assigns layer-wise pruning ratios while protecting high-score layers. Both continuous programs have unique globally optimal solutions characterized by one dual variable and computable in $O(K\log(1/\varepsilon))$ time by bisection. We also prove a quadratic transfer-regret bound: when source and target score vectors differ by at most $\delta$, the target surrogate cost of the transferred decision is within $O(\delta^2)$ of the target optimum. Experiments on Mistral-7B and Gemma-7B show clear allocation gains in some settings and competitive, though mixed, pruning performance. The framework therefore replaces an empirical score-to-decision heuristic with a budget-feasible optimization procedure whose guarantees apply to the stated continuous surrogates. Code is available on github repo - [TKAI-LAB-Mali/Curvature-Weighted-Capacity-Allocation](https://github.com/TKAI-LAB-Mali/Curvature-Weighted-Capacity-Allocation.git)

cs.IT↗

arXiv2025

Integral Signatures of Activation Functions: A 9-Dimensional Taxonomy and Stability Theory for Deep Learning

Activation functions govern the expressivity and stability of neural networks, yet existing comparisons remain largely heuristic. We propose a rigorous framework for their classification via a nine-dimensional integral signature S_sigma(phi), combining Gaussian propagation statistics (m1, g1, g2, m2, eta), asymptotic slopes (alpha_plus, alpha_minus), and regularity measures (TV(phi'), C(phi)). This taxonomy establishes well-posedness, affine reparameterization laws with bias, and closure under bounded slope variation. Dynamical analysis yields Lyapunov theorems with explicit descent constants and identifies variance stability regions through (m2', g2). From a kernel perspective, we derive dimension-free Hessian bounds and connect smoothness to bounded variation of phi'. Applying the framework, we classify eight standard activations (ReLU, leaky-ReLU, tanh, sigmoid, Swish, GELU, Mish, TeLU), proving sharp distinctions between saturating, linear-growth, and smooth families. Numerical Gauss-Hermite and Monte Carlo validation confirms theoretical predictions. Our framework provides principled design guidance, moving activation choice from trial-and-error to provable stability and kernel conditioning.

cs.LG↗

arXiv2025

Realizable Circuit Complexity: Embedding Computation in Space-Time

Classical circuit complexity characterizes parallel computation in purely combinatorial terms, ignoring the physical constraints that govern real hardware. The standard classes $\mathbf{NC}$, $\mathbf{AC}$, and $\mathbf{TC}$ treat unlimited fan-in, free interconnection, and polynomial gate counts as feasible -- assumptions that conflict with geometric, energetic, and thermodynamic realities. We introduce the family of realizable circuit classes $\mathbf{RC}_d$, which model computation embedded in physical $d$-dimensional space. Each circuit in $\mathbf{RC}_d$ obeys conservative realizability laws: volume scales as $\mathcal{O}(t^d)$, cross-boundary information flux is bounded by $\mathcal{O}(t^{d-1})$ per unit time, and growth occurs through local, physically constructible edits. These bounds apply to all causal systems, classical or quantum. Within this framework, we show that algorithms with runtime $\omega(n^{d/(d-1)})$ cannot scale to inputs of maximal entropy, and that any $d$-dimensional parallel implementation offers at most a polynomial speed-up of degree $(d-1)$ over its optimal sequential counterpart. In the limit $d\to\infty$, $\mathbf{RC}_\infty(\mathrm{polylog})=\mathbf{NC}$, recovering classical parallelism as a non-physical idealization. By unifying geometry, causality, and information flow, $\mathbf{RC}_d$ extends circuit complexity into the physical domain, revealing universal scaling laws for computation.

cs.CC↗

arXiv2025

Rethinking Reasoning in LLMs: Neuro-Symbolic Local RetoMaton Beyond ICL and CoT

Prompt-based reasoning strategies such as Chain-of-Thought (CoT) and In-Context Learning (ICL) have become widely used for eliciting reasoning capabilities in large language models (LLMs). However, these methods rely on fragile, implicit mechanisms often yielding inconsistent outputs across seeds, formats, or minor prompt variations making them fundamentally unreliable for tasks requiring stable, interpretable reasoning. In contrast, automata-based neuro-symbolic frameworks like RetoMaton offer a more structured and trustworthy alternative by grounding retrieval in symbolic memory with deterministic transitions. In this work, we extend RetoMaton by replacing its global datastore with a local, task-adaptive Weighted Finite Automaton (WFA), constructed directly from external domain corpora. This local automaton structure promotes robust, context-aware retrieval while preserving symbolic traceability and low inference overhead. Unlike prompting, which entangles context and memory in opaque ways, our approach leverages the explicit structure of WFAs to provide verifiable and modular retrieval behavior, making it better suited for domain transfer and interoperability. We evaluate this local RetoMaton variant on two pretrained LLMs LLaMA-3.2-1B and Gemma-3-1B-PT across three reasoning tasks: TriviaQA (reading comprehension), GSM8K (multi-step math), and MMLU (domain knowledge). Compared to the base model and prompting-based methods, augmenting these setups with local RetoMaton consistently improves performance while enabling transparent and reproducible retrieval dynamics. Our results highlight a promising shift toward trustworthy, symbolic reasoning in modern LLMs via lightweight, automaton-guided memory.

cs.CL↗

arXiv2025

Investigating Pedagogical Teacher and Student LLM Agents: Genetic Adaptation Meets Retrieval Augmented Generation Across Learning Style

Effective teaching requires adapting instructional strategies to accommodate the diverse cognitive and behavioral profiles of students, a persistent challenge in education and teacher training. While Large Language Models (LLMs) offer promise as tools to simulate such complex pedagogical environments, current simulation frameworks are limited in two key respects: (1) they often reduce students to static knowledge profiles, and (2) they lack adaptive mechanisms for modeling teachers who evolve their strategies in response to student feedback. To address these gaps, \textbf{we introduce a novel simulation framework that integrates LLM-based heterogeneous student agents with a self-optimizing teacher agent}. The teacher agent's pedagogical policy is dynamically evolved using a genetic algorithm, allowing it to discover and refine effective teaching strategies based on the aggregate performance of diverse learners. In addition, \textbf{we propose Persona-RAG}, a Retrieval Augmented Generation module that enables student agents to retrieve knowledge tailored to their individual learning styles. Persona-RAG preserves the retrieval accuracy of standard RAG baselines while enhancing personalization, an essential factor in modeling realistic educational scenarios. Through extensive experiments, we demonstrate how our framework supports the emergence of distinct and interpretable teaching patterns when interacting with varied student populations. Our results highlight the potential of LLM-driven simulations to inform adaptive teaching practices and provide a testbed for training human educators in controlled, data-driven environments.

cs.AI↗

arXiv2025

Bridging Predictive Coding and MDL: A Two-Part Code Framework for Deep Learning

We present the first theoretical framework that connects predictive coding (PC), a biologically inspired local learning rule, with the minimum description length (MDL) principle in deep networks. We prove that layerwise PC performs block-coordinate descent on the MDL two-part code objective, thereby jointly minimizing empirical risk and model complexity. Using Hoeffding's inequality and a prefix-code prior, we derive a novel generalization bound of the form $R(\theta) \le \hat{R}(\theta) + \frac{L(\theta)}{N}$, capturing the tradeoff between fit and compression. We further prove that each PC sweep monotonically decreases the empirical two-part codelength, yielding tighter high-probability risk bounds than unconstrained gradient descent. Finally, we show that repeated PC updates converge to a block-coordinate stationary point, providing an approximate MDL-optimal solution. To our knowledge, this is the first result offering formal generalization and convergence guarantees for PC-trained deep models, positioning PC as a theoretically grounded and biologically plausible alternative to backpropagation.

cs.LG↗

arXiv2024

TeLU Activation Function for Fast and Stable Deep Learning

We propose the Hyperbolic Tangent Exponential Linear Unit (TeLU), a neural network hidden activation function defined as TeLU(x)=xtanh(exp(x)). TeLU's design is grounded in the core principles of key activation functions, achieving strong convergence by closely approximating the identity function in its active region while effectively mitigating the vanishing gradient problem in its saturating region. Its simple formulation enhances computational efficiency, leading to improvements in scalability and convergence speed. Unlike many modern activation functions, TeLU seamlessly combines the simplicity and effectiveness of ReLU with the smoothness and analytic properties essential for learning stability in deep neural networks. TeLU's ability to mimic the behavior and optimal hyperparameter settings of ReLU, while introducing the benefits of smoothness and curvature, makes it an ideal drop-in replacement. Its analytic nature positions TeLU as a powerful universal approximator, enhancing both robustness and generalization across a multitude of experiments. We rigorously validate these claims through theoretical analysis and experimental validation, demonstrating TeLU's performance across challenging benchmarks; including ResNet18 on ImageNet, Dynamic-Pooling Transformers on Text8, and Recurrent Neural Networks (RNNs) on the Penn TreeBank dataset. These results highlight TeLU's potential to set a new standard in activation functions, driving more efficient and stable learning in deep neural networks, thereby accelerating scientific discoveries across various fields.

cs.LG↗

arXiv2024

Tight Stability, Convergence, and Robustness Bounds for Predictive Coding Networks

Energy-based learning algorithms, such as predictive coding (PC), have garnered significant attention in the machine learning community due to their theoretical properties, such as local operations and biologically plausible mechanisms for error correction. In this work, we rigorously analyze the stability, robustness, and convergence of PC through the lens of dynamical systems theory. We show that, first, PC is Lyapunov stable under mild assumptions on its loss and residual energy functions, which implies intrinsic robustness to small random perturbations due to its well-defined energy-minimizing dynamics. Second, we formally establish that the PC updates approximate quasi-Newton methods by incorporating higher-order curvature information, which makes them more stable and able to converge with fewer iterations compared to models trained via backpropagation (BP). Furthermore, using this dynamical framework, we provide new theoretical bounds on the similarity between PC and other algorithms, i.e., BP and target propagation (TP), by precisely characterizing the role of higher-order derivatives. These bounds, derived through detailed analysis of the Hessian structures, show that PC is significantly closer to quasi-Newton updates than TP, providing a deeper understanding of the stability and efficiency of PC compared to conventional learning methods.

cs.LG↗

arXiv2024

Precision, Stability, and Generalization: A Comprehensive Assessment of RNNs learnability capability for Classifying Counter and Dyck Languages

This study investigates the learnability of Recurrent Neural Networks (RNNs) in classifying structured formal languages, focusing on counter and Dyck languages. Traditionally, both first-order (LSTM) and second-order (O2RNN) RNNs have been considered effective for such tasks, primarily based on their theoretical expressiveness within the Chomsky hierarchy. However, our research challenges this notion by demonstrating that RNNs primarily operate as state machines, where their linguistic capabilities are heavily influenced by the precision of their embeddings and the strategies used for sampling negative examples. Our experiments revealed that performance declines significantly as the structural similarity between positive and negative examples increases. Remarkably, even a basic single-layer classifier using RNN embeddings performed better than chance. To evaluate generalization, we trained models on strings up to a length of 40 and tested them on strings from lengths 41 to 500, using 10 unique seeds to ensure statistical robustness. Stability comparisons between LSTM and O2RNN models showed that O2RNNs generally offer greater stability across various scenarios. We further explore the impact of different initialization strategies revealing that our hypothesis is consistent with various RNNs. Overall, this research questions established beliefs about RNNs' computational capabilities, highlighting the importance of data structure and sampling techniques in assessing neural networks' potential for language classification tasks. It emphasizes that stronger constraints on expressivity are crucial for understanding true learnability, as mere expressivity does not capture the essence of learning.

cs.CL↗

arXiv2024

Exploring Learnability in Memory-Augmented Recurrent Neural Networks: Precision, Stability, and Empirical Insights

This study explores the learnability of memory-less and memory-augmented RNNs, which are theoretically equivalent to Pushdown Automata. Empirical results show that these models often fail to generalize on longer sequences, relying more on precision than mastering symbolic grammar. Experiments on fully trained and component-frozen models reveal that freezing the memory component significantly improves performance, achieving state-of-the-art results on the Penn Treebank dataset (test perplexity reduced from 123.5 to 120.5). Models with frozen memory retained up to 90% of initial performance on longer sequences, compared to a 60% drop in standard models. Theoretical analysis suggests that freezing memory stabilizes temporal dependencies, leading to robust convergence. These findings stress the need for stable memory designs and long-sequence evaluations to understand RNNs true learnability limits.

cs.CL↗

arXiv2024

A Unified Framework for Continual Learning and Unlearning

Continual learning and machine unlearning are crucial challenges in machine learning, typically addressed separately. Continual learning focuses on adapting to new knowledge while preserving past information, whereas unlearning involves selectively forgetting specific subsets of data. In this paper, we introduce a new framework that jointly tackles both tasks by leveraging controlled knowledge distillation. Our approach enables efficient learning with minimal forgetting and effective targeted unlearning. By incorporating a fixed memory buffer, the system supports learning new concepts while retaining prior knowledge. The distillation process is carefully managed to ensure a balance between acquiring new information and forgetting specific data as needed. Experimental results on benchmark datasets show that our method matches or exceeds the performance of existing approaches in both continual learning and machine unlearning. This unified framework is the first to address both challenges simultaneously, paving the way for adaptable models capable of dynamic learning and forgetting while maintaining strong overall performance. Source code: \textcolor{blue}{https://respailab.github.io/CLMUL}

cs.LG↗

arXiv2024

Investigating Symbolic Capabilities of Large Language Models

Prompting techniques have significantly enhanced the capabilities of Large Language Models (LLMs) across various complex tasks, including reasoning, planning, and solving math word problems. However, most research has predominantly focused on language-based reasoning and word problems, often overlooking the potential of LLMs in handling symbol-based calculations and reasoning. This study aims to bridge this gap by rigorously evaluating LLMs on a series of symbolic tasks, such as addition, multiplication, modulus arithmetic, numerical precision, and symbolic counting. Our analysis encompasses eight LLMs, including four enterprise-grade and four open-source models, of which three have been pre-trained on mathematical tasks. The assessment framework is anchored in Chomsky's Hierarchy, providing a robust measure of the computational abilities of these models. The evaluation employs minimally explained prompts alongside the zero-shot Chain of Thoughts technique, allowing models to navigate the solution process autonomously. The findings reveal a significant decline in LLMs' performance on context-free and context-sensitive symbolic tasks as the complexity, represented by the number of symbols, increases. Notably, even the fine-tuned GPT3.5 exhibits only marginal improvements, mirroring the performance trends observed in other models. Across the board, all models demonstrated a limited generalization ability on these symbol-intensive tasks. This research underscores LLMs' challenges with increasing symbolic complexity and highlights the need for specialized training, memory and architectural adjustments to enhance their proficiency in symbol-based reasoning tasks.

cs.CL↗

arXiv2024

Neuro-mimetic Task-free Unsupervised Online Learning with Continual Self-Organizing Maps

An intelligent system capable of continual learning is one that can process and extract knowledge from potentially infinitely long streams of pattern vectors. The major challenge that makes crafting such a system difficult is known as catastrophic forgetting - an agent, such as one based on artificial neural networks (ANNs), struggles to retain previously acquired knowledge when learning from new samples. Furthermore, ensuring that knowledge is preserved for previous tasks becomes more challenging when input is not supplemented with task boundary information. Although forgetting in the context of ANNs has been studied extensively, there still exists far less work investigating it in terms of unsupervised architectures such as the venerable self-organizing map (SOM), a neural model often used in clustering and dimensionality reduction. While the internal mechanisms of SOMs could, in principle, yield sparse representations that improve memory retention, we observe that, when a fixed-size SOM processes continuous data streams, it experiences concept drift. In light of this, we propose a generalization of the SOM, the continual SOM (CSOM), which is capable of online unsupervised learning under a low memory budget. Our results, on benchmarks including MNIST, Kuzushiji-MNIST, and Fashion-MNIST, show almost a two times increase in accuracy, and CIFAR-10 demonstrates a state-of-the-art result when tested on (online) unsupervised class incremental learning setting.

cs.LG↗

arXiv2024

A Review of Neuroscience-Inspired Machine Learning

One major criticism of deep learning centers around the biological implausibility of the credit assignment schema used for learning -- backpropagation of errors. This implausibility translates into practical limitations, spanning scientific fields, including incompatibility with hardware and non-differentiable implementations, thus leading to expensive energy requirements. In contrast, biologically plausible credit assignment is compatible with practically any learning condition and is energy-efficient. As a result, it accommodates hardware and scientific modeling, e.g. learning with physical systems and non-differentiable behavior. Furthermore, it can lead to the development of real-time, adaptive neuromorphic processing systems. In addressing this problem, an interdisciplinary branch of artificial intelligence research that lies at the intersection of neuroscience, cognitive science, and machine learning has emerged. In this paper, we survey several vital algorithms that model bio-plausible rules of credit assignment in artificial neural networks, discussing the solutions they provide for different scientific fields as well as their advantages on CPUs, GPUs, and novel implementations of neuromorphic hardware. We conclude by discussing the future challenges that will need to be addressed in order to make such algorithms more useful in practical applications.

cs.NE↗

arXiv2024

Stable and Robust Deep Learning By Hyperbolic Tangent Exponential Linear Unit (TeLU)

In this paper, we introduce the Hyperbolic Tangent Exponential Linear Unit (TeLU), a novel neural network activation function, represented as $f(x) = x{\cdot}tanh(e^x)$. TeLU is designed to overcome the limitations of conventional activation functions like ReLU, GELU, and Mish by addressing the vanishing and, to an extent, the exploding gradient problems. Our theoretical analysis and empirical assessments reveal that TeLU outperforms existing activation functions in stability and robustness, effectively adjusting activation outputs' mean towards zero for enhanced training stability and convergence. Extensive evaluations against popular activation functions (ReLU, GELU, SiLU, Mish, Logish, Smish) across advanced architectures, including Resnet-50, demonstrate TeLU's lower variance and superior performance, even under hyperparameter conditions optimized for other functions. In large-scale tests with challenging datasets like CIFAR-10, CIFAR-100, and TinyImageNet, encompassing 860 scenarios, TeLU consistently showcased its effectiveness, positioning itself as a potential new standard for neural network activation functions, boosting stability and performance in diverse deep learning applications.

cs.LG↗

arXiv2024

Stability Analysis of Various Symbolic Rule Extraction Methods from Recurrent Neural Network

This paper analyzes two competing rule extraction methodologies: quantization and equivalence query. We trained $3600$ RNN models, extracting $18000$ DFA with a quantization approach (k-means and SOM) and $3600$ DFA by equivalence query($L^{*}$) methods across $10$ initialization seeds. We sampled the datasets from $7$ Tomita and $4$ Dyck grammars and trained them on $4$ RNN cells: LSTM, GRU, O2RNN, and MIRNN. The observations from our experiments establish the superior performance of O2RNN and quantization-based rule extraction over others. $L^{*}$, primarily proposed for regular grammars, performs similarly to quantization methods for Tomita languages when neural networks are perfectly trained. However, for partially trained RNNs, $L^{*}$ shows instability in the number of states in DFA, e.g., for Tomita 5 and Tomita 6 languages, $L^{*}$ produced more than $100$ states. In contrast, quantization methods result in rules with number of states very close to ground truth DFA. Among RNN cells, O2RNN produces stable DFA consistently compared to other cells. For Dyck Languages, we observe that although GRU outperforms other RNNs in network performance, the DFA extracted by O2RNN has higher performance and better stability. The stability is computed as the standard deviation of accuracy on test sets on networks trained across $10$ seeds. On Dyck Languages, quantization methods outperformed $L^{*}$ with better stability in accuracy and the number of states. $L^{*}$ often showed instability in accuracy in the order of $16\% - 22\%$ for GRU and MIRNN while deviation for quantization methods varied in $5\% - 15\%$. In many instances with LSTM and GRU, DFA's extracted by $L^{*}$ even failed to beat chance accuracy ($50\%$), while those extracted by quantization method had standard deviation in the $7\%-17\%$ range. For O2RNN, both rule extraction methods had deviation in the $0.5\% - 3\%$ range.

cs.LG↗

arXiv2023

A Robust Backpropagation-Free Framework for Images

While current deep learning algorithms have been successful for a wide variety of artificial intelligence (AI) tasks, including those involving structured image data, they present deep neurophysiological conceptual issues due to their reliance on the gradients that are computed by backpropagation of errors (backprop). Gradients are required to obtain synaptic weight adjustments but require knowledge of feed-forward activities in order to conduct backward propagation, a biologically implausible process. This is known as the "weight transport problem". Therefore, in this work, we present a more biologically plausible approach towards solving the weight transport problem for image data. This approach, which we name the error kernel driven activation alignment (EKDAA) algorithm, accomplishes through the introduction of locally derived error transmission kernels and error maps. Like standard deep learning networks, EKDAA performs the standard forward process via weights and activation functions; however, its backward error computation involves adaptive error kernels that propagate local error signals through the network. The efficacy of EKDAA is demonstrated by performing visual-recognition tasks on the Fashion MNIST, CIFAR-10 and SVHN benchmarks, along with demonstrating its ability to extract visual features from natural color images. Furthermore, in order to demonstrate its non-reliance on gradient computations, results are presented for an EKDAA trained CNN that employs a non-differentiable activation function.

cs.NE↗