Aman Bhargava

Aman Bhargava, Cameron Witkowski, Shi-Zhuo Looi et al.

Prompt engineering is crucial for deploying LLMs but is poorly understood mathematically. We formalize LLM systems as a class of discrete stochastic dynamical systems to explore prompt engineering through the lens of control theory. We offer a mathematical analysis of the limitations on the controllability of self-attention as a function of the singular values of the parameter matrices. We present complementary empirical results on the controllability of a panel of LLMs, including Falcon-7b, Llama-7b, and Falcon-40b. Given initial state $\mathbf x_0$ from Wikitext and prompts of length $k \leq 10$ tokens, we find that the "correct" next token is reachable at least 97% of the time, and that the top 75 most likely next tokens are reachable at least 85% of the time. Intriguingly, short prompt sequences can dramatically alter the likelihood of specific outputs, even making the least likely tokens become the most likely ones. This control-theoretic analysis of LLMs demonstrates the significant and poorly understood role of input sequences in steering output probabilities, offering a foundational perspective for enhancing language model system capabilities.

Zitong Jerry Wang, Alexander M. Xu, Aman Bhargava et al.

The tumor microenvironment (TME) significantly impacts cancer prognosis due to its immune composition. While therapies for altering the immune composition, including immunotherapies, have shown exciting results for treating hematological cancers, they are less effective for immunologically-cold, solid tumors. Spatial omics technologies capture the spatial organization of the TME with unprecedented molecular detail, revealing the relationship between immune cell localization and molecular signals. Here, we formulate T-cell infiltration prediction as a self-supervised machine learning problem and develop a counterfactual optimization strategy that leverages large scale spatial omics profiles of patient tumors to design tumor perturbations predicted to boost T-cell infiltration. A convolutional neural network predicts T-cell distribution based on signaling molecules in the TME provided by imaging mass cytometry. Gradient-based counterfactual generation, then, computes perturbations predicted to boost T-cell abundance. We apply our framework to melanoma, colorectal cancer liver metastases, and breast tumor data, discovering combinatorial perturbations predicted to support T-cell infiltration across tens to hundreds of patients. This work presents a paradigm for counterfactual-based prediction and design of cancer therapeutics using spatial omics data.

Aman Bhargava, Cameron Witkowski, Alexander Detkov et al.

Two primary ways to change LLM behavior are prompting and weight updates (e.g., fine-tuning). Prompting LLMs is simple and effective, specifying the desired changes explicitly in natural language, whereas weight updates provide more expressive and permanent behavior changes, specified implicitly via training on large datasets. We present a technique for "baking" prompts into the weights of an LLM. Prompt Baking converts a prompt $u$ and initial weights $θ$ to a new set of weights $θ_u$ such that new "baked" LLM behaves like the original prompted LLM. Mathematically, we minimize the KL divergence between $P_θ(\cdot | u)$ and $P_{θ_u}(\cdot)$, where $P$ is the LLM's probability distribution over token sequences. Across all our experiments, we find prompts can be readily baked into weight updates. Baking chain-of-thought prompts improves zero-shot performance on GSM8K, ASDiv, MBPP, ARC-Easy, ARC-Challenge, and CommonsenseQA benchmarks. Baking news headlines directly updates an LLM's knowledge. And baking instructions & personas alleviates "prompt forgetting" over long sequences. Furthermore, stopping baking early creates "half-baked" models, continuously scaling prompt strength. Baked models retain their sensitivity to further prompting and baking, including re-prompting with the baked-in prompt. Surprisingly, the re-prompted models yield further performance gains in instruction following, as well as math reasoning and coding benchmarks. Taking re-prompting and re-baking to the limit yields a form of iterative self-improvement we call Prompt Pursuit, and preliminary results on instruction following exhibit dramatic performance gains. Finally, we discuss implications for AI safety, continuous model updating, enhancing real-time learning capabilities in LLM-based agents, and generating more stable AI personas.

Pantelis Vafidis, Aman Bhargava, Antonio Rangel

Intelligent perception and interaction with the world hinges on internal representations that capture its underlying structure (''disentangled'' or ''abstract'' representations). Disentangled representations serve as world models, isolating latent factors of variation in the world along approximately orthogonal directions, thus facilitating feature-based generalization. We provide experimental and theoretical results guaranteeing the emergence of disentangled representations in agents that optimally solve multi-task evidence accumulation classification tasks, canonical in the neuroscience literature. The key conceptual finding is that, by producing accurate multi-task classification estimates, a system implicitly represents a set of coordinates specifying a disentangled representation of the underlying latent state of the data it receives. The theory provides conditions for the emergence of these representations in terms of noise, number of tasks, and evidence accumulation time. We experimentally validate these predictions in RNNs trained to multi-task, which learn disentangled representations in the form of continuous attractors, leading to zero-shot out-of-distribution (OOD) generalization in predicting latent factors. We demonstrate the robustness of our framework across autoregressive architectures, decision boundary geometries and in tasks requiring classification confidence estimation. We find that transformers are particularly suited for disentangling representations, which might explain their unique world understanding abilities. Overall, our framework establishes a formal link between competence at multiple tasks and the formation of disentangled, interpretable world models in both biological and artificial systems, and helps explain why ANNs often arrive at human-interpretable concepts, and how they both may acquire exceptional zero-shot generalization capabilities.

Aman Bhargava, Alice X. Zhou, Adam Carnaffan et al.

The vibrations generated from scratching and tapping on surfaces can be highly expressive and recognizable, and have therefore been proposed as a method of natural user interface (NUI). Previous systems require custom sensor hardware such as contact microphones and have struggled with gesture classification accuracy. We propose a deep learning approach to scratch input. Using smartphones and tablets laid on tabletops or other similar surfaces, our system achieved a gesture classification accuracy of 95.8\%, substantially reducing gesture misclassification from previous works. Further, our system achieved this performance when tested on a wide variety of surfaces, mobile devices, and in high noise environments. The results indicate high potential for the application of deep learning techniques to natural user interface (NUI) systems that can readily convert large unpowered surfaces into a user interface using just a smartphone with no special-purpose sensors or hardware.

Aman Bhargava, Mohammad R. Rezaei, Milad Lankarany

An ongoing challenge in neural information processing is: how do neurons adjust their connectivity to improve task performance over time (i.e., actualize learning)? It is widely believed that there is a consistent, synaptic-level learning mechanism in specific brain regions that actualizes learning. However, the exact nature of this mechanism remains unclear. Here we propose an algorithm based on reinforcement learning (RL) to generate and apply a simple synaptic-level learning policy for multi-layer perceptron (MLP) models. In this algorithm, the action space for each MLP synapse consists of a small increase, decrease, or null action on the synapse weight, and the state for each synapse consists of the last two actions and reward signals. A binary reward signal indicates improvement or deterioration in task performance. The static policy produces superior training relative to the adaptive policy and is agnostic to activation function, network shape, and task. Trained MLPs yield character recognition performance comparable to identically shaped networks trained with gradient descent. 0 hidden unit character recognition tests yielded an average validation accuracy of 88.28%, 1.86$\pm$0.47% higher than the same MLP trained with gradient descent. 32 hidden unit character recognition tests yielded an average validation accuracy of 88.45%, 1.11$\pm$0.79% lower than the same MLP trained with gradient descent. The robustness and lack of reliance on gradient computations opens the door for new techniques for training difficult-to-differentiate artificial neural networks such as spiking neural networks (SNNs) and recurrent neural networks (RNNs). Further, the method's simplicity provides a unique opportunity for further development of local rule-driven multi-agent connectionist models for machine intelligence analogous to cellular automata.