BPC by chatGPT <3

gistfile1.txt

i need help with the following document 

•	Broadening Participation in Computing plan, must include roles for all PIs and co-PIs. 
o	Each plan should begin with the heading “Broadening Participation in Computing (BPC) Plan –” followed by either “Standalone” or “Connected”.
	A Standalone BPC Plan does not include Departmental BPC Plans. Instead, the BPC activities of all PIs are listed in a single document that is up to 3 pages for the whole project and specifically addresses all five elements of a BPC plan: (1) the goal and context of the proposed activity, (2) intended population(s), (3) strategy, (4) measurement, and (5) PI engagement. This option must be used if one or more of the collaborating institutions do not have a Departmental BPC Plan verified by BPCnet.
	A Connected BPC Plan may be used when each PI and co-PI will engage in an activity listed in a Verified Departmental BPC Plan from their institution. Note that the (1) goal and context, (2) intended population, (3) strategy, and (4) measurement are already addressed in Verified Departmental BPC Plans. Connected BPC Plan only has to address the following, organized as:
•	up to 2 pages that describe (5) what strategies in the departmental plan the PI and co-PIs will focus on, their specific roles, and their preparation for their work;
	To be followed by the verified Departmental BPC Plans from each institution.
o	Should answer positively to the following five elements
	Goal and Context: Does the plan describe a goal and the data from your institution(s) or local community that justifies that goal?
	Intended population(s): Does the plan identify the characteristics of participants from an underrepresented group listed above, including school level (e.g., African American undergraduates or female high-school students)?
	Strategy: Does the plan describe activities that address the stated goal(s) and intended population(s)?
	Measurement: Is there a plan to measure the outcome(s) of the activities?
	PI Engagement: Is there a clear role for each PI and co-PI? Does the plan describe how the PI is prepared (or will prepare or collaborate) to do the proposed work?

this is an NSF proposal that's collaborative among PI Papailiopoulos (UW-Madison), PI Oymak (UMichigan), and PI Lee (Princeton).

whatever inforamtion youi can use from the bvelow research use it, what you can't find make up to be believable
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%\vspace{-0.3cm}
\section*{Introduction}


Transformers (TFs) have recently gained significant traction in machine learning tasks, establishing state-of-the-art results in Natural Language Processing (NLP) and Computer Vision (CV)~\cite{vaswani2017attention,khan2022transformers,yuan2021tokens,dosovitskiy2020image}. Their attention mechanisms, attributed to part of their success, can capture higher-order relationships and long-range dependencies, making them highly effective in tasks such as machine translation and language modeling~\cite{vaswani2017attention,kenton2019bert}. 

One of the most remarkable aspects of Large Language Models (LLMs) such as GPT-3/4, PaLM, and LaMDA, which are all based on transformer architectures, is their ability to demonstrate emergent reasoning properties as the scale of training data and model size increases~\cite{brown2020language, chowdhery2022palm, thoppilan2022lamda}. These capabilities pertain to numerous downstream tasks, including language and code translation,  basic arithmetic operations and problem solving, and complex question answering; these tasks are not explicitly incorporated in the training objective~\cite{webb2022emergent, nye2021show, wei2022chain, shi2022language, wang2022self, srivastava2022beyond, chen2023teaching}. The key utility of these emergent abilities lies in their potential to {\it bypass the need for model fine-tuning} to perform such tasks. In the past, a base model would need to undergo extensive fine-tuning to acquire these skills. However, with the advent of modern LLMs, a base model can effectively serve as a {\it universal reasoning engine} without the need for weight fine-tuning, as long as an appropriate prompt (\ie model input) is presented that urges the model to perform the task of interest.

These emergent abilities are intriguing because they are not explicitly built into the model's training objective. They arise from training procedures that usually employ an auto-regressive, next-token-prediction loss, commonly defined as the cross-entropy loss between predicted and actual subsequent tokens, based on a conditional probability induced by a parameterised model on a given sequence of tokens $x_1, x_2, \dots, x_n$. For a model parameterized by $\mathbf{W}$, the auto-regressive loss is as follows: $$\mathcal{L}(\mathbf{W}, {\bf x}) = -\sum_{i=1}^{n-1} \log P_{\mathbf{W}}(x_{i+1}|x_1, x_2, \dots, x_i).$$ This loss function does not inherently optimize for specific tasks due to its unsupervised nature. Instead, it focuses on generating plausible tokens, given the prior sequence of tokens as input, regardless of the task's nature or context. Therefore, it is surprising that this loss can implicitly encourage the model to comprehend the underlying logic or reasoning required for intricate tasks like arithmetic operations or semantic understanding for translation.


The emergence of compositional reasoning as a powerful capability in Large Language Models (LLMs) serves as the main focus of this proposal. Compositional reasoning, viewed through the lens of the Chain of Thought (CoT), enables LLMs to tackle complex tasks by decomposing them into a series of intermediate reasoning steps. In this approach, a target function is divided into a sequence of simpler functions, allowing the model to process and combine these functions in a stepwise manner. For example, instead of directly learning a complex function $f_T(f_{T-1}(...(f_1(x))))$, the model learns to reason by first applying $f_1(x)$, then $f_2(f_1(x))$, and so on, until the final output is produced. CoT prompting not only includes input-output pairs but also intermediate reasoning steps in the provided examples, enabling LLMs to learn and generate these thought chains. This emergent capability is especially intriguing since it allows LLMs to serve as universal reasoning engines without the need for extensive fine-tuning and offers a more interpretable insight into the model's behavior.

Our research, motivated by the potential of compositional reasoning and its impact on the downstream capabilities of LLMs, seeks to investigate the theoretical foundations of compositional learning with transformers. We aim to explore the expressive capacity of transformer models when augmented with loops, memory, and external tools, which constitute critical components of compositional logic. In addition, we will examine the statistical properties of autoregressive training using compositional data to understand the limits and benefits of this approach. By studying compositionality from an integrated perspective, our project aims to produce new learning guarantees, algorithms, architectures, and design principles that will significantly advance the development of more capable and interpretable transformer systems, ultimately unlocking their full potential for complex reasoning tasks.



The team brings a targeted and complementary research expertise to accomplish the timely challenges proposed in this project. Relevant to proposed research, the team already has preliminary research on expressivity \cite{giannou2023looped}, sample complexity \cite{li2023transformers,li2023dissecting}, and optimization foundations \cite{malladi2023finetuning} of transformers; spanning topics of in-context learning \cite{li2023transformers}, compositionality and looping \cite{giannou2023looped,yang2023looped, li2023dissecting}, optimization geometry \cite{damian2023smoothing,jin2023understanding,du2018power}, and efficient algorithms \cite{wang2021pufferfish,wang2023cuttlefish,malladi2023finetuning,yang2023predictive}. 




\begin{figure}[t]
%\vspace{-0.5cm}
\centering
\begin{tikzpicture}
\node at (0,0) {\includegraphics[width=0.98\linewidth]{fig/medium_overview.pdf}};
\node at (-8.15,1.2) [rotate=0,anchor=west,scale=1]{\tiny{$\bullet$ \text{How can \textbf{loops and memory} augment frozen LLMs?}}};
\node at (-8.15,0.9) [rotate=0,anchor=west,scale=1]{\tiny{$\bullet$ To what extent looping can \textbf{enhance expressivity}?}};
\node at (-8.15,0.6) [rotate=0,anchor=west,scale=1]{\tiny{$\bullet$ Enhancing LLMs with \textbf{external tools and new skills}}};
\node at (-2.45,1.3) [rotate=0,anchor=west,scale=1]{\tiny{$\bullet$ \textbf{Statistical limits} of compositional learning}};
\node at (-2.45,1.0) [rotate=0,anchor=west,scale=1]{\tiny{$\bullet$ Can compositionality enable \textbf{out-of-distribution}}};
\node at (-2.25,0.75) [rotate=0,anchor=west,scale=1]{\tiny{generalization to novel problems?}};
\node at (-2.45,0.45) [rotate=0,anchor=west,scale=1]{\tiny{$\bullet$ The role of \textbf{attention and skills} in generalization?}};
\node at (3.0,1.2) [rotate=0,anchor=west,scale=1]{\tiny{$\bullet$ How does compositionality catalyze optimization?}};
\node at (3.0,0.9) [rotate=0,anchor=west,scale=1]{\tiny{$\bullet$ What compositional data models SGD can learn?}};
\node at (3.0,0.6) [rotate=0,anchor=west,scale=1]{\tiny{$\bullet$ Harnessing compositional struture in fine-tuning}};
\end{tikzpicture}
\caption{\small This project will develop theoretical foundations of compositional learning with transformers through approximation, optimization, and statistical viewpoints. By studying compositionality from an integrated perspective, the project will yield new learning guarantees, algorithms, architectures, and design principles that will significantly advance the development of more capable and interpretable transformer systems.}
\label{fig:overview}
\vspace{-0.1cm}
\end{figure}


\subsection*{Intellectual Merit}
This research project focuses on the theoretical foundations that characterize and enhance the compositional learning capabilities of transformer models, with key areas including model expressivity, statistical learning theory, and optimization. The project will result in both theoretical breakthroughs and practical algorithms that improve transformer efficiency and reasoning abilities, offering valuable insights into transformer intelligence and guiding the design of more capable artificial intelligence systems.

The intellectual merit of the project lies in its multidisciplinary approach, combining expertise from various fields such as machine learning theory, optimization, statistics, approximation theory, and deep learning. By investigating the theoretical underpinnings of compositional reasoning techniques and examining optimization geometry and generalization properties of transformers, this research project promises substantial advancements in the development of more data-efficient, robust, and interpretable AI systems.

The broader impacts of this research project extend beyond theoretical contributions, integrating research findings into academic curricula and fostering a diverse and informed community around transformer models and their applications. By running an inclusive Research Experience for Undergraduates program and engaging with the local community through hands-on public events, interactive exhibits, and extended STEM learning activities, the project will cultivate widespread educational enrichment and further conversations around the responsible application of AI systems. Additionally, cross-disciplinary workshops and events will provide a platform for experts from theory, practice, academia, and industry to collaborate and exchange knowledge in the area of large language models.

The following thrusts summarize our \textbf{basic research objectives}:

\begin{itemize}
\item \textbf{\redd{Thrust I: Expressive Capacity of Augmented Transformers.}} 
This thrust focuses on exploring the expressive capacity of transformers augmented with loops, longer context, external memory, and specific skills. This research aims to better understand the in-context learning capabilities of large language models (LLMs), which have shown impressive emergent reasoning abilities through chain-of-thought prompting. However, the underlying mechanics of these capabilities remain largely unexplored. By incorporating loop constructs and recursion, along with external memory, this thrust seeks to enhance the compositional logic and expressive capacity of LLMs.

\item \textbf{\redd{Thrust II: Statistical Foundations of Compositional Learning.}} Focusing on the statistical aspects of compositional learning in autoregressive transformer models, this thrust addresses key questions concerning sample efficiency, skill reusability, problem decomposition, and out-of-distribution generalization. By analyzing the statistical limits and benefits of autoregressive training with compositional data, this research aims to unveil the reasoning capabilities of these models, particularly in their ability to tackle novel, complex tasks. The proposed "Zero-Shot Compositional Learning (ZCL)" theory will explore the role of skill acquisition, selection, and attention mechanisms in zero-shot generalization, fostering a deeper understanding of transformer intelligence.


%draws inspiration from the mixture-of-experts literature, this theory conceptualizes an autoregressive language model as a 'mixture-of-skills,' allowing the model to selectively apply these skills to various tasks. 
\item \textbf{\redd{Thrust III: Optimization Theory and Algorithms for Transformers.}} This thrust targets the development of next-generation optimization theories and algorithms for transformers that leverage compositionality. We will investigate the role of compositional data in accelerating optimization and uncover the optimization geometry of transformers when trained by Stochastic Gradient Descent (SGD). Additionally, we plan to develop efficient compositional zeroth-order optimization methods that compete with SGD while offering affordability and accessibility advantages. These findings will not only advance optimization foundations but also illuminate the synergies between compositionality and optimization, paving the way for innovative zeroth-order methods in training and deploying transformers.

\end{itemize}




\subsection*{Qualifications of the team}



%

\textbf{PI Papailiopoulos (DP)} is an Associate Professor at the University of Wisconsin, Madison. He brings unique expertise in large-scale optimization techniques, information theory, large language models. \textbf{PI Oymak (SO)} is an Assistant Professor at the University of Michigan, Ann Arbor, with an expertise in optimization theory, statistical learning theory, and temporally-dependent/sequential data. \textbf{PI Lee (JDL)} is an Associate Professor at Princeton University, with an expertise in deep learning, statistics, and optimization theory. The PIs have a strong track record of working together that lays the groundwork for this project. PIs DP and SO have co-authored some of the first rigorous guarantees on in-context learning and chain-of-thought ability of transformers \cite{li2023transformers,li2023dissecting}. PIs DP and JDL developed the \emph{looped transformers} framework \cite{giannou2023looped} and demonstrated the benefit of compositionality for accelerated transformer training \cite{lee2023teaching}. The team has strong complementary expertise in all aspects of machine learning theory (optimization, approximation, statistics) and is uniquely positioned to accomplish this project. The PIs also have a history of organizing conferences (\eg MLSys), workshops at top ML venues (ICML, NeurIPS, and Dagtuhl), and seminars on topics related to this project.




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\section{Broader Impacts}

Our program will offer a paradigm shift in the way that compositional learning with language models is approached, with a focus on understanding compositional reasoning in LLMs. The resulting theory will have broad impacts on the choice of model architecture, on augmenting current models with additional skills, and on the diversity of ways that LLMs are used as reasoning engines. Moreover, the proposed broadening participation activities emphasize accessibility and broad dissemination, via 1) curriculum development; 2) interdisciplinary workshops; 3) outreach activities for youth.

\vspace{-0.15cm}
\paragraph{Curriculum Development:} The PIs aim to attract a wider group of graduate students to the mathematical foundations of deep learning and transformers by incorporating the results of the project and recent advances in the field into their existing courses on optimization, ML, and data science. The PIs will also collaboratively design a new graduate-level course titled “Foundations of Transformers and Large Language Models”. This is a course that is largely useful, but absent from current curricula; the aim is to emphasize on foundational advances, mathematical background (statistics, optimization), and broader applications (beyond NLP and vision) to signal processing and control/RL.

\vspace{-0.1cm}
\paragraph{Research Dissemination:} We will publish results from our work at a variety of top-tier machine learning, deep learning, and information theory meetings (e.g., NeurIPS, ICML, ICLR, MLSys). The PIs have a strong track record across all these venues. As discussed in the data management plan, we plan to release free, publicly available, open-source software implementations of our algorithms and data generated by the project.

\vspace{-0.1cm}
\paragraph{Fostering Interdisciplinarity:} The PIs are actively involved in bridging interdisciplinary divides in their research and teaching. Students from a variety of departments participate in their courses. The PI Papailiopoulos is part of the organizing team of a weekly lunch meeting called SILO seminars (Systems, Information, Learning, and Optimization), hosting presentations by visiting researchers from departments including CS, ECE, Math, Statistics, and more. Bringing researchers across different fields in the greater midwest area will also be a focus of our activities, as PI Papailiopoulos was the program co-chair for the 2019 Midwest Machine Learning Symposium that gathered more than 300 participants, and has been a cofounder of the Machine Learning and Systems (MLSys) conference currently running its 7th year with more than 700 participants. 

\vspace{-0.2cm}
\paragraph{Workshop and Conference Organization:} As part of our disseminating and interdisciplinarity efforts, the PIs will submit a Foundations of Large Language Models Workshop in ICML and NeurIPS 2024 and 2025, respectively. PI Papailiopoulos has a history of co-organizing events that bridge the areas of machine learning and coding and information theory, such as a Dagstuhl Workshop 18112, "Coding Theory for Inference, Learning and Optimization," and the first Coding for ML workshop, in ICML 2019. PI Oymak has organized an ICASSP tutorial on ``High-Dimensional Phenomena in Estimation and Learning''.

\vspace{-0.2cm}
\paragraph{Outreach Programs:} The team of PIs plans to conduct several outreach activities across the three institutions. PI Papailiopoulos plans to base his outreach activities on an already established rich outreach program at UW-Madison through the Wisconsin Institute for Discovery (WID), which offers extensive support programs for women and URM students. The PI will collaborate with Discovery Outreach at UW, a collaboration of the Morgridge Institute for Research and the Wisconsin Alumni Research Foundation, to organize a Saturday Science program centered around the theme of fairness in ML. In 2017, more than 12,000 people attended Saturday Science programs designed for families and children ages 5 to 13.

PI Oymak will work with SURE and Engineering OnRamp at Michigan for K-12 outreach. PI Oymak has previously advised Hispanic students from community colleges through UC Riverside's RISE program and organized undergraduate ML workshops, including those targeted towards female students.

PI Lee will work with high school teachers to develop a machine learning curriculum that can be taught in public high school classrooms. This work will be done in collaboration with the Princeton Teachers as Scholars Program (PTSP), led by Dr. Anne Catena. PTSP has extensive experience organizing seminars with faculty instructors and high school teachers. It works with 14 different school districts across central NJ, including many from minority communities and socioeconomically disadvantaged districts, such as the Camden and Trenton school districts.

\vspace{-0.2cm}
\paragraph{Improving Disability Accommodation in Academia:} As a disabled faculty member who suffers from fibromyalgia, low-vision, mobility impairments, and chronic fatigue, and a member of Disability in AI, PI Lee has invaluable firsthand experience with disability accommodations. He is working towards improving these accommodations and raising awareness of ableism in academia. 

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\paragraph{Collaboration with Industry Partners:} The PIs have a track record of translating new theory and methods into practice, both in academia and industry. For example, PI Papailiopoulos collaborated with researchers at Facebook to apply state-of-the-art distributed data storage solutions to improve data availability and system reliability. The presented methods and algorithms will be tested in real AI systems through existing collaborations with Google Deepmind, Anthropic, and Microsoft Research, ensuring that the developed solutions have practical applications and can be integrated into real-world systems.

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\paragraph{Mentoring and Supporting Students:} The PIs are committed to mentoring and supporting students from diverse backgrounds, including women and underrepresented minorities. They will provide research opportunities, guidance, and resources to help students succeed in their academic and professional careers. By fostering an inclusive and supportive environment, the PIs aim to increase diversity and representation in the field of machine learning.

In conclusion, the broader impacts of this proposal span various aspects, including curriculum development, research dissemination, fostering interdisciplinarity, outreach programs, improving disability accommodation in academia, collaboration with industry partners, and mentoring and supporting students. The PIs are committed to ensuring that the results of this project have a lasting and positive impact on the field of machine learning, as well as on the students and communities they engage with.
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again the instructions for you are

i need help with the following document 

•	Broadening Participation in Computing plan, must include roles for all PIs and co-PIs. 
o	Each plan should begin with the heading “Broadening Participation in Computing (BPC) Plan –” followed by either “Standalone” or “Connected”.
	A Standalone BPC Plan does not include Departmental BPC Plans. Instead, the BPC activities of all PIs are listed in a single document that is up to 3 pages for the whole project and specifically addresses all five elements of a BPC plan: (1) the goal and context of the proposed activity, (2) intended population(s), (3) strategy, (4) measurement, and (5) PI engagement. This option must be used if one or more of the collaborating institutions do not have a Departmental BPC Plan verified by BPCnet.
	A Connected BPC Plan may be used when each PI and co-PI will engage in an activity listed in a Verified Departmental BPC Plan from their institution. Note that the (1) goal and context, (2) intended population, (3) strategy, and (4) measurement are already addressed in Verified Departmental BPC Plans. Connected BPC Plan only has to address the following, organized as:
•	up to 2 pages that describe (5) what strategies in the departmental plan the PI and co-PIs will focus on, their specific roles, and their preparation for their work;
	To be followed by the verified Departmental BPC Plans from each institution.
o	Should answer positively to the following five elements
	Goal and Context: Does the plan describe a goal and the data from your institution(s) or local community that justifies that goal?
	Intended population(s): Does the plan identify the characteristics of participants from an underrepresented group listed above, including school level (e.g., African American undergraduates or female high-school students)?
	Strategy: Does the plan describe activities that address the stated goal(s) and intended population(s)?
	Measurement: Is there a plan to measure the outcome(s) of the activities?
	PI Engagement: Is there a clear role for each PI and co-PI? Does the plan describe how the PI is prepared (or will prepare or collaborate) to do the proposed work?


i want you to write it in latex, and i want you to prepare it based on this intro of an nsf proposal

this is an NSF proposal that's collaborative among PI Papailiopoulos (UW-Madison), PI Oymak (UMichigan), and PI Lee (Princeton).
some info Papailiopoulos will lead T1 and contribute to T2 and T3, and the two other PIs will mostly work on T2 and T3
whatever inforamtion youi can use from the bvelow research use it, what you can't find make up to be believable