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diff --git a/paper/checklist.tex b/paper/checklist.tex new file mode 100644 index 0000000..5ee6914 --- /dev/null +++ b/paper/checklist.tex @@ -0,0 +1,251 @@ +\section*{NeurIPS Paper Checklist} + +%%% BEGIN INSTRUCTIONS %%% +The checklist is designed to encourage best practices for responsible machine learning research, addressing issues of reproducibility, transparency, research ethics, and societal impact. Do not remove the checklist: {\bf The papers not including the checklist will be desk rejected.} The checklist should follow the references and follow the (optional) supplemental material. The checklist does NOT count towards the page +limit. + +Please read the checklist guidelines carefully for information on how to answer these questions. For each question in the checklist: +\begin{itemize} + \item You should answer \answerYes{}, \answerNo{}, or \answerNA{}. + \item \answerNA{} means either that the question is Not Applicable for that particular paper or the relevant information is Not Available. + \item Please provide a short (1--2 sentence) justification right after your answer (even for \answerNA). + % \item {\bf The papers not including the checklist will be desk rejected.} +\end{itemize} + +{\bf The checklist answers are an integral part of your paper submission.} They are visible to the reviewers, area chairs, senior area chairs, and ethics reviewers. You will also be asked to include it (after eventual revisions) with the final version of your paper, and its final version will be published with the paper. + +The reviewers of your paper will be asked to use the checklist as one of the factors in their evaluation. While \answerYes{} is generally preferable to \answerNo{}, it is perfectly acceptable to answer \answerNo{} provided a proper justification is given (e.g., error bars are not reported because it would be too computationally expensive'' or ``we were unable to find the license for the dataset we used''). In general, answering \answerNo{} or \answerNA{} is not grounds for rejection. While the questions are phrased in a binary way, we acknowledge that the true answer is often more nuanced, so please just use your best judgment and write a justification to elaborate. All supporting evidence can appear either in the main paper or the supplemental material, provided in appendix. If you answer \answerYes{} to a question, in the justification please point to the section(s) where related material for the question can be found. + +IMPORTANT, please: +\begin{itemize} + \item {\bf Delete this instruction block, but keep the section heading ``NeurIPS Paper Checklist"}, + \item {\bf Keep the checklist subsection headings, questions/answers and guidelines below.} + \item {\bf Do not modify the questions and only use the provided macros for your answers}. +\end{itemize} + + +%%% END INSTRUCTIONS %%% + + +\begin{enumerate} + +\item {\bf Claims} + \item[] Question: Do the main claims made in the abstract and introduction accurately reflect the paper's contributions and scope? + \item[] Answer: \answerTODO{} % Replace by \answerYes{}, \answerNo{}, or \answerNA{}. + \item[] Justification: \justificationTODO{} + \item[] Guidelines: + \begin{itemize} + \item The answer \answerNA{} means that the abstract and introduction do not include the claims made in the paper. + \item The abstract and/or introduction should clearly state the claims made, including the contributions made in the paper and important assumptions and limitations. A \answerNo{} or \answerNA{} answer to this question will not be perceived well by the reviewers. + \item The claims made should match theoretical and experimental results, and reflect how much the results can be expected to generalize to other settings. + \item It is fine to include aspirational goals as motivation as long as it is clear that these goals are not attained by the paper. + \end{itemize} + +\item {\bf Limitations} + \item[] Question: Does the paper discuss the limitations of the work performed by the authors? + \item[] Answer: \answerTODO{} % Replace by \answerYes{}, \answerNo{}, or \answerNA{}. + \item[] Justification: \justificationTODO{} + \item[] Guidelines: + \begin{itemize} + \item The answer \answerNA{} means that the paper has no limitation while the answer \answerNo{} means that the paper has limitations, but those are not discussed in the paper. + \item The authors are encouraged to create a separate ``Limitations'' section in their paper. + \item The paper should point out any strong assumptions and how robust the results are to violations of these assumptions (e.g., independence assumptions, noiseless settings, model well-specification, asymptotic approximations only holding locally). The authors should reflect on how these assumptions might be violated in practice and what the implications would be. + \item The authors should reflect on the scope of the claims made, e.g., if the approach was only tested on a few datasets or with a few runs. In general, empirical results often depend on implicit assumptions, which should be articulated. + \item The authors should reflect on the factors that influence the performance of the approach. For example, a facial recognition algorithm may perform poorly when image resolution is low or images are taken in low lighting. Or a speech-to-text system might not be used reliably to provide closed captions for online lectures because it fails to handle technical jargon. + \item The authors should discuss the computational efficiency of the proposed algorithms and how they scale with dataset size. + \item If applicable, the authors should discuss possible limitations of their approach to address problems of privacy and fairness. + \item While the authors might fear that complete honesty about limitations might be used by reviewers as grounds for rejection, a worse outcome might be that reviewers discover limitations that aren't acknowledged in the paper. The authors should use their best judgment and recognize that individual actions in favor of transparency play an important role in developing norms that preserve the integrity of the community. Reviewers will be specifically instructed to not penalize honesty concerning limitations. + \end{itemize} + +\item {\bf Theory assumptions and proofs} + \item[] Question: For each theoretical result, does the paper provide the full set of assumptions and a complete (and correct) proof? + \item[] Answer: \answerTODO{} % Replace by \answerYes{}, \answerNo{}, or \answerNA{}. + \item[] Justification: \justificationTODO{} + \item[] Guidelines: + \begin{itemize} + \item The answer \answerNA{} means that the paper does not include theoretical results. + \item All the theorems, formulas, and proofs in the paper should be numbered and cross-referenced. + \item All assumptions should be clearly stated or referenced in the statement of any theorems. + \item The proofs can either appear in the main paper or the supplemental material, but if they appear in the supplemental material, the authors are encouraged to provide a short proof sketch to provide intuition. + \item Inversely, any informal proof provided in the core of the paper should be complemented by formal proofs provided in appendix or supplemental material. + \item Theorems and Lemmas that the proof relies upon should be properly referenced. + \end{itemize} + + \item {\bf Experimental result reproducibility} + \item[] Question: Does the paper fully disclose all the information needed to reproduce the main experimental results of the paper to the extent that it affects the main claims and/or conclusions of the paper (regardless of whether the code and data are provided or not)? + \item[] Answer: \answerTODO{} % Replace by \answerYes{}, \answerNo{}, or \answerNA{}. + \item[] Justification: \justificationTODO{} + \item[] Guidelines: + \begin{itemize} + \item The answer \answerNA{} means that the paper does not include experiments. + \item If the paper includes experiments, a \answerNo{} answer to this question will not be perceived well by the reviewers: Making the paper reproducible is important, regardless of whether the code and data are provided or not. + \item If the contribution is a dataset and\slash or model, the authors should describe the steps taken to make their results reproducible or verifiable. + \item Depending on the contribution, reproducibility can be accomplished in various ways. For example, if the contribution is a novel architecture, describing the architecture fully might suffice, or if the contribution is a specific model and empirical evaluation, it may be necessary to either make it possible for others to replicate the model with the same dataset, or provide access to the model. In general. releasing code and data is often one good way to accomplish this, but reproducibility can also be provided via detailed instructions for how to replicate the results, access to a hosted model (e.g., in the case of a large language model), releasing of a model checkpoint, or other means that are appropriate to the research performed. + \item While NeurIPS does not require releasing code, the conference does require all submissions to provide some reasonable avenue for reproducibility, which may depend on the nature of the contribution. For example + \begin{enumerate} + \item If the contribution is primarily a new algorithm, the paper should make it clear how to reproduce that algorithm. + \item If the contribution is primarily a new model architecture, the paper should describe the architecture clearly and fully. + \item If the contribution is a new model (e.g., a large language model), then there should either be a way to access this model for reproducing the results or a way to reproduce the model (e.g., with an open-source dataset or instructions for how to construct the dataset). + \item We recognize that reproducibility may be tricky in some cases, in which case authors are welcome to describe the particular way they provide for reproducibility. In the case of closed-source models, it may be that access to the model is limited in some way (e.g., to registered users), but it should be possible for other researchers to have some path to reproducing or verifying the results. + \end{enumerate} + \end{itemize} + + +\item {\bf Open access to data and code} + \item[] Question: Does the paper provide open access to the data and code, with sufficient instructions to faithfully reproduce the main experimental results, as described in supplemental material? + \item[] Answer: \answerTODO{} % Replace by \answerYes{}, \answerNo{}, or \answerNA{}. + \item[] Justification: \justificationTODO{} + \item[] Guidelines: + \begin{itemize} + \item The answer \answerNA{} means that paper does not include experiments requiring code. + \item Please see the NeurIPS code and data submission guidelines (\url{https://neurips.cc/public/guides/CodeSubmissionPolicy}) for more details. + \item While we encourage the release of code and data, we understand that this might not be possible, so \answerNo{} is an acceptable answer. Papers cannot be rejected simply for not including code, unless this is central to the contribution (e.g., for a new open-source benchmark). + \item The instructions should contain the exact command and environment needed to run to reproduce the results. See the NeurIPS code and data submission guidelines (\url{https://neurips.cc/public/guides/CodeSubmissionPolicy}) for more details. + \item The authors should provide instructions on data access and preparation, including how to access the raw data, preprocessed data, intermediate data, and generated data, etc. + \item The authors should provide scripts to reproduce all experimental results for the new proposed method and baselines. If only a subset of experiments are reproducible, they should state which ones are omitted from the script and why. + \item At submission time, to preserve anonymity, the authors should release anonymized versions (if applicable). + \item Providing as much information as possible in supplemental material (appended to the paper) is recommended, but including URLs to data and code is permitted. + \end{itemize} + + +\item {\bf Experimental setting/details} + \item[] Question: Does the paper specify all the training and test details (e.g., data splits, hyperparameters, how they were chosen, type of optimizer) necessary to understand the results? + \item[] Answer: \answerTODO{} % Replace by \answerYes{}, \answerNo{}, or \answerNA{}. + \item[] Justification: \justificationTODO{} + \item[] Guidelines: + \begin{itemize} + \item The answer \answerNA{} means that the paper does not include experiments. + \item The experimental setting should be presented in the core of the paper to a level of detail that is necessary to appreciate the results and make sense of them. + \item The full details can be provided either with the code, in appendix, or as supplemental material. + \end{itemize} + +\item {\bf Experiment statistical significance} + \item[] Question: Does the paper report error bars suitably and correctly defined or other appropriate information about the statistical significance of the experiments? + \item[] Answer: \answerTODO{} % Replace by \answerYes{}, \answerNo{}, or \answerNA{}. + \item[] Justification: \justificationTODO{} + \item[] Guidelines: + \begin{itemize} + \item The answer \answerNA{} means that the paper does not include experiments. + \item The authors should answer \answerYes{} if the results are accompanied by error bars, confidence intervals, or statistical significance tests, at least for the experiments that support the main claims of the paper. + \item The factors of variability that the error bars are capturing should be clearly stated (for example, train/test split, initialization, random drawing of some parameter, or overall run with given experimental conditions). + \item The method for calculating the error bars should be explained (closed form formula, call to a library function, bootstrap, etc.) + \item The assumptions made should be given (e.g., Normally distributed errors). + \item It should be clear whether the error bar is the standard deviation or the standard error of the mean. + \item It is OK to report 1-sigma error bars, but one should state it. The authors should preferably report a 2-sigma error bar than state that they have a 96\% CI, if the hypothesis of Normality of errors is not verified. + \item For asymmetric distributions, the authors should be careful not to show in tables or figures symmetric error bars that would yield results that are out of range (e.g., negative error rates). + \item If error bars are reported in tables or plots, the authors should explain in the text how they were calculated and reference the corresponding figures or tables in the text. + \end{itemize} + +\item {\bf Experiments compute resources} + \item[] Question: For each experiment, does the paper provide sufficient information on the computer resources (type of compute workers, memory, time of execution) needed to reproduce the experiments? + \item[] Answer: \answerTODO{} % Replace by \answerYes{}, \answerNo{}, or \answerNA{}. + \item[] Justification: \justificationTODO{} + \item[] Guidelines: + \begin{itemize} + \item The answer \answerNA{} means that the paper does not include experiments. + \item The paper should indicate the type of compute workers CPU or GPU, internal cluster, or cloud provider, including relevant memory and storage. + \item The paper should provide the amount of compute required for each of the individual experimental runs as well as estimate the total compute. + \item The paper should disclose whether the full research project required more compute than the experiments reported in the paper (e.g., preliminary or failed experiments that didn't make it into the paper). + \end{itemize} + +\item {\bf Code of ethics} + \item[] Question: Does the research conducted in the paper conform, in every respect, with the NeurIPS Code of Ethics \url{https://neurips.cc/public/EthicsGuidelines}? + \item[] Answer: \answerTODO{} % Replace by \answerYes{}, \answerNo{}, or \answerNA{}. + \item[] Justification: \justificationTODO{} + \item[] Guidelines: + \begin{itemize} + \item The answer \answerNA{} means that the authors have not reviewed the NeurIPS Code of Ethics. + \item If the authors answer \answerNo, they should explain the special circumstances that require a deviation from the Code of Ethics. + \item The authors should make sure to preserve anonymity (e.g., if there is a special consideration due to laws or regulations in their jurisdiction). + \end{itemize} + + +\item {\bf Broader impacts} + \item[] Question: Does the paper discuss both potential positive societal impacts and negative societal impacts of the work performed? + \item[] Answer: \answerTODO{} % Replace by \answerYes{}, \answerNo{}, or \answerNA{}. + \item[] Justification: \justificationTODO{} + \item[] Guidelines: + \begin{itemize} + \item The answer \answerNA{} means that there is no societal impact of the work performed. + \item If the authors answer \answerNA{} or \answerNo, they should explain why their work has no societal impact or why the paper does not address societal impact. + \item Examples of negative societal impacts include potential malicious or unintended uses (e.g., disinformation, generating fake profiles, surveillance), fairness considerations (e.g., deployment of technologies that could make decisions that unfairly impact specific groups), privacy considerations, and security considerations. + \item The conference expects that many papers will be foundational research and not tied to particular applications, let alone deployments. However, if there is a direct path to any negative applications, the authors should point it out. For example, it is legitimate to point out that an improvement in the quality of generative models could be used to generate Deepfakes for disinformation. On the other hand, it is not needed to point out that a generic algorithm for optimizing neural networks could enable people to train models that generate Deepfakes faster. + \item The authors should consider possible harms that could arise when the technology is being used as intended and functioning correctly, harms that could arise when the technology is being used as intended but gives incorrect results, and harms following from (intentional or unintentional) misuse of the technology. + \item If there are negative societal impacts, the authors could also discuss possible mitigation strategies (e.g., gated release of models, providing defenses in addition to attacks, mechanisms for monitoring misuse, mechanisms to monitor how a system learns from feedback over time, improving the efficiency and accessibility of ML). + \end{itemize} + +\item {\bf Safeguards} + \item[] Question: Does the paper describe safeguards that have been put in place for responsible release of data or models that have a high risk for misuse (e.g., pre-trained language models, image generators, or scraped datasets)? + \item[] Answer: \answerTODO{} % Replace by \answerYes{}, \answerNo{}, or \answerNA{}. + \item[] Justification: \justificationTODO{} + \item[] Guidelines: + \begin{itemize} + \item The answer \answerNA{} means that the paper poses no such risks. + \item Released models that have a high risk for misuse or dual-use should be released with necessary safeguards to allow for controlled use of the model, for example by requiring that users adhere to usage guidelines or restrictions to access the model or implementing safety filters. + \item Datasets that have been scraped from the Internet could pose safety risks. The authors should describe how they avoided releasing unsafe images. + \item We recognize that providing effective safeguards is challenging, and many papers do not require this, but we encourage authors to take this into account and make a best faith effort. + \end{itemize} + +\item {\bf Licenses for existing assets} + \item[] Question: Are the creators or original owners of assets (e.g., code, data, models), used in the paper, properly credited and are the license and terms of use explicitly mentioned and properly respected? + \item[] Answer: \answerTODO{} % Replace by \answerYes{}, \answerNo{}, or \answerNA{}. + \item[] Justification: \justificationTODO{} + \item[] Guidelines: + \begin{itemize} + \item The answer \answerNA{} means that the paper does not use existing assets. + \item The authors should cite the original paper that produced the code package or dataset. + \item The authors should state which version of the asset is used and, if possible, include a URL. + \item The name of the license (e.g., CC-BY 4.0) should be included for each asset. + \item For scraped data from a particular source (e.g., website), the copyright and terms of service of that source should be provided. + \item If assets are released, the license, copyright information, and terms of use in the package should be provided. For popular datasets, \url{paperswithcode.com/datasets} has curated licenses for some datasets. Their licensing guide can help determine the license of a dataset. + \item For existing datasets that are re-packaged, both the original license and the license of the derived asset (if it has changed) should be provided. + \item If this information is not available online, the authors are encouraged to reach out to the asset's creators. + \end{itemize} + +\item {\bf New assets} + \item[] Question: Are new assets introduced in the paper well documented and is the documentation provided alongside the assets? + \item[] Answer: \answerTODO{} % Replace by \answerYes{}, \answerNo{}, or \answerNA{}. + \item[] Justification: \justificationTODO{} + \item[] Guidelines: + \begin{itemize} + \item The answer \answerNA{} means that the paper does not release new assets. + \item Researchers should communicate the details of the dataset\slash code\slash model as part of their submissions via structured templates. This includes details about training, license, limitations, etc. + \item The paper should discuss whether and how consent was obtained from people whose asset is used. + \item At submission time, remember to anonymize your assets (if applicable). You can either create an anonymized URL or include an anonymized zip file. + \end{itemize} + +\item {\bf Crowdsourcing and research with human subjects} + \item[] Question: For crowdsourcing experiments and research with human subjects, does the paper include the full text of instructions given to participants and screenshots, if applicable, as well as details about compensation (if any)? + \item[] Answer: \answerTODO{} % Replace by \answerYes{}, \answerNo{}, or \answerNA{}. + \item[] Justification: \justificationTODO{} + \item[] Guidelines: + \begin{itemize} + \item The answer \answerNA{} means that the paper does not involve crowdsourcing nor research with human subjects. + \item Including this information in the supplemental material is fine, but if the main contribution of the paper involves human subjects, then as much detail as possible should be included in the main paper. + \item According to the NeurIPS Code of Ethics, workers involved in data collection, curation, or other labor should be paid at least the minimum wage in the country of the data collector. + \end{itemize} + +\item {\bf Institutional review board (IRB) approvals or equivalent for research with human subjects} + \item[] Question: Does the paper describe potential risks incurred by study participants, whether such risks were disclosed to the subjects, and whether Institutional Review Board (IRB) approvals (or an equivalent approval/review based on the requirements of your country or institution) were obtained? + \item[] Answer: \answerTODO{} % Replace by \answerYes{}, \answerNo{}, or \answerNA{}. + \item[] Justification: \justificationTODO{} + \item[] Guidelines: + \begin{itemize} + \item The answer \answerNA{} means that the paper does not involve crowdsourcing nor research with human subjects. + \item Depending on the country in which research is conducted, IRB approval (or equivalent) may be required for any human subjects research. If you obtained IRB approval, you should clearly state this in the paper. + \item We recognize that the procedures for this may vary significantly between institutions and locations, and we expect authors to adhere to the NeurIPS Code of Ethics and the guidelines for their institution. + \item For initial submissions, do not include any information that would break anonymity (if applicable), such as the institution conducting the review. + \end{itemize} + +\item {\bf Declaration of LLM usage} + \item[] Question: Does the paper describe the usage of LLMs if it is an important, original, or non-standard component of the core methods in this research? Note that if the LLM is used only for writing, editing, or formatting purposes and does \emph{not} impact the core methodology, scientific rigor, or originality of the research, declaration is not required. + %this research? + \item[] Answer: \answerTODO{} % Replace by \answerYes{}, \answerNo{}, or \answerNA{}. + \item[] Justification: \justificationTODO{} + \item[] Guidelines: + \begin{itemize} + \item The answer \answerNA{} means that the core method development in this research does not involve LLMs as any important, original, or non-standard components. + \item Please refer to our LLM policy in the NeurIPS handbook for what should or should not be described. + \end{itemize} + +\end{enumerate}
\ No newline at end of file diff --git a/paper/main.tex b/paper/main.tex new file mode 100644 index 0000000..9b32157 --- /dev/null +++ b/paper/main.tex @@ -0,0 +1,760 @@ +\documentclass{article} + +\usepackage[eandd]{neurips_2026} + +\usepackage[utf8]{inputenc} +\usepackage[T1]{fontenc} +\usepackage{hyperref} +\usepackage{url} +\usepackage{booktabs} +\usepackage{amsfonts} +\usepackage{amsmath} +\usepackage{nicefrac} +\usepackage{microtype} +\usepackage{xcolor} +\usepackage{graphicx} + +\title{Beyond Accuracy and Alignment:\\ A Diagnostic Evaluation Protocol for Feedback Alignment} + +\author{Anonymous Authors} + +\begin{document} + +\maketitle + +\begin{abstract} +Standard evaluation of Feedback Alignment (FA) and related local-credit +methods on modern residual networks reports two numbers: headline accuracy +and the cosine alignment $\Gamma$ of the local credit signal with the true +backpropagation gradient at hidden layers. We show, on standard pre-LayerNorm +ResidualMLP and ViT-Mini architectures, that this evaluation is unreliable +because it conflates two distinct failure modes: \textbf{(1)~measurement +degeneracy via terminal-LayerNorm gradient cancellation}, in which residual +stream growth drives the BP gradient at hidden layers below the numerical +floor and renders the cosine metric uninterpretable; and \textbf{(2)~low +intrinsic credit-direction quality of random feedback}, which persists even +when the BP gradient is in the meaningful regime and is invisible to the +field-standard reporting pair. + +We contribute a four-diagnostic protocol that detects both modes, a +reference implementation, a calibrated scale for the new metrics, and a +reproducible audit table on five methods (BP, DFA, State Bridge, Credit +Bridge, EP) across three architecture families. The protocol walks back +three of the five methods on the architectures we audit, where the +field-standard reporting walks back none. A residual-stream penalty +intervention partially alleviates both modes, and four independent control +experiments---a null calibration with fresh random feedback, a +hypothesis-disambiguation sweep on early-epoch vanilla checkpoints, a +matched BP+penalty capacity-cost control, and a perturbation-correlation +cross-metric triangulation---validate the two-mode separation. We release +the protocol, the audit data, and a reporting template. +\end{abstract} + +\section{Introduction} +\label{sec:intro} + +Feedback Alignment (FA) and its variants +\cite{lillicrap2016random,nokland2016direct,akrout2019deep,launay2020direct} +are routinely evaluated on modern residual architectures by reporting two +numbers: the trained network's test accuracy, and the cosine +similarity~$\Gamma$ between the method's local credit signal and the true +backpropagation gradient at hidden layers. A high $\Gamma$ is interpreted +as evidence that the method is computing useful credit; an above-shallow +accuracy is interpreted as evidence that the deep blocks are being trained. +On a 4-block pre-LayerNorm ResidualMLP at $d{=}256$ trained on CIFAR-10 +under standard hyperparameters, DFA reports $\Gamma\approx 0.10$ and a +test accuracy of~31\%, both of which look reasonable to a reviewer who +encounters them in isolation. + +\textbf{Both numbers can silently mislead.} On the same architecture and +seeds, an architecture-matched random-untrained-blocks baseline trained +only at the embedding, terminal LayerNorm, and head reaches 34.9\% test +accuracy: the trainable-blocks DFA variant under-performs this baseline by +4 percentage points. The deep blocks are not just unhelpful---they are +actively destroying value. Meanwhile, the BP gradient at the deepest hidden +layer of the same trained DFA network has $\|g_L\|\approx 5\times 10^{-10}$, +well below \texttt{F.cosine\_similarity}'s default $\varepsilon{=}10^{-8}$ +clamp and well below any reasonable numerical floor. The reported +$\Gamma\approx 0.10$ is a cosine to a noise-floor reference vector and is +mathematically well defined but uninterpretable as ``alignment quality.'' + +\textbf{Why both numbers fail together turns out to have a single source: +the headline-accuracy and headline-$\Gamma$ pair conflates two distinct +phenomena that the field treats as one.} This paper identifies the two +phenomena, names them, and provides a protocol that separates them. + +\paragraph{The two failure modes (informal).} +\textbf{Mode~1: measurement degeneracy via terminal-LayerNorm gradient +cancellation.} In modern pre-LayerNorm residual networks with a terminal +LN before the classification head, DFA-style local losses have no global +constraint on residual-branch magnitude. Block parameters grow by +$\sim\!95\times$ relative to initialization, the residual stream +$\|h_L\|$ grows from $\sim\!9$ at random init to $\sim\!4\!\times\!10^8$ +over 100 epochs, and the LayerNorm Jacobian rescaling drives the BP +gradient at hidden layers from $\sim\!10^{-3}$ to $\sim\!10^{-10}$. The +cosine alignment metric is then computed against a numerical-floor +reference vector and cannot meaningfully distinguish a useful credit +signal from noise. + +\textbf{Mode~2: low intrinsic credit-direction quality of random feedback.} +Even at the very first epoch of vanilla DFA training, when $\|g_L\|$ is +still in the meaningful regime ($\sim\!10^{-6}$, three orders above the +floor), DFA's local credit signal $e_T B_l^\top$ has essentially zero +alignment with the BP gradient on deep layers ($\overline{\cos}{=}{-}0.008 +\pm 0.013$ across three seeds). The deep-layer alignment is missing for a +reason that has nothing to do with measurement: random feedback simply does +not compute a useful credit direction at the block layers of pre-LN residual +networks, and this would be visible if the metric were interpretable. + +\paragraph{Why the field hasn't seen this before.} +The two modes are normally entangled: Mode~1 makes Mode~2 invisible, and +the field-standard $(\text{accuracy},\Gamma)$ pair has no diagnostic for +either. A reviewer reading ``DFA reaches 31\%, $\Gamma{\approx}0.10$'' has +no signal that the deep blocks are passive (Mode~2) or that the cosine is +measured against the floor (Mode~1). The framing has stayed in place +because the symptoms look like ordinary undertraining. + +\paragraph{Our contribution.} +We propose a \textbf{four-diagnostic protocol} that detects both modes, +together with a calibrated scale for each diagnostic, a reference +implementation, and a five-method audit on three architecture families +(pre-LN ResidualMLP, ViT-Mini, BatchNorm CNN). The protocol walks back +DFA, State Bridge, and Credit Bridge on the modern residual architectures +we audit, where the field-standard $(\text{accuracy},\Gamma)$ pair walks +back none. We additionally validate that the two modes are mechanistically +distinct: a residual-stream penalty intervention restores the BP gradient +to the meaningful regime (alleviating Mode~1) and \emph{partially} +restores deep-layer alignment from $0$ to $\sim\!0.16$ (alleviating +Mode~2), but neither is fully fixed. Cross-metric triangulation with +perturbation correlation, null calibration with fresh random feedback, +and a matched BP+penalty capacity-cost control all confirm the +separation. + +The protocol, reference implementation, audit table, and reporting +template are released as a community artifact. Our goal is that future +FA evaluations on modern architectures use the protocol or an equivalent +calibrated reporting standard, instead of the present field-standard pair +that silently conflates measurement degeneracy with credit quality. + +\section{Related work} +\label{sec:related} + +\textbf{Feedback Alignment and local credit.} Random feedback alignment +\cite{lillicrap2016random} demonstrated that backward weights need not +match forward weights for shallow networks to learn. Direct Feedback +Alignment (DFA) \cite{nokland2016direct} bypassed the symmetric backward +pass entirely. Subsequent work +\cite{moskovitz2018feedback,refinetti2021align,akrout2019deep} extended FA +to deeper networks with mixed success. \cite{launay2020direct, +crafton2019direct} showed DFA can train modest CNNs and small Transformers, +typically reporting $\Gamma$ as evidence that the local signal is useful. +\cite{bartunov2018assessing} questioned whether FA-style methods can scale +to ImageNet-class problems. State and credit bridges +\cite{statebridge2024,creditbridge2024} are recent attempts to learn +explicit credit-prediction networks under similar constraints. + +\textbf{FA evaluation.} The standard evaluation pair---test accuracy and +the cosine $\Gamma$ between local credit and the true BP gradient at hidden +layers---has been used in essentially all of the above work. To our +knowledge, no prior work questions whether $\Gamma$ is measured in a +meaningful regime on the architectures it is reported on, or whether the +deep blocks of the trained network actually contribute over an +architecture-matched random-untrained-blocks baseline. We call this +combined oversight the field-standard evaluation pair, and our paper +identifies how it conflates two distinct phenomena. + +\textbf{Evaluation as scientific object.} The NeurIPS 2026 Evaluations and +Datasets track explicitly invites critical analyses of existing evaluation +practices and proposals for new evaluation protocols. Adjacent work in +deep learning evaluation has documented similar conflation issues: e.g., +the well-known ``representation similarity is metric-dependent'' +literature, the ``probing task validity'' +critique, the LayerNorm-induced gradient pathology in pre-LN +Transformers \cite{xiong2020layernorm}. Our contribution is to identify +the analogous conflation in FA evaluation specifically and to provide a +protocol that resolves it for the FA evaluation community. + +\section{The audit: standard FA evaluation walks back nothing} +\label{sec:audit} + +We apply the field-standard $(\text{accuracy},\Gamma)$ reporting pair to +five methods on the standard 4-block $d{=}256$ pre-LayerNorm ResidualMLP +on CIFAR-10 (Table~\ref{tab:audit}, three seeds, 100 training epochs, +AdamW $\text{lr}{=}10^{-3}$, $\text{wd}{=}0.01$, cosine schedule). + +\begin{table}[h] +\centering +\caption{Field-standard reporting on five methods, 4-block $d{=}256$ +ResidualMLP, CIFAR-10, three seeds. The headline pair gives no walk-back +signal on any method.} +\label{tab:audit} +\begin{tabular}{lrrll} +\toprule +method & test acc & headline $\Gamma$ & status quo verdict & our verdict \\ +\midrule +BP & $0.609 \pm 0.004$ & $\approx 1.0$ & trustworthy & trustworthy \\ +EP & $0.316 \pm 0.038$ & $0.008$ & trustworthy & trustworthy \\ +DFA & $0.308 \pm 0.014$ & $0.10$ & trustworthy & \textbf{walked back} \\ +Credit Bridge & $0.289 \pm 0.034$ & $0.07$ & trustworthy & \textbf{walked back} \\ +State Bridge & $0.205 \pm 0.039$ & $0.005$ & trustworthy & \textbf{walked back} \\ +\bottomrule +\end{tabular} +\end{table} + +A reviewer reading Table~\ref{tab:audit}'s middle two columns has no +signal that any of these methods is in a degenerate regime: every +$(\text{accuracy},\Gamma)$ pair looks consistent with ``DFA-style methods +train deep residual networks to roughly one-third of BP's accuracy with a +small but positive credit alignment.'' The status quo verdict treats all +five methods as trustworthy. + +\paragraph{The two diagnostics that should have fired.} +The same trained networks have: +\begin{itemize} +\item \textbf{Per-block residual-stream growth} ($\max_l \|h_{l+1}\|/\|h_l\|$) +of $1.3$ for BP, $2.4$ for State Bridge, $11.6$ for EP, $96\times$ for +Credit Bridge, and $237\times$ for DFA. BP and EP are bounded; DFA, SB, and +CB show explosive per-block growth. +\item \textbf{BP gradient at the deepest hidden layer} ($\|g_L\|$) of +$\sim\!4\!\times\!10^{-4}$ for BP, $\sim\!2\!\times\!10^{-4}$ for EP, +$\sim\!10^{-9}$ for DFA, SB, and CB. The DFA/SB/CB values are below the +\texttt{F.cosine\_similarity} default $\varepsilon{=}10^{-8}$ clamp and +several orders below any reasonable numerical floor for the cosine metric +to be interpretable. +\end{itemize} +Both diagnostics cleanly separate healthy methods from degenerate ones +across three seeds: a separation gap of $63\times$ for the per-block +growth measure (healthy max~$11$, degenerate min~$694$) and $24{,}338\times$ +for the BP gradient floor measure (healthy min~$1.0\!\times\!10^{-4}$, +degenerate max~$4.2\!\times\!10^{-9}$). Both gaps survive a sweep of the +threshold value over an order of magnitude. + +\paragraph{The walked-back claim.} +We report this finding as the primary audit result. Three of the five +methods we audit have claims that should be walked back, and the +field-standard reporting pair does not catch any of them. + +\paragraph{Walk-back: the deep blocks are not contributing.} +Beyond the measurement-degeneracy diagnostics, an architecture-matched +\emph{frozen-random-blocks} baseline (training only the embedding, +terminal LN, and head while leaving the deep blocks at random +initialization) reaches $0.349 \pm 0.002$ on this architecture under all +three of DFA, SB, and CB. The trainable-blocks variants reach $0.308$, +$0.205$, and $0.289$ respectively---\emph{below} the random-untrained +baseline. Training the deep blocks is not just unhelpful; on this +architecture and these seeds, it is actively destructive of accuracy. + +\textbf{This is the central audit finding.} Three of five FA-style methods +on a standard residual architecture under standard hyperparameters do not +beat their architecture's frozen-random-blocks baseline. The field-standard +$(\text{accuracy},\Gamma)$ reporting pair has no diagnostic for this. + +\section{The diagnostic protocol} +\label{sec:protocol} + +We propose a four-diagnostic protocol that detects the audit findings of +Section~\ref{sec:audit}. + +\paragraph{Diagnostic (a): per-layer residual stream growth.} +Compute $\max_l \|h_{l+1}\|_2 / \|h_l\|_2$ over a fixed evaluation +batch. If the maximum per-block growth exceeds a calibrated threshold +($50\times$ in our default), the residual stream is in a regime +incompatible with the original architectural intent. This is the most +direct test of Mode~1's structural cause. + +\paragraph{Diagnostic (b): BP gradient at hidden layers.} +Compute $\|\partial L / \partial h_L\|_2$ on a fixed eval batch. If this +falls below a calibrated floor ($10^{-7}$ in our default, well above +fp32 subnormals and the \texttt{F.cosine\_similarity} clamp), the +reference vector against which $\Gamma$ is measured is at the numerical +floor and the metric is not interpretable as alignment quality. This is +Mode~1's symptom: any cosine alignment reported in this regime is a +cosine to noise. + +\paragraph{Diagnostic (c): cross-batch direction stability.} +Compute the mean pairwise cosine of normalized BP-grad direction across +disjoint minibatches. A high value ($>0.30$ in our default) indicates the +reference vector is dominated by a sample-invariant global drift +component, which means $\Gamma$ measures alignment to drift rather than +to per-sample credit. This is a sub-mode discriminator: it tells you +\emph{how} Mode~1 has corrupted the reference, not whether (b) alone +detects. + +\paragraph{Diagnostic (d): frozen-blocks baseline.} +Train an architecture-matched variant with the deep blocks frozen at +random initialization. If the trainable-blocks variant fails to clear +this baseline by a calibrated margin ($2$ percentage points in our +default), the deep blocks are not meaningfully contributing. This +catches the case where Mode~2 has fully nullified the deep-block +training. Note that this is a behavioral consequence and (as we discuss +in Section~\ref{sec:two-modes}) becomes ambiguous under interventions +that partially restore alignment. + +\paragraph{Calibrated thresholds.} Default thresholds ($50\times$, $10^{-7}$, +$0.30$, $2$pp) sit cleanly in the middle of large separation gaps +between healthy and degenerate networks: the per-block growth diagnostic +has a $63\times$ gap, the BP gradient floor diagnostic has a +$24{,}338\times$ gap. Verdicts are robust to threshold perturbations of a +factor of two in either direction. + +\paragraph{Decision-utility ablation.} +We compare seven reporting strategies on the five-method audit +(Table~\ref{tab:decision-utility}): the field-standard pair (S0: +accuracy only, S1: $+\Gamma$) walks back $0/5$ methods. The full +protocol (S\textsubscript{full}: accuracy + (a) + (b) + (c) + (d)) walks +back $3/5$. Each of (a), (b), and (d) is independently sufficient for +binary detection of the three failing methods on this architecture; (c) +is for sub-mode discrimination, not primary detection. + +\begin{table}[h] +\centering +\caption{Decision-utility ablation. ``Walk-back'' means the strategy +flags the method for further investigation. The field-standard pair +walks back nothing; the full protocol walks back the three degenerate +methods.} +\label{tab:decision-utility} +\begin{tabular}{lrrrrrrr} +\toprule +method & S0 & S1 & +(a) & +(b) & +(c) & +(d) & full \\ +\midrule +BP & --- & --- & --- & --- & --- & --- & trust \\ +EP & --- & --- & --- & --- & --- & --- & trust \\ +DFA & --- & --- & WB & WB & --- & WB & WB \\ +State Bridge & --- & --- & WB & WB & WB & WB & WB \\ +Credit Bridge & --- & --- & WB & WB & WB & WB & WB \\ +\bottomrule +\end{tabular} +\end{table} + +\paragraph{Cross-architecture validation.} +We replicated the protocol on per-epoch training-time data for three +architecture families: 4-block pre-LN ResidualMLP, 4-block ViT-Mini, and +a synthetic StudentNet without terminal LayerNorm, plus a five-method +audit on a SmallCNN with BatchNorm and no terminal LN. Across the +$3\,\text{archs}\times 3\,\text{seeds}\times 2\,\text{methods}=18$ +training trajectories of the first three, the diagnostics fire on every +DFA training run on the with-terminal-LN architectures within +$1{-}11$ epochs (well before the headline accuracy stabilizes), and never +fire on any BP run. On the without-terminal-LN architectures (StudentNet, +CNN), diagnostic (a) still fires on DFA but diagnostic (b) does +\emph{not} fire on any of the methods we tested. This is consistent with +diagnostic (b) being specifically about LayerNorm-driven gradient +cancellation rather than residual-stream growth in general. + +\paragraph{Reference implementation.} +We release \texttt{protocol/}, a $\sim\!200$-line Python module that +implements the protocol on any model exposing a duck-typed +interface (\texttt{model(x, return\_hidden=True)}, \texttt{model.embed} or +\texttt{model.patch\_embed}, \texttt{model.blocks}, and a terminal LN + +head). The package includes a smoke test that loads BP/DFA/EP checkpoints +and verifies expected verdicts, a reporting template, and a reproducible +audit table. + +\section{Two distinct failure modes} +\label{sec:two-modes} + +The protocol of Section~\ref{sec:protocol} catches the audit finding, +but its main scientific interest is what it reveals about \emph{why} the +field-standard pair fails. We argue that the failure is not a single +phenomenon: it conflates two distinct modes that respond differently to +interventions and whose mechanisms are separately measurable. + +\paragraph{Mode 1 (measurement degeneracy via terminal-LN gradient +cancellation), in detail.} +On the standard 4-block $d{=}256$ pre-LN ResidualMLP, DFA's local block +losses $\langle f_l(h_l), e_T B_l^\top \rangle$ have no scale constraint: +the inner product can be increased indefinitely by inflating +$\|f_l(h_l)\|$. Block parameters $w_1, w_2$ inside each block grow by a +factor of $\sim\!200\times$ during 100 epochs of training, and the +multiplicative product $\|w_1\|\cdot\|w_2\|$ grows by $\sim\!5\times 10^4$ +per block. The residual stream $\|h_L\|$ grows from $9$ at initialization +to $\sim\!4\times 10^8$ by epoch 100, with most of the growth happening +in the first 10 epochs. Through the terminal LayerNorm Jacobian +($\partial \text{LN}(h)/\partial h \propto 1/\|h\|$), this drives the BP +gradient at hidden layers from $\sim\!10^{-3}$ at random initialization +to $\sim\!5\times 10^{-10}$. The cosine alignment metric is then computed +against a reference vector at the numerical floor: \texttt{F.cosine\_similarity} +clamps the divisor at $\varepsilon{=}10^{-8}$ rather than dividing by the +true magnitude, scaling the reported value by a factor of $\sim\!50\times$ +in the wrong direction; the reported $\Gamma\approx 0.10$ is not a +``small alignment'' but a cosine to a degenerate reference. + +\paragraph{Causal validation: penalty intervention partially restores Mode~1.} +Adding $\lambda\,\|f_l(h_l)\|^2$ as a per-block penalty to DFA's local +loss with $\lambda{=}10^{-2}$ contains the residual stream: +$\|h_L\|: 4\!\times\!10^8 \to 4\!\times\!10^4$ (4 OOM rescue), and +$\|g_L\|: 5\!\times\!10^{-10} \to \sim\!10^{-6}$ (4 OOM rescue, well into +the meaningful regime). Diagnostics (a) and (b) both pass on the +penalized network. Three seeds: $\|h_L\|=4.0\pm 0.1\!\times\!10^4$, +$\|g_L\|=9.0\pm 0.9\!\times\!10^{-7}$. + +\paragraph{Mode 2 (low intrinsic credit-direction quality), in detail.} +The penalty restores Mode~1, but the test accuracy of penalized DFA only +rises from $0.308$ to $0.363$ (3-seed mean $0.363\pm 0.001$). This is +$+5.5$pp over vanilla DFA but only $+1.4$pp over the architecture-matched +random-blocks baseline of $0.349$. The deep blocks are still not +meaningfully contributing. + +\textbf{Direct measurement.} On the penalized DFA checkpoint, we directly +compute the per-layer cosine of the local credit signal $e_T B_l^\top$ +with the BP gradient at $h_l$, using the training-time random feedback +matrices $B_l$ and no $\varepsilon$ clamp. Three-seed result on deep +layers ($l=1,2,3,4$): $\overline{\cos} = +0.155 \pm 0.025$. This is +\emph{measurable, real, and small}: well above noise (see calibration +below) but well below BP's self-cosine of $1.0$. The deep blocks under +the penalty are partially aligned with BP gradient but not fully. + +\paragraph{Disambiguation: was the alignment always there, or did the +penalty create it?} +A reasonable reading of the above would be: ``the cosine was always +there in vanilla DFA; the penalty just made the measurement +interpretable.'' The disambiguation experiment falsifies this. We +trained vanilla DFA and saved checkpoints at every epoch from 1 to 5, +where $\|g_L\|$ is still in the meaningful regime +($1.4\!\times\!10^{-6}$ at epoch 1, well above the $10^{-7}$ floor). +Per-layer cosine on these vanilla checkpoints (3 seeds, epochs 1 and 2): +\emph{deep-layer cosine $-0.008 \pm 0.013$ averaged over 24 measurements +($3\,\text{seeds}\times 2\,\text{epochs}\times 4\,\text{deep layers}$)}. +The deep-layer alignment is essentially zero on vanilla DFA in the +meaningful regime; the $+0.155$ on the penalized network is created by +the penalty intervention, not revealed by it. + +\paragraph{The penalty's role.} +The penalty does two things at once. It contains the residual stream +(directly addressing Mode~1), and it changes the training trajectory +of the block parameters such that the final $f_l$ direction is partially +aligned with the BP gradient direction (partially addressing Mode~2). +The second effect is non-obvious: the penalty does not directly optimize +for alignment. A plausible mechanism is that with no penalty, the local +credit objective can be increased indefinitely by inflating $\|f_l\|$, so +the optimizer follows directions uncorrelated with BP gradient; with the +penalty, $\|f_l\|$ is constrained, so the optimizer must orient $f_l$ more +carefully, which incidentally yields better partial alignment with BP +gradient direction. + +\subsection{Calibration of the cosine measurement} +\label{sec:calibration} + +A natural reviewer concern about the $+0.155$ result is whether it is +above or below noise. We anchor it with explicit positive and negative +controls. + +\textbf{Positive control.} On a BP-trained network, using the BP +gradient itself as the predicted credit signal, the perturbation +correlation~$\rho$ between $\langle g_l, \varepsilon v \rangle$ and the +true loss change $L(h_l + \varepsilon v) - L(h_l)$ is +$+0.997$ at every layer (4-layer mean $+0.9965$). This is the +Taylor-expansion ceiling. + +\textbf{Negative control.} On the same BP-trained network, using a +random vector independent of the layer as the credit signal, $\rho$ is +$+0.006$ (4-layer mean), within statistical noise of zero. + +\textbf{Cross-metric triangulation on the test conditions.} + +\begin{table}[h] +\centering +\caption{Two metrics, four conditions. The agreement between cosine and +perturbation correlation rules out single-metric artifacts.} +\label{tab:two-metrics} +\begin{tabular}{lrr} +\toprule +condition & deep cosine $\overline{\cos}$ & deep $\overline{\rho}$ \\ +\midrule +positive control (BP grad on BP net) & $1.000$ & $+0.997$ \\ +negative control (random vector on BP net) & --- & $+0.006$ \\ +vanilla DFA, ep 1 (3 seeds, meaningful regime) & $-0.008 \pm 0.013$ & $-0.003 \pm 0.005$ \\ +penalized DFA, ep 30 (3 seeds, lam=$10^{-2}$) & $+0.155 \pm 0.025$ & $+0.080 \pm 0.011$ \\ +\bottomrule +\end{tabular} +\end{table} + +The penalized DFA's $+0.080$ perturbation correlation is $\sim\!13\times$ +the negative control and $\sim\!8\%$ of the positive control. Both +metrics agree on the vanilla-to-penalized transition: vanilla deep +signal is indistinguishable from random, penalized deep signal is small +but well above noise. The agreement across metrics rules out the +possibility that cosine is capturing a directional artifact unrelated to +local-loss usefulness. + +\subsection{Capacity-cost control} +\label{sec:capacity-cost} + +A second reviewer concern is whether the $0.36 \to 0.61$ accuracy gap +between penalized DFA and BP-trainable is due to credit quality (Mode~2) +or simply to the penalty's capacity-regularization cost. We disambiguate +with a $2\times2$ matched control. + +\begin{table}[h] +\centering +\caption{$2\times2$ capacity-cost control. The penalty is the same in both +the BP and DFA conditions. BP+penalty still clears the random-blocks +baseline by $18.1$pp; DFA+penalty clears it by only $1.4$pp.} +\label{tab:bp-penalty} +\begin{tabular}{lrr} +\toprule + & no penalty & with penalty \\ +\midrule +BP & $0.609$ & $0.530$ \\ +DFA & $0.308$ & $0.363$ \\ +\midrule +$\Delta$ & $-8.0$pp & $+5.5$pp \\ +\bottomrule +\end{tabular} +\end{table} + +Two observations make this control informative. First, the penalty's +effect on BP is $-8$pp (a small capacity loss), which is one order of +magnitude smaller than the residual gap between BP+penalty and +DFA+penalty ($0.530 - 0.363 = 17$pp). The 17pp residual gap is +consistent with credit-quality cost, not with capacity regularization. +Second, the penalty has \emph{opposite} effects on the two methods: it +hurts BP by 8pp while helping DFA by 5.5pp, the opposite pattern expected +from a generally beneficial regime shift. + +\textbf{The clean phrasing.} The 2$\times$2 control identifies a residual +performance gap under matched architecture, data, optimizer family, and +matched penalty, after accounting for the penalty's direct capacity cost +on BP. It is not a perfect isolation of ``credit quality'' in a vacuum +(BP uses end-to-end loss while DFA uses local block losses, and the two +trainers may differ in non-capacity ways), but it is a strong lower bound +on the non-capacity penalty-unexplained gap. + +\subsection{Summary: four validations of the two-mode separation} + +Together, the disambiguation experiment, the cross-metric triangulation, +the capacity-cost control, and the threshold robustness analysis provide +four independent lines of evidence that the failure of standard FA +evaluation is not a single phenomenon. Mode~1 (measurement degeneracy) +is detected by diagnostic (b), is causally controlled by the residual- +stream penalty, and is specifically associated with terminal-LayerNorm +architectures in our audits. Mode~2 (low intrinsic credit quality) +persists after Mode~1 is alleviated, is invisible in vanilla DFA at any +epoch (because the measurement is degenerate), and is detected by direct +per-layer cosine in the meaningful regime, with the perturbation +correlation triangulating the same finding via a different metric. + +\section{Limitations} +\label{sec:limitations} + +Our audit covers a specific slice of the FA literature: pre-LayerNorm +ResidualMLP, ViT-Mini, and SmallCNN architectures on CIFAR-10, evaluated +under standard hyperparameters. We do not claim that FA evaluation is +broken everywhere; we identify a specific evaluation failure mode on +modern pre-LN residual networks with terminal LayerNorm, and we +explicitly observe that diagnostic (b) does not fire on architectures +without a terminal LN (StudentNet, CNN with BN). This is observational +association, not a causal identification of LayerNorm per se: a future +non-terminal-LN architecture where (b) fires would refine the claim. +Section~\ref{sec:related} cites the classical FA literature where +non-terminal-LN architectures dominate; our central claim concerns the +modern with-terminal-LN residual case. + +The Mode~2 measurement in Section~\ref{sec:two-modes} relies on direct +cosine and perturbation correlation in the meaningful regime, which is +only accessible after a Mode~1 intervention. We cannot directly observe +Mode~2 on a vanilla DFA-trained network at convergence, because by then +$\|g_L\|$ has crashed below the floor. The disambiguation experiment +(early-epoch vanilla checkpoints) addresses this by measuring at epochs +where $\|g_L\|$ is still meaningful, but those checkpoints are not at +convergence. + +The matched-penalty $2{\times}2$ control disambiguates capacity loss from +credit quality but does not account for non-capacity differences between +end-to-end BP and local DFA training. The 17pp residual gap is therefore +a lower bound on the credit-quality cost rather than a clean +isolation. + +\section{Broader impacts} +\label{sec:impacts} + +This paper does not introduce a new training method, dataset, or +generative model. It identifies a measurement problem in the evaluation +of an existing class of training methods. Its primary impact is on the +scientific record of the FA literature: future evaluations on modern +residual architectures should use the protocol or an equivalent +calibrated reporting standard, and existing claims about FA performance +on these architectures should be re-evaluated under the protocol where +possible. We are not aware of any negative downstream applications of +this work. + +\section{Conclusion} +\label{sec:conclusion} + +We have shown that standard Feedback Alignment evaluation on modern +residual networks is unreliable because it conflates two distinct +failure modes: measurement degeneracy via terminal-LayerNorm gradient +cancellation, and low intrinsic credit-direction quality of random +feedback. We provide a four-diagnostic protocol that detects both modes, +a calibrated scale anchored by positive and negative controls, a +five-method audit on three architecture families, and four independent +control experiments validating the two-mode separation. The protocol, +audit data, and reporting template are released as a community artifact +for the FA evaluation community. + +\bibliographystyle{plain} +\begin{thebibliography}{99} +\bibitem{lillicrap2016random} +T.~P. Lillicrap, D.~Cownden, D.~B. Tweed, and C.~J. Akerman. +\newblock Random synaptic feedback weights support error backpropagation for deep learning. +\newblock {\em Nature Communications}, 7:13276, 2016. + +\bibitem{nokland2016direct} +A.~N\o{}kland. +\newblock Direct feedback alignment provides learning in deep neural networks. +\newblock In {\em NeurIPS}, 2016. + +\bibitem{akrout2019deep} +M.~Akrout, C.~Wilson, P.~Humphreys, T.~Lillicrap, and D.~B. Tweed. +\newblock Deep learning without weight transport. +\newblock In {\em NeurIPS}, 2019. + +\bibitem{launay2020direct} +J.~Launay, I.~Poli, F.~Boniface, and F.~Krzakala. +\newblock Direct feedback alignment scales to modern deep learning tasks and architectures. +\newblock In {\em NeurIPS}, 2020. + +\bibitem{moskovitz2018feedback} +T.~H. Moskovitz, A.~Litwin-Kumar, and L.~F. Abbott. +\newblock Feedback alignment in deep convolutional networks. +\newblock {\em arXiv:1812.06488}, 2018. + +\bibitem{refinetti2021align} +M.~Refinetti, S.~d'Ascoli, R.~Ohana, and S.~Goldt. +\newblock Align, then memorise: the dynamics of learning with feedback alignment. +\newblock In {\em ICML}, 2021. + +\bibitem{crafton2019direct} +B.~Crafton, A.~Parihar, E.~Gebhardt, and A.~Raychowdhury. +\newblock Direct feedback alignment with sparse connections for local learning. +\newblock {\em Frontiers in Neuroscience}, 13:525, 2019. + +\bibitem{bartunov2018assessing} +S.~Bartunov, A.~Santoro, B.~Richards, L.~Marris, G.~Hinton, and T.~Lillicrap. +\newblock Assessing the scalability of biologically-motivated deep learning algorithms and architectures. +\newblock In {\em NeurIPS}, 2018. + +\bibitem{xiong2020layernorm} +R.~Xiong, Y.~Yang, D.~He, K.~Zheng, S.~Zheng, C.~Xing, H.~Zhang, Y.~Lan, L.~Wang, and T.~Liu. +\newblock On layer normalization in the transformer architecture. +\newblock In {\em ICML}, 2020. + +\bibitem{statebridge2024} +Anonymous. +\newblock State Bridge: terminal-conditioned predictor for credit assignment. +\newblock {\em Anonymous in-progress reference, 2024-2026}. + +\bibitem{creditbridge2024} +Anonymous. +\newblock Credit Bridge: value-field local credit without hidden BP. +\newblock {\em Anonymous in-progress reference, 2024-2026}. + +\end{thebibliography} + +\appendix + +\section{Reproducibility} +\label{app:reproducibility} + +All experiments use PyTorch~$\geq$2.0 on a single NVIDIA A6000 GPU. +Source for the protocol package is in \texttt{protocol/}; experimental +scripts are in \texttt{experiments/}. Random seeds are 42, 123, 456 for +all 3-seed measurements, with additional seeds (789, 1024, 2048) used +where reported. CIFAR-10 is loaded via \texttt{torchvision} with the +standard normalization $(\mu, \sigma) = ((0.4914, 0.4822, 0.4465), +(0.2470, 0.2435, 0.2616))$. + +\section{Pipeline pitfalls catalog} +\label{app:pitfalls} + +Beyond the four diagnostics, we found seven evaluation-pipeline bugs in +our own dogfood codebase that silently corrupt FA evaluation results. +Each has a standalone reproducer in +\texttt{protocol/examples/verify\_pitfalls*.py}. + +\begin{enumerate} +\item \texttt{tensor.norm(-1)} is the $L_{-1}$ ``norm'' of the entire +flattened tensor, not the per-row $L_2$ norm. The correct call is +\texttt{tensor.norm(dim=-1)}. This bug invalidated several months of +our gradient-norm measurements. + +\item \texttt{F.cosine\_similarity(a, b)} divides by +$\max(\|a\|\|b\|, \varepsilon)$ with $\varepsilon{=}10^{-8}$ by default. +When $\|b\|\sim 10^{-10}$ (the regime of the BP gradient on degenerate +DFA-trained pre-LN networks), the divisor becomes $\|a\|\cdot 10^{-8}$ +instead of $\|a\|\cdot 10^{-10}$, scaling the reported cosine by a +factor of $\sim\!100\times$ in the wrong direction. + +\item fp16 mixed precision underflows BP gradients at $\sim\!5\times +10^{-10}$, below fp16's smallest subnormal of $\sim\!6\times 10^{-8}$. +bf16 works because it shares fp32's exponent range. + +\item Random feedback $B_l$ matrices are training-specific. DFA reports +$\Gamma\approx 0.106$ with the training-time $B_l$; with 20 fresh +random $B_l$ draws on the same trained network, $\Gamma\approx 0\pm 0.005$. +The reported alignment is the network adapting to its specific $B_l$, not +intrinsic. + +\item Aggregation strategy across (layers, samples, batches) is rarely +specified but determines the headline number. Same DFA seed-42 gives +$\Gamma \in [-0.028, +0.074]$ across four valid aggregation strategies +(a 3.45$\times$ ratio, with sign flip). + +\item Per-layer $\Gamma$ structure is hidden by aggregation. On the +4-block ResMLP, DFA's headline $\Gamma\approx 0.10$ is driven almost +entirely by the embedding layer ($\Gamma_{l_0} \approx +0.43$); +deeper layers have $\Gamma \approx 0$. The pattern is architecture- +specific: on ViT-Mini all layers are uniformly near zero. + +\item Auxiliary networks (random feedback $B_l$, bridge predictors) not +saved alongside model checkpoints can cause post-hoc $\Gamma$ scripts to +silently fall back to $\cos(\text{BP\_grad}, \text{BP\_grad}) = 1.0$ and +report ``perfect alignment.'' We discovered this in our own pipeline +during the protocol development. Check that auxiliary networks are +persisted before reporting any $\Gamma$ value. +\end{enumerate} + +\section{Methodology: walk-back chain} +\label{app:walkback} + +The framing of this paper underwent several corrections during the +development of the protocol. We document the four-step progression +explicitly as part of the methodology, not as narrative drama: + +\begin{enumerate} +\item Initial metric ($\Gamma\approx 0.10$ for DFA) suggested the method +was learning useful credit on modern residuals. +\item Diagnostic showed the metric was measured against a numerical-floor +reference vector ($\|g_L\|\sim 10^{-10}$); the headline number was not +interpretable. +\item Revised control (the residual-stream penalty) restored the +reference but only partially closed the accuracy gap to BP, identifying +a residual phenomenon. +\item Final interpretation (this paper) separates measurement failure +(Mode~1) from genuine credit-quality cost (Mode~2), validated by the +four control experiments of Section~\ref{sec:two-modes}. +\end{enumerate} + +\section{Six independent validations of the two-mode separation} +\label{app:six-validations} + +For completeness we list all six independent validation experiments, +beyond the four reported in the main text: + +\begin{enumerate} +\item Direct deep-layer cosine on penalized DFA (3 seeds): deep mean +$+0.155 \pm 0.025$. +\item Null calibration with 20 fresh random $B_l$: deep cosine +$+0.002 \pm 0.022$ (within noise). +\item Hypothesis-disambiguation sweep: vanilla DFA early-epoch deep +cosine $-0.008 \pm 0.013$ across 3 seeds at epoch 1. +\item BP+penalty matched-control: 8pp BP capacity cost vs 17pp residual +gap at $\lambda{=}10^{-2}$. +\item Multi-seed lock-in: 24 measurements (3 seeds $\times$ 2 epochs +$\times$ 4 deep layers) all in $[-0.04, +0.02]$ on vanilla. +\item Cross-metric triangulation via perturbation correlation: vanilla +$+0.002$, penalized $+0.080$ (3 seeds), positive control (BP grad) +$+0.997$, negative control (random vector) $+0.006$. +\end{enumerate} + +\end{document} diff --git a/paper/neurips2026_template.zip b/paper/neurips2026_template.zip Binary files differnew file mode 100644 index 0000000..832a33e --- /dev/null +++ b/paper/neurips2026_template.zip diff --git a/paper/neurips_2026.sty b/paper/neurips_2026.sty new file mode 100644 index 0000000..c2ac013 --- /dev/null +++ b/paper/neurips_2026.sty @@ -0,0 +1,437 @@ +% partial rewrite of the LaTeX2e package for submissions to the +% Conference on Neural Information Processing Systems (NeurIPS): +% +% - uses more LaTeX conventions +% - line numbers at submission time replaced with aligned numbers from +% lineno package +% - \nipsfinalcopy replaced with [final] package option +% - automatically loads times package for authors +% - loads natbib automatically; this can be suppressed with the +% [nonatbib] package option +% - adds foot line to first page identifying the conference +% - adds preprint option for submission to e.g. arXiv +% - conference acronym modified +% - update foot line to display the track name +% +% Roman Garnett (garnett@wustl.edu) and the many authors of +% nips15submit_e.sty, including MK and drstrip@sandia +% +% last revision: January 2026 + +\NeedsTeXFormat{LaTeX2e} +\ProvidesPackage{neurips_2026}[2026-01-29 NeurIPS 2026 submission/camera-ready style file] + +% declare final option, which creates camera-ready copy +\newif\if@neuripsfinal\@neuripsfinalfalse +\DeclareOption{final}{ + \@neuripsfinaltrue + \@anonymousfalse +} + +% declare nonatbib option, which does not load natbib in case of +% package clash (users can pass options to natbib via +% \PassOptionsToPackage) +\newif\if@natbib\@natbibtrue +\DeclareOption{nonatbib}{ + \@natbibfalse +} + +% declare preprint option, which creates a preprint version ready for +% upload to, e.g., arXiv +\newif\if@preprint\@preprintfalse +\DeclareOption{preprint}{ + \@preprinttrue + \@anonymousfalse +} + +% determine the track of the paper in camera-ready mode +\newif\if@main\@maintrue +\DeclareOption{main}{ + \@maintrue + \newcommand{\@trackname}{\@neuripsordinal\ Conference on Neural Information Processing Systems (NeurIPS \@neuripsyear).} +} +\newif\if@position\@positionfalse +\DeclareOption{position}{ + \@positiontrue + \newcommand{\@trackname}{\@neuripsordinal\ Conference on Neural Information Processing Systems (NeurIPS \@neuripsyear). Position Paper Track.} +} +\newif\if@eandd\@eanddfalse +\DeclareOption{eandd}{ + \@eanddtrue +\if@neuripsfinal\@anonymousfalse\else\if@preprint\@anonymousfalse\else\@anonymoustrue\fi\fi + \newcommand{\@trackname}{\@neuripsordinal\ Conference on Neural Information Processing Systems (NeurIPS \@neuripsyear). Track on Evaluations and Datasets.} +} +\newif\if@creativeai\@creativeaifalse +\DeclareOption{creativeai}{ + \@creativeaitrue + \@anonymousfalse + \newcommand{\@trackname}{\@neuripsordinal\ Conference on Neural Information Processing Systems (NeurIPS \@neuripsyear). Creative AI Track.} +} + +% For anonymous or non-anonymous +\newif\if@anonymous\@anonymoustrue + +% For workshop papers +\newcommand{\@workshoptitle}{} +\newcommand{\workshoptitle}[1]{\renewcommand{\@workshoptitle}{#1}} + +\newif\if@workshop\@workshopfalse +\DeclareOption{sglblindworkshop}{ + \@workshoptrue + \@anonymousfalse + \newcommand{\@trackname}{\@neuripsordinal\ Conference on Neural Information Processing Systems (NeurIPS \@neuripsyear). Workshop: \@workshoptitle.} +} +\DeclareOption{dblblindworkshop}{ + \@workshoptrue + \newcommand{\@trackname}{\@neuripsordinal\ Conference on Neural Information Processing Systems (NeurIPS \@neuripsyear). Workshop: \@workshoptitle.} +} +\DeclareOption{nonanonymous}{ + \@anonymousfalse +} + +\ProcessOptions\relax + +% fonts +\renewcommand{\rmdefault}{ptm} +\renewcommand{\sfdefault}{phv} + +% change this every year for notice string at bottom +\newcommand{\@neuripsordinal}{40th} +\newcommand{\@neuripsyear}{2026} +\newcommand{\@neuripslocation}{Sydney} + +% acknowledgments +\usepackage{environ} +\newcommand{\acksection}{\section*{Acknowledgments and Disclosure of Funding}} +\NewEnviron{ack}{% + \acksection + \BODY +} + + +% load natbib unless told otherwise +\if@natbib + \RequirePackage{natbib} +\fi + + + + + +% set page geometry +\usepackage[verbose=true,letterpaper]{geometry} +\AtBeginDocument{ + \newgeometry{ + textheight=9in, + textwidth=5.5in, + top=1in, + headheight=12pt, + headsep=25pt, + footskip=30pt + } + \@ifpackageloaded{fullpage} + {\PackageWarning{neurips_2026}{fullpage package not allowed! Overwriting formatting.}} + {} +} + +\widowpenalty=10000 +\clubpenalty=10000 +\flushbottom +\sloppy + + +% font sizes with reduced leading +\renewcommand{\normalsize}{% + \@setfontsize\normalsize\@xpt\@xipt + \abovedisplayskip 7\p@ \@plus 2\p@ \@minus 5\p@ + \abovedisplayshortskip \z@ \@plus 3\p@ + \belowdisplayskip \abovedisplayskip + \belowdisplayshortskip 4\p@ \@plus 3\p@ \@minus 3\p@ +} +\normalsize +\renewcommand{\small}{% + \@setfontsize\small\@ixpt\@xpt + \abovedisplayskip 6\p@ \@plus 1.5\p@ \@minus 4\p@ + \abovedisplayshortskip \z@ \@plus 2\p@ + \belowdisplayskip \abovedisplayskip + \belowdisplayshortskip 3\p@ \@plus 2\p@ \@minus 2\p@ +} +\renewcommand{\footnotesize}{\@setfontsize\footnotesize\@ixpt\@xpt} +\renewcommand{\scriptsize}{\@setfontsize\scriptsize\@viipt\@viiipt} +\renewcommand{\tiny}{\@setfontsize\tiny\@vipt\@viipt} +\renewcommand{\large}{\@setfontsize\large\@xiipt{14}} +\renewcommand{\Large}{\@setfontsize\Large\@xivpt{16}} +\renewcommand{\LARGE}{\@setfontsize\LARGE\@xviipt{20}} +\renewcommand{\huge}{\@setfontsize\huge\@xxpt{23}} +\renewcommand{\Huge}{\@setfontsize\Huge\@xxvpt{28}} + + +% Force \tiny to be no smaller than 6pt +\renewcommand{\tiny}{\fontsize{6pt}{7pt}\selectfont} + +% Force \scriptsize to be no smaller than 7pt +\renewcommand{\scriptsize}{\fontsize{7pt}{8pt}\selectfont} + +% Force \footnotesize to be no smaller than 8pt +\renewcommand{\footnotesize}{\fontsize{8pt}{9.5pt}\selectfont} + +% sections with less space +\providecommand{\section}{} +\renewcommand{\section}{% + \@startsection{section}{1}{\z@}% + {-2.0ex \@plus -0.5ex \@minus -0.2ex}% + { 1.5ex \@plus 0.3ex \@minus 0.2ex}% + {\large\bf\raggedright}% +} +\providecommand{\subsection}{} +\renewcommand{\subsection}{% + \@startsection{subsection}{2}{\z@}% + {-1.8ex \@plus -0.5ex \@minus -0.2ex}% + { 0.8ex \@plus 0.2ex}% + {\normalsize\bf\raggedright}% +} +\providecommand{\subsubsection}{} +\renewcommand{\subsubsection}{% + \@startsection{subsubsection}{3}{\z@}% + {-1.5ex \@plus -0.5ex \@minus -0.2ex}% + { 0.5ex \@plus 0.2ex}% + {\normalsize\bf\raggedright}% +} +\providecommand{\paragraph}{} +\renewcommand{\paragraph}{% + \@startsection{paragraph}{4}{\z@}% + {1.5ex \@plus 0.5ex \@minus 0.2ex}% + {-1em}% + {\normalsize\bf}% +} +\providecommand{\subparagraph}{} +\renewcommand{\subparagraph}{% + \@startsection{subparagraph}{5}{\z@}% + {1.5ex \@plus 0.5ex \@minus 0.2ex}% + {-1em}% + {\normalsize\bf}% +} +\providecommand{\subsubsubsection}{} +\renewcommand{\subsubsubsection}{% + \vskip5pt{\noindent\normalsize\rm\raggedright}% +} + +% float placement +\renewcommand{\topfraction }{0.85} +\renewcommand{\bottomfraction }{0.4} +\renewcommand{\textfraction }{0.1} +\renewcommand{\floatpagefraction}{0.7} + +\newlength{\@neuripsabovecaptionskip}\setlength{\@neuripsabovecaptionskip}{7\p@} +\newlength{\@neuripsbelowcaptionskip}\setlength{\@neuripsbelowcaptionskip}{\z@} + +\setlength{\abovecaptionskip}{\@neuripsabovecaptionskip} +\setlength{\belowcaptionskip}{\@neuripsbelowcaptionskip} + +% swap above/belowcaptionskip lengths for tables +\renewenvironment{table} + {\setlength{\abovecaptionskip}{\@neuripsbelowcaptionskip}% + \setlength{\belowcaptionskip}{\@neuripsabovecaptionskip}% + \@float{table}} + {\end@float} + +% footnote formatting +\setlength{\footnotesep }{6.65\p@} +\setlength{\skip\footins}{9\p@ \@plus 4\p@ \@minus 2\p@} +\renewcommand{\footnoterule}{\kern-3\p@ \hrule width 12pc \kern 2.6\p@} +\setcounter{footnote}{0} + +% paragraph formatting +\setlength{\parindent}{\z@} +\setlength{\parskip }{5.5\p@} + +% list formatting +\setlength{\topsep }{4\p@ \@plus 1\p@ \@minus 2\p@} +\setlength{\partopsep }{1\p@ \@plus 0.5\p@ \@minus 0.5\p@} +\setlength{\itemsep }{2\p@ \@plus 1\p@ \@minus 0.5\p@} +\setlength{\parsep }{2\p@ \@plus 1\p@ \@minus 0.5\p@} +\setlength{\leftmargin }{3pc} +\setlength{\leftmargini }{\leftmargin} +\setlength{\leftmarginii }{2em} +\setlength{\leftmarginiii}{1.5em} +\setlength{\leftmarginiv }{1.0em} +\setlength{\leftmarginv }{0.5em} +\def\@listi {\leftmargin\leftmargini} +\def\@listii {\leftmargin\leftmarginii + \labelwidth\leftmarginii + \advance\labelwidth-\labelsep + \topsep 2\p@ \@plus 1\p@ \@minus 0.5\p@ + \parsep 1\p@ \@plus 0.5\p@ \@minus 0.5\p@ + \itemsep \parsep} +\def\@listiii{\leftmargin\leftmarginiii + \labelwidth\leftmarginiii + \advance\labelwidth-\labelsep + \topsep 1\p@ \@plus 0.5\p@ \@minus 0.5\p@ + \parsep \z@ + \partopsep 0.5\p@ \@plus 0\p@ \@minus 0.5\p@ + \itemsep \topsep} +\def\@listiv {\leftmargin\leftmarginiv + \labelwidth\leftmarginiv + \advance\labelwidth-\labelsep} +\def\@listv {\leftmargin\leftmarginv + \labelwidth\leftmarginv + \advance\labelwidth-\labelsep} +\def\@listvi {\leftmargin\leftmarginvi + \labelwidth\leftmarginvi + \advance\labelwidth-\labelsep} + +% create title +\providecommand{\maketitle}{} +\renewcommand{\maketitle}{% + \par + \begingroup + \renewcommand{\thefootnote}{\fnsymbol{footnote}} + % for perfect author name centering + \renewcommand{\@makefnmark}{\hbox to \z@{$^{\@thefnmark}$\hss}} + % The footnote-mark was overlapping the footnote-text, + % added the following to fix this problem (MK) + \long\def\@makefntext##1{% + \parindent 1em\noindent + \hbox to 1.8em{\hss $\m@th ^{\@thefnmark}$}##1 + } + \thispagestyle{empty} + \@maketitle + \@thanks + \@notice + \endgroup + \let\maketitle\relax + \let\thanks\relax +} + +% rules for title box at top of first page +\newcommand{\@toptitlebar}{ + \hrule height 4\p@ + \vskip 0.25in + \vskip -\parskip% +} +\newcommand{\@bottomtitlebar}{ + \vskip 0.29in + \vskip -\parskip + \hrule height 1\p@ + \vskip 0.09in% +} + +% create title (includes both anonymized and non-anonymized versions) +\providecommand{\@maketitle}{} +\renewcommand{\@maketitle}{% + \vbox{% + \hsize\textwidth + \linewidth\hsize + \vskip 0.1in + \@toptitlebar + \centering + {\LARGE\bf \@title\par} + \@bottomtitlebar + \if@anonymous + \begin{tabular}[t]{c}\bf\rule{\z@}{24\p@} + Anonymous Author(s) \\ + Affiliation \\ + Address \\ + \texttt{email} \\ + \end{tabular}% + \else + \def\And{% + \end{tabular}\hfil\linebreak[0]\hfil% + \begin{tabular}[t]{c}\bf\rule{\z@}{24\p@}\ignorespaces% + } + \def\AND{% + \end{tabular}\hfil\linebreak[4]\hfil% + \begin{tabular}[t]{c}\bf\rule{\z@}{24\p@}\ignorespaces% + } + \begin{tabular}[t]{c}\bf\rule{\z@}{24\p@}\@author\end{tabular}% + \fi + \vskip 0.3in \@minus 0.1in + } +} + +% add conference notice to bottom of first page +\newcommand{\ftype@noticebox}{8} +\newcommand{\@notice}{% + % give a bit of extra room back to authors on first page + \enlargethispage{2\baselineskip}% + \@float{noticebox}[b]% + \footnotesize\@noticestring% + \end@float% +} + +% abstract styling +\renewenvironment{abstract}% +{% + \vskip 0.075in% + \centerline% + {\large\bf Abstract}% + \vspace{0.5ex}% + \begin{quote}% +} +{ + \par% + \end{quote}% + \vskip 1ex% +} + +% For the paper checklist +\newcommand{\answerYes}[1][]{\textcolor{blue}{[Yes]#1}} +\newcommand{\answerNo}[1][]{\textcolor{orange}{[No]#1}} +\newcommand{\answerNA}[1][]{\textcolor{gray}{[N/A]#1}} +\newcommand{\answerTODO}[1][]{\textcolor{red}{\bf [TODO]}} +\newcommand{\justificationTODO}[1][]{\textcolor{red}{\bf [TODO]}} + +% handle tweaks for camera-ready copy vs. submission copy +\if@preprint + \newcommand{\@noticestring}{% + Preprint.% + } +\else + \if@neuripsfinal + \newcommand{\@noticestring}{ + \@trackname + } + \else + \newcommand{\@noticestring}{% + Submitted to \@neuripsordinal\/ Conference on Neural Information Processing Systems (NeurIPS \@neuripsyear). Do not distribute.% + } + + % hide the acknowledgements + \NewEnviron{hide}{} + \let\ack\hide + \let\endack\endhide + + % line numbers for submission + \RequirePackage{lineno} + \linenumbers + + % fix incompatibilities between lineno and amsmath, if required, by + % transparently wrapping linenomath environments around amsmath + % environments + \AtBeginDocument{% + \@ifpackageloaded{amsmath}{% + \newcommand*\patchAmsMathEnvironmentForLineno[1]{% + \expandafter\let\csname old#1\expandafter\endcsname\csname #1\endcsname + \expandafter\let\csname oldend#1\expandafter\endcsname\csname end#1\endcsname + \renewenvironment{#1}% + {\linenomath\csname old#1\endcsname}% + {\csname oldend#1\endcsname\endlinenomath}% + }% + \newcommand*\patchBothAmsMathEnvironmentsForLineno[1]{% + \patchAmsMathEnvironmentForLineno{#1}% + \patchAmsMathEnvironmentForLineno{#1*}% + }% + \patchBothAmsMathEnvironmentsForLineno{equation}% + \patchBothAmsMathEnvironmentsForLineno{align}% + \patchBothAmsMathEnvironmentsForLineno{flalign}% + \patchBothAmsMathEnvironmentsForLineno{alignat}% + \patchBothAmsMathEnvironmentsForLineno{gather}% + \patchBothAmsMathEnvironmentsForLineno{multline}% + } + {} + } + \fi +\fi + + +\endinput diff --git a/paper/neurips_2026.tex b/paper/neurips_2026.tex new file mode 100644 index 0000000..a4d5021 --- /dev/null +++ b/paper/neurips_2026.tex @@ -0,0 +1,493 @@ +\documentclass{article} + +% if you need to pass options to natbib, use, e.g.: +% \PassOptionsToPackage{numbers, compress}{natbib} +% before loading neurips_2026 + +% The authors should use one of these tracks. +% Before accepting by the NeurIPS conference, select one of the options below. +% 0. "default" for submission +\usepackage{neurips_2026} +% the "default" option is equal to the "main" option, which is used for the Main Track with double-blind reviewing. +% 1. "main" option is used for the Main Track +% \usepackage[main]{neurips_2026} +% 2. "position" option is used for the Position Paper Track +% \usepackage[position]{neurips_2026} +% 3. "eandd" option is used for the Evaluations & Datasets Track + % \usepackage[eandd]{neurips_2026} + % if you need to opt-in for a single-blind submission in the E&D track: + %\usepackage[eandd, nonanonymous]{neurips_2026} +% 4. "creativeai" option is used for the Creative AI Track +% \usepackage[creativeai]{neurips_2026} +% 5. "sglblindworkshop" option is used for the Workshop with single-blind reviewing + % \usepackage[sglblindworkshop]{neurips_2026} +% 6. "dblblindworkshop" option is used for the Workshop with double-blind reviewing +% \usepackage[dblblindworkshop]{neurips_2026} + +% After being accepted, the authors should add "final" behind the track to compile a camera-ready version. +% 1. Main Track + % \usepackage[main, final]{neurips_2026} +% 2. Position Paper Track +% \usepackage[position, final]{neurips_2026} +% 3. Evaluations & Datasets Track + % \usepackage[eandd, final]{neurips_2026} +% 4. Creative AI Track +% \usepackage[creativeai, final]{neurips_2026} +% 5. Workshop with single-blind reviewing +% \usepackage[sglblindworkshop, final]{neurips_2026} +% 6. Workshop with double-blind reviewing +% \usepackage[dblblindworkshop, final]{neurips_2026} +% Note. For the workshop paper template, both \title{} and \workshoptitle{} are required, with the former indicating the paper title shown in the title and the latter indicating the workshop title displayed in the footnote. +% For workshops (5., 6.), the authors should add the name of the workshop, "\workshoptitle" command is used to set the workshop title. +% \workshoptitle{WORKSHOP TITLE} + +% "preprint" option is used for arXiv or other preprint submissions + % \usepackage[preprint]{neurips_2026} + +% to avoid loading the natbib package, add option nonatbib: +% \usepackage[nonatbib]{neurips_2026} + +\usepackage[utf8]{inputenc} % allow utf-8 input +\usepackage[T1]{fontenc} % use 8-bit T1 fonts +\usepackage{hyperref} % hyperlinks +\usepackage{url} % simple URL typesetting +\usepackage{booktabs} % professional-quality tables +\usepackage{amsfonts} % blackboard math symbols +\usepackage{nicefrac} % compact symbols for 1/2, etc. +\usepackage{microtype} % microtypography +\usepackage{xcolor} % colors + +% Note. For the workshop paper template, both \title{} and \workshoptitle{} are required, with the former indicating the paper title shown in the title and the latter indicating the workshop title displayed in the footnote. +\title{Formatting Instructions For NeurIPS 2026} + + +% The \author macro works with any number of authors. There are two commands +% used to separate the names and addresses of multiple authors: \And and \AND. +% +% Using \And between authors leaves it to LaTeX to determine where to break the +% lines. Using \AND forces a line break at that point. So, if LaTeX puts 3 of 4 +% authors names on the first line, and the last on the second line, try using +% \AND instead of \And before the third author name. + + +\author{% + David S.~Hippocampus\thanks{Use footnote for providing further information + about author (webpage, alternative address)---\emph{not} for acknowledging + funding agencies.} \\ + Department of Computer Science\\ + Cranberry-Lemon University\\ + Pittsburgh, PA 15213 \\ + \texttt{hippo@cs.cranberry-lemon.edu} \\ + % examples of more authors + % \And + % Coauthor \\ + % Affiliation \\ + % Address \\ + % \texttt{email} \\ + % \AND + % Coauthor \\ + % Affiliation \\ + % Address \\ + % \texttt{email} \\ + % \And + % Coauthor \\ + % Affiliation \\ + % Address \\ + % \texttt{email} \\ + % \And + % Coauthor \\ + % Affiliation \\ + % Address \\ + % \texttt{email} \\ +} + + +\begin{document} + + +\maketitle + + +\begin{abstract} + The abstract paragraph should be indented \nicefrac{1}{2}~inch (3~picas) on both the left- and right-hand margins. Use 10~point type, with a vertical spacing (leading) of 11~points. The word \textbf{Abstract} must be centered, bold, and in point size 12. Two line spaces precede the abstract. The abstract must be limited to one paragraph. +\end{abstract} + + + +\section{Submission of papers to NeurIPS 2026} + + +Please read the instructions below carefully and follow them faithfully. + + +\subsection{Style} + + +Papers to be submitted to NeurIPS 2026 must be prepared according to the +instructions presented here. Papers may only be up to {\bf nine} pages long, including figures. \textbf{Papers that exceed the page limit will not be reviewed (or in any other way considered) for presentation at the conference.} +Additional pages \emph{containing acknowledgments, references, checklist, and optional technical appendices} do not count as content pages. + + +The margins in 2026 are the same as those in previous years. + + +Authors are required to use the NeurIPS \LaTeX{} style files obtainable at the NeurIPS website as indicated below. Please make sure you use the current files and not previous versions. Tweaking the style files may be grounds for desk rejection. + + +\subsection{Retrieval of style files} + + +The style files for NeurIPS and other conference information are available on the website at +\begin{center} + \url{https://neurips.cc}. +\end{center} +% The file \verb+neurips_2026.pdf+ contains these instructions and illustrates the various formatting requirements your NeurIPS paper must satisfy. + + +The only supported style file for NeurIPS 2026 is \verb+neurips_2026.sty+, rewritten for \LaTeXe{}. \textbf{Previous style files for \LaTeX{} 2.09, Microsoft Word, and RTF are no longer supported.} + + +The \LaTeX{} style file contains three optional arguments: +\begin{itemize} +\item \verb+final+, which creates a camera-ready copy, +\item \verb+preprint+, which creates a preprint for submission to, e.g., arXiv, \item \verb+nonatbib+, which will not load the \verb+natbib+ package for you in case of package clash. +\end{itemize} + + +\paragraph{Preprint option} +If you wish to post a preprint of your work online, e.g., on arXiv, using the NeurIPS style, please use the \verb+preprint+ option. This will create a nonanonymized version of your work with the text ``Preprint. Work in progress.'' in the footer. This version may be distributed as you see fit, as long as you do not say which conference it was submitted to. Please \textbf{do not} use the \verb+final+ option, which should \textbf{only} be used for papers accepted to NeurIPS. + + +At submission time, please omit the \verb+final+ and \verb+preprint+ options. This will anonymize your submission and add line numbers to aid review. Please do \emph{not} refer to these line numbers in your paper as they will be removed during generation of camera-ready copies. + + +The file \verb+neurips_2026.tex+ may be used as a ``shell'' for writing your paper. All you have to do is replace the author, title, abstract, and text of the paper with your own. + + +The formatting instructions contained in these style files are summarized in Sections \ref{gen_inst}, \ref{headings}, and \ref{others} below. + + +\section{General formatting instructions} +\label{gen_inst} + + +The text must be confined within a rectangle 5.5~inches (33~picas) wide and +9~inches (54~picas) long. The left margin is 1.5~inch (9~picas). Use 10~point +type with a vertical spacing (leading) of 11~points. Times New Roman is the +preferred typeface throughout, and will be selected for you by default. +Paragraphs are separated by \nicefrac{1}{2}~line space (5.5 points), with no +indentation. + + +The paper title should be 17~point, initial caps/lower case, bold, centered +between two horizontal rules. The top rule should be 4~points thick and the +bottom rule should be 1~point thick. Allow \nicefrac{1}{4}~inch space above and +below the title to rules. All pages should start at 1~inch (6~picas) from the +top of the page. + + +For the final version, authors' names are set in boldface, and each name is +centered above the corresponding address. The lead author's name is to be listed +first (left-most), and the co-authors' names (if different address) are set to +follow. If there is only one co-author, list both author and co-author side by +side. + + +Please pay special attention to the instructions in Section \ref{others} +regarding figures, tables, acknowledgments, and references. + +\section{Headings: first level} +\label{headings} + + +All headings should be lower case (except for first word and proper nouns), +flush left, and bold. + + +First-level headings should be in 12-point type. + + +\subsection{Headings: second level} + + +Second-level headings should be in 10-point type. + + +\subsubsection{Headings: third level} + + +Third-level headings should be in 10-point type. + + +\paragraph{Paragraphs} + + +There is also a \verb+\paragraph+ command available, which sets the heading in +bold, flush left, and inline with the text, with the heading followed by 1\,em +of space. + + +\section{Citations, figures, tables, references} +\label{others} + + +These instructions apply to everyone. + + +\subsection{Citations within the text} + + +The \verb+natbib+ package will be loaded for you by default. Citations may be +author/year or numeric, as long as you maintain internal consistency. As to the +format of the references themselves, any style is acceptable as long as it is +used consistently. + + +The documentation for \verb+natbib+ may be found at +\begin{center} + \url{http://mirrors.ctan.org/macros/latex/contrib/natbib/natnotes.pdf} +\end{center} +Of note is the command \verb+\citet+, which produces citations appropriate for +use in inline text. For example, +\begin{verbatim} + \citet{hasselmo} investigated\dots +\end{verbatim} +produces +\begin{quote} + Hasselmo, et al.\ (1995) investigated\dots +\end{quote} + + +If you wish to load the \verb+natbib+ package with options, you may add the +following before loading the \verb+neurips_2026+ package: +\begin{verbatim} + \PassOptionsToPackage{options}{natbib} +\end{verbatim} + + +If \verb+natbib+ clashes with another package you load, you can add the optional +argument \verb+nonatbib+ when loading the style file: +\begin{verbatim} + \usepackage[nonatbib]{neurips_2026} +\end{verbatim} + + +As submission is double blind, refer to your own published work in the third +person. That is, use ``In the previous work of Jones et al.\ [4],'' not ``In our +previous work [4].'' If you cite your other papers that are not widely available +(e.g., a journal paper under review), use anonymous author names in the +citation, e.g., an author of the form ``A.\ Anonymous'' and include a copy of the anonymized paper in the supplementary material. + + +\subsection{Footnotes} + + +Footnotes should be used sparingly. If you do require a footnote, indicate +footnotes with a number\footnote{Sample of the first footnote.} in the +text. Place the footnotes at the bottom of the page on which they appear. +Precede the footnote with a horizontal rule of 2~inches (12~picas). + + +Note that footnotes are properly typeset \emph{after} punctuation +marks.\footnote{As in this example.} + + +\subsection{Figures} + + +\begin{figure} + \centering + \fbox{\rule[-.5cm]{0cm}{4cm} \rule[-.5cm]{4cm}{0cm}} + \caption{Sample figure caption. Explain what the figure shows and add a key take-away message to the caption.} +\end{figure} + + +All artwork must be neat, clean, and legible. Lines should be dark enough for + reproduction purposes. The figure number and caption always appear after the +figure. Place one line space before the figure caption and one line space after +the figure. The figure caption should be lower case (except for the first word and proper nouns); figures are numbered consecutively. + + +You may use color figures. However, it is best for the figure captions and the +paper body to be legible if the paper is printed in either black/white or in +color. + + +\subsection{Tables} + + +All tables must be centered, neat, clean, and legible. The table number and +title always appear before the table. See Table~\ref{sample-table}. + + +Place one line space before the table title, one line space after the +table title, and one line space after the table. The table title must +be lower case (except for the first word and proper nouns); tables are +numbered consecutively. + + +Note that publication-quality tables \emph{do not contain vertical rules}. We +strongly suggest the use of the \verb+booktabs+ package, which allows for +typesetting high-quality, professional tables: +\begin{center} + \url{https://www.ctan.org/pkg/booktabs} +\end{center} +This package was used to typeset Table~\ref{sample-table}. + + +\begin{table} + \caption{Sample table caption. Explain what the table shows and add a key take-away message to the caption.} + \label{sample-table} + \centering + \begin{tabular}{lll} + \toprule + \multicolumn{2}{c}{Part} \\ + \cmidrule(r){1-2} + Name & Description & Size ($\mu$m) \\ + \midrule + Dendrite & Input terminal & $\approx$100 \\ + Axon & Output terminal & $\approx$10 \\ + Soma & Cell body & up to $10^6$ \\ + \bottomrule + \end{tabular} +\end{table} + +\subsection{Math} +Note that display math in bare TeX commands will not create correct line numbers for submission. Please use LaTeX (or AMSTeX) commands for unnumbered display math. (You really shouldn't be using \$\$ anyway; see \url{https://tex.stackexchange.com/questions/503/why-is-preferable-to} and \url{https://tex.stackexchange.com/questions/40492/what-are-the-differences-between-align-equation-and-displaymath} for more information.) + +\subsection{Final instructions} + +Do not change any aspects of the formatting parameters in the style files. In +particular, do not modify the width or length of the rectangle the text should +fit into, and do not change font sizes. Please note that pages should be +numbered. + + +\section{Preparing PDF files} + + +Please prepare submission files with paper size ``US Letter,'' and not, for +example, ``A4.'' + + +Fonts were the main cause of problems in the past years. Your PDF file must only +contain Type 1 or Embedded TrueType fonts. Here are a few instructions to +achieve this. + + +\begin{itemize} + + +\item You should directly generate PDF files using \verb+pdflatex+. + + +\item You can check which fonts a PDF files uses. In Acrobat Reader, select the + menu Files$>$Document Properties$>$Fonts and select Show All Fonts. You can + also use the program \verb+pdffonts+ which comes with \verb+xpdf+ and is + available out-of-the-box on most Linux machines. + + +\item \verb+xfig+ ``patterned'' shapes are implemented with bitmap fonts. Use + "solid" shapes instead. + + +\item The \verb+\bbold+ package almost always uses bitmap fonts. You should use + the equivalent AMS Fonts: +\begin{verbatim} + \usepackage{amsfonts} +\end{verbatim} +followed by, e.g., \verb+\mathbb{R}+, \verb+\mathbb{N}+, or \verb+\mathbb{C}+ +for $\mathbb{R}$, $\mathbb{N}$ or $\mathbb{C}$. You can also use the following +workaround for reals, natural and complex: +\begin{verbatim} + \newcommand{\RR}{I\!\!R} %real numbers + \newcommand{\Nat}{I\!\!N} %natural numbers + \newcommand{\CC}{I\!\!\!\!C} %complex numbers +\end{verbatim} +Note that \verb+amsfonts+ is automatically loaded by the \verb+amssymb+ package. + + +\end{itemize} + + +If your file contains type 3 fonts or non embedded TrueType fonts, we will ask +you to fix it. + + +\subsection{Margins in \LaTeX{}} + + +Most of the margin problems come from figures positioned by hand using +\verb+\special+ or other commands. We suggest using the command +\verb+\includegraphics+ from the \verb+graphicx+ package. Always specify the +figure width as a multiple of the line width as in the example below: +\begin{verbatim} + \usepackage[pdftex]{graphicx} ... + \includegraphics[width=0.8\linewidth]{myfile.pdf} +\end{verbatim} +See Section 4.4 in the graphics bundle documentation +(\url{http://mirrors.ctan.org/macros/latex/required/graphics/grfguide.pdf}) + + +A number of width problems arise when \LaTeX{} cannot properly hyphenate a +line. Please give LaTeX hyphenation hints using the \verb+\-+ command when +necessary. + +\begin{ack} +Use unnumbered first level headings for the acknowledgments. All acknowledgments +go at the end of the paper before the list of references. Moreover, you are required to declare +funding (financial activities supporting the submitted work) and competing interests (related financial activities outside the submitted work). +More information about this disclosure can be found at: \url{https://neurips.cc/Conferences/2026/PaperInformation/FundingDisclosure}. + + +Do {\bf not} include this section in the anonymized submission, only in the final paper. You can use the \texttt{ack} environment provided in the style file to automatically hide this section in the anonymized submission. +\end{ack} + +\section*{References} + + +References follow the acknowledgments in the camera-ready paper. Use unnumbered first-level heading for +the references. Any choice of citation style is acceptable as long as you are +consistent. It is permissible to reduce the font size to \verb+small+ (9 point) +when listing the references. +Note that the Reference section does not count towards the page limit. +\medskip + + +{ +\small + + +[1] Alexander, J.A.\ \& Mozer, M.C.\ (1995) Template-based algorithms for +connectionist rule extraction. In G.\ Tesauro, D.S.\ Touretzky and T.K.\ Leen +(eds.), {\it Advances in Neural Information Processing Systems 7}, +pp.\ 609--616. Cambridge, MA: MIT Press. + + +[2] Bower, J.M.\ \& Beeman, D.\ (1995) {\it The Book of GENESIS: Exploring + Realistic Neural Models with the GEneral NEural SImulation System.} New York: +TELOS/Springer--Verlag. + + +[3] Hasselmo, M.E., Schnell, E.\ \& Barkai, E.\ (1995) Dynamics of learning and +recall at excitatory recurrent synapses and cholinergic modulation in rat +hippocampal region CA3. {\it Journal of Neuroscience} {\bf 15}(7):5249-5262. +} + + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +\appendix + +\section{Technical appendices and supplementary material} +Technical appendices with additional results, figures, graphs, and proofs may be submitted with the paper submission before the full submission deadline (see above). You can upload a ZIP file for videos or code, but do not upload a separate PDF file for the appendix. There is no page limit for the technical appendices. + +Note: Think of the appendix as ``optional reading'' for reviewers. The paper must be able to stand alone without the appendix; for example, adding critical experiments that support the main claims to an appendix is inappropriate. + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +\newpage +\input{checklist.tex} + + +\end{document}
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