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<!DOCTYPE html>
<html>
<head>
<title>Learning</title>
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# Lifelong Learning:<br>What is it anyway?
<br>
PI: Joshua T. Vogelstein, [JHU](https://www.jhu.edu/) <br>
Co-PI: Vova Braverman, [JHU](https://www.jhu.edu/) <br>
Jayanta Dey, Ali Geisa, Will LeVine, Hayden Helm, Ronak Mehta, Haoran Li, Aditya Krishnan, Rahul Ramesh, Pratik Chaudhari, Ashwin De Silva, Jingfeng Wu,
Carey E. Priebe
<!-- | Joshua T. Vogelstein <br> -->
<!-- [Microsoft Research](https://www.microsoft.com/en-us/research/): Weiwei Yang | Jonathan Larson | Bryan Tower | Chris White -->
<img src="images/neurodata_blue.png" width="20%" style="vertical-align: top">
<img src="images/jhu.png" width="8%" style="vertical-align: top">
---
<img src="images/L2M_hava.png" width="1000">
---
## Formalizing Learning
- Assume $(X\_i,Y\_i) \sim^{iid} P, \quad i \in [n]$
- Let $f((X_i,Y_i)^n) \rightarrow h_n$
- Let R (risk) be expected loss
- Let $\delta, \epsilon > 0$
- a learner .ye[weakly] learns if $\, \exists N$ s.t. $\forall n > N$
$$Pr[ R(h\_n) < R\_{chance} ] \geq 1 - \delta$$
- a learner .ye[strongly] learns if $\, \exists N$ s.t. $\forall n > N$
$$Pr[ R(h\_n) - R^* < \epsilon ] \geq 1 - \delta$$
- strong learner thm: if $f$ weakly learns, it also strongly learns
- implication: if your AI is doing ok, just get more data!
---
## So learning is solved?
- No.
- In lifelong learning, the samples are not all from the same distribution.
- Consider the simplest possible generalization:
- we have 2 datasets from two different distributions
- We want to know whether we learn about one from the other
- This is called '.ye[out of distribution]' learning
- Lifelong learning is a special (sequential) case
---
## Formalizing OOD Learning
- Assume $(X\_i,Y\_i) \sim^{iid} P, \quad i \in [n]$
- Assume $(X\_i,Y\_i) \sim^{iid} Q, \quad i \in ${$n+1, \ldots, n+m$}
- Let $f((X\_i,Y\_i)^{n+m}) \rightarrow h\_{n,m}$
- a learner .ye[weakly] learns about $P$ from $Q$ if $\, \exists M$ s.t. $\forall m > M$
$$Pr[ R(h\_{n,m}) < R(h\_n) ] \geq 1 - \delta$$
- a learner .ye[strongly] learns about $P$ from $Q$ if $\, \exists M$ s.t. $\forall m > M$
$$Pr[ R(h\_{n,m}) - R^* < \epsilon ] \geq 1 - \delta$$
- strong OOD learner thm: if $f$ weakly learns, it does not necessarily strongly learn
- implications: more data does not necessarily help!
.footnote[.small[Geisa, et al., Towards a theory of out-of-distribution learning. 2021]]
---
### A generalized definition of learning
- Let $S = (X\_i,Y\_i) \sim^{iid} P, \, \forall i \in [n]$
- Let $S' = (X\_i,Y\_i) \sim^{iid} Q, \, \forall i \in ${$n+1,\ldots, n+m$}
- Let $\mathcal{E}^t_f(S)$ := expected risk for task $t$ of learner $f$ using data $S$
- Let .ye[Learning Efficiency] be defined:
$$LE^t_f(S,S') = \frac{ \mathcal{E}^t_f(S)}{\mathcal{E}^t_f(S')}$$
- $f$ .ye[learns] about $P$ from $Q$ whenever $\log LE^t_f(S,S') >0$
- $f$ .ye[forgets] about $P$ from $Q$ whenever $\log LE^t_f(S,S') < 0$
- .ye[catastrophic forgetting]: $LE \ll 0$
- forward transfer, backward transfer, performance relative to STE, etc. are special cases
.footnote[.small[Vogelstein, et al. arxiv, 2020]]
---
### Fundamental Question of OOD Learning
- Assume $S = (X\_i,Y\_i) \sim^{iid} P, \quad i \in [n]$
- Assume $T = (X\_i,Y\_i) \sim^{iid} Q, \quad i \in ${$n+1, \ldots, n+m$}
- Assume $S \perp T$
<!-- the $n$ samples from $P$ and the $m$ samples from $Q$ are independent of each other -->
- What are the conditions on $P, Q, n, m$ such that $f$ can learn about $P$ from $Q$ (i.e., achieve $\log LE > 0$)?
We hope that for a given $P, Q, n$, there exists an $M$ such that if $m > M$, then data from $Q$ makes $f$ learn about (rather than forget about) $P$
---
## The simplest example
- $P$ is two gaussians
- $Q$ is two gaussians shifted by $\Delta$
<img src="https://github.com/neurodata/ood-tl/blob/main/reports/figures/gausstask_fig.png?raw=true" width="700">
<!--  -->
---
## A terrible thing
<img src="https://github.com/neurodata/ood-tl/blob/main/reports/figures/gaussian_task_analytical_plot.svg?raw=true" width="1000">
- Sometimes, for a fixed $\Delta$, error is non-monotonic wrt $m$
- implications: just because a little OOD data helps, does not mean that more will help!
.footnote[.small[de Silva, et al. Non-monotonic Out-of-Distribution Risk, in prep]]
---
## Not just in simulated data
- CIFAR 10
- Task 1: Bird vs. Cat
- Task 2: Deer vs. Dog
<img src="https://github.com/neurodata/ood-tl/blob/main/reports/figures/bridcat_deerdog.svg?raw=true" width="1000">
---
## Summary so far
- OOD learning is different in kind from in-distribution learning
- More data is not necessarily adequate to get arbitrary performance
- More data can actually hurt
- Time to think carefully about how much data of different kinds to use, and how to combine datasets, rather than throwing everything in a bucket
---
###
<img src="images/S1.png" width="1200">
---
###
<img src="images/S2.png" width="1200">
---
###
<img src="images/S3.png" width="1200">
---
.small[
### Publications
1. A. Geisa et al. [Towards a theory of out-of-distribution learning](https://arxiv.org/abs/2109.14501), arXiv, 2021.
1. J. T. Vogelstein et al. [Representation Ensembling for Synergistic Lifelong Learning with Quasilinear Complexity](https://arxiv.org/abs/2004.12908), arXiv, 2022.
1. H. Xu et al. [Simplest Streaming Trees](https://arxiv.org/abs/2110.08483), arXiv, 2022.
1. J. Dey et al. [Out-of-distribution and in-distribution posterior calibration using Kernel Density Polytopes](https://arxiv.org/abs/2201.13001), arXiv, 2022.
1. C. E. Priebe et al. [Modern Machine Learning: Partition and Vote](https://doi.org/10.1101/2020.04.29.068460), 2020.
1. R. Guo, et al. [Estimating Information-Theoretic Quantities with Uncertainty Forests](https://arxiv.org/abs/1907.00325). arXiv, 2019.
1. R. Perry, et al. [Manifold Forests: Closing the Gap on Neural Networks](https://openreview.net/forum?id=B1xewR4KvH). arXiv, 2019.
1. C. Shen and J. T. Vogelstein. [Decision Forests Induce Characteristic Kernels](https://arxiv.org/abs/1812.00029). arXiv, 2019.
1. M. Madhya, et al. [Geodesic Learning via Unsupervised Decision Forests](https://arxiv.org/abs/1907.02844). arXiv, 2019.
1. M. Madhya, et al. [PACSET (Packed Serialized Trees): Reducing Inference Latency for Tree Ensemble Deployment](https://arxiv.org/abs/2011.05383). arXiv, 2020.
<!-- ### Conferences -->
1. J. T. Vogelstein et al. A biological implementation of lifelong learning in the pursuit of artificial general intelligence. NAISys, 2020.
2. B. Pedigo et al. A quantitative comparison of a complete connectome to artificial intelligence architectures. NAISys, 2020.
3. L. Haoran, et al. [Lifelong Learning with Sketched Structural Regularization](https://arxiv.org/abs/2104.08604). ACML, 2021.
]
---
#### Acknowledgements
<!-- <div class="small-container">
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##### JHU
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##### HRL & Microsoft Research
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##### DARPA L2M
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---
background-image: url(images/l_and_v.jpeg)
.footnote[Questions?]
---
class: middle
# .center[Appendix]
---
### Biological learning is on top
<img src="images/learning-table.png" width="1000">
---
### Spoken Digit dataset
.pull-left[
- *Spoken Digit* contains recording from 6 different speakers.
- Each digit has 50 recordings (3000 total recordings).
- For each recording spectrogram was extracted using using Hanning windows of duration 16 ms with an overlap of 4 ms.
- The spectrograms were resized down to 28×28.
]
.pull-right[
<img src="images/spectrogram.png" style="left:500px; width:400px;"/>
]
---
### Synergistic Algorithms on Spoken Digit Task
<img src="images/spoken_digit.png" width="1000">
<!-- ![:scale 105%]() -->
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