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Title: Backpropamine: training self-modifying neural networks with differentiable neuromodulated plasticity

Paper content:
The impressive lifelong learning in animal brains is primarily enabled by plastic changes in synaptic connectivity.
Importantly, these changes are not passive, but are actively controlled by neuromodulation, which is itself under the control of the brain.
The resulting self-modifying abilities of the brain play an important role in learning and adaptation, and are a major basis for biological reinforcement learning.
Here we show for the first time that artificial neural networks with such neuromodulated plasticity can be trained with gradient descent.
Extending previous work on differentiable Hebbian plasticity, we propose a differentiable formulation for the neuromodulation of plasticity.
We show that neuromodulated plasticity improves the performance of neural networks on both reinforcement learning and supervised learning tasks.
In one task, neuromodulated plastic LSTMs with millions of parameters outperform standard LSTMs on a benchmark language modeling task (controlling for the number of parameters).
We conclude that differentiable neuromodulation of plasticity offers a powerful new framework for training neural networks.
Neural networks that deal with temporally extended tasks must be able to store traces of past events.
Often this memory of past events is maintained by neural activity reverberating through recurrent connections; other methods for handling temporal information exist, including memory networks BID36 or temporal convolutions BID21 .
However, in nature, the primary basis for long-term learning and memory in the brain is synaptic plasticity -the automatic modification of synaptic weights as a function of ongoing activity BID16 BID14 .
Plasticity is what enables the brain to store information over the long-term about its environment that would be impossible or impractical for evolution to imprint directly into innate connectivity (e.g. things that are different within each life, such as the language one speaks).Importantly
, these modifications are not a passive process, but are actively modulated on a momentto-moment basis by dedicated systems and mechanisms: the brain can "decide" where and when to modify its own connectivity, as a function of its inputs and computations. This neuromodulation
of plasticity, which involves several chemicals (particularly dopamine; BID1 He et al. 2015; BID13 BID43 , plays an important role in learning and adaptation BID22 BID32 Kreitzer & Malenka, 2008) . By allowing the brain
to control its own modification as a function of ongoing states and events, the neuromodulation of plasticity can filter out irrelevant events while selectively incorporating important information, combat catastrophic forgetting of previously acquired knowledge, and implement a self-contained reinforcement learning algorithm by altering its own connectivity in a reward-dependent manner BID31 BID24 BID7 Hoerzer et al., 2014; BID19 BID4 BID38 .The complex organization
of neuromodulated plasticity is not accidental: it results from a long process of evolutionary optimization. Evolution has not only designed
the general connection pattern of the brain, but has also sculpted the machinery that controls neuromodulation, endowing the brain with carefully tuned self-modifying abilities and enabling efficient lifelong learning. In effect, this coupling of evolution
and plasticity is a meta-learning process (the original and by far most powerful example of meta-learning), whereby a simple but powerful optimization process (evolution guided by natural selection) discovered how to arrange elementary building blocks to produce remarkably efficient learning agents.Taking inspiration from nature, several authors have shown that evolutionary algorithms can design small neural networks (on the order of hundreds of connections) with neuromodulated plasticity (see the "Related Work" section below). However, many of the spectacular recent
advances in machine learning make use of gradient-based methods (which can directly translate error signals into weight gradients) rather than evolution (which has to discover the gradients through random weight-space exploration). If we could make plastic, neuromodulated
networks amenable to gradient descent, we could leverage gradient-based methods for optimizing and studying neuromodulated plastic networks, expanding the abilities of current deep learning architectures to include these important biologically inspired self-modifying abilities.Here we build on the differentiable plasticity framework BID19 BID20 to implement differentiable neuromodulated plasticity. As a result, for the first time to our knowledge
, we are able to train neuromodulated plastic networks with gradient descent. We call our framework backpropamine in reference
to its ability to emulate the effects of natural neuromodulators (like dopamine) in artificial neural networks trained by backpropagation. Our experimental results establish that neuromodulated
plastic networks outperform both non-plastic and non-modulated plastic networks, both on simple reinforcement learning tasks and on a complex language modeling task involving a multi-million parameter network. By showing that neuromodulated plasticity can be optimized
through gradient descent, the backpropamine framework potentially provides more powerful types of neural networks, both recurrent and feedforward, for use in all the myriad domains in which neural networks have had tremendous impact.
This paper introduces a biologically-inspired method for training networks to self-modify their weights.
Building upon the differentiable plasticity framework, which already improved performance (sometimes dramatically) over non-plastic architectures on various supervised and RL tasks BID18 BID20 , here we introduce neuromodulated plasticity to let the network control its own weight changes.
As a result, for the first time, neuromodulated plastic networks can be trained with gradient descent, opening up a new research direction into optimizing large-scale self-modifying neural networks.As a complement to the benefits in the simple RL domains investigated, our finding that plastic and neuromodulated LSTMs outperform standard LSTMs on a benchmark language modeling task (importantly, a central domain of application of LSTMs) is potentially of great importance.
LSTMs are used in real-world applications with massive academic and economic impact.
Therefore, if plasticity and neuromodulation consistently improve LSTM performance (for a fixed search space size), the potential benefits could be considerable.
We intend to pursue this line of investigation and test plastic LSTMs (both neuromodulated and non) on other problems for which LSTMs are commonly used, such as forecasting.Conceptually, an important comparison point is the "Learning to Reinforcement Learn" (L2RL) framework introduced by BID39 .
In this meta-learning framework, the weights do not change during episodes: all within-episode learning occurs through updates to the activity state of the network.
This framework is explicitly described BID40 as a model of the slow sculpting of prefrontal cortex by the reward-based dopamine system, an analogy facilitated by the features of the A2C algorithm used for meta-training (such as the use of a value signal and modulation of weight changes by a reward prediction error).
As described in the RL experiments above, our approach adds more flexibility to this model by allowing the system to store state information with weight changes, in addition to hidden state changes.
However, because our framework allows the network to update its own connectivity, we might potentially extend the L2RL model one level higher: rather than using A2C as a hand-designed reward-based weight-modification scheme, the system could now determine its own arbitrary weight-modification scheme, which might make use of any signal it can compute (reward predictions, surprise, saliency, etc.) This emergent weight-modifying algorithm (designed over many episodes/lifetimes by the "outer loop" meta-training algorithm) might in turn sculpt network connectivity to implement the meta-learning process described by BID40 .
Importantly, this additional level of learning (or "meta-meta-learning") is not just a pure flight of fancy: it has undoubtedly taken place in evolution.
Because humans (and other animals) can perform meta-learning ("learning-to-learn") during their lifetime (Harlow, 1949; BID40 , and because humans are themselves the result of an optimization process (evolution), then meta-meta-learning has not only occurred, but may be the key to some of the most advanced human mental functions.
Our framework opens the tantalizing possibility of studying this process, while allowing us to replace evolution with any gradient-based method in the outermost optimization loop.To investigate the full potential of our approach, the framework described above requires several improvements.
These include: implementing multiple neuromodulatory signals (each with their own inputs and outputs), as seems to be the case in the brain BID12 Howe & Dombeck, 2016; BID27 ; introducing more complex tasks that could make full use of the flexibility of the framework, including the eligibility traces afforded by retroactive modulation and the several levels of learning mentioned above; and addressing the pitfalls in the implementation of reinforcement learning with reward-modulated Hebbian plasticity (e.g. the inherent interference between the unsupervised component of Hebbian learning and reward-based modifications; BID9 BID8 , so as to facilitate the automatic design of efficient, selfcontained reinforcement learning systems.
Finally, it might be necessary to allow the meta-training algorithm to design the overall architecture of the system, rather than simply the parameters of a fixed, hand-designed architecture.
With such a rich potential for extension, our framework for neuromodulated plastic networks opens many avenues of exciting research.
DISPLAYFORM0 j t , f t and o t are used for controlling the data-flow through the LSTM and i t is the actual data.
Therefore, plasticity is introduced in the path that goes through i t (adding plasticity to the control paths of LSTM is for future-work) .
The corresponding pre-synaptic and post-synaptic activations (denoted by x i (t − 1) and x j (t) respectively in equations 1 and
2) are h t−1 and i t .
A layer of size 200 has 40k (200×200) plastic connections.
Each plastic connection has its own individual η (used in equation
2) that is learned through backpropagation.
The plasticity coefficients (α i,j ) are used as shown in equation 1.

assistant: text: Neural networks can be trained to modify their own connectivity, improving their online learning performance on challenging tasks.