Recent experiments revealed that the fruit fly Drosophila melanogaster has a dedicated mechanism for forgetting: blocking the G-protein Rac leads to slower and activating Rac to faster forgetting. This active form of forgetting lacks a satisfactory functional explanation. We investigated optimal decision making for an agent adapting to a stochastic environment where a stimulus may switch between being indicative of reward or punishment. Like Drosophila, an optimal agent shows forgetting with a rate that is linked to the time scale of changes in the environment. Moreover, to reduce the odds of missing future reward, an optimal agent may trade the risk of immediate pain for information gain and thus forget faster after aversive conditioning. A simple neuronal network reproduces these features. Our theory shows that forgetting in Drosophila appears as an optimal adaptive behavior in a changing environment. This is in line with the view that forgetting is adaptive rather than a consequence of limitations of the memory system.

I study Genki 1 with a tutor, I'm almost at the end of it, but I don't remember half of the words and kanji from previous lessons. We take new lesson each 1,5 - 2 weeks and every time I really learn everything, do the exersises, but when I start new lesson all knowledge from previous lessons vanishes. I don't want to lose my progress, but I just don't know what to do to keep this information in my head.


Full Movie Lessons In Forgetting


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The same neural circuitry appears to be involved in forgetting and remembering. If that is properly understood, students and teachers can adopt strategies to reduce memory leaks and reinforce learning.

Drosophila melanogaster forgets [1], [2]. In itself this is unremarkable because forgetting as a behavioral phenomenon appears in any adaptive system of limited capacity; storing new associations will lead to interference with existing memories. Forgetting, in this sense, is just the flip side of learning. When capacity is not an issue, forgetting may nevertheless be caused by a useful mechanism: one that keeps a low memory load and thus prevents a slowdown of retrieval [3], [4]. Consequently, capacity or retrieval limitations lie at the heart of standard theories of non-pathological forgetting [5], [6], which focus on interference and decay explanations. Alternatively, forgetting has been proposed to be an adaptive strategy that has evolved in response to the demands of a changing environment [7]. It is the latter explanation that seems to apply to Drosophila where the experimental evidence suggests that the cause underlying forgetting is an active process which is modulated by the learning task and not by internal constraints of the memory system; in particular in olfactory conditioning tasks, reversal learning leads to faster forgetting [8] whereas spaced training leads to slower forgetting compared to single or massed training [9]. Further, forgetting in Drosophila seems rather idiosyncratic in that aversive conditioning is forgotten approximately twice as quickly as appetitive conditioning [10], [11].

A The environmental state changes stochastically with rates between being rewarding, neutral or punishing. Unless mentioned otherwise, we choose and . B Based on a policy (with forgetting, without forgetting) which may depend on past observations of the environmental state and current costs of responding, an agent shows the appetitive reaction (upward arrow) or the aversive reaction (downward arrow). The stochastic costs (i.i.d. with an exponential distribution with scale parameter ) for the appetitive/aversive reaction are shown above/below the white line. An agent with a policy that involves forgetting accumulates more reward than an agent without forgetting or immediate forgetting. C In an emulation of a classical conditioning experiment, the agent experiences a defined environmental state, and after a waiting period of length the agent has to react according to the internal policy. D Different policies lead to different outcomes in classical conditioning experiments. Shown is the fraction of agents choosing the conditioned response (conditioned resp.) at time after conditioning for agents subject to individual costs of responding.

That Drosophila has a dedicated mechanism to control forgetting was convincingly demonstrated by Shuai et al. [8] and Berry et al. [2]. Inhibition of the small G-protein Rac leads to slower decay of memory, extending it from a few hours to more than one day [8]. Conversely, elevated Rac activity leads to faster forgetting [8]. Similar results were achieved by modulation of a small subset of Dopamine neurons [2]. Stimulating these neurons leads to faster forgetting after aversive and appetitive conditioning, while silencing these neurons leads to slower forgetting [2].

Given the importance of decision making, it appears unlikely that forgetting in Drosophila is a behavioral trait which is maladaptive in an ecological sense. Hence we investigated what generic model of the environment would justify the observed forgetting and in particular the asymmetry between aversive and appetitive conditioning. For this we mathematically determined optimal decision making strategies in environments with different associations between stimulus and reinforcement.

If the agent knew the environmental state, the best policy would be simple: choose the appetitive (aversive) reaction if the environmental state is rewarding (punishing). Typically however, the agent does not know the actual environmental state but, at best, maintains a belief about it (see Fig. 2A and Methods). In our model, the belief consists of the probabilities , and to receive rewarding, neutral or punishing reinforcement, respectively, after selecting the appetitive reaction. Geometrically, the belief can be represented as a position in a 2-dimensional belief space that stepwise changes after the appetitive reaction and thus gaining new information about the current environmental state and otherwise drifts towards an equilibrium (forgetting), see Fig. 2B (note that, since the three probabilities sum to one, the probability of the neutral state can be computed given the probabilities of the rewarding and punishing state, i.e. ).

While the difference in forgetting speed after appetitive and aversive forgetting could be a consequence of different transition rates and , such a difference also arises if these rates are equal but the agent uses a provident policy, i.e. a policy that also takes into account future rewards. In the long run the provident policy is superior to the greedy policy (Fig. 4B). We therefore determined numerically a policy which approximately maximizes the reward rate, i.e. the total reward accumulated over a long period divided by the length of this period (see Methods). The resulting policy is such that there are beliefs for which the appetitive reaction is chosen, even when the probability of punishment is larger than the probability of reward, i.e. , and the costs of responding are equal for both actions (Fig. 2C bottom, middle). The reason for this becomes clearer when we look at what economists call the opportunity cost, i.e. the additional gain that has not been harvested because of missing to choose the (often by hindsight) better option [14]. For the appetitive reaction, the agent's opportunity cost is given by the potentially lower cost for the aversive reaction. But for the aversive reaction, the agent's opportunity cost is not only the potentially lower cost for the appetitive reaction but also the lack of further information about the actual environmental state. This information is required for best exploitation in future trials. Assume, for instance, that at some point in time the agent believes that punishment is slightly more probable than reward and therefore sticks to the aversive reaction. Now, if the actual environmental state would be rewarding, the agent would not only miss the current reward but also misses subsequent rewards that could potentially be harvested while the state is still rewarding. When taking this opportunity cost into account, the agent will choose the appetitive reaction despite the belief state slightly favoring the aversive reaction. For an external observer this optimal choice behavior appears as a faster forgetting of the aversive memory. In short, the asymmetry in forgetting after aversive and appetitive conditioning (Fig. 4) arises because choosing the appetitive reaction is always informative about the current environmental state whereas choosing the aversive reaction is not.

So far we have assumed that the transition rates between the environmental states are fixed. This is not an assumption Drosophila seems to make and in fact, would be an unrealistic model of the environment. The experiments by Tully et al. [9] show that forgetting depends not only on the number of conditioning trials but also on their frequency. In particular, forgetting is slower when the same number of learning trials is spaced out over a longer period of time. Spaced training is more informative about the environment being in a slowly changing mode than the temporally compressed massed training. Furthermore, reversal training during which in fast succession an odor is aversively, neutral and again aversively conditioned [8] results in faster forgetting and is informative about a fast changing environment. So the observed behavior provides rather direct evidence that adaptation in Drosophila does indeed take non-stationarity into account.

A In an extended model the rate of change depends on a slowly changing meta variable , which can be in a slow or fast state. B As observed in experiments with Drosophila, our model agents show slowest forgetting after spaced training and fastest forgetting of the last association after reversal training. In our model, this result appears as a consequence of spaced training being most informative about slow transitions, whereas reversal training is most informative about fast transitions. be457b7860

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